Daily Papers

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

Best-of-N inference scaling (drawing N candidate answers from a language model and returning the one a reward model ranks highest) improves accuracy by an amount that varies across models, but predicting that amount in advance currently requires running the procedure end-to-end. Prior work links cheap statistics of a model's sampled outputs and validation-set correctness (how often samples agree, how diverse they are, how confident the model is, and where correct samples appear) to model behavior, but does not isolate which of these form a stable, compact predictor of best-of-N gain. We fit ridge predictors on features computed from a single labeled validation-set sampling pass, use bootstrap-Lasso as a stability analysis of the candidate feature set, and give a concentration analysis with an explicit linear-approximation residual. Across three base-model families, six post-training methods, and math and reasoning task domains, the stability analysis identifies a strict three-feature core spanning prompt-level agreement spread, label-assisted first-correct-sample position, and completion-length variance; a compact ridge predictor built from this core plus an entropy add-on reaches Spearman ρ= 0.90 with actual best-of-N gain under a reward-model verifier. The intended use is labeled validation-set screening of candidate configurations before paying the full reward-model scoring cost.

Evaluating image-text alignment while reflecting human preferences across multiple aspects is a significant issue for the development of reliable vision-language applications. It becomes especially crucial in real-world scenarios where multiple valid descriptions exist depending on contexts or user needs. However, research progress is hindered by the lack of comprehensive benchmarks and existing evaluation predictors lacking at least one of these key properties: (1) Alignment with human judgments, (2) Long-sequence processing, (3) Inference efficiency, and (4) Applicability to multi-objective scoring. To address these challenges, we propose a plug-and-play architecture to build a robust predictor, MULTI-TAP (Multi-Objective Task-Aware Predictor), capable of both multi and single-objective scoring. MULTI-TAP can produce a single overall score, utilizing a reward head built on top of a large vision-language model (LVLMs). We show that MULTI-TAP is robust in terms of application to different LVLM architectures, achieving significantly higher performance than existing metrics and even on par with the GPT-4o-based predictor, G-VEval, with a smaller size (7-8B). By training a lightweight ridge regression layer on the frozen hidden states of a pre-trained LVLM, MULTI-TAP can produce fine-grained scores for multiple human-interpretable objectives. MULTI-TAP performs better than VisionREWARD, a high-performing multi-objective reward model, in both performance and efficiency on multi-objective benchmarks and our newly released text-image-to-text dataset, EYE4ALL. Our new dataset, consisting of chosen/rejected human preferences (EYE4ALLPref) and human-annotated fine-grained scores across seven dimensions (EYE4ALLMulti), can serve as a foundation for developing more accessible AI systems by capturing the underlying preferences of users, including blind and low-vision (BLV) individuals.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples (x, f(x)) presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from +0.46 on ETTm2 to -0.19 on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay. Specifically, we prove that the following stages occur: (i) the model overfits the training data early during training; (ii) poor generalization persists long after overfitting has manifested; and (iii) the generalization error eventually becomes arbitrarily small. Moreover, we show, both theoretically and empirically, that grokking can be amplified or eliminated in a principled manner through proper hyperparameter tuning. To the best of our knowledge, these are the first rigorous quantitative bounds on the generalization delay (which we refer to as the "grokking time") in terms of training hyperparameters. Lastly, going beyond the linear setting, we empirically demonstrate that our quantitative bounds also capture the behavior of grokking on non-linear neural networks. Our results suggest that grokking is not an inherent failure mode of deep learning, but rather a consequence of specific training conditions, and thus does not require fundamental changes to the model architecture or learning algorithm to avoid.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

This study analyzes Sri Lankan migration and remittances over 32 years (1994-2025). Using a 384-month harmonized dataset, we apply exploratory data analysis, stationarity corrected time-series modeling (ADF, Johansen, VAR/VECM), and supervised learning. Results reveal remittance inflows are primarily driven by external macroeconomic variables, specifically exchange rate dynamics and global oil prices, rather than domestic indicators. Impulse response analysis confirms the asymmetric impact of currency depreciation and oil price shocks. Predictively, multivariate machine learning models outperform traditional univariate approaches; Ridge Regression achieves a 73.8% accuracy improvement over SARIMA (Annualized RMSE: USD 494.8 Mn). The optimized framework projects 2026 remittances at USD 9,001 million under stable conditions. These findings highlight the structural dependence of remittances on global economies, emphasizing the need for robust exchange rate policies, skilled migration, and formal financial channels to enhance long-term economic resilience.

Evaluating neural network performance is critical to deep neural network design but a costly procedure. Neural predictors provide an efficient solution by treating architectures as samples and learning to estimate their performance on a given task. However, existing predictors are task-dependent, predominantly estimating neural network performance on image classification benchmarks. They are also search-space dependent; each predictor is designed to make predictions for a specific architecture search space with predefined topologies and set of operations. In this paper, we propose a novel All-in-One Predictor (AIO-P), which aims to pretrain neural predictors on architecture examples from multiple, separate computer vision (CV) task domains and multiple architecture spaces, and then transfer to unseen downstream CV tasks or neural architectures. We describe our proposed techniques for general graph representation, efficient predictor pretraining and knowledge infusion techniques, as well as methods to transfer to downstream tasks/spaces. Extensive experimental results show that AIO-P can achieve Mean Absolute Error (MAE) and Spearman's Rank Correlation (SRCC) below 1% and above 0.5, respectively, on a breadth of target downstream CV tasks with or without fine-tuning, outperforming a number of baselines. Moreover, AIO-P can directly transfer to new architectures not seen during training, accurately rank them and serve as an effective performance estimator when paired with an algorithm designed to preserve performance while reducing FLOPs.

The pulp and paper manufacturing industry requires precise quality control to ensure pure, contaminant-free end products suitable for various applications. Fungal spore concentration is a crucial metric that affects paper usability, and current testing methods are labor-intensive with delayed results, hindering real-time control strategies. To address this, a machine learning algorithm utilizing time-series data and domain knowledge was proposed. The optimal model employed Ridge Regression achieving an MSE of 2.90 on training and validation data. This approach could lead to significant improvements in efficiency and sustainability by providing real-time predictions for fungal spore concentrations. This paper showcases a promising method for real-time fungal spore concentration prediction, enabling stringent quality control measures in the pulp-and-paper industry.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (cf. Mallinar et al. 2022).

Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues, one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics.

Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.

Large-scale kernel ridge regression (KRR) is limited by the need to store a large kernel matrix K_t. To avoid storing the entire matrix K_t, Nystrom methods subsample a subset of columns of the kernel matrix, and efficiently find an approximate KRR solution on the reconstructed matrix. The chosen subsampling distribution in turn affects the statistical and computational tradeoffs. For KRR problems, recent works show that a sampling distribution proportional to the ridge leverage scores (RLSs) provides strong reconstruction guarantees for the approximation. While exact RLSs are as difficult to compute as a KRR solution, we may be able to approximate them well enough. In this paper, we study KRR problems in a sequential setting and introduce the INK-ESTIMATE algorithm, that incrementally computes the RLSs estimates. INK-ESTIMATE maintains a small sketch of K_t, that at each step is used to compute an intermediate estimate of the RLSs. First, our sketch update does not require access to previously seen columns, and therefore a single pass over the kernel matrix is sufficient. Second, the algorithm requires a fixed, small space budget to run dependent only on the effective dimension of the kernel matrix. Finally, our sketch provides strong approximation guarantees on the distance between the true kernel matrix and its approximation, and on the statistical risk of the approximate KRR solution at any time, because all our guarantees hold at any intermediate step.

One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space complexity to O(nm) by sampling m columns from K_n. Uniform sampling preserves KRR accuracy (up to epsilon) only when m is proportional to the maximum degree of freedom of K_n, which may require O(n) columns for datasets with high coherence. Sampling columns according to their ridge leverage scores (RLS) gives accurate Nystrom approximations with m proportional to the effective dimension, but computing exact RLS also requires O(n^2) space. (Calandriello et al. 2016) propose INK-Estimate, an algorithm that processes the dataset incrementally and updates RLS, effective dimension, and Nystrom approximations on-the-fly. Its space complexity scales with the effective dimension but introduces a dependency on the largest eigenvalue of K_n, which in the worst case is O(n). In this paper we introduce SQUEAK, a new algorithm that builds on INK-Estimate but uses unnormalized RLS. As a consequence, the algorithm is simpler, does not need to estimate the effective dimension for normalization, and achieves a space complexity that is only a constant factor worse than exact RLS sampling.

Structured tabular data dominates clinical medicine, yet existing benchmarks fail to reflect real-world properties like complex survey sampling, demographic oversampling, and subgroup fairness. We introduce the NHANES Accelerometry Cardiometabolic Benchmark, derived from NHANES 2003-2006, comprising 1,381 adults with hip-worn accelerometry, fasting laboratory biomarkers, dietary intake, and anthropometrics. We evaluate three tabular learning methods -- ridge regression, XGBoost, and the foundation model TabPFN v2 -- to predict glycated haemoglobin (HbA1c), fasting triglycerides, and C-reactive protein (CRP) from activity phenotypes and lifestyle covariates. TabPFN v2 achieves the best overall performance (HbA1c R^2=0.156, CRP R^2=0.383), while triglycerides remain largely unpredictable (R^2 < 0.05), consistent with known genetic dominance. We apply split conformal prediction to generate distribution-free 90% prediction intervals and evaluate demographic coverage equity across sex and race/ethnicity subgroups. Marginal coverage aligns with the 90% target for CRP and HbA1c but falls below for triglycerides. At the subgroup level, we observe localized undercoverage (e.g., HbA1c for Mexican American participants), illustrating the gap between marginal guarantees and the conditional coverage required for clinical fairness. Code and data are at https://github.com/felizzi/nhanes-accel-cardiometabolic-benchmark.

Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a linearly parameterized single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.

This paper models the availability of bikes at San Francisco Bay Area Bike Share stations using machine learning algorithms. Random Forest (RF) and Least-Squares Boosting (LSBoost) were used as univariate regression algorithms, and Partial Least-Squares Regression (PLSR) was applied as a multivariate regression algorithm. The univariate models were used to model the number of available bikes at each station. PLSR was applied to reduce the number of required prediction models and reflect the spatial correlation between stations in the network. Results clearly show that univariate models have lower error predictions than the multivariate model. However, the multivariate model results are reasonable for networks with a relatively large number of spatially correlated stations. Results also show that station neighbors and the prediction horizon time are significant predictors. The most effective prediction horizon time that produced the least prediction error was 15 minutes.

In the field of autonomous driving, even a meticulously trained model can encounter failures when faced with unfamiliar sceanrios. One of these scenarios can be formulated as an online continual learning (OCL) problem. That is, data come in an online fashion, and models are updated according to these streaming data. Two major OCL challenges are catastrophic forgetting and data imbalance. To address these challenges, in this paper, we propose an Analytic Exemplar-Free Online Continual Learning (AEF-OCL). The AEF-OCL leverages analytic continual learning principles and employs ridge regression as a classifier for features extracted by a large backbone network. It solves the OCL problem by recursively calculating the analytical solution, ensuring an equalization between the continual learning and its joint-learning counterpart, and works without the need to save any used samples (i.e., exemplar-free). Additionally, we introduce a Pseudo-Features Generator (PFG) module that recursively estimates the deviation of real features. The PFG generates offset pseudo-features following a normal distribution, thereby addressing the data imbalance issue. Experimental results demonstrate that despite being an exemplar-free strategy, our method outperforms various methods on the autonomous driving SODA10M dataset. Source code is available at https://github.com/ZHUANGHP/Analytic-continual-learning.

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function f_{rho}^{*} in [H]^{s}, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) H for some sin (0,1). The existing minimax optimal results require |f_{rho}^{*}|_{L^{infty}}<infty which implicitly requires s > alpha_{0} where alpha_{0}in (0,1) is the embedding index, a constant depending on H. Whether the KRR is optimal for all sin (0,1) is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any sin (0,1) when the H is a Sobolev RKHS.

Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the radial basis function neural network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link. https://github.com/dannyzx/Gaussian-RBFNN

We investigate the predictability of large language model (LLM) capabilities: given records of past experiments using different model families, numbers of parameters, tasks, and numbers of in-context examples, can we accurately predict LLM performance on new experiment configurations? Answering this question has practical implications for LLM users (e.g., deciding which models to try), developers (e.g., prioritizing evaluation on representative tasks), and the research community (e.g., identifying hard-to-predict capabilities that warrant further investigation). We study the performance prediction problem on experiment records from BIG-bench. On a random train-test split, an MLP-based predictor achieves an R^2 score greater than 95%, indicating the presence of learnable patterns within the experiment records. We then formulate the problem of searching for "small-bench," an informative subset of BIG-bench tasks from which the performance on the full set can be maximally recovered. We find a subset as informative as BIG-bench Hard for evaluating new model families, while being 3times smaller. Additionally, we find competitive subsets by clustering task representations learned by our MLP-based predictor and selecting tasks close to cluster centroids, highlighting the importance of task diversity in constructing "small-bench."

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

This research investigates how Machine Learning (ML) algorithms can assist in workload allocation strategies by detecting tasks with node affinity operators (referred to as constraint operators), which constrain their execution to a limited number of nodes. Using real-world Google Cluster Data (GCD) workload traces and the AGOCS framework, the study extracts node attributes and task constraints, then analyses them to identify suitable node-task pairings. It focuses on tasks that can be executed on either a single node or fewer than a thousand out of 12.5k nodes in the analysed GCD cluster. Task constraint operators are compacted, pre-processed with one-hot encoding, and used as features in a training dataset. Various ML classifiers, including Artificial Neural Networks, K-Nearest Neighbours, Decision Trees, Naive Bayes, Ridge Regression, Adaptive Boosting, and Bagging, are fine-tuned and assessed for accuracy and F1-scores. The final ensemble voting classifier model achieved 98% accuracy and a 1.5-1.8% misclassification rate for tasks with a single suitable node.

The recent surge in Time Series Foundation Models has rapidly advanced the field, yet the heterogeneous training setups across studies make it difficult to attribute improvements to architectural innovations versus data engineering. In this work, we investigate the potential of a standard patch Transformer, demonstrating that this generic architecture achieves state-of-the-art zero-shot forecasting performance using a straightforward training protocol. We conduct a comprehensive ablation study that covers model scaling, data composition, and training techniques to isolate the essential ingredients for high performance. Our findings identify the key drivers of performance, while confirming that the generic architecture itself demonstrates excellent scalability. By strictly controlling these variables, we provide comprehensive empirical results on model scaling across multiple dimensions. We release our open-source model and detailed findings to establish a transparent, reproducible baseline for future research.

ML models often exhibit unexpectedly poor behavior when they are deployed in real-world domains. We identify underspecification as a key reason for these failures. An ML pipeline is underspecified when it can return many predictors with equivalently strong held-out performance in the training domain. Underspecification is common in modern ML pipelines, such as those based on deep learning. Predictors returned by underspecified pipelines are often treated as equivalent based on their training domain performance, but we show here that such predictors can behave very differently in deployment domains. This ambiguity can lead to instability and poor model behavior in practice, and is a distinct failure mode from previously identified issues arising from structural mismatch between training and deployment domains. We show that this problem appears in a wide variety of practical ML pipelines, using examples from computer vision, medical imaging, natural language processing, clinical risk prediction based on electronic health records, and medical genomics. Our results show the need to explicitly account for underspecification in modeling pipelines that are intended for real-world deployment in any domain.

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and the number of samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is obligatory: near-optimal performance can only be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural tangent kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization, overfitting, and more data in random feature models.

Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under multicollinearity, and overfitting in meta-learning pipelines. We propose a regularized meta-learning framework that addresses these challenges through a four-stage pipeline combining redundancy-aware projection, statistical meta-feature augmentation, and cross-validated regularized meta-models (Ridge, Lasso, and ElasticNet). Our multi-metric de-duplication strategy removes near-collinear predictors using correlation and MSE thresholds (τ_{corr}=0.95), reducing the effective condition number of the meta-design matrix while preserving predictive diversity. Engineered ensemble statistics and interaction terms recover higher-order structure unavailable to raw prediction columns. A final inverse-RMSE blending stage mitigates regularizer-selection variance. On the Playground Series S6E1 benchmark (100K samples, 72 base models), the proposed framework achieves an out-of-fold RMSE of 8.582, improving over simple averaging (8.894) and conventional Ridge stacking (8.627), while matching greedy hill climbing (8.603) with substantially lower runtime (4 times faster). Conditioning analysis shows a 53.7\% reduction in effective matrix condition number after redundancy projection. Comprehensive ablations demonstrate consistent contributions from de-duplication, statistical meta-features, and meta-ensemble blending. These results position regularized meta-learning as a stable and deployment-efficient stacking strategy for high-dimensional ensemble systems.

Deep neural networks are often applied to medical images to automate the problem of medical diagnosis. However, a more clinically relevant question that practitioners usually face is how to predict the future trajectory of a disease. Current methods for prognosis or disease trajectory forecasting often require domain knowledge and are complicated to apply. In this paper, we formulate the prognosis prediction problem as a one-to-many prediction problem. Inspired by a clinical decision-making process with two agents -- a radiologist and a general practitioner -- we predict prognosis with two transformer-based components that share information with each other. The first transformer in this framework aims to analyze the imaging data, and the second one leverages its internal states as inputs, also fusing them with auxiliary clinical data. The temporal nature of the problem is modeled within the transformer states, allowing us to treat the forecasting problem as a multi-task classification, for which we propose a novel loss. We show the effectiveness of our approach in predicting the development of structural knee osteoarthritis changes and forecasting Alzheimer's disease clinical status directly from raw multi-modal data. The proposed method outperforms multiple state-of-the-art baselines with respect to performance and calibration, both of which are needed for real-world applications. An open-source implementation of our method is made publicly available at https://github.com/Oulu-IMEDS/CLIMATv2.

Dataset distillation methods have achieved remarkable success in distilling a large dataset into a small set of representative samples. However, they are not designed to produce a distilled dataset that can be effectively used for facilitating self-supervised pre-training. To this end, we propose a novel problem of distilling an unlabeled dataset into a set of small synthetic samples for efficient self-supervised learning (SSL). We first prove that a gradient of synthetic samples with respect to a SSL objective in naive bilevel optimization is biased due to the randomness originating from data augmentations or masking. To address this issue, we propose to minimize the mean squared error (MSE) between a model's representations of the synthetic examples and their corresponding learnable target feature representations for the inner objective, which does not introduce any randomness. Our primary motivation is that the model obtained by the proposed inner optimization can mimic the self-supervised target model. To achieve this, we also introduce the MSE between representations of the inner model and the self-supervised target model on the original full dataset for outer optimization. Lastly, assuming that a feature extractor is fixed, we only optimize a linear head on top of the feature extractor, which allows us to reduce the computational cost and obtain a closed-form solution of the head with kernel ridge regression. We empirically validate the effectiveness of our method on various applications involving transfer learning.

Transformers have become a standard architecture in machine learning, demonstrating strong in-context learning (ICL) abilities that allow them to learn from the prompt at inference time. However, uncertainty quantification for ICL remains an open challenge, particularly in noisy regression tasks. This paper investigates whether ICL can be leveraged for distribution-free uncertainty estimation, proposing a method based on conformal prediction to construct prediction intervals with guaranteed coverage. While traditional conformal methods are computationally expensive due to repeated model fitting, we exploit ICL to efficiently generate confidence intervals in a single forward pass. Our empirical analysis compares this approach against ridge regression-based conformal methods, showing that conformal prediction with in-context learning (CP with ICL) achieves robust and scalable uncertainty estimates. Additionally, we evaluate its performance under distribution shifts and establish scaling laws to guide model training. These findings bridge ICL and conformal prediction, providing a theoretically grounded and new framework for uncertainty quantification in transformer-based models.

We introduce NeuralProphet, a successor to Facebook Prophet, which set an industry standard for explainable, scalable, and user-friendly forecasting frameworks. With the proliferation of time series data, explainable forecasting remains a challenging task for business and operational decision making. Hybrid solutions are needed to bridge the gap between interpretable classical methods and scalable deep learning models. We view Prophet as a precursor to such a solution. However, Prophet lacks local context, which is essential for forecasting the near-term future and is challenging to extend due to its Stan backend. NeuralProphet is a hybrid forecasting framework based on PyTorch and trained with standard deep learning methods, making it easy for developers to extend the framework. Local context is introduced with auto-regression and covariate modules, which can be configured as classical linear regression or as Neural Networks. Otherwise, NeuralProphet retains the design philosophy of Prophet and provides the same basic model components. Our results demonstrate that NeuralProphet produces interpretable forecast components of equivalent or superior quality to Prophet on a set of generated time series. NeuralProphet outperforms Prophet on a diverse collection of real-world datasets. For short to medium-term forecasts, NeuralProphet improves forecast accuracy by 55 to 92 percent.

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

This article investigates signal estimation in wireless transmission (i.e., receive beamforming) from the perspective of statistical machine learning, where the transmit signals may be from an integrated sensing and communication system; that is, 1) signals may be not only discrete constellation points but also arbitrary complex values; 2) signals may be spatially correlated. Particular attention is paid to handling various uncertainties such as the uncertainty of the transmit signal covariance, the uncertainty of the channel matrix, the uncertainty of the channel noise covariance, the existence of channel impulse noises, and the limited sample size of pilots. To proceed, a distributionally robust machine learning framework that is insensitive to the above uncertainties is proposed, which reveals that channel estimation is not a necessary operation. For optimal linear estimation, the proposed framework includes several existing beamformers as special cases such as diagonal loading and eigenvalue thresholding. For optimal nonlinear estimation, estimators are limited in reproducing kernel Hilbert spaces and neural network function spaces, and corresponding uncertainty-aware solutions (e.g., kernelized diagonal loading) are derived. In addition, we prove that the ridge and kernel ridge regression methods in machine learning are distributionally robust against diagonal perturbation in feature covariance.

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the-art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer's favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks. From a delivery standpoint, we operationalize the above four dimensions (4D) of exploration within a unified, scalable open-source toolbox called 4DBInfer. We conclude by presenting evaluations using 4DBInfer, the results of which highlight the importance of considering each such dimension in the design of RDB predictive models, as well as the limitations of more naive approaches such as simply joining adjacent tables. Our source code is released at https://github.com/awslabs/multi-table-benchmark .

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models. This view will have various implications for NNs, e.g. providing an explanation for why convergence problems arise in NNs, and it gives rough guidance on avoiding overfitting. In addition, we use this phenomenon to predict and confirm a multicollinearity property of NNs not previously reported in the literature. Most importantly, given this loose correspondence, one may choose to routinely use polynomial models instead of NNs, thus avoiding some major problems of the latter, such as having to set many tuning parameters and dealing with convergence issues. We present a number of empirical results; in each case, the accuracy of the polynomial approach matches or exceeds that of NN approaches. A many-featured, open-source software package, polyreg, is available.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Foundation models for predictive machine learning on tabular data have recently gained significant traction in academia and industry. Research communities across disciplines are increasingly evaluating tabular foundation models on diverse datasets and tasks. However, these task- and discipline-specific evaluations remain largely inaccessible to model researchers because benchmark software and evaluation protocols are fragmented. As a result, model researchers rely on standard benchmarks, which are mostly defined for tasks where tabular foundation models already excel. The most challenging scenarios are excluded, limiting meaningful progress in the field by focusing on marginal improvements on IID data rather than on broader, more demanding challenges. To overcome this, we introduce BeyondArena, the first unified holistic benchmark for tabular data that supports diverse task types (IID, temporal, grouped), across sample size and feature dimensionality scales, with diverse feature types (with text, with high cardinality) from a broad range of disciplines. To enable unified benchmarking beyond standard benchmarks, we introduce Data Foundry, a Python framework and metadata schema for curating tabular datasets for predictive machine learning. Our results across 11 models and 142 curated datasets show that existing tabular foundation models excel on tiny- to medium-sized IID data, while traditional tree-based and deep learning models still dominate on non-IID, large, and high-dimensional datasets. BeyondArena guides model research for the most demanding challenges in tabular data, enabling progress towards truly foundational tabular models.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

We present the findings of "The Alzheimer's Disease Prediction Of Longitudinal Evolution" (TADPOLE) Challenge, which compared the performance of 92 algorithms from 33 international teams at predicting the future trajectory of 219 individuals at risk of Alzheimer's disease. Challenge participants were required to make a prediction, for each month of a 5-year future time period, of three key outcomes: clinical diagnosis, Alzheimer's Disease Assessment Scale Cognitive Subdomain (ADAS-Cog13), and total volume of the ventricles. The methods used by challenge participants included multivariate linear regression, machine learning methods such as support vector machines and deep neural networks, as well as disease progression models. No single submission was best at predicting all three outcomes. For clinical diagnosis and ventricle volume prediction, the best algorithms strongly outperform simple baselines in predictive ability. However, for ADAS-Cog13 no single submitted prediction method was significantly better than random guesswork. Two ensemble methods based on taking the mean and median over all predictions, obtained top scores on almost all tasks. Better than average performance at diagnosis prediction was generally associated with the additional inclusion of features from cerebrospinal fluid (CSF) samples and diffusion tensor imaging (DTI). On the other hand, better performance at ventricle volume prediction was associated with inclusion of summary statistics, such as the slope or maxima/minima of biomarkers. TADPOLE's unique results suggest that current prediction algorithms provide sufficient accuracy to exploit biomarkers related to clinical diagnosis and ventricle volume, for cohort refinement in clinical trials for Alzheimer's disease. However, results call into question the usage of cognitive test scores for patient selection and as a primary endpoint in clinical trials.

We introduce Moirai 2.0, a decoder-only time-series foundation model trained on a new corpus of 36M series. The model adopts quantile forecasting and multi-token prediction, improving both probabilistic accuracy and inference efficiency. On the Gift-Eval benchmark, it ranks among the top pretrained models while achieving a strong trade-off between accuracy, speed, and model size. Compared to Moirai 1.0, Moirai 2.0 replaces masked-encoder training, multi-patch inputs, and mixture-distribution outputs with a simpler decoder-only architecture, single patch, and quantile loss. Ablation studies isolate these changes -- showing that the decoder-only backbone along with recursive multi-quantile decoding contribute most to the gains. Additional experiments show that Moirai 2.0 outperforms larger models from the same family and exhibits robust domain-level results. In terms of efficiency and model size, Moirai 2.0 is twice as fast and thirty times smaller than its prior best version, Moirai 1.0-Large, while also performing better. Model performance plateaus with increasing parameter count and declines at longer horizons, motivating future work on data scaling and long-horizon modeling. We release code and evaluation details to support further research.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

In many industries, predicting metric outcomes of large systems is a fundamental problem, driven largely by traditional tabular regression. However, such methods struggle on complex systems data in the wild such as configuration files or system logs, where feature engineering is often infeasible. We propose text-to-text regression as a general, scalable alternative. For predicting resource efficiency on Borg, Google's massive compute cluster scheduling system, a 60M parameter encoder-decoder, trained from random initialization, achieves up to a near perfect 0.99 (0.9 average) rank correlation across the entire fleet, and 100x lower MSE than tabular approaches. The model also easily adapts to new tasks in only 500 few-shot examples and captures the densities of complex outcome distributions. Ablation studies highlight the importance of using encoders, increasing sequence length, and the model's inherent uncertainty quantification. These findings pave the way for universal simulators of real-world outcomes.

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

In this report, we introduce Piccolo2, an embedding model that surpasses other models in the comprehensive evaluation over 6 tasks on CMTEB benchmark, setting a new state-of-the-art. Piccolo2 primarily leverages an efficient multi-task hybrid loss training approach, effectively harnessing textual data and labels from diverse downstream tasks. In addition, Piccolo2 scales up the embedding dimension and uses MRL training to support more flexible vector dimensions. The latest information of piccolo models can be accessed via: https://huggingface.co/sensenova/

Most kernel-based methods, such as kernel or Gaussian process regression, kernel PCA, ICA, or k-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix K_n requires at least O(n^2) time and space for n samples. Recent works show that sampling points with replacement according to their ridge leverage scores (RLS) generates small dictionaries of relevant points with strong spectral approximation guarantees for K_n. The drawback of RLS-based methods is that computing exact RLS requires constructing and storing the whole kernel matrix. In this paper, we introduce SQUEAK, a new algorithm for kernel approximation based on RLS sampling that sequentially processes the dataset, storing a dictionary which creates accurate kernel matrix approximations with a number of points that only depends on the effective dimension d_{eff}(γ) of the dataset. Moreover since all the RLS estimations are efficiently performed using only the small dictionary, SQUEAK is the first RLS sampling algorithm that never constructs the whole matrix K_n, runs in linear time mathcal{O}(nd_{eff}(γ)^3) w.r.t. n, and requires only a single pass over the dataset. We also propose a parallel and distributed version of SQUEAK that linearly scales across multiple machines, achieving similar accuracy in as little as mathcal{O}(log(n)d_{eff}(γ)^3) time.

Automated feature engineering plays a critical role in improving predictive model performance for tabular learning tasks. Traditional automated feature engineering methods are limited by their reliance on pre-defined transformations within fixed, manually designed search spaces, often neglecting domain knowledge. Recent advances using Large Language Models (LLMs) have enabled the integration of domain knowledge into the feature engineering process. However, existing LLM-based approaches use direct prompting or rely solely on validation scores for feature selection, failing to leverage insights from prior feature discovery experiments or establish meaningful reasoning between feature generation and data-driven performance. To address these challenges, we propose LLM-FE, a novel framework that combines evolutionary search with the domain knowledge and reasoning capabilities of LLMs to automatically discover effective features for tabular learning tasks. LLM-FE formulates feature engineering as a program search problem, where LLMs propose new feature transformation programs iteratively, and data-driven feedback guides the search process. Our results demonstrate that LLM-FE consistently outperforms state-of-the-art baselines, significantly enhancing the performance of tabular prediction models across diverse classification and regression benchmarks.

We present Δ-UQ -- a novel, general-purpose uncertainty estimator using the concept of anchoring in predictive models. Anchoring works by first transforming the input into a tuple consisting of an anchor point drawn from a prior distribution, and a combination of the input sample with the anchor using a pretext encoding scheme. This encoding is such that the original input can be perfectly recovered from the tuple -- regardless of the choice of the anchor. Therefore, any predictive model should be able to predict the target response from the tuple alone (since it implicitly represents the input). Moreover, by varying the anchors for a fixed sample, we can estimate uncertainty in the prediction even using only a single predictive model. We find this uncertainty is deeply connected to improper sampling of the input data, and inherent noise, enabling us to estimate the total uncertainty in any system. With extensive empirical studies on a variety of use-cases, we demonstrate that Δ-UQ outperforms several competitive baselines. Specifically, we study model fitting, sequential model optimization, model based inversion in the regression setting and out of distribution detection, & calibration under distribution shifts for classification.

Regression, the task of predicting a continuous scalar target y based on some features x is one of the most fundamental tasks in machine learning and statistics. It has been observed and theoretically analyzed that the classical approach, meansquared error minimization, can lead to suboptimal results when training neural networks. In this work, we propose a new method to improve the training of these models on regression tasks, with continuous scalar targets. Our method is based on casting this task in a different fashion, using a target encoder, and a prediction decoder, inspired by approaches in classification and clustering. We showcase the performance of our method on a wide range of real-world datasets.

Genome-wide association studies are pivotal in understanding the genetic underpinnings of complex traits and diseases. Collaborative, multi-site GWAS aim to enhance statistical power but face obstacles due to the sensitive nature of genomic data sharing. Current state-of-the-art methods provide a privacy-focused approach utilizing computationally expensive methods such as Secure Multi-Party Computation and Homomorphic Encryption. In this context, we present a novel algorithm PP-GWAS designed to improve upon existing standards in terms of computational efficiency and scalability without sacrificing data privacy. This algorithm employs randomized encoding within a distributed architecture to perform stacked ridge regression on a Linear Mixed Model to ensure rigorous analysis. Experimental evaluation with real world and synthetic data indicates that PP-GWAS can achieve computational speeds twice as fast as similar state-of-the-art algorithms while using lesser computational resources, all while adhering to a robust security model that caters to an all-but-one semi-honest adversary setting. We have assessed its performance using various datasets, emphasizing its potential in facilitating more efficient and private genomic analyses.

In medical applications, deep learning methods are built to automate diagnostic tasks. However, a clinically relevant question that practitioners usually face, is how to predict the future trajectory of a disease (prognosis). Current methods for such a problem often require domain knowledge, and are complicated to apply. In this paper, we formulate the prognosis prediction problem as a one-to-many forecasting problem from multimodal data. Inspired by a clinical decision-making process with two agents -- a radiologist and a general practitioner, we model a prognosis prediction problem with two transformer-based components that share information between each other. The first block in this model aims to analyze the imaging data, and the second block leverages the internal representations of the first one as inputs, also fusing them with auxiliary patient data. We show the effectiveness of our method in predicting the development of structural knee osteoarthritis changes over time. Our results show that the proposed method outperforms the state-of-the-art baselines in terms of various performance metrics. In addition, we empirically show that the existence of the multi-agent transformers with depths of 2 is sufficient to achieve good performances. Our code is publicly available at https://github.com/MIPT-Oulu/CLIMAT.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Predictor-based methods have substantially enhanced Neural Architecture Search (NAS) optimization. The efficacy of these predictors is largely influenced by the method of encoding neural network architectures. While traditional encodings used an adjacency matrix describing the graph structure of a neural network, novel encodings embrace a variety of approaches from unsupervised pretraining of latent representations to vectors of zero-cost proxies. In this paper, we categorize and investigate neural encodings from three main types: structural, learned, and score-based. Furthermore, we extend these encodings and introduce unified encodings, that extend NAS predictors to multiple search spaces. Our analysis draws from experiments conducted on over 1.5 million neural network architectures on NAS spaces such as NASBench-101 (NB101), NB201, NB301, Network Design Spaces (NDS), and TransNASBench-101. Building on our study, we present our predictor FLAN: Flow Attention for NAS. FLAN integrates critical insights on predictor design, transfer learning, and unified encodings to enable more than an order of magnitude cost reduction for training NAS accuracy predictors. Our implementation and encodings for all neural networks are open-sourced at https://github.com/abdelfattah-lab/flan_nas{https://github.com/abdelfattah-lab/flan\_nas}.

Building predictive models for companies often relies on inference using historical data of companies in the same industry sector. However, companies are similar across a variety of dimensions that should be leveraged in relevant prediction problems. This is particularly true for large, complex organizations which may not be well defined by a single industry and have no clear peers. To enable prediction using company information across a variety of dimensions, we create an embedding of company stocks, Stock2Vec, which can be easily added to any prediction model that applies to companies with associated stock prices. We describe the process of creating this rich vector representation from stock price fluctuations, and characterize what the dimensions represent. We then conduct comprehensive experiments to evaluate this embedding in applied machine learning problems in various business contexts. Our experiment results demonstrate that the four features in the Stock2Vec embedding can readily augment existing cross-company models and enhance cross-company predictions.

Pretrained transformers exhibit the remarkable ability of in-context learning (ICL): they can learn tasks from just a few examples provided in the prompt without updating any weights. This raises a foundational question: can ICL solve fundamentally new tasks that are very different from those seen during pretraining? To probe this question, we examine ICL's performance on linear regression while varying the diversity of tasks in the pretraining dataset. We empirically demonstrate a task diversity threshold for the emergence of ICL. Below this threshold, the pretrained transformer cannot solve unseen regression tasks, instead behaving like a Bayesian estimator with the non-diverse pretraining task distribution as the prior. Beyond this threshold, the transformer significantly outperforms this estimator; its behavior aligns with that of ridge regression, corresponding to a Gaussian prior over all tasks, including those not seen during pretraining. Thus, when pretrained on data with task diversity greater than the threshold, transformers can optimally solve fundamentally new tasks in-context. Importantly, this capability hinges on it deviating from the Bayes optimal estimator with the pretraining distribution as the prior. This study also explores the effect of regularization, model capacity and task structure and underscores, in a concrete example, the critical role of task diversity, alongside data and model scale, in the emergence of ICL. Code is available at https://github.com/mansheej/icl-task-diversity.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

We present a conceptual framework, datamodeling, for analyzing the behavior of a model class in terms of the training data. For any fixed "target" example x, training set S, and learning algorithm, a datamodel is a parameterized function 2^S to R that for any subset of S' subset S -- using only information about which examples of S are contained in S' -- predicts the outcome of training a model on S' and evaluating on x. Despite the potential complexity of the underlying process being approximated (e.g., end-to-end training and evaluation of deep neural networks), we show that even simple linear datamodels can successfully predict model outputs. We then demonstrate that datamodels give rise to a variety of applications, such as: accurately predicting the effect of dataset counterfactuals; identifying brittle predictions; finding semantically similar examples; quantifying train-test leakage; and embedding data into a well-behaved and feature-rich representation space. Data for this paper (including pre-computed datamodels as well as raw predictions from four million trained deep neural networks) is available at https://github.com/MadryLab/datamodels-data .

Multivariate time series classification is a crucial task in data mining, attracting growing research interest due to its broad applications. While many existing methods focus on discovering discriminative patterns in time series, real-world data does not always present such patterns, and sometimes raw numerical values can also serve as discriminative features. Additionally, the recent success of Transformer models has inspired many studies. However, when applying to time series classification, the self-attention mechanisms in Transformer models could introduce classification-irrelevant features, thereby compromising accuracy. To address these challenges, we propose a novel method, VSFormer, that incorporates both discriminative patterns (shape) and numerical information (value). In addition, we extract class-specific prior information derived from supervised information to enrich the positional encoding and provide classification-oriented self-attention learning, thereby enhancing its effectiveness. Extensive experiments on all 30 UEA archived datasets demonstrate the superior performance of our method compared to SOTA models. Through ablation studies, we demonstrate the effectiveness of the improved encoding layer and the proposed self-attention mechanism. Finally, We provide a case study on a real-world time series dataset without discriminative patterns to interpret our model.

A delayed feedback reservoir (DFR) is a hardwarefriendly reservoir computing system. Implementing DFRs in embedded hardware requires efficient online training. However, two main challenges prevent this: hyperparameter selection, which is typically done by offline grid search, and training of the output linear layer, which is memory-intensive. This paper introduces a fast and accurate parameter optimization method for the reservoir layer utilizing backpropagation and gradient descent by adopting a modular DFR model. A truncated backpropagation strategy is proposed to reduce memory consumption associated with the expansion of the recursive structure while maintaining accuracy. The computation time is significantly reduced compared to grid search. Additionally, an in-place Ridge regression for the output layer via 1-D Cholesky decomposition is presented, reducing memory usage to be 1/4. These methods enable the realization of an online edge training and inference system of DFR on an FPGA, reducing computation time by about 1/13 and power consumption by about 1/27 compared to software implementation on the same board.

Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.

Recent advances in deep learning have driven rapid progress in time series forecasting, yet many state-of-the-art models continue to struggle with robust performance in real-world applications, even when they achieve strong results on standard benchmark datasets. This persistent gap can be attributed to the black-box nature of deep learning architectures and the inherent limitations of current evaluation frameworks, which frequently lack the capacity to provide clear, quantitative insights into the specific strengths and weaknesses of different models, thereby complicating the selection of appropriate models for particular forecasting scenarios. To address these issues, we propose a synthetic data-driven evaluation paradigm, SynTSBench, that systematically assesses fundamental modeling capabilities of time series forecasting models through programmable feature configuration. Our framework isolates confounding factors and establishes an interpretable evaluation system with three core analytical dimensions: (1) temporal feature decomposition and capability mapping, which enables systematic evaluation of model capacities to learn specific pattern types; (2) robustness analysis under data irregularities, which quantifies noise tolerance thresholds and anomaly recovery capabilities; and (3) theoretical optimum benchmarking, which establishes performance boundaries for each pattern type-enabling direct comparison between model predictions and mathematical optima. Our experiments show that current deep learning models do not universally approach optimal baselines across all types of temporal features.The code is available at https://github.com/TanQitai/SynTSBench

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

Tabular Foundation Models have recently established the state of the art in supervised tabular learning, by leveraging pretraining to learn generalizable representations of numerical and categorical structured data. However, they lack native support for unstructured modalities such as text and image, and rely on frozen, pretrained embeddings to process them. On established Multimodal Tabular Learning benchmarks, we show that tuning the embeddings to the task improves performance. Existing benchmarks, however, often focus on the mere co-occurrence of modalities; this leads to high variance across datasets and masks the benefits of task-specific tuning. To address this gap, we introduce MulTaBench, a benchmark of 40 datasets, split equally between image-tabular and text-tabular tasks. We focus on predictive tasks where the modalities provide complementary predictive signal, and where generic embeddings lose critical information, necessitating Target-Aware Representations that are aligned with the task. Our experimental results demonstrate that the gains from target-aware representation tuning generalize across both text and image modalities, several tabular learners, encoder scales, and embedding dimensions. MulTaBench constitutes the largest image-tabular benchmarking effort to date, spanning high-impact domains such as healthcare and e-commerce. It is designed to enable the research of novel architectures which incorporate joint modeling and target-aware representations, paving the way for the development of novel Multimodal Tabular Foundation Models.

Strictly proper scoring rules identify the true conditional class distribution at population level, but their curvature can alter optimization and finite-sample behavior. We study three multiclass objectives: a class-aware quadratic Bregman score (CAPM), a strongly convex generator with constrained log-cosh ridges (HPG), and an HPG objective with an annealed probability-margin penalty (APMS). CAPM is treated as a structured instance of established quadratic scoring-rule theory. We derive conditional-regret, curvature, range, and logit-gradient bounds for CAPM and HPG, and prove exact penalty-range and conditional-target displacement bounds for APMS. Controlled five-seed experiments use Digits, Wisconsin breast cancer, and synthetic confusion and long-tail problems under clean labels, symmetric and pair-flip corruption, class imbalance, calibration evaluation, input corruption, and first-order adversarial perturbations. The candidates are close to cross-entropy on clean data and show descriptive gains in some noisy-label cells, but the five-seed comparisons are interpreted descriptively rather than as significance evidence. The selected noisy-label baselines perform better on Digits with 40% symmetric label noise, and explicit prior-adjustment methods perform better in the 30:1 synthetic long-tail experiment. Ablations do not show a consistent benefit from the candidate-specific graph, ridge, or margin components. The mathematical analysis establishes the stated properties, and the experiments delimit the empirical evidence; together they do not support a claim of general superiority.

We introduce TabRepo, a new dataset of tabular model evaluations and predictions. TabRepo contains the predictions and metrics of 1310 models evaluated on 200 classification and regression datasets. We illustrate the benefit of our dataset in multiple ways. First, we show that it allows to perform analysis such as comparing Hyperparameter Optimization against current AutoML systems while also considering ensembling at marginal cost by using precomputed model predictions. Second, we show that our dataset can be readily leveraged to perform transfer-learning. In particular, we show that applying standard transfer-learning techniques allows to outperform current state-of-the-art tabular systems in accuracy, runtime and latency.

Machine learning techniques are effective for building predictive models because they identify patterns in large datasets. Development of a model for complex real-life problems often stop at the point of publication, proof of concept or when made accessible through some mode of deployment. However, a model in the medical domain risks becoming obsolete as patient demographics, systems and clinical practices change. The maintenance and monitoring of predictive model performance post-publication is crucial to enable their safe and effective long-term use. We will assess the infrastructure required to monitor the outputs of a machine learning algorithm, and present two scenarios with examples of monitoring and updates of models, firstly on a breast cancer prognosis model trained on public longitudinal data, and secondly on a neurodegenerative stratification algorithm that is currently being developed and tested in clinic.

Methods for neural network hyperparameter optimization and meta-modeling are computationally expensive due to the need to train a large number of model configurations. In this paper, we show that standard frequentist regression models can predict the final performance of partially trained model configurations using features based on network architectures, hyperparameters, and time-series validation performance data. We empirically show that our performance prediction models are much more effective than prominent Bayesian counterparts, are simpler to implement, and are faster to train. Our models can predict final performance in both visual classification and language modeling domains, are effective for predicting performance of drastically varying model architectures, and can even generalize between model classes. Using these prediction models, we also propose an early stopping method for hyperparameter optimization and meta-modeling, which obtains a speedup of a factor up to 6x in both hyperparameter optimization and meta-modeling. Finally, we empirically show that our early stopping method can be seamlessly incorporated into both reinforcement learning-based architecture selection algorithms and bandit based search methods. Through extensive experimentation, we empirically show our performance prediction models and early stopping algorithm are state-of-the-art in terms of prediction accuracy and speedup achieved while still identifying the optimal model configurations.

Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) jacot2018neural. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK arora2019exact. However, the equivalence is only known for ridge regression currently arora2019harnessing, while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalences between NNs and a broad family of ell_2 regularized KMs with finite-width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) non-vacuous generalization bound of NN via the corresponding KM; (ii) non-trivial robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression. Our code for the experiments is available at https://github.com/leslie-CH/equiv-nn-svm.

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to 20times sim 5000times. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and non-stationarity, creating bottlenecks for models like Gradient Boosting Decision Trees and requiring laborious manual feature engineering. We introduce KMLP, a hybrid deep architecture integrating a shallow Kolmogorov-Arnold Network (KAN) front-end with a Gated Multilayer Perceptron (gMLP) backbone. The KAN front-end uses learnable activation functions to automatically model complex non-linear transformations for each feature, while the gMLP backbone captures high-order interactions. Experiments on public benchmarks and an industrial dataset with billions of samples show KMLP achieves state-of-the-art performance, with advantages over baselines like GBDTs increasing at larger scales, validating KMLP as a scalable deep learning paradigm for large-scale web tabular data.

Geological borehole descriptions contain detailed textual information about the composition of the subsurface. However, their unstructured format presents significant challenges for extracting relevant features into a structured format. This paper introduces GEOBERTje: a domain adapted large language model trained on geological borehole descriptions from Flanders (Belgium) in the Dutch language. This model effectively extracts relevant information from the borehole descriptions and represents it into a numeric vector space. Showcasing just one potential application of GEOBERTje, we finetune a classifier model on a limited number of manually labeled observations. This classifier categorizes borehole descriptions into a main, second and third lithology class. We show that our classifier outperforms both a rule-based approach and GPT-4 of OpenAI. This study exemplifies how domain adapted large language models enhance the efficiency and accuracy of extracting information from complex, unstructured geological descriptions. This offers new opportunities for geological analysis and modeling using vast amounts of data.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

Table foundation models bring high hopes to data science: pre-trained on tabular data to embark knowledge or priors, they should facilitate downstream tasks on tables. One specific challenge is that of data semantics: numerical entries take their meaning from context, e.g., column name. Pre-trained neural networks that jointly model column names and table entries have recently boosted prediction accuracy. While these models outline the promises of world knowledge to interpret table values, they lack the convenience of popular foundation models in text or vision. Indeed, they must be fine-tuned to bring benefits, come with sizeable computation costs, and cannot easily be reused or combined with other architectures. Here we introduce TARTE, a foundation model that transforms tables to knowledge-enhanced vector representations using the string to capture semantics. Pre-trained on large relational data, TARTE yields representations that facilitate subsequent learning with little additional cost. These representations can be fine-tuned or combined with other learners, giving models that push the state-of-the-art prediction performance and improve the prediction/computation performance trade-off. Specialized to a task or a domain, TARTE gives domain-specific representations that facilitate further learning. Our study demonstrates an effective approach to knowledge pre-training for tabular learning.

In recent years, the development of robust multi-source models has emerged in the Earth Observation (EO) field. These are models that leverage data from diverse sources to improve predictive accuracy when there is missing data. Despite these advancements, the factors influencing the varying effectiveness of such models remain poorly understood. In this study, we evaluate the predictive performance of six state-of-the-art multi-source models in predicting scenarios where either a single data source is missing or only a single source is available. Our analysis reveals that the efficacy of these models is intricately tied to the nature of the task, the complementarity among data sources, and the model design. Surprisingly, we observe instances where the removal of certain data sources leads to improved predictive performance, challenging the assumption that incorporating all available data is always beneficial. These findings prompt critical reflections on model complexity and the necessity of all collected data sources, potentially shaping the way for more streamlined approaches in EO applications.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

Tabular data prediction is a fundamental machine learning task for many applications. Existing methods predominantly employ discriminative modeling and operate under the assumption of a fixed target column, necessitating re-training for every new predictive task. Inspired by the generative power of large language models (LLMs), this paper exploits the idea of building universal tabular data predictors based on generative modeling, namely UniPredict. Here, we demonstrate the scalability of an LLM to extensive tabular datasets, enabling it to comprehend diverse tabular inputs and predict target variables following the provided instructions. Specifically, we train a single LLM on an aggregation of 169 tabular datasets with diverse targets and compare its performance against baselines that are trained on each dataset separately. We observe this versatile UniPredict model demonstrates an advantage over other models, ranging from 5.4% to 13.4%, when compared with the best tree-boosting baseline and the best neural network baseline, respectively. We further test UniPredict in few-shot learning settings on another 62 tabular datasets. Our method achieves strong performance in quickly adapting to new tasks. In low-resource few-shot setup, we observed a 100%+ performance advantage compared with XGBoost, and significant margin over all baselines. We envision that UniPredict sheds light on developing a universal tabular data prediction system that learns from data at scale and serves a wide range of prediction tasks.

Pretrained time series models have enabled inference-only forecasting systems that produce accurate predictions without task-specific training. However, existing approaches largely focus on univariate forecasting, limiting their applicability in real-world scenarios where multivariate data and covariates play a crucial role. We present Chronos-2, a pretrained model capable of handling univariate, multivariate, and covariate-informed forecasting tasks in a zero-shot manner. Chronos-2 employs a group attention mechanism that facilitates in-context learning (ICL) through efficient information sharing across multiple time series within a group, which may represent sets of related series, variates of a multivariate series, or targets and covariates in a forecasting task. These general capabilities are achieved through training on synthetic datasets that impose diverse multivariate structures on univariate series. Chronos-2 delivers state-of-the-art performance across three comprehensive benchmarks: fev-bench, GIFT-Eval, and Chronos Benchmark II. On fev-bench, which emphasizes multivariate and covariate-informed forecasting, Chronos-2's universal ICL capabilities lead to substantial improvements over existing models. On tasks involving covariates, it consistently outperforms baselines by a wide margin. Case studies in the energy and retail domains further highlight its practical advantages. The in-context learning capabilities of Chronos-2 establish it as a general-purpose forecasting model that can be used "as is" in real-world forecasting pipelines.

Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new closed-form predictor variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at 100 and 300 epochs (top-1 linear accuracy on ImageNet).

Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning". In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We then explore the significance of TabPFN to the field of statistics: We show that an out-of-the-box application of TabPFN can sometimes outperform specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. As a partial explanation for the predictive effectiveness of TabPFN, we show that it can simultaneously adapt to both nonparametric structure and parametric structure, for instance, sometimes outperforming LASSO even when assumptions are correctly specified. All experiments can be reproduced using the code provided at https://github.com/qinglong-tian/tabpfn_study (https://github.com/qinglong-tian/tabpfn_study).

This paper introduces WeatherFormer, a transformer encoder-based model designed to learn robust weather features from minimal observations. It addresses the challenge of modeling complex weather dynamics from small datasets, a bottleneck for many prediction tasks in agriculture, epidemiology, and climate science. WeatherFormer was pretrained on a large pretraining dataset comprised of 39 years of satellite measurements across the Americas. With a novel pretraining task and fine-tuning, WeatherFormer achieves state-of-the-art performance in county-level soybean yield prediction and influenza forecasting. Technical innovations include a unique spatiotemporal encoding that captures geographical, annual, and seasonal variations, adapting the transformer architecture to continuous weather data, and a pretraining strategy to learn representations that are robust to missing weather features. This paper for the first time demonstrates the effectiveness of pretraining large transformer encoder models for weather-dependent applications across multiple domains.

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Breast cancer survival prediction in computational pathology presents a remarkable challenge due to tumor heterogeneity. For instance, different regions of the same tumor in the pathology image can show distinct morphological and molecular characteristics. This makes it difficult to extract representative features from whole slide images (WSIs) that truly reflect the tumor's aggressive potential and likely survival outcomes. In this paper, we present PathoHR, a novel pipeline for accurate breast cancer survival prediction that enhances any size of pathological images to enable more effective feature learning. Our approach entails (1) the incorporation of a plug-and-play high-resolution Vision Transformer (ViT) to enhance patch-wise WSI representation, enabling more detailed and comprehensive feature extraction, (2) the systematic evaluation of multiple advanced similarity metrics for comparing WSI-extracted features, optimizing the representation learning process to better capture tumor characteristics, (3) the demonstration that smaller image patches enhanced follow the proposed pipeline can achieve equivalent or superior prediction accuracy compared to raw larger patches, while significantly reducing computational overhead. Experimental findings valid that PathoHR provides the potential way of integrating enhanced image resolution with optimized feature learning to advance computational pathology, offering a promising direction for more accurate and efficient breast cancer survival prediction. Code will be available at https://github.com/AIGeeksGroup/PathoHR.

The paper shows that the application of the fixed-effect multiple linear regression model to an overparameterized dataset is equivalent to fitting the data with a hyper-curve parameterized by a single scalar parameter. This equivalence allows for a predictor-focused approach, where each predictor is described by a function of the chosen parameter. It is proven that a linear model will produce exact predictions even in the presence of nonlinear dependencies that violate the model assumptions. Parameterization in terms of the dependent variable and the monomial basis in the predictor function space are applied here to both synthetic and experimental data. The hyper-curve approach is especially suited for the regularization of problems with noise in predictor variables and can be used to remove noisy and "improper" predictors from the model.

Data organized in tabular format is ubiquitous in real-world applications, and users often craft tables with biased feature definitions and flexibly set prediction targets of their interests. Thus, a rapid development of a robust, effective, dataset-versatile, user-friendly tabular prediction approach is highly desired. While Gradient Boosting Decision Trees (GBDTs) and existing deep neural networks (DNNs) have been extensively utilized by professional users, they present several challenges for casual users, particularly: (i) the dilemma of model selection due to their different dataset preferences, and (ii) the need for heavy hyperparameter searching, failing which their performances are deemed inadequate. In this paper, we delve into this question: Can we develop a deep learning model that serves as a "sure bet" solution for a wide range of tabular prediction tasks, while also being user-friendly for casual users? We delve into three key drawbacks of deep tabular models, encompassing: (P1) lack of rotational variance property, (P2) large data demand, and (P3) over-smooth solution. We propose ExcelFormer, addressing these challenges through a semi-permeable attention module that effectively constrains the influence of less informative features to break the DNNs' rotational invariance property (for P1), data augmentation approaches tailored for tabular data (for P2), and attentive feedforward network to boost the model fitting capability (for P3). These designs collectively make ExcelFormer a "sure bet" solution for diverse tabular datasets. Extensive and stratified experiments conducted on real-world datasets demonstrate that our model outperforms previous approaches across diverse tabular data prediction tasks, and this framework can be friendly to casual users, offering ease of use without the heavy hyperparameter tuning.

Accurate prediction of biochemical recurrence (BCR) after radical prostatectomy is critical for guiding adjuvant treatment and surveillance decisions in prostate cancer. However, existing clinicopathological risk models reduce complex morphology to relatively coarse descriptors, leaving substantial prognostic information embedded in routine histopathology underexplored. We present a deep learning-based biomarker that predicts continuous, patient-specific risk of BCR directly from H&E-stained whole-slide prostatectomy specimens. Trained end-to-end on time-to-event outcomes and evaluated across four independent international cohorts, our model demonstrates robust generalization across institutions and patient populations. When integrated with the CAPRA-S clinical risk score, the deep learning risk score consistently improved discrimination for BCR, increasing concordance indices from 0.725-0.772 to 0.749-0.788 across cohorts. To support clinical interpretability, outcome-grounded analyses revealed subtle histomorphological patterns associated with recurrence risk that are not captured by conventional clinicopathological risk scores. This multicohort study demonstrates that deep learning applied to routine prostate histopathology can deliver reproducible and clinically generalizable biomarkers that augment postoperative risk stratification, with potential to support personalized management of prostate cancer in real-world clinical settings.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Predictive models play a crucial role in the financial industry, enabling risk prediction, fraud detection, and personalized recommendations, where slight changes in core model performance can result in billions of dollars in revenue or losses. While financial institutions have access to enormous amounts of user data (e.g., bank transactions, in-app events, and customer support logs), leveraging this data effectively remains challenging due to its complexity and scale. Thus, in many financial institutions, most production models follow traditional machine learning (ML) approaches by converting unstructured data into manually engineered tabular features. Conversely, other domains (e.g., natural language processing) have effectively utilized self-supervised learning (SSL) to learn rich representations from raw data, removing the need for manual feature extraction. In this paper, we investigate using transformer-based representation learning models for transaction data, hypothesizing that these models, trained on massive data, can provide a novel and powerful approach to understanding customer behavior. We propose a new method enabling the use of SSL with transaction data by adapting transformer-based models to handle both textual and structured attributes. Our approach, denoted nuFormer, includes an end-to-end fine-tuning method that integrates user embeddings with existing tabular features. Our experiments demonstrate improvements for large-scale recommendation problems at Nubank. Notably, these gains are achieved solely through enhanced representation learning rather than incorporating new data sources.

The growing popularity of Contrastive Language-Image Pretraining (CLIP) has led to its widespread application in various visual downstream tasks. To enhance CLIP's effectiveness and versatility, efficient few-shot adaptation techniques have been widely adopted. Among these approaches, training-free methods, particularly caching methods exemplified by Tip-Adapter, have gained attention for their lightweight adaptation without the need for additional fine-tuning. In this paper, we revisit Tip-Adapter from a kernel perspective, showing that caching methods function as local adapters and are connected to a well-established kernel literature. Drawing on this insight, we offer a theoretical understanding of how these methods operate and suggest multiple avenues for enhancing the Tip-Adapter baseline. Notably, our analysis shows the importance of incorporating global information in local adapters. Therefore, we subsequently propose a global method that learns a proximal regularizer in a reproducing kernel Hilbert space (RKHS) using CLIP as a base learner. Our method, which we call ProKeR (Proximal Kernel ridge Regression), has a closed form solution and achieves state-of-the-art performances across 11 datasets in the standard few-shot adaptation benchmark.

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

Evolving borrower behaviors, shifting economic conditions, and changing regulatory landscapes continuously reshape the data distributions underlying modern credit-scoring systems. Conventional explainability techniques, such as SHAP, assume static data and fixed background distributions, making their explanations unstable and potentially unfair when concept drift occurs. This study addresses that challenge by developing adaptive explanation frameworks that recalibrate interpretability and fairness in dynamically evolving credit models. Using a multi-year credit dataset, we integrate predictive modeling via XGBoost with three adaptive SHAP variants: (A) per-slice explanation reweighting that adjusts for feature distribution shifts, (B) drift-aware SHAP rebaselining with sliding-window background samples, and (C) online surrogate calibration using incremental Ridge regression. Each method is benchmarked against static SHAP explanations using metrics of predictive performance (AUC, F1), directional and rank stability (cosine, Kendall tau), and fairness (demographic parity and recalibration). Results show that adaptive methods, particularly rebaselined and surrogate-based explanations, substantially improve temporal stability and reduce disparate impact across demographic groups without degrading predictive accuracy. Robustness tests, including counterfactual perturbations, background sensitivity analysis, and proxy-variable detection, confirm the resilience of adaptive explanations under real-world drift conditions. These findings establish adaptive explainability as a practical mechanism for sustaining transparency, accountability, and ethical reliability in data-driven credit systems, and more broadly, in any domain where decision models evolve with population change.

Open weight models, which are ubiquitous, rarely provide access to their training data or loss function. This makes modifying such models for tasks such as pruning or unlearning constrained by this unavailability an active area of research. Existing techniques typically require gradients or ground-truth labels, rendering them infeasible in settings with limited computational resources. In this work, we investigate the fundamental question of identifying components that are critical to the model's predictive performance, without access to either gradients or the loss function, and with only distributional access such as synthetic data. We theoretically demonstrate that the global reconstruction error is linearly bounded by local reconstruction errors for Lipschitz-continuous networks such as CNNs and well-trained Transformers (which, contrary to existing literature, we find exhibit Lipschitz continuity). This motivates using the locally reconstructive behavior of component subsets to quantify their global importance, via a metric that we term Subset Fidelity. In the uncorrelated features setting, selecting individual components via their Subset Fidelity scores is optimal, which we use to propose ModHiFi, an algorithm for model modification that requires no training data or loss function access. ModHiFi-P, for structured pruning, achieves an 11% speedup over the current state of the art on ImageNet models and competitive performance on language models. ModHiFi-U, for classwise unlearning, achieves complete unlearning on CIFAR-10 without fine-tuning and demonstrates competitive performance on Swin Transformers.

We present a transformer architecture-based foundation model for tasks at high-energy particle colliders such as the Large Hadron Collider. We train the model to classify jets using a self-supervised strategy inspired by the Joint Embedding Predictive Architecture. We use the JetClass dataset containing 100M jets of various known particles to pre-train the model with a data-centric approach -- the model uses a fraction of the jet constituents as the context to predict the embeddings of the unseen target constituents. Our pre-trained model fares well with other datasets for standard classification benchmark tasks. We test our model on two additional downstream tasks: top tagging and differentiating light-quark jets from gluon jets. We also evaluate our model with task-specific metrics and baselines and compare it with state-of-the-art models in high-energy physics. Project site: https://hep-jepa.github.io/

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term K-RCPS, which allows to (i) provide entrywise calibrated intervals for future samples of any diffusion model, and (ii) control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Anticipating supply chain disruptions before they materialize is a core challenge for firms and policymakers alike. A key difficulty is learning to reason reliably about infrequent, high-impact events from noisy and unstructured inputs - a setting where general-purpose models struggle without task-specific adaptation. We introduce an end-to-end framework that trains LLMs to produce calibrated probabilistic forecasts using realized disruption outcomes as supervision. The resulting model substantially outperforms strong baselines - including GPT-5 - on accuracy, calibration, and precision. We also show that training induces more structured and reliable probabilistic reasoning without explicit prompting. These results suggest a general pathway for training domain-specific forecasting models that produce decision-ready signals. To support transparency we open-source the evaluation dataset used in this study. Dataset: https://huggingface.co/datasets/LightningRodLabs/supply-chain-predictions

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

Tabular data underpins most high-value prediction problems in science and industry, and TabPFN has driven the foundation model revolution for this modality. Designed with feedback from our users, TabPFN-3 builds on this foundation to scale state-of-the-art performance to datasets with 1M training rows and substantially reduce training and inference time. Pretrained exclusively on synthetic data from our prior, TabPFN-3 dramatically pushes the frontier of tabular prediction and brings substantial gains on time series, relational, and tabular-text data. On the standard tabular benchmark TabArena, a forward pass of TabPFN-3 outperforms all other models, including tuned and ensembled baselines, by a significant margin, and pareto-dominates the speed/performance frontier. On more diverse datasets, TabPFN-3 ranks first on datasets with many classes, and beats 8-hour-tuned gradient-boosted-tree baselines on datasets up to 1M training rows and 200 features. TabPFN-3 introduces test-time compute scaling to tabular foundation models. Our API offering TabPFN-3-Plus (Thinking) exploits this to beat all non-TabPFN models by over 200 Elo on TabArena, rising to 420 Elo on the largest data subset, and outperforms AutoGluon 1.5 extreme while being 10x faster, without using LLMs, real data, internet search or any other model besides TabPFN. TabPFN-3 extends the capabilities of our models, enabling SOTA prediction on relational data (new SOTA foundation model on RelBenchV1) and tabular-text data (SOTA on TabSTAR via TabPFN-3-Plus); and improves existing integrations: a specialized checkpoint, TabPFN-TS-3, ranks 2nd on the time-series benchmark fev-bench, and SHAP-value computation is up to 120x faster. TabPFN-3 achieves this performance while being up to 20x faster than TabPFN-2.5. In addition, a reduced KV cache and row-chunking scale to 1M rows on one H100 with fast inference speed.

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pretrained transformer-based models in generating equations as sequences, leveraging large-scale pretraining on synthetic datasets and offering notable advantages in terms of inference time over GP-based methods. However, these models primarily rely on supervised pretraining goals borrowed from text generation and overlook equation-specific objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise

Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

Time series forecasting is central to decision-making in domains as diverse as energy, finance, climate, and public health. In practice, forecasters face thousands of short, noisy series that vary in frequency, quality, and horizon, where the dominant cost lies not in model fitting, but in the labor-intensive preprocessing, validation, and ensembling required to obtain reliable predictions. Prevailing statistical and deep learning models are tailored to specific datasets or domains and generalize poorly. A general, domain-agnostic framework that minimizes human intervention is urgently in demand. In this paper, we introduce TimeSeriesScientist (TSci), the first LLM-driven agentic framework for general time series forecasting. The framework comprises four specialized agents: Curator performs LLM-guided diagnostics augmented by external tools that reason over data statistics to choose targeted preprocessing; Planner narrows the hypothesis space of model choice by leveraging multi-modal diagnostics and self-planning over the input; Forecaster performs model fitting and validation and, based on the results, adaptively selects the best model configuration as well as ensemble strategy to make final predictions; and Reporter synthesizes the whole process into a comprehensive, transparent report. With transparent natural-language rationales and comprehensive reports, TSci transforms the forecasting workflow into a white-box system that is both interpretable and extensible across tasks. Empirical results on eight established benchmarks demonstrate that TSci consistently outperforms both statistical and LLM-based baselines, reducing forecast error by an average of 10.4% and 38.2%, respectively. Moreover, TSci produces a clear and rigorous report that makes the forecasting workflow more transparent and interpretable.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

Large language models are increasingly applied to materials science, yet fundamental questions remain about their reliability and knowledge encoding. Evaluating 25 LLMs across four materials science tasks -- over 200 base and fine-tuned configurations -- we find that output modality fundamentally determines model behavior. For symbolic tasks, fine-tuning converges to consistent, verifiable answers with reduced response entropy, while for numerical tasks, fine-tuning improves prediction accuracy but models remain inconsistent across repeated inference runs, limiting their reliability as quantitative predictors. For numerical regression, we find that better performance can be obtained by extracting embeddings directly from intermediate transformer layers than from model text output, revealing an ``LLM head bottleneck,'' though this effect is property- and dataset-dependent. Finally, we present a longitudinal study of GPT model performance in materials science, tracking four models over 18 months and observing 9--43\% performance variation that poses reproducibility challenges for scientific applications.

In this paper, we introduce PredBench, a benchmark tailored for the holistic evaluation of spatio-temporal prediction networks. Despite significant progress in this field, there remains a lack of a standardized framework for a detailed and comparative analysis of various prediction network architectures. PredBench addresses this gap by conducting large-scale experiments, upholding standardized and appropriate experimental settings, and implementing multi-dimensional evaluations. This benchmark integrates 12 widely adopted methods with 15 diverse datasets across multiple application domains, offering extensive evaluation of contemporary spatio-temporal prediction networks. Through meticulous calibration of prediction settings across various applications, PredBench ensures evaluations relevant to their intended use and enables fair comparisons. Moreover, its multi-dimensional evaluation framework broadens the analysis with a comprehensive set of metrics, providing deep insights into the capabilities of models. The findings from our research offer strategic directions for future developments in the field. Our codebase is available at https://github.com/OpenEarthLab/PredBench.

We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensors-to-image which enables us to take advantage of Computer Vision architectures and training processes. In addition to this data preparation methodology, we explore the use of state-of-the-art architectures to generate regression outputs to predict agricultural crop continuous yield information. Finally, we compare with some of the top models reported in MLCAS2021. We found that using a straightforward training process, we were able to accomplish an MAE of 4.394, RMSE of 5.945, and R^2 of 0.861.

Checklists are simple decision aids that are often used to promote safety and reliability in clinical applications. In this paper, we present a method to learn checklists for clinical decision support. We represent predictive checklists as discrete linear classifiers with binary features and unit weights. We then learn globally optimal predictive checklists from data by solving an integer programming problem. Our method allows users to customize checklists to obey complex constraints, including constraints to enforce group fairness and to binarize real-valued features at training time. In addition, it pairs models with an optimality gap that can inform model development and determine the feasibility of learning sufficiently accurate checklists on a given dataset. We pair our method with specialized techniques that speed up its ability to train a predictive checklist that performs well and has a small optimality gap. We benchmark the performance of our method on seven clinical classification problems, and demonstrate its practical benefits by training a short-form checklist for PTSD screening. Our results show that our method can fit simple predictive checklists that perform well and that can easily be customized to obey a rich class of custom constraints.

Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data. Technically, equation discovery is implemented by symbolic regression algorithms. Performance of symbolic regression for equation discovery is measured along two dimensions: Prediction accuracy on test data, and recovery of known groundtruth formulas. For standard regression, accuracy is typically measured on in-domain test data, for instance, by splitting a data set randomly into training and test data. While this makes sense for in-domain interpolation, which is the common goal in ordinary regression, it can be a misleading proxy for true model discovery and generalization. The obvious alternative is to measure out-of-domain accuracy. However, obtaining challenging out-of-domain test data is a non-trivial problem. Therefore, we focus on equation recovery for evaluating symbolic regression algorithms for equation discovery. The rationale is that symbolic regression algorithms that perform well in recovering known groundtruth formulas are good candidates to perform well in unknown equation discovery. Existing benchmarks for symbolic regression include equation recovery tasks, however, with only a small number of groundtruth formulas that are publicly known. Moreover, these benchmarks place less emphasis on evaluating the robustness of algorithms in terms of their behavior under changing dimensionality, sampling size, sampling distribution and sampling domain. This, however, is of central importance to practitioners wanting to discover equations for modeling natural phenomena, since data is almost certainly noisy and comes from diverse domains, distributions, and sample sizes. To fill this gap, we introduce the Equation Recovery Benchmark (ERBench), a new evaluation framework designed to rigorously assess algorithms explicitly targeting the task of equation discovery.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.