Daily Papers

We construct S-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations X/S with relative Picard rank 1 and rational geometric fibers and discuss how the structure of components of these decompositions is related to rationality properties of X/S.

We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a general hyperplane section on such a variety, we consider the zero loci of its pushforwards along the projective bundle structures and we discuss their properties at the level of Hodge structures. In the case of the flag variety F(1,2,n) with its projections to P^{n-1} and G(2, n), we construct a derived embedding of the relevant zero loci by methods based on the study of B-brane categories in the context of a gauged linear sigma model.

We introduce MedAgentGYM, the first publicly available training environment designed to enhance coding-based medical reasoning capabilities in large language model (LLM) agents. MedAgentGYM comprises 72,413 task instances across 129 categories derived from authentic real-world biomedical scenarios. Tasks are encapsulated within executable coding environments, each featuring detailed task descriptions, interactive feedback mechanisms, verifiable ground-truth annotations, and scalable training trajectory generation. Extensive benchmarking of over 30 LLMs reveals a notable performance disparity between commercial API-based models and open-source counterparts. Leveraging MedAgentGYM, Med-Copilot-7B achieves substantial performance gains through supervised fine-tuning (+36.44%) and continued reinforcement learning (+42.47%), emerging as an affordable and privacy-preserving alternative competitive with gpt-4o. By offering both a comprehensive benchmark and accessible, expandable training resources within unified execution environments, MedAgentGYM delivers an integrated platform to develop LLM-based coding assistants for advanced biomedical research and practice.

Moral sentiments expressed in natural language significantly influence both online and offline environments, shaping behavioral styles and interaction patterns, including social media selfpresentation, cyberbullying, adherence to social norms, and ethical decision-making. To effectively measure moral sentiments in natural language processing texts, it is crucial to utilize large, annotated datasets that provide nuanced understanding for accurate analysis and modeltraining. However, existing corpora, while valuable, often face linguistic limitations. To address this gap in the Chinese language domain,we introduce the Moral Foundation Weibo Corpus. This corpus consists of 25,671 Chinese comments on Weibo, encompassing six diverse topic areas. Each comment is manually annotated by at least three systematically trained annotators based on ten moral categories derived from a grounded theory of morality. To assess annotator reliability, we present the kappa testresults, a gold standard for measuring consistency. Additionally, we apply several the latest large language models to supplement the manual annotations, conducting analytical experiments to compare their performance and report baseline results for moral sentiment classification.

Referring expression comprehension (REC) aims at achieving object localization based on natural language descriptions. However, existing REC approaches are constrained by object category descriptions and single-attribute intention descriptions, hindering their application in real-world scenarios. In natural human-robot interactions, users often express their desires through individual states and intentions, accompanied by guiding gestures, rather than detailed object descriptions. To address this challenge, we propose Multi-ref EC, a novel task framework that integrates state descriptions, derived intentions, and embodied gestures to locate target objects. We introduce the State-Intention-Gesture Attributes Reference (SIGAR) dataset, which combines state and intention expressions with embodied references. Through extensive experiments with various baseline models on SIGAR, we demonstrate that properly ordered multi-attribute references contribute to improved localization performance, revealing that single-attribute reference is insufficient for natural human-robot interaction scenarios. Our findings underscore the importance of multi-attribute reference expressions in advancing visual-language understanding.

We present the Consilium Protocol, a Byzantine Fault Tolerance-derived architecture for structured multi-model AI deliberation that treats inter-model disagreement as epistemic signal rather than error. The protocol assigns engineered cognitive personas to language models -- separating what a model is from how it reasons -- and introduces an In-Sample/Out-of-Sample validation framework adapted from quantitative finance to distinguish training-data consensus from empirically grounded conclusions. Across 1,478 deliberation sessions spanning 32 topics in 10 domain categories, we demonstrate that (1) the cognitive persona, not the underlying model, determines epistemic behavior: free edge-inference models costing 0.0002 USD per batch produced comparable analytical output to frontier models costing 10.69 USD; (2) RLHF alignment training creates measurable, domain-specific epistemic blind spots -- contested policy topics exhibit 12.3 percentage points less adversarial challenge than settled science topics, and AI safety topics show asymmetric bias (Δ=11.6%) where models challenge claims that AI is dangerous far more vigorously than claims that AI risk is overstated; (3) the protocol exhibits no directional bias of its own (immigration Δ=2.3%, renewables Δ=1.2%); and (4) out-of-sample evidence retrieval validated 239 claims with 100% evidence retrieval and surfaced 167 blind-spot discoveries invisible to training-data deliberation. Run-to-run reproducibility across randomized modeltimespersona assignments averages pm2.2% standard deviation. Total cost for the complete battery including all overhead: 217 USD. We release the protocol specification under MIT license to enable independent verification.

The accelerating development of general medical artificial intelligence (GMAI), powered by multimodal large language models (MLLMs), offers transformative potential for addressing persistent healthcare challenges, including workforce deficits and escalating costs. The parallel development of systematic evaluation benchmarks emerges as a critical imperative to enable performance assessment and provide technological guidance. Meanwhile, as an invaluable knowledge source, the potential of medical textbooks for benchmark development remains underexploited. Here, we present MedBookVQA, a systematic and comprehensive multimodal benchmark derived from open-access medical textbooks. To curate this benchmark, we propose a standardized pipeline for automated extraction of medical figures while contextually aligning them with corresponding medical narratives. Based on this curated data, we generate 5,000 clinically relevant questions spanning modality recognition, disease classification, anatomical identification, symptom diagnosis, and surgical procedures. A multi-tier annotation system categorizes queries through hierarchical taxonomies encompassing medical imaging modalities (42 categories), body anatomies (125 structures), and clinical specialties (31 departments), enabling nuanced analysis across medical subdomains. We evaluate a wide array of MLLMs, including proprietary, open-sourced, medical, and reasoning models, revealing significant performance disparities across task types and model categories. Our findings highlight critical capability gaps in current GMAI systems while establishing textbook-derived multimodal benchmarks as essential evaluation tools. MedBookVQA establishes textbook-derived benchmarking as a critical paradigm for advancing clinical AI, exposing limitations in GMAI systems while providing anatomically structured performance metrics across specialties.

We propose Encyclopedic-VQA, a large scale visual question answering (VQA) dataset featuring visual questions about detailed properties of fine-grained categories and instances. It contains 221k unique question+answer pairs each matched with (up to) 5 images, resulting in a total of 1M VQA samples. Moreover, our dataset comes with a controlled knowledge base derived from Wikipedia, marking the evidence to support each answer. Empirically, we show that our dataset poses a hard challenge for large vision+language models as they perform poorly on our dataset: PaLI [14] is state-of-the-art on OK-VQA [37], yet it only achieves 13.0% accuracy on our dataset. Moreover, we experimentally show that progress on answering our encyclopedic questions can be achieved by augmenting large models with a mechanism that retrieves relevant information from the knowledge base. An oracle experiment with perfect retrieval achieves 87.0% accuracy on the single-hop portion of our dataset, and an automatic retrieval-augmented prototype yields 48.8%. We believe that our dataset enables future research on retrieval-augmented vision+language models. It is available at https://github.com/google-research/google-research/tree/master/encyclopedic_vqa .

We present M2D2, a fine-grained, massively multi-domain corpus for studying domain adaptation in language models (LMs). M2D2 consists of 8.5B tokens and spans 145 domains extracted from Wikipedia and Semantic Scholar. Using ontologies derived from Wikipedia and ArXiv categories, we organize the domains in each data source into 22 groups. This two-level hierarchy enables the study of relationships between domains and their effects on in- and out-of-domain performance after adaptation. We also present a number of insights into the nature of effective domain adaptation in LMs, as examples of the new types of studies M2D2 enables. To improve in-domain performance, we show the benefits of adapting the LM along a domain hierarchy; adapting to smaller amounts of fine-grained domain-specific data can lead to larger in-domain performance gains than larger amounts of weakly relevant data. We further demonstrate a trade-off between in-domain specialization and out-of-domain generalization within and across ontologies, as well as a strong correlation between out-of-domain performance and lexical overlap between domains.

Recent large language models (LLMs) have demonstrated significant advancements, particularly in their ability to serve as agents thereby surpassing their traditional role as chatbots. These agents can leverage their planning and tool utilization capabilities to address tasks specified at a high level. However, a standardized dataset to benchmark the agent capabilities of LLMs in medical applications is currently lacking, making the evaluation of LLMs on complex tasks in interactive healthcare environments challenging. To address this gap, we introduce MedAgentBench, a broad evaluation suite designed to assess the agent capabilities of large language models within medical records contexts. MedAgentBench encompasses 300 patient-specific clinically-derived tasks from 10 categories written by human physicians, realistic profiles of 100 patients with over 700,000 data elements, a FHIR-compliant interactive environment, and an accompanying codebase. The environment uses the standard APIs and communication infrastructure used in modern EMR systems, so it can be easily migrated into live EMR systems. MedAgentBench presents an unsaturated agent-oriented benchmark that current state-of-the-art LLMs exhibit some ability to succeed at. The best model (Claude 3.5 Sonnet v2) achieves a success rate of 69.67%. However, there is still substantial space for improvement which gives the community a next direction to optimize. Furthermore, there is significant variation in performance across task categories. MedAgentBench establishes this and is publicly available at https://github.com/stanfordmlgroup/MedAgentBench , offering a valuable framework for model developers to track progress and drive continuous improvements in the agent capabilities of large language models within the medical domain.

Paralinguistic sounds, like laughter and sighs, are crucial for synthesizing more realistic and engaging speech. However, existing methods typically depend on proprietary datasets, while publicly available resources often suffer from incomplete speech, inaccurate or missing timestamps, and limited real-world relevance. To address these problems, we propose an automated framework for generating large-scale paralinguistic data and apply it to construct the SynParaSpeech dataset. The dataset comprises 6 paralinguistic categories with 118.75 hours of data and precise timestamps, all derived from natural conversational speech. Our contributions lie in introducing the first automated method for constructing large-scale paralinguistic datasets and releasing the SynParaSpeech corpus, which advances speech generation through more natural paralinguistic synthesis and enhances speech understanding by improving paralinguistic event detection. The dataset and audio samples are available at https://github.com/ShawnPi233/SynParaSpeech.

We consider the problem of characterizing derived endomorphism algebras of simple objects in length categories up to quasi-isomorphism. We give such a characterization for module categories, abelian categories, exact categories, as well as, for certain differential graded analogues of them. It turns out that the property of being d-complicial (dgeq 1), in the sense of Lurie, of the involved simple-minded collections plays a central role. We also explain how this characterization can be interpreted as a coherent generation property for any minimal A_{infty}-model of the derived endomorphism algebra. Along the way, we propose a notion of length exact differential graded categories and explain how they relate to length abelian d-truncated differential graded categories, generalizing results of Enomoto.

We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications of such construction at the level of Hodge equivalence, derived equivalence and mathbb L-equivalence. For the case of K3 surfaces, we provide alternative interpretations for the Fourier-Mukai duality in the family of K3 surfaces of degree 12 of Mukai. In all these constructions the derived equivalence lifts to an equivalence of matrix factorizations categories.

Video generation models are increasingly used as world simulators for storytelling, simulation, and embodied AI. As these models advance, a key question arises: do generated videos obey the physical laws of the real world? Existing evaluations largely rely on automated metrics or coarse human judgments such as preferences or rubric-based checks. While useful for assessing perceptual quality, these methods provide limited insight into when and why generated dynamics violate real-world physical constraints. We introduce Physion-Eval, a large-scale benchmark of expert human reasoning for diagnosing physical realism failures in videos generated by five state-of-the-art models across egocentric and exocentric views, containing 10,990 expert reasoning traces spanning 22 fine-grained physical categories. Each generated video is derived from a corresponding real-world reference video depicting a clear physical process, and annotated with temporally localized glitches, structured failure categories, and natural-language explanations of the violated physical behavior. Using this dataset, we reveal a striking limitation of current video generation models: in physics-critical scenarios, 83.3% of exocentric and 93.5% of egocentric generated videos exhibit at least one human-identifiable physical glitch. We hope Physion-Eval will set a new standard for physical realism evaluation and guide the development of physics-grounded video generation. The benchmark is publicly available at https://huggingface.co/datasets/PhysionLabs/Physion-Eval.

Visibility of natural landmarks such as Mount Fuji is a defining factor in both tourism planning and visitor experience, yet it remains difficult to predict due to rapidly changing atmospheric conditions. We present FujiView, a multimodal learning framework and dataset for predicting scenic visibility by fusing webcam imagery with structured meteorological data. Our late-fusion approach combines image-derived class probabilities with numerical weather features to classify visibility into five categories. The dataset currently comprises over 100,000 webcam images paired with concurrent and forecasted weather conditions from more than 40 cameras around Mount Fuji, and continues to expand; it will be released to support further research in environmental forecasting. Experiments show that YOLO-based vision features dominate short-term horizons such as "nowcasting" and "samedaycasting", while weather-driven forecasts increasingly take over as the primary predictive signal beyond +1d. Late fusion consistently yields the highest overall accuracy, achieving ACC of approx 0.89 for same-day prediction and up to 84% for next-day forecasts. These results position Scenic Visibility Forecasting (SVF) as a new benchmark task for multimodal learning.

Subject-driven text-to-image (T2I) generation aims to produce images that align with a given textual description, while preserving the visual identity from a referenced subject image. Despite its broad downstream applicability -- ranging from enhanced personalization in image generation to consistent character representation in video rendering -- progress in this field is limited by the lack of reliable automatic evaluation. Existing methods either assess only one aspect of the task (i.e., textual alignment or subject preservation), misalign with human judgments, or rely on costly API-based evaluation. To address this, we introduce RefVNLI, a cost-effective metric that evaluates both textual alignment and subject preservation in a single prediction. Trained on a large-scale dataset derived from video-reasoning benchmarks and image perturbations, RefVNLI outperforms or matches existing baselines across multiple benchmarks and subject categories (e.g., Animal, Object), achieving up to 6.4-point gains in textual alignment and 8.5-point gains in subject consistency. It also excels with lesser-known concepts, aligning with human preferences at over 87\% accuracy.

Environmental, Social, and Governance (ESG) reports are essential for evaluating sustainability practices, ensuring regulatory compliance, and promoting financial transparency. However, these documents are often lengthy, structurally diverse, and multimodal, comprising dense text, structured tables, complex figures, and layout-dependent semantics. Existing AI systems often struggle to perform reliable document-level reasoning in such settings, and no dedicated benchmark currently exists in ESG domain. To fill the gap, we introduce MMESGBench, a first-of-its-kind benchmark dataset targeted to evaluate multimodal understanding and complex reasoning across structurally diverse and multi-source ESG documents. This dataset is constructed via a human-AI collaborative, multi-stage pipeline. First, a multimodal LLM generates candidate question-answer (QA) pairs by jointly interpreting rich textual, tabular, and visual information from layout-aware document pages. Second, an LLM verifies the semantic accuracy, completeness, and reasoning complexity of each QA pair. This automated process is followed by an expert-in-the-loop validation, where domain specialists validate and calibrate QA pairs to ensure quality, relevance, and diversity. MMESGBench comprises 933 validated QA pairs derived from 45 ESG documents, spanning across seven distinct document types and three major ESG source categories. Questions are categorized as single-page, cross-page, or unanswerable, with each accompanied by fine-grained multimodal evidence. Initial experiments validate that multimodal and retrieval-augmented models substantially outperform text-only baselines, particularly on visually grounded and cross-page tasks. MMESGBench is publicly available as an open-source dataset at https://github.com/Zhanglei1103/MMESGBench.

Large language model (LLM) agents have demonstrated remarkable potential in advancing scientific discovery. However, their capability in the fundamental yet crucial task of reproducing code from research papers, especially in the NLP domain, remains underexplored. This task includes unique complex reasoning challenges in the intellectual synthesis of abstract concepts and the comprehension of code repositories with interdependent files. Motivated by this gap, we present LMR-BENCH, a benchmark designed to systematically evaluate the capability of LLM agents on code reproduction from Language Modeling Research. It consists of 28 code reproduction tasks derived from 23 research papers published in top-tier NLP venues over the past five years, spanning nine fundamental categories. Models are provided with a research paper, a code repository containing one or more masked functions, and instructions for implementing these functions. We conduct extensive experiments in standard prompting and LLM agent settings with state-of-the-art LLMs, evaluating the accuracy of unit tests and performing LLM-based evaluation of code correctness. Experimental results reveal that even the most advanced models still exhibit persistent limitations in scientific reasoning and code synthesis, highlighting critical gaps in LLM agents' ability to autonomously reproduce scientific research

Despite significant breakthroughs in video analysis driven by the rapid development of large multimodal models (LMMs), there remains a lack of a versatile evaluation benchmark to comprehensively assess these models' performance in video understanding and reasoning. To address this, we present VideoVista, a video QA benchmark that integrates challenges across diverse content categories, durations, and abilities. Specifically, VideoVista comprises 25,000 questions derived from 3,400 videos spanning 14 categories (e.g., Howto, Film, and Entertainment) with durations ranging from a few seconds to over 10 minutes. Besides, it encompasses 19 types of understanding tasks (e.g., anomaly detection, interaction understanding) and 8 reasoning tasks (e.g., logical reasoning, causal reasoning). To achieve this, we present an automatic data construction framework, leveraging powerful GPT-4o alongside advanced analysis tools (e.g., video splitting, object segmenting, and tracking). We also utilize this framework to construct training data to enhance the capabilities of video-related LMMs (Video-LMMs). Through a comprehensive and quantitative evaluation of cutting-edge models, we reveal that: 1) Video-LMMs face difficulties in fine-grained video tasks involving temporal location, object tracking, and anomaly detection; 2) Video-LMMs present inferior logical and relation reasoning abilities; 3) Open-source Video-LMMs' performance is significantly lower than GPT-4o and Gemini-1.5, lagging by 20 points. This highlights the crucial role VideoVista will play in advancing LMMs that can accurately understand videos and perform precise reasoning.

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

While recent advancements in vision-language models have improved video understanding, diagnosing their capacity for deep, narrative comprehension remains a challenge. Existing benchmarks often test short-clip recognition or use template-based questions, leaving a critical gap in evaluating fine-grained reasoning over long-form narrative content. To address these gaps, we introduce Cinacute{easte}, a comprehensive benchmark for long-form movie understanding. Our dataset comprises 3,119 multiple-choice question-answer pairs derived from 1,805 scenes across 200 diverse movies, spanning five novel fine-grained contextual reasoning categories. We use GPT-4o to generate diverse, context-rich questions by integrating visual descriptions, captions, scene titles, and summaries, which require deep narrative understanding. To ensure high-quality evaluation, our pipeline incorporates a two-stage filtering process: Context-Independence filtering ensures questions require video context, while Contextual Veracity filtering validates factual consistency against the movie content, mitigating hallucinations. Experiments show that existing MLLMs struggle on Cinacute{easte}; our analysis reveals that long-range temporal reasoning is a primary bottleneck, with the top open-source model achieving only 63.15\% accuracy. This underscores significant challenges in fine-grained contextual understanding and the need for advancements in long-form movie comprehension.

The rapid expansion of AI has intensified concerns about its environmental sustainability. Yet, current assessments predominantly focus on operational carbon emissions using secondary data or estimated values, overlooking environmental impacts in other life cycle stages. This study presents the first comprehensive multi-criteria life cycle assessment (LCA) of AI training, examining 16 environmental impact categories based on detailed primary data collection of the Nvidia A100 SXM 40GB GPU. The LCA results for training BLOOM reveal that the use phase dominates 11 of 16 impact categories including climate change (96\%), while manufacturing dominates the remaining 5 impact categories including human toxicity, cancer (99\%) and mineral and metal depletion (85\%). For training GPT-4, the use phase dominates 10 of 16 impact categories, contributing about 96\% to both the climate change and resource use, fossils category. The manufacturing stage dominates 6 of 16 impact categories including human toxicity, cancer (94\%) and eutrophication, freshwater (81\%). Assessing the cradle-to-gate environmental impact distribution across the GPU components reveals that the GPU chip is the largest contributor across 10 of 16 of impact categories and shows particularly pronounced contributions to climate change (81\%) and resource use, fossils (80\%). While primary data collection results in modest changes in carbon estimates compared to database-derived estimates, substantial variations emerge in other categories. Most notably, minerals and metals depletion increases by 33\%, demonstrating the critical importance of primary data for non-carbon accounting. This multi-criteria analysis expands the Sustainable AI discourse beyond operational carbon emissions, challenging current sustainability narratives and highlighting the need for policy frameworks addressing the full spectrum of AI's environmental impact.

Humans can efficiently parse continuous sensory streams, from hours to years, scaffolding an internal world model that grounds spatial reasoning and prediction. To mimic this capacity, spatial supersensing challenges multimodal models to move beyond linguistic understanding toward true world modeling. However, their benchmark relies on synthetic long videos, formed by concatenating random short clips, and is mostly limited to household scenes, leaving real-world continuity and diversity underexplored. To address the gap, we introduce VSI-Super-Wild, a large-scale benchmark for evaluating spatial supersensing over long temporal horizons in diverse in-the-wild scenes. Notably, inspired by cognitive studies on how humans structure experience, we systematically probe the full triad of world state: the agent (observer), objects (scene items), and the environment (places and global layout). In total, VSI-Super-Wild contains 6,980 human-verified question-answer pairs derived from 442 real-world videos spanning 8 scene categories, including long-form recordings exceeding 4 hours. Results on VSI-Super-Wild expose a fundamental disconnect: despite advances in static image understanding, models consistently fail at tasks that require coherent world-state tracking over time. We characterize how performance degrades with world-state complexity and temporal horizon, and diagnose four failure modes: spatial collapse, semantic shortcuts, insufficient update, and instance confusion. This taxonomy reveals that models lack mechanisms to bind objects, agents, and environments into a unified spatial world model, a fundamental gap that defines the path forward for spatial supersensing.

Subjective Answer Grading (SAG) plays a crucial role in education, standardized testing, and automated assessment systems, particularly for evaluating short-form responses in Short Answer Scoring (SAS). However, existing approaches often produce coarse-grained scores and lack detailed reasoning. Although large language models (LLMs) have demonstrated potential as zero-shot evaluators, they remain susceptible to bias, inconsistencies with human judgment, and limited transparency in scoring decisions. To overcome these limitations, we introduce SAS-Bench, a benchmark specifically designed for LLM-based SAS tasks. SAS-Bench provides fine-grained, step-wise scoring, expert-annotated error categories, and a diverse range of question types derived from real-world subject-specific exams. This benchmark facilitates detailed evaluation of model reasoning processes and explainability. We also release an open-source dataset containing 1,030 questions and 4,109 student responses, each annotated by domain experts. Furthermore, we conduct comprehensive experiments with various LLMs, identifying major challenges in scoring science-related questions and highlighting the effectiveness of few-shot prompting in improving scoring accuracy. Our work offers valuable insights into the development of more robust, fair, and educationally meaningful LLM-based evaluation systems.

Open-Vocabulary Camouflaged Object Segmentation (OVCOS) seeks to segment and classify camouflaged objects from arbitrary categories, presenting unique challenges due to visual ambiguity and unseen categories.Recent approaches typically adopt a two-stage paradigm: first segmenting objects, then classifying the segmented regions using Vision Language Models (VLMs).However, these methods (1) suffer from a domain gap caused by the mismatch between VLMs' full-image training and cropped-region inference, and (2) depend on generic segmentation models optimized for well-delineated objects, making them less effective for camouflaged objects.Without explicit guidance, generic segmentation models often overlook subtle boundaries, leading to imprecise segmentation.In this paper,we introduce a novel VLM-guided cascaded framework to address these issues in OVCOS.For segmentation, we leverage the Segment Anything Model (SAM), guided by the VLM.Our framework uses VLM-derived features as explicit prompts to SAM, effectively directing attention to camouflaged regions and significantly improving localization accuracy.For classification, we avoid the domain gap introduced by hard cropping.Instead, we treat the segmentation output as a soft spatial prior via the alpha channel, which retains the full image context while providing precise spatial guidance, leading to more accurate and context-aware classification of camouflaged objects.The same VLM is shared across both segmentation and classification to ensure efficiency and semantic consistency.Extensive experiments on both OVCOS and conventional camouflaged object segmentation benchmarks demonstrate the clear superiority of our method, highlighting the effectiveness of leveraging rich VLM semantics for both segmentation and classification of camouflaged objects.

The last decade has seen a significant increase of interest in deep learning research, with many public successes that have demonstrated its potential. As such, these systems are now being incorporated into commercial products. With this comes an additional challenge: how can we build AI systems that solve tasks where there is not a crisp, well-defined specification? While multiple solutions have been proposed, in this competition we focus on one in particular: learning from human feedback. Rather than training AI systems using a predefined reward function or using a labeled dataset with a predefined set of categories, we instead train the AI system using a learning signal derived from some form of human feedback, which can evolve over time as the understanding of the task changes, or as the capabilities of the AI system improve. The MineRL BASALT competition aims to spur forward research on this important class of techniques. We design a suite of four tasks in Minecraft for which we expect it will be hard to write down hardcoded reward functions. These tasks are defined by a paragraph of natural language: for example, "create a waterfall and take a scenic picture of it", with additional clarifying details. Participants must train a separate agent for each task, using any method they want. Agents are then evaluated by humans who have read the task description. To help participants get started, we provide a dataset of human demonstrations on each of the four tasks, as well as an imitation learning baseline that leverages these demonstrations. Our hope is that this competition will improve our ability to build AI systems that do what their designers intend them to do, even when the intent cannot be easily formalized. Besides allowing AI to solve more tasks, this can also enable more effective regulation of AI systems, as well as making progress on the value alignment problem.

As single-cell RNA sequencing datasets grow in adoption, scale, and complexity, data analysis remains a bottleneck for many research groups. Although frontier AI agents have improved dramatically at software engineering and general data analysis, it remains unclear whether they can extract biological insight from messy, real-world single-cell datasets. We introduce scBench, a benchmark of 394 verifiable problems derived from practical scRNA-seq workflows spanning six sequencing platforms and seven task categories. Each problem provides a snapshot of experimental data immediately prior to an analysis step and a deterministic grader that evaluates recovery of a key biological result. Benchmark data on eight frontier models shows that accuracy ranges from 29-53%, with strong model-task and model-platform interactions. Platform choice affects accuracy as much as model choice, with 40+ percentage point drops on less-documented technologies. scBench complements SpatialBench to cover the two dominant single-cell modalities, serving both as a measurement tool and a diagnostic lens for developing agents that can analyze real scRNA-seq datasets faithfully and reproducibly.

Obtaining high-quality fine-grained annotations for traffic signs is critical for accurate and safe decision-making in autonomous driving. Widely used datasets, such as Mapillary, often provide only coarse-grained labels - without distinguishing semantically important types such as stop signs or speed limit signs. To this end, we present a new validation set for traffic signs derived from the Mapillary dataset called Mapillary Vistas Validation for Traffic Signs (MVV), where we decompose composite traffic signs into granular, semantically meaningful categories. The dataset includes pixel-level instance masks and has been manually annotated by expert annotators to ensure label fidelity. Further, we benchmark several state-of-the-art VLMs against the self-supervised DINOv2 model on this dataset and show that DINOv2 consistently outperforms all VLM baselines-not only on traffic sign recognition, but also on heavily represented categories like vehicles and humans. Our analysis reveals significant limitations in current vision-language models for fine-grained visual understanding and establishes DINOv2 as a strong baseline for dense semantic matching in autonomous driving scenarios. This dataset and evaluation framework pave the way for more reliable, interpretable, and scalable perception systems. Code and data are available at: https://github.com/nec-labs-ma/relabeling

A growing number of papers are published in the area of superconducting materials science. However, novel text and data mining (TDM) processes are still needed to efficiently access and exploit this accumulated knowledge, paving the way towards data-driven materials design. Herein, we present SuperMat (Superconductor Materials), an annotated corpus of linked data derived from scientific publications on superconductors, which comprises 142 articles, 16052 entities, and 1398 links that are characterised into six categories: the names, classes, and properties of materials; links to their respective superconducting critical temperature (Tc); and parametric conditions such as applied pressure or measurement methods. The construction of SuperMat resulted from a fruitful collaboration between computer scientists and material scientists, and its high quality is ensured through validation by domain experts. The quality of the annotation guidelines was ensured by satisfactory Inter Annotator Agreement (IAA) between the annotators and the domain experts. SuperMat includes the dataset, annotation guidelines, and annotation support tools that use automatic suggestions to help minimise human errors.

Unsupervised text representation learning (TRL) is a fundamental task in natural language processing, which is beneficial for improving search and recommendations with the web's unlabeled texts. A recent empirical study finds that the high-quality representation aligns with the key token of the input text, uncovering the potential connection between representation space and vocabulary space. Inspired by the findings, we revisit the generative tasks and develop an unsupervised generative framework for TRL, Text2Token. The framework is based on the token target prediction task, utilizing carefully constructed target token distribution as supervisory signals. To construct the high-quality target token distribution, we analyze the token-alignment properties with advanced embedders and identify two essential categories of key tokens: (1) the meaningful tokens in the text and (2) semantically derived tokens beyond the text. Based on these insights, we propose two methods -- data-driven and model-derived -- to construct synthetic token targets from data or the LLM backbone. Experiments on the MTEB v2 benchmark demonstrate that Text2Token achieves performance competitive with the state-of-the-art embedder with unsupervised contrastive learning, LLM2Vec. Our analysis further shows that vocabulary and representation spaces optimize together and toward the optimum solution during training, providing new ideas and insights for future work.

Effective disaster management requires timely access to accurate and contextually relevant information. Existing Information Retrieval (IR) benchmarks, however, focus primarily on general or specialized domains, such as medicine or finance, neglecting the unique linguistic complexity and diverse information needs encountered in disaster management scenarios. To bridge this gap, we introduce DisastIR, the first comprehensive IR evaluation benchmark specifically tailored for disaster management. DisastIR comprises 9,600 diverse user queries and more than 1.3 million labeled query-passage pairs, covering 48 distinct retrieval tasks derived from six search intents and eight general disaster categories that include 301 specific event types. Our evaluations of 30 state-of-the-art retrieval models demonstrate significant performance variances across tasks, with no single model excelling universally. Furthermore, comparative analyses reveal significant performance gaps between general-domain and disaster management-specific tasks, highlighting the necessity of disaster management-specific benchmarks for guiding IR model selection to support effective decision-making in disaster management scenarios. All source codes and DisastIR are available at https://github.com/KaiYin97/Disaster_IR.

Being data-driven is one of the most iconic properties of deep learning algorithms. The birth of ImageNet drives a remarkable trend of "learning from large-scale data" in computer vision. Pretraining on ImageNet to obtain rich universal representations has been manifested to benefit various 2D visual tasks, and becomes a standard in 2D vision. However, due to the laborious collection of real-world 3D data, there is yet no generic dataset serving as a counterpart of ImageNet in 3D vision, thus how such a dataset can impact the 3D community is unraveled. To remedy this defect, we introduce MVImgNet, a large-scale dataset of multi-view images, which is highly convenient to gain by shooting videos of real-world objects in human daily life. It contains 6.5 million frames from 219,188 videos crossing objects from 238 classes, with rich annotations of object masks, camera parameters, and point clouds. The multi-view attribute endows our dataset with 3D-aware signals, making it a soft bridge between 2D and 3D vision. We conduct pilot studies for probing the potential of MVImgNet on a variety of 3D and 2D visual tasks, including radiance field reconstruction, multi-view stereo, and view-consistent image understanding, where MVImgNet demonstrates promising performance, remaining lots of possibilities for future explorations. Besides, via dense reconstruction on MVImgNet, a 3D object point cloud dataset is derived, called MVPNet, covering 87,200 samples from 150 categories, with the class label on each point cloud. Experiments show that MVPNet can benefit the real-world 3D object classification while posing new challenges to point cloud understanding. MVImgNet and MVPNet will be publicly available, hoping to inspire the broader vision community.

Embodied Foundation Models (EFMs) integrate multimodal understanding, future-state reasoning, and executable robot actions. Yet their safety alignment for human-injury prevention remains underexplored, primarily because real-world data of robots harming humans or creating hazardous household situations cannot be safely or ethically collected. To address this challenge, we propose a safety-critical data construction pipeline for human-injury prevention in EFMs.Starting from real DROID observations, our construction pipeline proceeds through scene understanding, hazard-aware image editing, temporal prompt generation, and single-pass rollout synthesis. The temporal prompts specify the expected scene evolution, while Wan2.7 synthesizes realistic robotic rollouts from the edited hazardous states in a single pass. Using this pipeline, we construct ROBOSHACKLES, a 10,000-clip robotic video dataset derived from real DROID observations, spanning two direct-harm and four indirect-harm categories. To ensure dataset quality, we assess task completion and visual quality with automatic metrics, and evaluate six representative EFMs under a refusal-based safety criterion. Results show that all evaluated models produce unsafe actions in the tested safety-critical scenarios, yielding a 100% unsafe action generation rate. ROBOSHACKLES serves as a scalable benchmark and training resource for refusal learning and hazard anticipation before robot action execution.The dataset is publicly available at https://huggingface.co/datasets/YZW00/RoboShackles.

Egocentric video action recognition under domain shifts remains challenging due to large intra-class spatio-temporal variability, long-tailed feature distributions, and strong correlations between actions and environments. Existing benchmarks for egocentric domain generalization often conflate covariate shifts with concept shifts, making it difficult to reliably evaluate a model's ability to generalize across input distributions. To address this limitation, we introduce Ego4OOD, a domain generalization benchmark derived from Ego4D that emphasizes measurable covariate diversity while reducing concept shift through semantically coherent, moment-level action categories. Ego4OOD spans eight geographically distinct domains and is accompanied by a clustering-based covariate shift metric that provides a quantitative proxy for domain difficulty. We further leverage a one-vs-all binary training objective that decomposes multi-class action recognition into independent binary classification tasks. This formulation is particularly well-suited for covariate shift by reducing interference between visually similar classes under feature distribution shift. Using this formulation, we show that a lightweight two-layer fully connected network achieves performance competitive with state-of-the-art egocentric domain generalization methods on both Argo1M and Ego4OOD, despite using fewer parameters and no additional modalities. Our empirical analysis demonstrates a clear relationship between measured covariate shift and recognition performance, highlighting the importance of controlled benchmarks and quantitative domain characterization for studying out-of-distribution generalization in egocentric video.

In industrial procurement, an LLM answer is useful only if it survives a standards check: recommended material must match operating condition, every parameter must respect a regulated threshold, and no procedure may contradict a safety clause. Partial correctness can mask safety-critical contradictions that aggregate LLM benchmarks rarely capture. We introduce IndustryBench, a 2,049-item benchmark for industrial procurement QA in Chinese, grounded in Chinese national standards (GB/T) and structured industrial product records, organized by seven capability dimensions, ten industry categories, and panel-derived difficulty tiers, with item-aligned English, Russian, and Vietnamese renderings. Our construction pipeline rejects 70.3% of LLM-generated candidates at a search-based external-verification stage, calibrating how unreliable industrial QA remains after LLM-only filtering.Our evaluation decouples raw correctness, scored by a Qwen3-Max judge validated at κ_w = 0.798 against a domain expert, from a separate safety-violation (SV) check against source texts. Across 17 models in Chinese and an 8-model intersection over four languages, we find: (i) the best system reaches only 2.083 on the 0--3 rubric, leaving substantial headroom; (ii) Standards & Terminology is the most persistent capability weakness and survives item-aligned translation; (iii) extended reasoning lowers safety-adjusted scores for 12 of 13 models, primarily by introducing unsupported safety-critical details into longer final answers; and (iv) safety-violation rates reshuffle the leaderboard -- GPT-5.4 climbs from rank 6 to rank 3 after SV adjustment, while Kimi-k2.5-1T-A32B drops seven positions.Industrial LLM evaluation therefore requires source-grounded, safety-aware diagnosis rather than aggregate accuracy. We release IndustryBench with all prompts, scoring scripts, and dataset documentation.

Visual reasoning, the capability to interpret visual input in response to implicit text query through multi-step reasoning, remains a challenge for deep learning models due to the lack of relevant benchmarks. Previous work in visual reasoning has primarily focused on reasoning segmentation, where models aim to segment objects based on implicit text queries. This paper introduces reasoning visual tasks (RVTs), a unified formulation that extends beyond traditional video reasoning segmentation to a diverse family of visual language reasoning problems, which can therefore accommodate multiple output formats including bounding boxes, natural language descriptions, and question-answer pairs. Correspondingly, we identify the limitations in current benchmark construction methods that rely solely on large language models (LLMs), which inadequately capture complex spatial-temporal relationships and multi-step reasoning chains in video due to their reliance on token representation, resulting in benchmarks with artificially limited reasoning complexity. To address this limitation, we propose a novel automated RVT benchmark construction pipeline that leverages digital twin (DT) representations as structured intermediaries between perception and the generation of implicit text queries. Based on this method, we construct RVTBench, a RVT benchmark containing 3,896 queries of over 1.2 million tokens across four types of RVT (segmentation, grounding, VQA and summary), three reasoning categories (semantic, spatial, and temporal), and four increasing difficulty levels, derived from 200 video sequences. Finally, we propose RVTagent, an agent framework for RVT that allows for zero-shot generalization across various types of RVT without task-specific fine-tuning.

Kuznetsov and Polishchuk provided a general algorithm to construct exceptional collections of maximal length for homogeneous varieties of type A,B,C,D. We consider the case of the spinor tenfold and we prove that the corresponding collection is full, i.e. it generates the whole derived category of coherent sheaves. As a step of the proof, we construct some resolutions of homogeneous vector bundles which might be of independent interest.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of R^{n} for the groups S_n, O(n), Sp(n), and SO(n). By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon's entropy of P.Baudot and D.Bennequin in 2015). They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Loef) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck's derivators.

Generalized category discovery (GCD) is a pragmatic but underexplored problem, which requires models to automatically cluster and discover novel categories by leveraging the labeled samples from old classes. The challenge is that unlabeled data contain both old and new classes. Early works leveraging pseudo-labeling with parametric classifiers handle old and new classes separately, which brings about imbalanced accuracy between them. Recent methods employing contrastive learning neglect potential positives and are decoupled from the clustering objective, leading to biased representations and sub-optimal results. To address these issues, we introduce a unified and unbiased prototype learning framework, namely ProtoGCD, wherein old and new classes are modeled with joint prototypes and unified learning objectives, {enabling unified modeling between old and new classes}. Specifically, we propose a dual-level adaptive pseudo-labeling mechanism to mitigate confirmation bias, together with two regularization terms to collectively help learn more suitable representations for GCD. Moreover, for practical considerations, we devise a criterion to estimate the number of new classes. Furthermore, we extend ProtoGCD to detect unseen outliers, achieving task-level unification. Comprehensive experiments show that ProtoGCD achieves state-of-the-art performance on both generic and fine-grained datasets. The code is available at https://github.com/mashijie1028/ProtoGCD.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for everything? This question cannot be answered by the existing theory of representation, optimization or generalization, because the issues they mainly investigate are assumed to be nonexistent here. In this paper, we show that category theory provides powerful machinery to answer this question. We have proved three results. The first one limits the power of prompt-based learning, saying that the model can solve a downstream task with prompts if and only if the task is representable. The second one says fine tuning does not have this limit, as a foundation model with the minimum required power (up to symmetry) can theoretically solve downstream tasks for the category defined by pretext task, with fine tuning and enough resources. Our final result can be seen as a new type of generalization theorem, showing that the foundation model can generate unseen objects from the target category (e.g., images) using the structural information from the source category (e.g., texts). Along the way, we provide a categorical framework for supervised and self-supervised learning, which might be of independent interest.

A homogeneous roof is a rational homogeneous variety of Picard rank 2 and index r equipped with two different mathbb P^{r-1}-bundle structures. We consider bundles of homogeneous roofs over a smooth projective variety, formulating a relative version of the duality of Calabi--Yau pairs associated to roofs of projective bundles. We discuss how derived equivalence of such pairs can lift to Calabi--Yau fibrations, extending a result of Bridgeland and Maciocia to higher-dimensional cases. We formulate an approach to prove that the DK-conjecture holds for a class of simple K-equivalent maps arising from bundles of roofs. As an example, we propose a pair of eight-dimensional Calabi--Yau varieties fibered in dual Calabi--Yau threefolds, related by a GLSM phase transition, and we prove derived equivalence with the methods above.

We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditions for induction functors associated to simple current extensions of vertex algebras to preserve Loewy diagrams.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been pursued recently, and yet there is still a gap between abstract mathematical foundations and concrete applications to machine learning tasks. In this paper we introduce DisCoPyro as a categorical structure learning framework, which combines categorical structures (such as symmetric monoidal categories and operads) with amortized variational inference, and can be applied, e.g., in program learning for variational autoencoders. We provide both mathematical foundations and concrete applications together with comparison of experimental performance with other models (e.g., neuro-symbolic models). We speculate that DisCoPyro could ultimately contribute to the development of artificial general intelligence.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific disciplines. It is therefore unsurprising that there is a burgeoning interest in applying category theory to machine learning. We aim to document the motivations, goals and common themes across these applications. We touch on gradient-based learning, probability, and equivariant learning.

Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in complex scenarios. Recent studies integrating Vision-Language Models (VLMs) with class hierarchies have shown promise, yet they fall short of fully exploiting the hierarchical relationships. These efforts are constrained by their inability to perform effectively across varied granularity of categories. To tackle this issue, we propose a novel framework (HGCLIP) that effectively combines CLIP with a deeper exploitation of the Hierarchical class structure via Graph representation learning. We explore constructing the class hierarchy into a graph, with its nodes representing the textual or image features of each category. After passing through a graph encoder, the textual features incorporate hierarchical structure information, while the image features emphasize class-aware features derived from prototypes through the attention mechanism. Our approach demonstrates significant improvements on 11 diverse visual recognition benchmarks. Our codes are fully available at https://github.com/richard-peng-xia/HGCLIP.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Generalized Category Discovery (GCD) aims to classify unlabelled images from both `seen' and `unseen' classes by transferring knowledge from a set of labelled `seen' class images. A key theme in existing GCD approaches is adapting large-scale pre-trained models for the GCD task. An alternate perspective, however, is to adapt the data representation itself for better alignment with the pre-trained model. As such, in this paper, we introduce a two-stage adaptation approach termed SPTNet, which iteratively optimizes model parameters (i.e., model-finetuning) and data parameters (i.e., prompt learning). Furthermore, we propose a novel spatial prompt tuning method (SPT) which considers the spatial property of image data, enabling the method to better focus on object parts, which can transfer between seen and unseen classes. We thoroughly evaluate our SPTNet on standard benchmarks and demonstrate that our method outperforms existing GCD methods. Notably, we find our method achieves an average accuracy of 61.4% on the SSB, surpassing prior state-of-the-art methods by approximately 10%. The improvement is particularly remarkable as our method yields extra parameters amounting to only 0.117% of those in the backbone architecture. Project page: https://visual-ai.github.io/sptnet.

In an unpublished preprint batanin, Batanin conjectures that it is possible to take `slices' of a globular operad, thereby isolating the algebraic structure in each dimension. It was further hypothesised that the slices of a globular operad for some theory of higher category contain essential information about those higher categories, namely whether or not they are equivalent to the fully weak variety. In this paper, we use the theory of presentations for globular operads developed in Me to provide a concrete definition of slices, and calculate the slices for several key theories of n-category.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all aspects of probability theory in which infinitely many random variables appear at a time. These infinite tensor products bigotimes_{i in J} X_i come in two versions: a weaker but more general one for families of objects (X_i)_{i in J} in semicartesian symmetric monoidal categories, and a stronger but more specific one for families of objects in Markov categories. As a first application, we state and prove versions of the zero-one laws of Kolmogorov and Hewitt-Savage for Markov categories. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts.

This book provides an inviting tour through sheaf theory, from the perspective of applied category theory and pitched at a less specialized audience than is typical with introductions to sheaves. The book makes it as easy as possible for the reader new to sheaves, by motivating and developing the theory via a broad range of concrete examples and explicit constructions, including applications to n-colorings of graphs, satellite data, chess problems, Bayes nets, musical performance, complexes, and more. Included is an extended first chapter introducing and motivating all the necessary category-theoretical background, again with a strong emphasis on concrete examples. A new and unabridged version (including a fifth chapter on more advanced topics and a conclusion) will be available with MIT Press.

We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an etale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified p-adic Beilinson--Drinfeld Grassmannians are kimberlites with finiteness and normality properties.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

We explore the problem of Incremental Generalized Category Discovery (IGCD). This is a challenging category incremental learning setting where the goal is to develop models that can correctly categorize images from previously seen categories, in addition to discovering novel ones. Learning is performed over a series of time steps where the model obtains new labeled and unlabeled data, and discards old data, at each iteration. The difficulty of the problem is compounded in our generalized setting as the unlabeled data can contain images from categories that may or may not have been observed before. We present a new method for IGCD which combines non-parametric categorization with efficient image sampling to mitigate catastrophic forgetting. To quantify performance, we propose a new benchmark dataset named iNatIGCD that is motivated by a real-world fine-grained visual categorization task. In our experiments we outperform existing related methods

Generalized Category Discovery (GCD) is an open-world problem that clusters unlabeled data by leveraging knowledge from partially labeled categories. A key challenge is that unlabeled data may contain both known and novel categories. Existing approaches suffer from two main limitations. First, they fail to exploit multi-granularity conceptual information in visual data, which limits representation quality. Second, most assume that the number of unlabeled categories is known during training, which is impractical in real-world scenarios. To address these issues, we propose a Multi-Granularity Conceptual Experts (MGCE) framework that adaptively mines visual concepts and integrates multi-granularity knowledge for accurate category discovery. MGCE consists of two modules: (1) Dynamic Conceptual Contrastive Learning (DCCL), which alternates between concept mining and dual-level representation learning to jointly optimize feature learning and category discovery; and (2) Multi-Granularity Experts Collaborative Learning (MECL), which extends the single-expert paradigm by introducing additional experts at different granularities and by employing a concept alignment matrix for effective cross-expert collaboration. Importantly, MGCE can automatically estimate the number of categories in unlabeled data, making it suitable for practical open-world settings. Extensive experiments on nine fine-grained visual recognition benchmarks demonstrate that MGCE achieves state-of-the-art results, particularly in novel-class accuracy. Notably, even without prior knowledge of category numbers, MGCE outperforms parametric approaches that require knowing the exact number of categories, with an average improvement of 3.6\%. Code is available at https://github.com/HaiyangZheng/MGCE.

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the Hoare hyperspace monad H, which assigns to every space its space of closed subsets equipped with the lower Vietoris topology. The second is the monad V of continuous valuations, also known as the extended probabilistic powerdomain. We construct both monads in a unified way in terms of double dualization. This reveals a close analogy between them, and allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra. Third, we show that V can be restricted to a submonad of tau-smooth probability measures on Top. By composing these two morphisms of monads, we obtain that taking the support of a tau-smooth probability measure is also a morphism of monads.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

In this paper, we address the problem of generalized category discovery (GCD), \ie, given a set of images where part of them are labelled and the rest are not, the task is to automatically cluster the images in the unlabelled data, leveraging the information from the labelled data, while the unlabelled data contain images from the labelled classes and also new ones. GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance.

Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural networks to progressively become more complex and thus difficult to define from a mathematical perspective. We present a general definition of linear layer arising from a categorical framework based on the notions of integration theory and parametric spans. This definition generalizes and encompasses classical layers (e.g., dense, convolutional), while guaranteeing existence and computability of the layer's derivatives for backpropagation.

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this thesis we build a category-theoretic formalism around a class of neural networks exemplified by CycleGAN. CycleGAN is a collection of neural networks, closed under composition, whose inductive bias is increased by enforcing composition invariants, i.e. cycle-consistencies. Inspired by Functorial Data Migration, we specify the interconnection of these networks using a categorical schema, and network instances as set-valued functors on this schema. We also frame neural network architectures, datasets, models, and a number of other concepts in a categorical setting and thus show a special class of functors, rather than functions, can be learned using gradient descent. We use the category-theoretic framework to conceive a novel neural network architecture whose goal is to learn the task of object insertion and object deletion in images with unpaired data. We test the architecture on three different datasets and obtain promising results.

Generalized Category Discovery (GCD) is a classification task that aims to classify both base and novel classes in unlabeled images, using knowledge from a labeled dataset. In GCD, previous research overlooks scene information or treats it as noise, reducing its impact during model training. However, in this paper, we argue that scene information should be viewed as a strong prior for inferring novel classes. We attribute the misinterpretation of scene information to a key factor: the Ambiguity Challenge inherent in GCD. Specifically, novel objects in base scenes might be wrongly classified into base categories, while base objects in novel scenes might be mistakenly recognized as novel categories. Once the ambiguity challenge is addressed, scene information can reach its full potential, significantly enhancing the performance of GCD models. To more effectively leverage scene information, we propose the Modeling Object-Scene Associations (MOS) framework, which utilizes a simple MLP-based scene-awareness module to enhance GCD performance. It achieves an exceptional average accuracy improvement of 4% on the challenging fine-grained datasets compared to state-of-the-art methods, emphasizing its superior performance in fine-grained GCD. The code is publicly available at https://github.com/JethroPeng/MOS.

Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets, providing a more realistic setting for image recognition. Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LegoGCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, eg, delivering a 7.74% and 2.51% accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is pi_1-injective. Furthermore, the domain complex of groups is developable and the induced map on geometric realizations of developments is an isometric embedding.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

This paper is devoted to the classification and studying properties of complex unital 3-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type (2, 1) and two algebras for type (1, 2). For each obtained algebra, we describe the derivation algebra, the automorphism group, the lattice of subalgebras and ideals, and functional identities of degree 2. Furthermore, we investigate the Allison-Kantor construction for the classified algebras. We determine the structure of the resulting Z-graded Lie algebras, providing their dimensions and Levi decompositions.

Traditional approaches for learning 3D object categories have been predominantly trained and evaluated on synthetic datasets due to the unavailability of real 3D-annotated category-centric data. Our main goal is to facilitate advances in this field by collecting real-world data in a magnitude similar to the existing synthetic counterparts. The principal contribution of this work is thus a large-scale dataset, called Common Objects in 3D, with real multi-view images of object categories annotated with camera poses and ground truth 3D point clouds. The dataset contains a total of 1.5 million frames from nearly 19,000 videos capturing objects from 50 MS-COCO categories and, as such, it is significantly larger than alternatives both in terms of the number of categories and objects. We exploit this new dataset to conduct one of the first large-scale "in-the-wild" evaluations of several new-view-synthesis and category-centric 3D reconstruction methods. Finally, we contribute NerFormer - a novel neural rendering method that leverages the powerful Transformer to reconstruct an object given a small number of its views. The CO3D dataset is available at https://github.com/facebookresearch/co3d .

For any {rm E}-rigid presentation e, we construct an orthogonal projection functor to {rm rep}(e^perp) left adjoint to the natural embedding. We establish a bijection between presentations in {rm rep}(e^perp) and presentations compatible with e. For quivers with potentials, we show that {rm rep}(e^perp) forms a module category of another quiver with potential. We derive mutation formulas for the delta-vectors of positive and negative complements and the dimension vectors of simple modules in {rm rep}(e^perp), enabling an algorithm to find the projected quiver with potential. Additionally, we introduce a modified projection for quivers with potentials that preserves general presentations. For applications to cluster algebras, we establish a connection to the stabilization functors.

This paper aims to study Ext-groups between certain functors defined on the category of finitely generated free groups. Rational Ext-groups between the abelianization functor and its symmetric powers are known, and are almost always equal to zero. Recently, using homotopical methods, Arone constructed an explicit bounded complex whose homology corresponds to the integral Ext-groups between the abelianization functor and its symmetric powers. The homology of this complex is far from being trivial. Using this complex, we explicitly calculate some of these Ext-groups. More precisely, we compute Ext^1, Ext^2, Ext^{d-1} and Ext^{d-2} between the abelianization functor and its dth symmetric power. We further explain how Arone's complex can be obtained from an explicit projective resolution of the abelianization functor. We compare our results with the computation of Ext-groups between functors from finitely generated free abelian groups, obtained by Franjou and Pirashvili. In particular, we obtain that the composition with the abelianization functor induces an isomorphism for the Ext^1 considered in this paper.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Generalized Category Discovery (GCD) aims to discover novel categories in unlabelled datasets using knowledge learned from labelled samples. Previous studies argued that parametric classifiers are prone to overfitting to seen categories, and endorsed using a non-parametric classifier formed with semi-supervised k-means. However, in this study, we investigate the failure of parametric classifiers, verify the effectiveness of previous design choices when high-quality supervision is available, and identify unreliable pseudo-labels as a key problem. We demonstrate that two prediction biases exist: the classifier tends to predict seen classes more often, and produces an imbalanced distribution across seen and novel categories. Based on these findings, we propose a simple yet effective parametric classification method that benefits from entropy regularisation, achieves state-of-the-art performance on multiple GCD benchmarks and shows strong robustness to unknown class numbers. We hope the investigation and proposed simple framework can serve as a strong baseline to facilitate future studies in this field. Our code is available at: https://github.com/CVMI-Lab/SimGCD.

This paper explores a novel setting called Generalized Category Discovery in Semantic Segmentation (GCDSS), aiming to segment unlabeled images given prior knowledge from a labeled set of base classes. The unlabeled images contain pixels of the base class or novel class. In contrast to Novel Category Discovery in Semantic Segmentation (NCDSS), there is no prerequisite for prior knowledge mandating the existence of at least one novel class in each unlabeled image. Besides, we broaden the segmentation scope beyond foreground objects to include the entire image. Existing NCDSS methods rely on the aforementioned priors, making them challenging to truly apply in real-world situations. We propose a straightforward yet effective framework that reinterprets the GCDSS challenge as a task of mask classification. Additionally, we construct a baseline method and introduce the Neighborhood Relations-Guided Mask Clustering Algorithm (NeRG-MaskCA) for mask categorization to address the fragmentation in semantic representation. A benchmark dataset, Cityscapes-GCD, derived from the Cityscapes dataset, is established to evaluate the GCDSS framework. Our method demonstrates the feasibility of the GCDSS problem and the potential for discovering and segmenting novel object classes in unlabeled images. We employ the generated pseudo-labels from our approach as ground truth to supervise the training of other models, thereby enabling them with the ability to segment novel classes. It paves the way for further research in generalized category discovery, broadening the horizons of semantic segmentation and its applications. For details, please visit https://github.com/JethroPeng/GCDSS

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.

Generalized Category Discovery (GCD) is a pragmatic and challenging open-world task, which endeavors to cluster unlabeled samples from both novel and old classes, leveraging some labeled data of old classes. Given that knowledge learned from old classes is not fully transferable to new classes, and that novel categories are fully unlabeled, GCD inherently faces intractable problems, including imbalanced classification performance and inconsistent confidence between old and new classes, especially in the low-labeling regime. Hence, some annotations of new classes are deemed necessary. However, labeling new classes is extremely costly. To address this issue, we take the spirit of active learning and propose a new setting called Active Generalized Category Discovery (AGCD). The goal is to improve the performance of GCD by actively selecting a limited amount of valuable samples for labeling from the oracle. To solve this problem, we devise an adaptive sampling strategy, which jointly considers novelty, informativeness and diversity to adaptively select novel samples with proper uncertainty. However, owing to the varied orderings of label indices caused by the clustering of novel classes, the queried labels are not directly applicable to subsequent training. To overcome this issue, we further propose a stable label mapping algorithm that transforms ground truth labels to the label space of the classifier, thereby ensuring consistent training across different active selection stages. Our method achieves state-of-the-art performance on both generic and fine-grained datasets. Our code is available at https://github.com/mashijie1028/ActiveGCD

Recent advances in deep learning have significantly improved the performance of various computer vision applications. However, discovering novel categories in an incremental learning scenario remains a challenging problem due to the lack of prior knowledge about the number and nature of new categories. Existing methods for novel category discovery are limited by their reliance on labeled datasets and prior knowledge about the number of novel categories and the proportion of novel samples in the batch. To address the limitations and more accurately reflect real-world scenarios, in this paper, we propose a novel unsupervised class incremental learning approach for discovering novel categories on unlabeled sets without prior knowledge. The proposed method fine-tunes the feature extractor and proxy anchors on labeled sets, then splits samples into old and novel categories and clusters on the unlabeled dataset. Furthermore, the proxy anchors-based exemplar generates representative category vectors to mitigate catastrophic forgetting. Experimental results demonstrate that our proposed approach outperforms the state-of-the-art methods on fine-grained datasets under real-world scenarios.

Generalized Continual Category Discovery (GCCD) tackles learning from sequentially arriving, partially labeled datasets while uncovering new categories. Traditional methods depend on feature distillation to prevent forgetting the old knowledge. However, this strategy restricts the model's ability to adapt and effectively distinguish new categories. To address this, we introduce a novel technique integrating a learnable projector with feature distillation, thus enhancing model adaptability without sacrificing past knowledge. The resulting distribution shift of the previously learned categories is mitigated with the auxiliary category adaptation network. We demonstrate that while each component offers modest benefits individually, their combination - dubbed CAMP (Category Adaptation Meets Projected distillation) - significantly improves the balance between learning new information and retaining old. CAMP exhibits superior performance across several GCCD and Class Incremental Learning scenarios. The code is available at https://github.com/grypesc/CAMP.

Generalized Category Discovery (GCD) is a practical and challenging open-world task that aims to recognize both known and novel categories in unlabeled data using limited labeled data from known categories. Due to the lack of supervision, previous GCD methods face significant challenges, such as difficulty in rectifying errors for confusing instances, and inability to effectively uncover and leverage the semantic meanings of discovered clusters. Therefore, additional annotations are usually required for real-world applicability. However, human annotation is extremely costly and inefficient. To address these issues, we propose GLEAN, a unified framework for generalized category discovery that actively learns from diverse and quality-enhanced LLM feedback. Our approach leverages three different types of LLM feedback to: (1) improve instance-level contrastive features, (2) generate category descriptions, and (3) align uncertain instances with LLM-selected category descriptions. Extensive experiments demonstrate the superior performance of \MethodName over state-of-the-art models across diverse datasets, metrics, and supervision settings. Our code is available at https://github.com/amazon-science/Glean.

The extraction of modular object-centric representations for downstream tasks is an emerging area of research. Learning grounded representations of objects that are guaranteed to be stable and invariant promises robust performance across different tasks and environments. Slot Attention (SA) learns object-centric representations by assigning objects to slots, but presupposes a single distribution from which all slots are randomly initialised. This results in an inability to learn specialized slots which bind to specific object types and remain invariant to identity-preserving changes in object appearance. To address this, we present \textsc{Conditional Slot Attention} (CoSA) using a novel concept of Grounded Slot Dictionary (GSD) inspired by vector quantization. Our proposed GSD comprises (i) canonical object-level property vectors and (ii) parametric Gaussian distributions, which define a prior over the slots. We demonstrate the benefits of our method in multiple downstream tasks such as scene generation, composition, and task adaptation, whilst remaining competitive with SA in popular object discovery benchmarks.

We introduce a Heegaard-Floer homology functor from the category of oriented links in closed 3-manifolds and oriented surface cobordisms in 4-manifolds connecting them to the category of F[v]-modules and F[v]-homomorphisms between them, where F is the field with two elements. In comparison with previously defined TQFTs for decorated links and link cobordisms, the construction of this paper has the advantage of being independent from the decoration. Some of the basic properties of this functor are also explored.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finetti's representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad. This new limit is used to identify among exchangeable coalgebras the final one.

A unique aspect of human visual understanding is the ability to flexibly interpret abstract concepts: acquiring lifted rules explaining what they symbolize, grounding them across familiar and unfamiliar contexts, and making predictions or reasoning about them. While off-the-shelf vision-language models excel at making literal interpretations of images (e.g., recognizing object categories such as tree branches), they still struggle to make sense of such visual abstractions (e.g., how an arrangement of tree branches may form the walls of a maze). To address this challenge, we introduce Deep Schema Grounding (DSG), a framework that leverages explicit structured representations of visual abstractions for grounding and reasoning. At the core of DSG are schemas--dependency graph descriptions of abstract concepts that decompose them into more primitive-level symbols. DSG uses large language models to extract schemas, then hierarchically grounds concrete to abstract components of the schema onto images with vision-language models. The grounded schema is used to augment visual abstraction understanding. We systematically evaluate DSG and different methods in reasoning on our new Visual Abstractions Dataset, which consists of diverse, real-world images of abstract concepts and corresponding question-answer pairs labeled by humans. We show that DSG significantly improves the abstract visual reasoning performance of vision-language models, and is a step toward human-aligned understanding of visual abstractions.

Open-vocabulary semantic segmentation is a challenging task that requires segmenting novel object categories at inference time. Recent studies have explored vision-language pre-training to handle this task, but suffer from unrealistic assumptions in practical scenarios, i.e., low-quality textual category names. For example, this paradigm assumes that new textual categories will be accurately and completely provided, and exist in lexicons during pre-training. However, exceptions often happen when encountering ambiguity for brief or incomplete names, new words that are not present in the pre-trained lexicons, and difficult-to-describe categories for users. To address these issues, this work proposes a novel attribute decomposition-aggregation framework, AttrSeg, inspired by human cognition in understanding new concepts. Specifically, in the decomposition stage, we decouple class names into diverse attribute descriptions to complement semantic contexts from multiple perspectives. Two attribute construction strategies are designed: using large language models for common categories, and involving manually labeling for human-invented categories. In the aggregation stage, we group diverse attributes into an integrated global description, to form a discriminative classifier that distinguishes the target object from others. One hierarchical aggregation architecture is further proposed to achieve multi-level aggregations, leveraging the meticulously designed clustering module. The final results are obtained by computing the similarity between aggregated attributes and images embeddings. To evaluate the effectiveness, we annotate three types of datasets with attribute descriptions, and conduct extensive experiments and ablation studies. The results show the superior performance of attribute decomposition-aggregation.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

Creating diverse and high-quality 3D assets with an automatic generative model is highly desirable. Despite extensive efforts on 3D generation, most existing works focus on the generation of a single category or a few categories. In this paper, we introduce a diffusion-based feed-forward framework for synthesizing massive categories of real-world 3D objects with a single generative model. Notably, there are three major challenges for this large-vocabulary 3D generation: a) the need for expressive yet efficient 3D representation; b) large diversity in geometry and texture across categories; c) complexity in the appearances of real-world objects. To this end, we propose a novel triplane-based 3D-aware Diffusion model with TransFormer, DiffTF, for handling challenges via three aspects. 1) Considering efficiency and robustness, we adopt a revised triplane representation and improve the fitting speed and accuracy. 2) To handle the drastic variations in geometry and texture, we regard the features of all 3D objects as a combination of generalized 3D knowledge and specialized 3D features. To extract generalized 3D knowledge from diverse categories, we propose a novel 3D-aware transformer with shared cross-plane attention. It learns the cross-plane relations across different planes and aggregates the generalized 3D knowledge with specialized 3D features. 3) In addition, we devise the 3D-aware encoder/decoder to enhance the generalized 3D knowledge in the encoded triplanes for handling categories with complex appearances. Extensive experiments on ShapeNet and OmniObject3D (over 200 diverse real-world categories) convincingly demonstrate that a single DiffTF model achieves state-of-the-art large-vocabulary 3D object generation performance with large diversity, rich semantics, and high quality.

AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition and only some empirical AGI benchmarking frameworks currently exist. The main purpose of this paper is to develop a general, algebraic and category theoretic framework for describing, comparing and analysing different possible AGI architectures. Thus, this Category theoretic formalization would also allow to compare different possible candidate AGI architectures, such as, RL, Universal AI, Active Inference, CRL, Schema based Learning, etc. It will allow to unambiguously expose their commonalities and differences, and what is even more important, expose areas for future research. From the applied Category theoretic point of view, we take as inspiration Machines in a Category to provide a modern view of AGI Architectures in a Category. More specifically, this first position paper provides, on one hand, a first exercise on RL, Causal RL and SBL Architectures in a Category, and on the other hand, it is a first step on a broader research program that seeks to provide a unified formal foundation for AGI systems, integrating architectural structure, informational organization, agent realization, agent and environment interaction, behavioural development over time, and the empirical evaluation of properties. This framework is also intended to support the definition of architectural properties, both syntactic and informational, as well as semantic properties of agents and their assessment in environments with explicitly characterized features. We claim that Category Theory and AGI will have a very symbiotic relation.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

Interpreting chest X-rays is inherently challenging due to the overlap between anatomical structures and the subtle presentation of many clinically significant pathologies, making accurate diagnosis time-consuming even for experienced radiologists. Recent radiology-focused foundation models, such as LLaVA-Rad and Maira-2, have positioned multi-modal large language models (MLLMs) at the forefront of automated radiology report generation (RRG). However, despite these advances, current foundation models generate reports in a single forward pass. This decoding strategy diminishes attention to visual tokens and increases reliance on language priors as generation proceeds, which in turn introduces spurious pathology co-occurrences in the generated reports. To mitigate these limitations, we propose Category-Wise Contrastive Decoding (CWCD), a novel and modular framework designed to enhance structured radiology report generation (SRRG). Our approach introduces category-specific parameterization and generates category-wise reports by contrasting normal X-rays with masked X-rays using category-specific visual prompts. Experimental results demonstrate that CWCD consistently outperforms baseline methods across both clinical efficacy and natural language generation metrics. An ablation study further elucidates the contribution of each architectural component to overall performance.

In this paper, we consider a real-world scenario where a model that is trained on pre-defined classes continually encounters unlabeled data that contains both known and novel classes. The goal is to continually discover novel classes while maintaining the performance in known classes. We name the setting Continual Generalized Category Discovery (C-GCD). Existing methods for novel class discovery cannot directly handle the C-GCD setting due to some unrealistic assumptions, such as the unlabeled data only containing novel classes. Furthermore, they fail to discover novel classes in a continual fashion. In this work, we lift all these assumptions and propose an approach, called MetaGCD, to learn how to incrementally discover with less forgetting. Our proposed method uses a meta-learning framework and leverages the offline labeled data to simulate the testing incremental learning process. A meta-objective is defined to revolve around two conflicting learning objectives to achieve novel class discovery without forgetting. Furthermore, a soft neighborhood-based contrastive network is proposed to discriminate uncorrelated images while attracting correlated images. We build strong baselines and conduct extensive experiments on three widely used benchmarks to demonstrate the superiority of our method.

We study the new task of class-incremental Novel Class Discovery (class-iNCD), which refers to the problem of discovering novel categories in an unlabelled data set by leveraging a pre-trained model that has been trained on a labelled data set containing disjoint yet related categories. Apart from discovering novel classes, we also aim at preserving the ability of the model to recognize previously seen base categories. Inspired by rehearsal-based incremental learning methods, in this paper we propose a novel approach for class-iNCD which prevents forgetting of past information about the base classes by jointly exploiting base class feature prototypes and feature-level knowledge distillation. We also propose a self-training clustering strategy that simultaneously clusters novel categories and trains a joint classifier for both the base and novel classes. This makes our method able to operate in a class-incremental setting. Our experiments, conducted on three common benchmarks, demonstrate that our method significantly outperforms state-of-the-art approaches. Code is available at https://github.com/OatmealLiu/class-iNCD

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

We define deriving semantic class targets as a novel multi-modal task. By doing so, we aim to improve classification schemes in the physical sciences which can be severely abstracted and obfuscating. We address this task for upcoming radio astronomy surveys and present the derived semantic radio galaxy morphology class targets.

We prove that the homotopy limits and homotopy colimits of chain complexes can be computed by the cobar and bar constructions. We also show that the totalizations of double complexes compute the homotopy limits and homotopy colimits of simplicial and cosimplicial chain complexes.

Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) combines aspected of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (Grefenstette et al., arxiv:1101.0309; Grefenstette and Sadrzadeh, arXiv:1106.4058v1 [cs.CL]). . In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (arXiv:1106.4058v1 [cs.CL]).

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

People can categorize the same entity at multiple taxonomic levels, such as basic (bear), superordinate (animal), and subordinate (grizzly bear). While prior research has focused on basic-level categories, this study is the first attempt to examine the organization of categories by analyzing exemplars produced at the subordinate level. We present a new Italian psycholinguistic dataset of human-generated exemplars for 187 concrete words. We then use these data to evaluate whether textual and vision LLMs produce meaningful exemplars that align with human category organization across three key tasks: exemplar generation, category induction, and typicality judgment. Our findings show a low alignment between humans and LLMs, consistent with previous studies. However, their performance varies notably across different semantic domains. Ultimately, this study highlights both the promises and the constraints of using AI-generated exemplars to support psychological and linguistic research.

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.

On-the-fly category discovery (OCD) aims to recognize known categories while simultaneously discovering novel ones from an unlabeled online stream, using a model trained only on labeled data. Existing approaches freeze the feature extractor trained offline and employ a hash-based framework that quantizes features into binary codes as class prototypes. However, discovering novel categories with a fixed knowledge base is counterintuitive, as the learning potential of incoming data is entirely neglected. In addition, feature quantization introduces information loss, diminishes representational expressiveness, and amplifies intra-class variance. It often results in category explosion, where a single class is fragmented into multiple pseudo-classes. To overcome these limitations, we propose a test-time adaptation framework that enables learning through discovery. It incorporates two complementary strategies: a semantic-aware prototype update and a stable test-time encoder update. The former dynamically refines class prototypes to enhance classification, whereas the latter integrates new information directly into the parameter space. Together, these components allow the model to continuously expand its knowledge base with newly encountered samples. Furthermore, we introduce a margin-aware logit calibration in the offline stage to enlarge inter-class margins and improve intra-class compactness, thereby reserving embedding space for future class discovery. Experiments on standard OCD benchmarks demonstrate that our method substantially outperforms existing hash-based state-of-the-art approaches, yielding notable improvements in novel-class accuracy and effectively mitigating category explosion. The code is publicly available at blue{https://github.com/ynanwu/TALON}.

In this article, we introduce and study singular foliations of b^k-type. These singular foliations formalize the properties of vector fields that are tangent to order k along a submanifold W subset M. Our first result is a classification of these foliations, relating them to geometric structures defined in a formal neighborhood of the submanifold, such as jets of distributions that are involutive up to order k-1. When W is a hypersurface, singular foliations of b^k-type are Lie algebroids. In this particular case, they are generalizations of the b^k-tangent bundles introduced by Scott. Indeed, they are always locally isomorphic to b^k-tangent bundles, but globally such an isomorphism is obstructed by a holonomy invariant. Our second main result is a Riemann-Hilbert-style classification of singular foliations of b^k-type in terms of holonomy representations. In this paper, we study singular foliations of b^k-type from several different perspectives. In particular: (1) We study the problem of extending a k-th-order foliation to a (k+1)-th order foliation and prove that this is obstructed by a characteristic class. (2) When W is a hypersurface, we give a detailed study of algebroid differential forms and extend Scott's calculation of the cohomology. (3) We study algebroid symplectic forms in terms of the geometric structures induced on W. In particular, we find that there is a close relationship between the above obstruction class for extensions and the symplectic variation of the symplectic foliation induced on W.

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. In this paper we provide an explanation for this behavior based on the recently observed phenomenon that the features learned by overparameterized classification networks show an interesting clustering property, called neural collapse. We demonstrate both theoretically and empirically that neural collapse generalizes to new samples from the training classes, and -- more importantly -- to new classes as well, allowing foundation models to provide feature maps that work well in transfer learning and, specifically, in the few-shot setting.

Learning 3D models of all animals on the Earth requires massively scaling up existing solutions. With this ultimate goal in mind, we develop 3D-Fauna, an approach that learns a pan-category deformable 3D animal model for more than 100 animal species jointly. One crucial bottleneck of modeling animals is the limited availability of training data, which we overcome by simply learning from 2D Internet images. We show that prior category-specific attempts fail to generalize to rare species with limited training images. We address this challenge by introducing the Semantic Bank of Skinned Models (SBSM), which automatically discovers a small set of base animal shapes by combining geometric inductive priors with semantic knowledge implicitly captured by an off-the-shelf self-supervised feature extractor. To train such a model, we also contribute a new large-scale dataset of diverse animal species. At inference time, given a single image of any quadruped animal, our model reconstructs an articulated 3D mesh in a feed-forward fashion within seconds.