CEREBRUM, Training-Free Knowledge Graph Reasoning

Every answer is a citable graph path. Not a prediction.

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Model Description

CEREBRUM is a training-free knowledge graph question answering (KGQA) framework that performs multi-hop reasoning via deterministic beam-search traversal guided by a 10-parameter Community-Structured Attention (CSA) formula.

Unlike supervised KGQA systems (EmbedKGQA, UniKGQA, NSM), CEREBRUM requires no labeled question-answer pairs, no gradient steps, and no dataset-specific configuration. Load any knowledge graph formatted as (head, relation, tail) triples and query it immediately.

Every answer includes the complete hop-by-hop reasoning path, every edge traversed, every score assigned, making the full reasoning process auditable, reproducible, and provable. The accuracy numbers (60.6% H@1 on MetaQA 3-hop, 87.9% H@10, 100% on Hetionet disease_associates_gene) are evidence for the above properties, not the headline.

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What matters depends on who you are.

	The claim	The evidence
Researchers	Your result is falsifiable. Every one.	Full hop-by-hop path, CSA weight per edge, community votes, pruned candidates — every answer is a complete reasoning record. Deterministic: same query, same graph → same path every time.
Scientists	You can't cite a hallucination. We don't make them.	Structural impossibility: answers can only be entities reachable via real graph edges. On Hetionet: 100% H@1 on disease_associates_gene, 95.3% 1-hop average, full provenance per answer.
Engineers	Load a CSV. Query immediately. Zero configuration.	ParameterInitializer derives all 9 scoring parameters from graph statistics in one O(E) pass. Adapters for CSV, Neo4j, RDF/SPARQL, NetworkX.
Students	$0.001 per 1K queries. No API key. No GPU.	Compute only. Runs on a laptop. Zero-config baseline: 56.8% H@1 on MetaQA 3-hop with no tuning. AGPL-3.0 — free for academic use.

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Key Properties

Property	Value
Training required	None
Hallucination risk	0% (deterministic graph traversal)
Reasoning transparency	Full hop-by-hop trace
Knowledge graph formats	CSV, Neo4j, RDF/SPARQL, NetworkX
Cost per 1K queries	~$0.001 (compute only)
GPU required	Optional (CPU-capable, GPU-accelerated)

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Benchmark Results

MetaQA, 3-hop (14,274 test questions)

System	3-hop H@1	3-hop H@10	MRR	Training
CEREBRUM v2.88.0 (full pipeline)	60.6%	87.9%	0.703	None
CEREBRUM (search only)	12.5%	50.3%	—	None
UniKGQA (Jiang et al., 2023) †	99.1%	—	—	Supervised
EmbedKGQA (Saxena et al., 2020) †	~94%	—	—	Supervised
MINERVA (Das et al., 2018) †	—	45.6%	—	RL-trained
GraftNet (Sun et al., 2018) †	22.8%	—	—	Supervised

† Black-box model: no auditable reasoning path; can produce confident wrong answers.

Note on the H@1 gap: The gap to supervised H@1 (99% vs 60.6%) is a ranking challenge, not a retrieval failure. CEREBRUM places the correct answer in its top-10 candidates 87.9% of the time, matching supervised recall, while requiring zero training data and returning a full reasoning trace.

MetaQA Dataset Stats

• 43,234 entities · 9 relation types · 186,217 triples
• Test split: 14,274 3-hop questions (full evaluation)
• Graph regime: hub_homogeneous (all seeds are movie entities)

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Hetionet, Biomedical KG (998 QA pairs, 6 templates)

Hetionet is a biomedical knowledge graph with 47,031 entities, 2,250,197 edges, and 24 relation types. Phase 209 full canonical validation (200q/template, sentence-transformers).

Hop	H@1	Notes
1-hop	95.3%	disease→gene, gene→pathway, compound→disease
2-hop	53.0%	disease→gene→pathway (+10pp vs random with sentence embeddings)
3-hop	49.2%	disease→compound→gene (cross-type ceiling†)

Per-template: disease_associates_gene 100% · gene_participates_pathway 98.5% · compound_treats_disease 89.0% · disease_gene_pathway 81.1% · compound_gene_disease 34.5%

† Cross-type 3-hop ceiling: cosine-similarity bias suppresses valid cross-type paths. Documented known limitation, not addressable by structural parameter tuning.

fANOVA finding: branch_bonus accounts for 81.9% of scoring variance on Hetionet, the highest single-parameter dominance across all benchmarks.

Hetionet Dataset Stats

• 47,031 nodes · 2,250,197 edges · 24 relation types
• 998 unique QA pairs across 6 templates
• Graph regime: typed_heterogeneous (biomedical ontology)

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WebQSP, Freebase 2-hop (1,628 test questions)

WebQSP is the standard benchmark for 2-hop open-world KGQA. The graph contains 3.79M entity-name triples from Freebase, 989 distinct relation types, typed-heterogeneous regime.

Phase 259 result, 1,628 questions, full evaluation: H@1=11.92%, H@10=20.47%, MRR=0.1516 (zero training data; zero-config baseline H@1=1.41%, +746% relative). Key milestones: Phase 255 Guaranteed 1-hop Pass (G1P) injects beam-pruned 1-hop neighbors back into the candidate pool; Phase 257 schema_top_k=32 (68.4% fANOVA dominance) expands PathSchemaIndex 2-hop coverage; Phase 259 idf_weight=0.073 + beta=0.649 + DPW=1.836 applies triple hub-suppression.

Why WebQSP is hard for training-free systems: Freebase uses CVT (compound-value-type) mediator nodes with opaque MID identifiers that break semantic attention on indirect 2-hop paths. The hop-reachability diagnostic showed 43.5% of beam misses are direct 1-hop neighbors pruned at beam_width — G1P targets this entire population.

WebQSP Dataset Stats

• 3.79M triples · 989 relation types · Freebase open-world KB
• Test split: 1,628 questions (full evaluation)
• Graph regime: typed_heterogeneous (Freebase ontology, 2-hop)

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How It Works

CEREBRUM reasons over a knowledge graph in three stages:

1. Graph Profiling, At build time, GraphProfiler analyzes the loaded graph: degree distribution, hub score, community modularity Q, and relation fan-out statistics. This auto-configures traversal strategy (hub_homogeneous, typed_heterogeneous, or mixed).

2. Community-Structured Attention, During traversal, each candidate edge is scored by the 10-parameter CSA formula, a sigmoid over a weighted sum of graph-structural features:

Feature	Role
Semantic similarity	Cosine distance between query and candidate entity
Community score	Structural membership in the traversal's target community
Edge-type weight	Per-relation importance derived from graph schema
Distance penalty	Penalizes edges that move away from the target
Hop decay	Reduces score as depth increases
PageRank	Global node importance prior
Temporal decay	Recency of the edge in time-stamped graphs
Node recency	How recently the node was visited in the beam
Synthesis-density penalty	Discounts over-reliance on synthesized edges
Grounding confidence	Provenance confidence of the underlying triple

3. Beam Traversal + Answer Extraction, Beam search (default width 10) follows the highest-scoring paths up to max_hop steps. The Schema-Derived Relation Boost (SDRB) dynamically upweights relations with high fan-out based on graph statistics, without any dataset-specific tuning.

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Novel Contributions

CEREBRUM introduces six original algorithmic contributions:

1. Community-Structured Attention (CSA), 10-parameter training-free attention formula using graph community topology as discrete attention heads.

2. Schema-Derived Relation Boost (SDRB), Derives per-relation scoring weights analytically from triple statistics: boost(r) = γ × fan_out(r)^β. Eliminates KB-specific configuration entirely.

3. Principled Hyperparameter Initialization (ParameterInitializer), Maps all 9 scoring parameters to measurable graph statistics via Bayesian evidence combination (branch_bonus ≈ 0.17), IDF theory (idf_weight = cv_d × 0.01), and Newman-Girvan modularity (vote_weight = 0.72 + 0.15·Q).

4. Experience-Dependent Graph Plasticity (Bridge Twins + STDP), Relay nodes form automatically on frequently-traversed inter-community paths, mimicking synaptic potentiation without training.

5. fANOVA Variance Decomposition Finding, Systematic fANOVA analysis of 200 tuner trials reveals branch_bonus accounts for 46.2% of scoring variance vs. 1.2% for beam width, 39× more influential. Per-relation tuning was masking this signal entirely.

6. PathSchemaIndex, Training-Free Pre-Traversal Schema Prediction (Phase 236), The first predictive reasoning signal in CEREBRUM. All prior signals steer or re-rank after beam traversal. PathSchemaIndex predicts the most likely (r1, r2) 2-hop relation path before any traversal begins, by encoding all graph schemas as natural-language embeddings and finding the closest match to the question embedding. Predicted schemas execute as targeted 2-hop traversals in parallel with the beam, adding high-precision candidates the beam may have pruned. The seed-filter (only schemas whose r1 is actually present on the seed entity) eliminates structurally inapplicable matches. On WebQSP: +3.5pp H@1 (6.0% → 9.5%), +4.0pp H@10.

7. BeamCheckpoint, Parameter-Free Structural Expansion Cache (Phase 241), Inspired by Behrouz et al. (2026) Memory Caching (arXiv:2602.24281), which proposes caching RNN hidden-state checkpoints so that recurrent models gain growing memory without re-processing the full input sequence. BeamCheckpoint applies the dual principle to graph traversal: the raw neighbor expansion at each hop is parameter-free (graph structure is fixed), so it is cached per entity and reused across any re-traversals with different CSA parameters. The scoring pass is then applied on the cached structural expansion, cleanly separating structure (what nodes are reachable) from attention (which ones to select). This eliminates redundant graph I/O for repeated seeds across tuner trials. The companion Sparse Selective Engram Consolidation (EngramConsolidator.sparse_consolidate()) applies the same sparsity principle to the Engram cache: instead of promoting all relation sequences above a count threshold, patterns are ranked by usage × confidence and only the top-k are materialized as canonical engrams.

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Installation

# Core engine with API and embeddings
pip install cerebrum-kg-core[api,embeddings]

# Full install including Studio UI
pip install cerebrum-kg-core[all]
pip install cerebrum-kg-studio

Requirements: Python ≥ 3.10, PyTorch ≥ 2.0, sentence-transformers (optional but recommended)

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Quick Start

from core.cerebrum_graph import CerebrumGraph

# Load any knowledge graph
graph = CerebrumGraph.build("my_graph.csv")

# Query with full trace
results = graph.query("What compound treats Diabetes?", max_hop=3)

for r in results:
    print(f"Answer: {r.entity} Score: {r.score:.3f}")
    for hop in r.path:
        print(f" → {hop.relation} → {hop.entity}")

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Supported Knowledge Graph Formats

Format	Adapter	Notes
CSV (head, relation, tail)	CSVAdapter	Default; zero config
Neo4j	Neo4jAdapter	Bolt protocol
RDF / SPARQL	SPARQLAdapter	Any SPARQL endpoint
NetworkX	NetworkXAdapter	In-memory graphs
Hetionet (biomedical)	CSVAdapter	Validated: 47,031 nodes, 24 relation types

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Use Cases

• Healthcare / Pharma, Drug-disease reasoning over biomedical KGs (Hetionet). Every conclusion citable to a specific graph edge.
• Legal, Case law and regulatory graphs. Full audit trail built-in.
• Financial, Entity relationship graphs for compliance. Reproducible reasoning.
• Scientific Research, Autonomous hypothesis generation with literature validation.
• Any domain, Load your own (head, relation, tail) CSV and query immediately.

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Architecture Overview

THALAMUS (Ingestion)
└─ IngestionPipeline → EmbeddingEngine → StructuralEncoder → CommunityEngine

CORTEX (Reasoning)
└─ PathSchemaIndex (pre-traversal schema prediction)
└─ CSAEngine (10-param) → BeamTraversal → SDRB → AnswerExtractor
└─ Schema channel merge (high-precision parallel traversal)

SDRB (Schema-Derived Relation Boost)
└─ fan_out(r) computed at load time → boost(r) = γ × fan_out(r)^β

Output
└─ Ranked answers + full hop-by-hop ReasoningTrace

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Citation

@misc{buchorn2026cerebrum,
  title = {CEREBRUM: Training-Free Multi-Hop Knowledge Graph Reasoning
           via Community-Structured Graph Attention},
  author = {Buchorn, Bryan Alexander},
  year = {2026},
  note = {arXiv preprint [ARXIV_ID_PLACEHOLDER]},
  url = {https://github.com/BrutalByte/CEREBRUM}
}

@misc{buchorn2026sdrb,
  title = {Schema-Derived Relation Boost and Principled Hyperparameter
           Initialization for Training-Free Multi-Hop Knowledge Graph Reasoning},
  author = {Buchorn, Bryan Alexander},
  year = {2026},
  note = {arXiv preprint [ARXIV_SDRB_ID_PLACEHOLDER]},
  url = {https://github.com/BrutalByte/CEREBRUM}
}

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References

Behrouz, A., Li, Z., Deng, Y., Zhong, P., Razaviyayn, M., & Mirrokni, V. (2026). Memory Caching: RNNs with Growing Memory. arXiv preprint arXiv:2602.24281. https://doi.org/10.48550/arXiv.2602.24281

Das, R., Dhuliawala, S., Zaheer, M., Vilnis, L., Durugkar, I., Krishnamurthy, A., Smola, A., & McCallum, A. (2018). Go for a walk and arrive at the answer. ICLR 2018. https://openreview.net/forum?id=Syg-YfWCW

Himmelstein, D. S., et al. (2017). Systematic integration of biomedical knowledge prioritizes drugs for repurposing. eLife, 6, e26726. https://doi.org/10.7554/eLife.26726

Hutter, F., Hoos, H., & Leyton-Brown, K. (2014). An efficient approach for assessing hyperparameter importance. ICML 2014. https://proceedings.mlr.press/v32/hutter14.html

Jiang, J., et al. (2023). UniKGQA. ICLR 2023. https://openreview.net/forum?id=Z63RvyAZ2Vh

Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113. https://doi.org/10.1103/PhysRevE.69.026113

Saxena, A., Tripathi, A., & Talukdar, P. (2020). Improving multi-hop QA over KGs. ACL 2020. https://aclanthology.org/2020.acl-main.412

Sun, H., et al. (2018). Open domain QA using early fusion of KBs and text. EMNLP 2018. https://aclanthology.org/D18-1455

Zhang, Y., et al. (2018). Variational reasoning for QA with knowledge graphs. AAAI 2018. https://arxiv.org/abs/1709.04071

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License

CEREBRUM is released under the GNU Affero General Public License v3.0 (AGPL-3.0).

Organizations that cannot comply with the AGPL's source-disclosure obligations (e.g., proprietary SaaS deployments) may obtain a commercial exception license. Inquiries: bryan.buchorn@gmail.com

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Built by one person. Open to the world. © 2026 Bryan Alexander Buchorn