Language-encoded network topology enables large language models to reason about complex networks

Introduction

• BioGlyph was designed to identify roles such as hubs, cut nodes, bridges, community cores and cross-community connectors, then describe their evidence and perturbation consequences without changing the network or language model.The method uses fixed rules and network topology alone, making its outputs interpretable to both researchers and language models.Source: Figure 1 · p. 2, Introduction · p. 3

BioGlyph improves reasoning over the yeast interactome and identifies biologically meaningful roles

• BioGlyph achieved 75.6% accuracy on the yeast benchmark, versus 47.3% without network information, 40.1% for edge lists, 37.5% for sentences, 36.1% for raw measurements and 49.2% for GraphSAGE-derived roles.Every BioGlyph description fit within the context window, and its advantage persisted on context-matched subsets.Source: BioGlyph improves reasoning over the… · pp. 3–4, Figure 3 · p. 5
• In yeast, cross-community connectors were 57.6% essential versus 30.9% network-wide and 12.9% for peripheral proteins, while matching-degree comparisons showed 57.6% enrichment versus 56.5% for highest-betweenness proteins.The connector role combined high betweenness with participation across multiple communities rather than applying one centrality measure alone.Source: Figure 3 · p. 5, BioGlyph improves reasoning over the… · p. 6

BioGlyph remains effective on a dense drug-interaction network

• BioGlyph achieved 77.7% accuracy on ChCh-Miner, versus 50.8% without network information, 41.7% for edge lists, 38.3% for sentences, 25.3% for raw measurements and 51.4% for GraphSAGE-derived roles.The median BioGlyph description contained 6,353 tokens and every description fit within the context window, unlike many alternative prompts.Source: BioGlyph remains effective on a dense… · p. 6, Figure 4 · p. 7

BioGlyph identifies structurally important proteins in a human pathway network

• In Reactome, removing EP300 detached 76 proteins, compared with 53 for GPLD1 and 51 for CTCF, and cut nodes were 13.3% selective dependencies versus 8.8% for other proteins.These structural predictions used topology alone and differed from rankings based only on degree or betweenness.Source: BioGlyph identifies structurally… · pp. 7–8, Figure 5 · p. 9

BioGlyph improves structural reasoning in a dense social network

• BioGlyph achieved 79.3% accuracy on ego-Facebook, versus 49.1% without network information, 39.5% for edge lists, 41.3% for sentences, 29.3% for raw measurements and 54.6% for GraphSAGE-derived roles.Accuracy remained stable as retrieved regions expanded from 120 to 300 individuals, at 78.6% and 79.9%, respectively.Source: BioGlyph improves structural reasoning… · pp. 8, 10, Figure 6 · p. 10

BioGlyph supports multi-turn reasoning on an email network

• 73.5% versus 62.6% accuracy favored BioGlyph over raw-measurement tables on 147 paired answers, with corresponding advantages over sentences, edge lists and GraphSAGE-derived roles.The comparisons were 74.4% versus 63.0% for sentences, 74.0% versus 51.4% for edge lists and 79.1% versus 46.2% for GraphSAGE-derived roles.Source: BioGlyph supports multi-turn reasoning… · p. 11
• 74.6% accuracy resulted when BioGlyph role names included supporting measurements and structural consequences, compared with 62.3% for names alone and 64.8% after adding measurements.Replacing meaningful role names with meaningless tokens reduced accuracy from 68.6% to 54.8%; BioGlyph reached 93.5% on cut-node questions, 85.9% on fragmentation and 83.0% on edge-removal questions.Source: BioGlyph supports multi-turn reasoning… · p. 11
• 59.9%, 71.7% and 52.5% accuracy across three turns showed BioGlyph outperforming raw measurements on follow-up and challenge turns despite similar initial performance.Raw graph measurements achieved 62.2%, 55.6% and 37.6% across the same turns.Source: BioGlyph supports multi-turn reasoning… · p. 11
• 75.2% accuracy across 219 eight-turn conversations showed that one initial BioGlyph description supported extended reasoning, while phrasing changes altered accuracy only from 68.6% to 67.9%.After challenges, models retained correct answers in 39.2% of cases and corrected incorrect answers in 9.7%; in the three-turn study, BioGlyph preserved 49.2% of initially correct answers versus 33.5% for raw measurements.Source: BioGlyph supports multi-turn reasoning… · p. 11

• BioGlyph reduced structural-reasoning limitations across 20 networks, with its largest improvement in dense or community-structured networks where direct representations were difficult to interpret or too long.The compiler identifies structural roles, supplies evidence for each assignment and states the role’s structural consequence.Source: Discussion · p. 11
• Selective compression and semantic interpretation drove BioGlyph’s gains: shorter prompts fit context windows, while meaningful role names and explicit consequences improved accuracy.Role names alone added little, arbitrary tokens reduced performance, and consequence statements substantially improved accuracy.Source: Discussion · pp. 11–13
• A single BioGlyph description supported eight-turn conversations and follow-up challenges, although models sometimes abandoned correct answers when challenged.Performance changed little when benchmark questions were rewritten in ordinary prose, whereas raw measurements were less effective and could fail when prompts exceeded context limits.Source: Figure 7 · p. 12, Discussion · p. 13
• Explicitly meaningful roles outperformed topology encodings without structural semantics: unsupervised graph-encoder roles stayed near the no-network baseline, and mismatched-node embeddings matched continuous embeddings.BioGlyph makes topology accessible to small frozen models without modifying the graph or language model.Source: Discussion · p. 13
• In biological networks, selected structural roles showed distinct associations with essentiality, cancer dependency and expression, but these relationships were not uniform and roles were not direct proxies for biological importance.Yeast connectors, cores and hubs were enriched for essential proteins while peripheral proteins were depleted; Reactome cut nodes had more selective cancer dependencies, with substantial protein-level variation.Source: Discussion · p. 13
• BioGlyph is best viewed as an auditable front end to exact graph algorithms, with limitations from sparse networks, prompt budgets, misleading feedback, larger models and benchmark design.Future systems could train readers, generate structurally justified candidates, or invoke exact algorithms for defined operations while using BioGlyph for explanation and multi-step reasoning.Source: Discussion · pp. 13–14

Conclusion

• BioGlyph improved structural reasoning across multi-domain networks, especially dense and community-structured networks, compared with edge lists, adjacency sentences, raw measurements, and unsupervised graph representations.The descriptions work with small, frozen language models without modifying the model or underlying network.Source: Conclusion · p. 14
• Ablations attributed the improvement to selective compression and explicit communication of structural consequences.Source: Conclusion · p. 14
• BioGlyph supported multi-turn reasoning and generated claims verifiable against exact graph analysis.Source: Conclusion · p. 14
• In biological networks, BioGlyph identified structural roles associated with independent measures of gene essentiality and dependency without access to those annotations.Source: Conclusion · p. 14
• BioGlyph is best understood as an interpretable interface between exact network analysis and natural-language reasoning, providing concise, accessible, and auditable structural evidence.The framework offers a practical foundation for language-model-assisted investigation of complex biomedical networks.Source: Conclusion · p. 14

Methods

• BioGlyph retrieves a target-centered region, computes graph signals, assigns eleven structural roles with fixed rules, and emits each role with triggering evidence and a structural consequence.The pipeline uses exact graph algorithms for graded answers, deterministic tie-breaking, and fixed seeds; roles cover nodes, edges, and communities.Source: Methods · p. 14, The BioGlyph compiler · p. 15

Structural signals

• Structural signals combine connectivity decompositions, centrality measures, k-core structure, and Leiden communities, with exact betweenness for n ≤5,000 and seeded 1,000-pivot estimates for larger graphs.Directed inputs preserve direction for degree, PageRank, and betweenness, while the reported experiments treat networks as undirected; participation and intra-community degree quantify community mixing and cohesion.Source: Structural signals · pp. 14–15

The BioGlyph compiler

• The compiler assigns structural roles, including exact CUT_NODE and BRIDGE_EDGE roles based on connectivity decompositions, alongside threshold roles using role-specific standard deviations compared within retrieved regions.Examples include HUB using degree with σ = 2.0 across all regional nodes, BOTTLENECK_LINK using edge betweenness with σ = 2.0 across regional edges, and COMMUNITY_CORE using intra-community degree with σ = 1.0 within communities of at least three nodes.Source: The BioGlyph compiler · p. 15

Retrieval and prompt construction

• Retrieval deterministically expands around named targets under 120- or 300-node caps, with family-specific rings or paths and sufficiency checks that test whether the graded predicate is supported.The benchmark prompt combines the rendered region, shared full-network target facts, and the question, subject to a 24,576-token prompt budget.Source: Retrieval and prompt construction · p. 16

Network representations

• The representation study holds each retrieved region, question, and language model fixed while comparing no graph, edge-list, sentence, raw-measurement, learned-role, and R5 BioGlyph renderings.R3 and R5 share the same structural-signal record, while BioGlyph additionally names roles, evidence, and structural consequences.Source: Network representations · pp. 16–17

Learned-role baselines

• Learned-role baselines use unsupervised eleven-dimensional graph features, two message-passing layers, and seeded clustering into K = 8 roles across GCN, GraphSAGE, GAT, and GIN architectures.The features omit articulation, bridge, community, and removal information, which BioGlyph derives explicitly; the main text reports GraphSAGE and supplementary results cover all architectures.Source: Learned-role baselines · p. 17

Benchmark construction and exact oracle

• The benchmark covers seven structural question families, samples answerable and unanswerable cases across eight networks, and contains 1,239 questions when all quotas are aggregated.Exact graph algorithms provide full-network answers for grading, while a separate region oracle determines whether each retrieved region is sufficient.Source: Benchmark construction and exact oracle · pp. 17–18

Language models, inference and grading

• Evaluation uses Qwen3-8B and Llama-3.1-8B-Instruct with deterministic parsing and exact-match grading, while additional experiments test three- and eight-turn conversations, natural-language answers, and challenge responses.The biological validation matches STRING-Yeast proteins to SGD essentiality annotations without exposing those annotations to the compiler or language models.Source: Language models, inference and grading · p. 18, Conversation experiments · p. 19

Biological validation

• Structural roles are compared with essential-protein prevalence using two-sided Fisher exact tests with Benjamini–Hochberg correction, including matched comparisons against degree, betweenness, and PageRank rankings.Role-specific essential fractions are compared with the full labeled network, and connector groups are matched in size to centrality-based groups.Source: Biological validation · p. 19
• The Reactome perturbation screen ranks proteins by the number of proteins separated from the largest remaining component after removal, then compares rankings with DepMap dependency data.Analyses are restricted to proteins in the Reactome main component that DepMap screened; dependency fraction is based on Chronos scores below −0.5.Source: Biological validation · p. 19
• Perturbation evaluation uses top-ranked proteins and retrieved 20–120-protein modules, scoring exact module-level detachment counts, median absolute error, and structural claims about cut nodes.The screen evaluates top-k selective-dependency enrichment against betweenness, degree, and overall rates, and compares screened cut nodes with other proteins for dependency and essentiality.Source: Biological validation · pp. 19–20

Statistical analysis

• Contrasts are paired by inner joins, with 3,000-resample within-network bootstrap intervals, 5,000-resample two-stage pooled intervals, and t-intervals across eight benchmark networks.The paired mean is the point estimate, while pooled resampling accounts for between-network variation and preserves shared-question correlation within networks.Source: Statistical analysis · p. 20

Datasets and implementation

• The benchmark contains 1,239 questions across eight networks from five domains, while ChCh-Miner is evaluated separately; Reactome FI supports the perturbation screen and BioGlyph runs with exact graph-analysis oracles.Datasets include protein, drug, friendship, email, and functional-interaction networks, with deterministic seed 0 used for stochastic procedures.Source: Datasets and implementation · p. 20

Public datasets

• The study analyzes public networks from protein-interaction, social, communication, biological, power-grid, citation, coauthorship, disease, patient-similarity, single-cell, and functional-interaction datasets.Sources include STRING, HuRI, PP-Pathways, SNAP, BioSNAP, Newman’s collection, PyTorch Geometric, Open Graph Benchmark, HuDiNe, TCGA, GEO accession GSE131928, and Reactome.Source: Data availability · p. 21

Validation data

• External validation used public gene-essentiality, gene-effect, tissue-expression, and approved-gene-symbol labels that were withheld from the models.The labels came from SGD, DepMap 24Q4, GTEx, and HGNC.Source: Data availability · p. 21

Released resources

• The authors release compiled descriptions, exact-answer question sets, every stored model reply, scored result tables, and analysis code.These materials support reproduction of the reported analyses and results.Source: Data availability · p. 21

Code availability

• The private Code Ocean capsule contains the complete BioGlyph implementation, including preprocessing, representation construction, model training and evaluation pipelines.It will become publicly available under a persistent digital object identifier upon publication.Source: Code availability · p. 21
• An interactive browser demonstration enables users to reproduce worked examples and apply BioGlyph to their own networks without local installation.Available at https://islamlab.org/bioglyph.Source: Code availability · p. 21

S1 The networks of the main text, and the result pooled over the whole benchmark

• The yeast interactome contains 363 cut nodes and 553 bridges among 3,384 proteins, whereas Ego-Facebook contains only 11 cut nodes among 4,039 people.These exact structural counts characterize dependence on single points and support using independently sourced SGD gene essentiality labels for validation; all twenty benchmark networks are listed in Table S2.Source: S1 The networks of the main text, and… · p. 24
• 70.6% of pooled questions were answered correctly with BIOGLYPH, versus 50.7% without a network, 48.7% with edge lists, and 39.5% with raw metrics.The benchmark included 1,239 questions across eight networks and five domains, evaluated with Qwen3-8B and Llama-3.1-8B; BIOGLYPH beat every encoder and raw-metric table in all 24 network-by-model combinations.Source: S1 The networks of the main text, and… · p. 24
• BIOGLYPH reached 70.6% pooled accuracy, compared with 74.8% for a trained graph neural network and 82.6% for the retrieval ceiling.BIOGLYPH beat adjacency text in 18 of 24 network-by-model combinations and came within one point of the graph neural network.Source: S1 The networks of the main text, and… · p. 24
• Adding removal-cost consequences raised accuracy from 61.9% with role names alone and 62.0% with measurements to 68.4%, improving performance on 19 of 20 networks.These three representation rungs were scored on a common question set across networks carrying the ladder.Source: S1 The networks of the main text, and… · p. 24
• BIOGLYPH led every representation in each model family, while raw measurements trailed; all six adjacency-text losses occurred on sparse citation and co-authorship graphs.Figure S2 and Table S3 report pooled accuracy, overflow share, and prompt length for each representation arm.Source: S1 The networks of the main text, and… · p. 24
• On the drug-interaction network, BIOGLYPH accuracy was 87.5% for Qwen3-8B, 71.8% for Gemma-3-12B, 67.9% for Llama-3.1-8B, and 57.7% for Mistral-Nemo-12B.Using raw measurements instead yielded 18.6%, 18.6%, 32.1%, and 15.1%, respectively.Source: S1 The networks of the main text, and… · p. 24
• On the yeast interactome, Qwen3-32B answered 90.7% of questions from BIOGLYPH versus 38.8% from the measurement table.The result extends the format advantage to a larger model family beyond the two 8B readers.Source: S1 The networks of the main text, and… · p. 24

Exchange examples

• Figures 2 and S3a–S3f show stored BioGlyph exchanges, including graded answers, lookups, opinions, push-back, successes and failures.The cards preserve replies from scored runs, with formatting simplified but no wording rewritten; evaluator verdicts and deterministic selection rules are retained.Source: S2 Talking to BIOGLYPH: the exchanges… · p. 24

What models saw

• Models received the compiled network description once with the first question, but not node identities or outside labels such as essentiality and dependency.Email-Eu-core was anonymized at source, so it had no identities to display.Source: S2 Talking to BIOGLYPH: the exchanges… · p. 24

Turn taxonomy

• The four turn types remain separate: graded turns are scored against oracle answers, lookups test reading, opinions are unscored, and push-back evaluates responses to disputed claims.This separation applies both to the cards and to every reported number.Source: S2 Talking to BIOGLYPH: the exchanges… · p. 28

Failure modes and checks

• The conversations expose practical failure modes, including a wrong email-network bottleneck lookup, capitulation under push-back, and raw-metric prompts that exceeded the token budget.Other examples include benchmark-style versus ordinary-prose questions and a knockout table with oracle counts, model answers and DepMap verdicts.Source: S2 Talking to BIOGLYPH: the exchanges… · p. 28, Figure S3d · p. 32, Figure S3e · p. 33

Failure interpretation

• Figure S3f frames two honest failures alongside pooled push-back rates, presenting them as examples of known frequencies rather than isolated anecdotes.The knockout examples list named Reactome-FI proteins, oracle detachment counts, BioGlyph model answers and external DepMap dependency shares.Source: S2 Talking to BIOGLYPH: the exchanges… · p. 28, Figure S3f · p. 34

S3 The raw-measurement table: where it fails, why, and what recovers it

• 41.7% of all raw-table prompts exceed 24,576 tokens, versus 0.3% for BIOGLYPH, with median lengths of 19,723 versus 6,229 tokens.The table is the longest rendering on every network, reaching a median length ratio of 7.0 on the yeast interactome at the wider retrieval setting.Source: S3 The raw-measurement table: where it… · p. 35
• A 131,072-token window reduces PP-Pathways table overflow from 40.7% to 1.6% and raises accuracy from 32.1% to 52.2%, matching BIOGLYPH at 52.6%.Qwen3-32B also brings feasible-question accuracy to parity with BIOGLYPH, at 77.0% versus 76.9%, despite lower all-question accuracy.Source: S3 The raw-measurement table: where it… · p. 35
• On shared feasible questions, the raw table reaches 61.4% accuracy versus 66.8% for BIOGLYPH, while its reasoning-error rate is 18.0% versus 13.6%.Restricting scores to questions both arms fit raises the table from 39.5% to 60.7%; the table also declines 60.2% of finished unanswerable questions, versus 32.1% for BIOGLYPH.Source: Table S4 · p. 35, S3 The raw-measurement table: where it… · p. 35

Across-network consistency

• The consequence step is positive on 19 of 20 networks and largest on 17, whereas naming is positive on only three studies and can significantly favor the negative direction.Across eight Table S5 studies, the consequence interval excludes zero in five, compared with three negative naming intervals.Source: S4 Which layer of the description does… · p. 37

Opaque control

• Named roles outperform meaningless tokens on all 11 tested networks, including accuracy gains from 55.1% to 58.0% on PP-Pathways and from 51.1% to 66.8% on the yeast interactome.The named prompts are consistently longer, so the improvement is not explained by saving context space.Source: S4 Which layer of the description does… · p. 37

Ladder comparison

• On eight main networks, accuracy rises from 63.6% with raw measurements to 68.4% with stated consequences, while names alone reach 61.9% and names with evidence 62.0%.Only the final consequence step has an interval excluding zero.Source: Table S5 · p. 37, S4 Which layer of the description does… · p. 37

Biological networks

• The STRING interactomes generally favored BioGlyph, whereas HuRI and DG-AssocMiner did not show a controlled advantage.STRING-Ecoli’s controlled comparison was 84.7% versus 76.6%, STRING-Human was 63.3% versus 62.3%, HuRI was 48.4% versus 49.7%, and DG-AssocMiner was 63.6% versus 65.3%.Source: S5 The sixteen further networks · pp. 37, 39
• In HuRI, BioGlyph’s cut nodes were enriched for common-essential genes at 10.4% versus a 7.6% background, with odds ratio 1.5 (95% CI 1.21 to 1.86).A 131,072-token window brought BioGlyph and the comparison arm level on the two interactomes.Source: S5 The sixteen further networks · p. 39, Figure S7 · p. 41

Patient networks

• BioGlyph led on patient-graph co-community questions at 17.1% versus 7.1% for HuDiNe and 35.2% versus 18.3% for TCGA-GBM-PSN.On the standard patient graphs, controlled accuracies were 76.5% versus 75.1% and 77.6% versus 75.2%; the single-cell graph remained difficult at 34.1% versus 15.9%.Source: S5 The sixteen further networks · p. 42, Table S7 · p. 42

Representation ladder

• The ladder’s gains depended on representation conditions: patient-similarity graphs showed large evidence-step gains, while sparse graphs had small net gains because naming steps were often negative.The results indicate that description helps when the raw view is unmanageable, but not uniformly across networks.Source: Figure S5 · p. 38, S5 The sixteen further networks · p. 42

Dense and sparse networks

• BioGlyph remained strongest on dense graphs, reaching 71.8%, 73.2%, and 79.6% versus raw tables at 33.2%, 28.8%, and 36.5% on Amazon-Photo, Wiki-Vote, and email-Enron.On the common feasible set, BioGlyph led at 70.2% versus 53.2%, 69.9% versus 58.5%, and 77.1% versus 71.7%, with consequence gains of 6.8–10.7 points.Source: Figure S6 · p. 40, S5 The sixteen further networks · p. 42
• On five sparse graphs, raw tables led BioGlyph on Cora, CiteSeer, and Power-Grid, while adjacency text led on ogbn-arxiv across all questions.The consequence step was positive on all five sparse graphs, but negative naming steps on four made the overall ladder yield little gain.Source: S5 The sixteen further networks · p. 42

Model families and scale

• Mistral retains a controlled advantage over the table and adjacency text, whereas Gemma is at parity and Qwen3-32B lifts every arm while closing the description–table gap.For Mistral, the controlled comparisons are 56.3% versus 49.8% and 55.1% versus 46.6%; Gemma’s corresponding comparisons are 60.2% versus 62.6% and 61.3% versus 58.5%, with intervals crossing zero for Gemma.Source: S6 Model families and scale, and the… · p. 42

The frontier ceiling

• Among hosted frontier readers, the description leads the table in one of twelve network-by-reader cells, matches it in four, and trails it in seven, with gaps from 6.6 below to 0.6 above.All arms score between 73.9% and 87.8%, and the networks fit within the readers’ context windows.Source: S6 Model families and scale, and the… · pp. 42–43, Table S8 · p. 43

Model families and scale

• 68.0% versus 35.2% and 49.2% for Gemma-3-12B, and 60.3% versus 30.1% and 41.5% for Mistral-Nemo-12B, on BIOGLYPH versus the raw table and adjacency text.The result is reported for two further open model families across the eight main networks; Table S8 collects these controls.Source: S6 Model families and scale, and the… · p. 42, Table S8 · p. 43

S7 Conversation statistics: threads, the three-turn study and prose

• 73.5% of questions answered by BioGlyph in three-turn follow-ups were answered versus 75.5% alone, while the table fell to 58.7% from 72.6%.BioGlyph started all conversations, whereas the raw-measurement table failed to start 17.8% because the region did not fit at turn 1.Source: S7 Conversation statistics: threads,… · p. 43, Table S9 · p. 45, Figure S9 · p. 46
• In eight-turn threads, Qwen3-8B answered 87.8% of graded turns versus 61.4% for Llama-3.1-8B, and accuracy did not decline along threads.Late-half accuracy exceeded early-half accuracy for both models, indicating positional dips reflected harder turns rather than conversational degradation.Source: S7 Conversation statistics: threads,… · p. 43, Figure S9 · p. 46
• BioGlyph’s advantage survived prose phrasing: it scored 68.8% versus 41.1% for the table, and 65.9% versus 60.1% on fitted, finished prose questions.Canonicalizing answers raised measured accuracy from 42.6% to 65.6%, while the prose extractor recovered answers from 98.6% of replies.Source: S7 Conversation statistics: threads,… · pp. 43, 45, Figure S9 · p. 46

S8 The Reactome-FI knockout screen, in full

• 13.3% of Reactome-FI cut nodes were selectively essential versus 8.8% of other screened proteins (one-sided Fisher p = 2.4×10−3).The deterministic ranking identified known regulators including EP300, GPLD1, CTCF, YY1, and TP53.Source: S8 The Reactome-FI knockout screen, in… · p. 45, Table S10 · p. 47
• 87.1% of BioGlyph node-level disconnection claims agreed with exact Reactome-FI analysis, versus 36.7% for adjacency text, 22.2% for edge lists, and 10.6% for raw tables.Across three models, BioGlyph was within two proteins of the oracle on 47.8% of cases, with median error 2.0.Source: S8 The Reactome-FI knockout screen, in… · p. 45

S9 Learned roles, fusion and the trained yardstick

• 81.4% accuracy for the compiled description exceeded 47.4% for discrete learned roles, while continuous embeddings performed like shuffled tokens at 43.9% versus 44.2%.Learned-role encoders remained near the blind floor, and fusing them into the compiled description changed nothing.Source: S9 Learned roles, fusion and the… · pp. 45, 47
• 74.8% accuracy from a trained graph neural network was close to 74.1% for frozen BioGlyph readers overall, but the systems won different question families.The trained model led on edge removal and counterfactual reachability, whereas frozen readers led on degree comparison and compositional questions.Source: S9 Learned roles, fusion and the… · p. 47
• The retrieval ceiling was 82.6% overall, rising to 88.0% on dense networks and falling to 72.6% on sparse ones.This ceiling bounded performance for a perfect reader of the retrieved region and contextualized the trained-yardstick comparison.Source: S9 Learned roles, fusion and the… · p. 47

S10 Retrieval

• Oracle-free personalized-PageRank retrieval preserved the arm ordering: BioGlyph reached 49.9% versus 33.0% for the raw table across 1,471 questions.On jointly answerable questions, the corresponding accuracies were 44.9% versus 39.1%, and the main results did not depend on the verification loop.Source: S10 Retrieval · p. 47
• Under oracle-free retrieval, BioGlyph scored 52.5% on the two families shared with the main benchmark, compared with 51.5% under standard retrieval.Adjacency text caught up with the description under the controlled view.Source: S10 Retrieval · p. 47
• The wider retrieval setting raised the ceiling from 78.7% to 86.6%, whereas BioGlyph remained essentially unchanged because it never exceeded the retrieval budget.The wider setting increased overflow for every long arm.Source: S10 Retrieval · p. 47, Figure S11 · p. 49

S12 The candidate-knockout screen: a biology-graded pick, pre-registered

• The candidate-knockout screen used five anonymous proteins per question, one biologically labeled candidate, three separate 300-question experiments, and a 20% chance baseline.The design, arms, policies, and five predictions were pre-registered; the registered Qwen3-32B leg did not run, leaving two 8B models.Source: S12 The candidate-knockout screen: a… · p. 50, Table S11 · p. 52
• The biology-graded screen tested whether models could use whole-network structural position, with a degree-only arm representing the strongest single deterministic policy.Structural arms rendered the compiler’s whole-network output for the retrieved region’s nodes.Source: S12 The candidate-knockout screen: a… · p. 50

S11 One region in every representation

• The same deterministically selected yeast-interactome region was rendered as an edge list, adjacency text, raw measurements, three compiled-description rungs, and an opaque control.Each rendering included token counts, making the model-visible inputs and the raw table’s greater length explicit.Source: S11 One region in every representation · p. 50, Figure S12 · p. 51

S12 The candidate-knockout screen: a biology-graded pick, pre-registered

• 46.5% adjacency text led both structural arms in common-essentiality, while BioGlyph reached 39.3% versus 46.2% for degree-only; no arm meaningfully beat the degree policy.Across the three experiments, the no-graph control stayed below chance, and yeast results showed no reliable separation between arms.Source: S12 The candidate-knockout screen: a… · p. 50, Table S11 · p. 52