Foundation Molecular Grammar: Is Asking a Multimodal Model to Write Molecular Grammars Really Interpretable?

0. Verified links and evidence boundaries

These URLs were visited on 2026-09-06. Numbers come only from PDFs downloaded and read page by page; web pages verify venues, versions, and released assets. Core evidence follows the 52-page ICML 2025 PMLR final version. arXiv has only v1，2025‑05‑29, consistent with the final text. The OpenReview URL is reachable but currently returns browser verification, so its existence is recorded without using it to verify the text. Not found means no item was located through PMLR, arXiv, author repositories, or exact-title search, rather than proof of nonexistence.

Index cross-check: the core paper's Semantic Scholar entryis linked from arXiv metadata. Exact-title searches found no dedicated entry in Hugging Face Daily Papers or Papers with Code, so these are marked not indexed / not found, without sourcing numbers from snippets. ACL Anthology does not index this ICML paper. Candidates were assembled from ICML 2025 PMLR proceedings, checked against OpenReview, and queried in arXiv, Hugging Face, Papers with Code, and Semantic Scholar for versions or duplicates.

1. Candidate pool, deduplication, and random selection

First read ml-report-index.mdto exclude closely related topics and papers covered in the preceding 14 days, including KLDM crystal generation, TIMING time-series interpretation, DreamGen robot world models, QServe/Lumos systems, and DocVXQA document interpretation . Earlier coverage of multimodal protein language models was also avoided. These 24 candidates are all ICML 2025 main-conference long papers within 24 months. Full numbers, titles, and official URLs are saved in 2026-09-06_candidates.tsv. Running shuf -i 1-24 -n 1returned 21, selecting FMG. Its final paper, code, main results, three-layer ablations, and expert-review materials are available, so no redraw was needed。

1. From Mechanistic Interpretability to Mechanistic Biology
2. Raptor: Train‑Free Embeddings for 3D Medical Volumes
3. BounDr.E: Predicting Drug‑likeness
4. A Variational Perspective on Generative Protein Fitness Optimization
5. DiffMS: Molecules Conditioned on Mass Spectra
6. Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching
7. Generalists vs. Specialists for Biophysical Sequence Optimization
8. An All‑Atom Generative Model for Designing Protein Complexes
9. Hierarchical Graph Tokenization for Molecule‑Language Alignment
10. Flexible Models of Genetic Variant Effects
11. InfoSEM for Gene Regulatory Network Inference
12. Predicting Mutational Effects on Protein Binding
13. Dictionary Learning from Microscopy Foundation Models
14. Retrieval‑Augmented Zero‑Shot Enzyme Generation
15. MF‑LAL for Drug Compound Generation
16. OneForecast for Global and Regional Weather
17. EEG‑Language Pretraining for Clinical Phenotyping
18. Static‑Dynamic Fusion for Protein Graphs
19. Steering Protein Language Models
20. Multi‑Reward Structure‑Based Drug Design
21. Foundation Molecular Grammar
22. Offline Model‑Based Optimization for Molecular Discovery
23. UniSim for Time‑Coarsened Biomolecular Dynamics
24. CellFlux for Cellular Morphology Simulation

2. Motivation: small-data molecular generation needs more than another large model

Molecular generation faces three constraints. First,syntax: valence, bond types, and connectivity must be valid. Second,semantics: candidates must be synthesizable and belong to the target chemical class. Third,data: real materials projects may have only a dozen expert-confirmed examples. FMG’s three small datasets contain Isocyanates with 11 examples, Acrylates with 32 examples, and Chain Extenders with 11 training examples; even the two real-world HOPV and PTC sets contain only 316/348 (core PDF printed p.6, Tables 1,2). At this scale, end-to-end VAEs readily collapse: JT-VAE uniqueness across the three small sets is only 5.8%、0.5%、2.3%, while MolT5 achieves just 0.9%、0.3%、7.1%(p.6, Table 1).

Grammar methods encode hard constraints in the generator. MHG uses molecular hypergraphs and HRG to guarantee 100% validity, but its automatic decomposition emphasizes fine-grained atom/bond structures rather than familiar functional groups. DEG learns a decomposition policy and can optimize diversity and Retro*, but decisions come from an opaque neural sampler. RW instead asks experts for motifs, making grammar trajectories readable while restoring a manual knowledge-acquisition bottleneck.

FMG asks whether a chemically knowledgeable multimodal model can identify meaningful groups in place of an expert while remaining inside an algorithm that always constructs valid HRGs. It does not ask GPT-4o to emit SMILES directly. The direct GPT-4 ICL control has average validity of only 91%on small sets and 71%on HOPV/PTC, whereas FMG achieves 100%throughout. Formal machinery supplies validity while the model primarily supplies semantic choices (pp.6–7, Tables 1,2).

3. Argument, assumptions, and trade-offs

The pipeline has five steps. Convert each molecule into a hypergraph wherebonds are nodes and shared-atom relations are hyperedges. Extract maximal cliques and triangulate to ensure a clique tree satisfying the running-intersection property exists. GPT-4o then examines RDKit images to merge cliques into functional groups, remove semantically weaker interactions in cycles, and choose a root motif representing the class. Natural-language explanations form a design story. Repeat each molecule K times, then use another LLM judge to compare stories, with Swiss tournaments and Bradley–Terry ranking selecting the top-k specialized grammars. During generation, available rules are sampled in proportion to their frequencies in the training corpus (pp.2–6, Figures 1–3, §3).

Three assumptions underpin the design:

• Representation: RDKit 2D images help an MMFM recognize local motifs and global context more readily than SMILES.
• Knowledge: GPT-4o's pretrained chemical priors compensate for having only 11–348 examples.
• Auditability: Written design narratives help another model rank candidates and serve as human-readable quality certificates.

The first two assumptions receive partial empirical support; the third is weakest. Image-based FMG generally outperforms FMG-Text across 24 non-validity metrics in Tables 1–2; FMG-Text still wins 13/24 columns when FMG is excluded (p.9, §5.2). Yet this does not establish that visual explanations faithfully reflect decisions. A design story acts simultaneously asdecision input, ranking evidence, and explanation output, so performance and interpretability are not independently validated. The trade-off is clear: complex, class-specific right-hand sides increase membership but reduce rule reuse. Adding more k grammars raises diversity and RS while diluting class motifs (pp.7–8, §4–5.1; Appendix E, pp.17–18).

4. Formalization and algorithm

Let the molecular hypergraph be H=(V_H,E_H)：V_H denotes chemical bonds; two bonds sharing an atom form a binary hyperedge, and each smallest ring is a separate hyperedge. For H , extract maximal cliques from its ordinary graph G_H to obtain G_C=(V_C,E_C). A clique tree T must cover every original node, place each hyperedge entirely in exactly one tree node, and ensure that tree nodes containing any shared node v form a connected subtree—the running-intersection property (core PDF printed p.3, §3.1).

A hyperedge-replacement grammar is written as:

G = (N, T, S, P)
N: nonterminal hyperedge labels; T: terminal labels; S: start nonterminal; P: productions
p ∈ P : A → R

Each parent–child clique relation becomes a production. For molecule i and random run r , obtain clique tree G_C^(i,r) and specialized rule set P(G_C^(i,r)). The narrative COT_r^(i) concatenates explanations from all steps. The judge produces pairwise outcomes y_ab, and Bradley–Terry estimates ability parameters:

Pr(a beats b) = exp(θ_a) / [exp(θ_a)+exp(θ_b)]
ranking = argsort_r θ_r
P_D(k) = ⊎_i ⊎_{r ∈ Top-k(i)} P(G_C^(i,r))

⊎ is multiset union preserving multiplicities. If the currently applicable rules at generation state g_t are A(g_t), sample them by corpus frequency:

Pr(p | g_t) = count_D(p) / Σ_{q∈A(g_t)} count_D(q),  p∈A(g_t)
g_{t+1} = Apply(g_t,p)

Thus, GPT-4o does not directly choose each generation sample. It changes rule granularity, tree structure, and root selection during grammar induction. Subsequent generation is auditable frequency-based sampling. Formal guarantees come from triangulation, clique trees, and Kajino's HRG-to-molecule conversion, not LLM accuracy.

Pseudocode

for molecule H_i in dataset D:
    base_cliques ← bonds ∪ minimal_rings
    G_C ← CLIQUE(TRIANGULATE(G_H))
    for r = 1..K:
        while meaningful_pair_exists:
            render highlighted motifs
            (u,v,reason) ← GPT-4o(pair-selection prompt)
            merge(u,v); log(reason)
        while G_C has cycle:
            render highlighted interactions
            (edge,reason) ← GPT-4o(least-important-edge prompt)
            delete(edge); verify running-intersection
        (root,reason) ← GPT-4o(root-motif prompt)
        P_i,r ← TreeToHRG(G_C,root)
        story_i,r ← summarize(all logged reasons)
    ranking_i ← SwissTournament(story_i, BradleyTerry)
P_D ← multiset union of Top-k P_i,r
sample molecules by frequency-weighted applicable HRG rules

5. Key mechanisms and engineering details

Baselines are adapted in three ways: train VAEs from scratch (T), fine-tune pretrained models (FT), or fit a Gaussian to small-data latent encodings and use posterior interpolation (I). GPT-4 ICL uses all small-set examples or random subsets of the real-world sets. MolT5/Text+Chem T5 sample five training molecules per call, with maximum generation length 512 (Appendix B, printed p.13). Each small dataset generates 10,000 molecules; HOPV/PTC generate 1,000 each (p.6, footnote 1; Appendix C). Training hardware, total API calls, token counts, dollar costs, and wall-clock time are allNot reported。

6. Datasets, benchmarks, and metrics

Metrics: Validity/Unique/Novelty measure valid structures, distinct outputs, and outputs absent from training. Diversity is mean pairwise Tanimoto distance. RS is the fraction for which Retro* finds a synthesis route. Membership is the fraction satisfying target-class rules (p.6, §4). RS is amodel-based proxy, not laboratory success. High validity indicates parseable graph/valence rules, not stability, nontoxicity, or manufacturability. The authors explicitly acknowledge that HOPV/PTC membership is not strictly defined (p.7).

7. Complete main-results matrices

7.1 Three small-sample benchmarks (ICML final Table 1, printed p.6)

This table retains all five metric types for six representative methods. Each triple is Isocyanates / Acrylates / Chain Extenders; validity is averaged across tasks. Bold indicates column-wise best within this subset only. The full original table also includes JT-VAE, Hier-VAE, MHG, STONED, MoLeR(I), two T5 models, and FMG-Text.

Relative to DEG, the closest automated-grammar baseline, FMG improves RS by +34.5、+49.1、+31.6 pp, corresponding to relative gains of +126.84%、+111.85%、+46.81%; membership increases by +3.3、+30.4、+6.3 pp. Diversity, however, decreases by −0.13、−0.40、−0.08, corresponding to relative gains of −15.12%、−46.51%、−8.60%. Thus, easier Retro* planning and stronger target-class resemblance are supported, but broader chemical-space coverage is not. Acrylates diversity falls from 0.86 to 0.46, nearly halving.

7.2 HOPV and PTC (ICML final Table 2, printed p.7)

Each cell is HOPV / PTC. Six methods illustrate different trade-offs; the complete original table also contains JT-VAE, Hier-VAE, MoLeR(I), MolGPT, MolT5, Text+Chem T5, and FMG-Text.

Compared with RW, FMG's RS changes by +12/+18 pp, corresponding to relative gains of +20.69%/+30.00%, supporting better-plannable samples without expert motifs. However, HOPV membership falls from 71% to 38% (−33 pp, −46.48%), whereas PTC rises from 22% to 46% (+24 pp). Opposite effects on the same metric across datasets indicate dependence on class definitions and prompts, rather than a stable universal grammar advantage.

7.3 MOSES distribution stress test (Appendix Table 8, printed p.19)

FMG is strong in unconditional validity, uniqueness, diversity, and novelty, but its FCD is 50.58 timesCharRNN's (26.30 versus 0.52), and even worse than HMM's 25.43 by 3.42%; SNN is only 0.29. The authors explicitly caution against direct comparisons. This table establishes thatgrammars can expand tiny datasets while departing substantially from the target distribution, rather than establishing MOSES state of the art.

8. Layered ablations, hyperparameter sensitivity, and transitions

8.1 Images versus text

FMG-Text replaces images with atom-indexed SMILES and motif atom lists. On small datasets, FMG's RS versus FMG-Text is 61.7 vs 33.1、93.0 vs 87.1、99.1 vs 98.5, an absolute change of +28.6/+5.9/+0.6 pp; diversity is almost identical (0.73/0.46/0.85 versus 0.73/0.46/0.84). Real-world RS is higher by only 1/1 pp(70/78 versus 69/77), while membership is lower on HOPV by 5 ppand higher on PTC by 13 pp(Tables 1–2). Images are not uniformly better: the clearest benefit is Isocyanates RS, not every dataset and metric.

Appendix F records a failed initial Tagged-SMILES attempt: GPT-4o misread a cyclopentane motif with ring closure as the linear chain CCCCC. The second attempt indexed all atoms (printed p.18). This supports images as a natural way to emphasize local structure, but also shows that the text baseline is not the only or necessarily strongest molecular sequence encoding.

8.2 Merge / Edge / Root (Table 4, printed p.9)

k=5 , FMG Avg achieves small-dataset RS of 44.3±3.4 / 87.4±1.5 / 91.9±3.8. Removing merge gives 32.6±5.7 / 91.0±2.0 / 97.4±0.8: Isocyanates drops by 11.7 pp, while the other two improve. Membership changes from 60.14±13.63 / 35.48±4.02 / 28.30±13.25 to 95.75±4.16 / 16.61±0.78 / 15.48±1.11. Merge therefore redistributes RS and class specificity rather than simply improving quality.

Replacing edge selection with MST yields RS of 57.9±6.5 / 93.5±1.8 / 99.9±5.4, exceeding FMG Avg in all three columns, but membership becomes 45.81±15.34 / 37.44±5.32 / 38.56±10.58, again a mixed result. The paper's phrase only slightly worse does not characterize every column. Removing root selection raises diversity to 0.79±0.03 / 0.85±0 / 0.83±0.02，RS 49.1±7.0 / 89.5±2.6 / 91.9±10.9but generally lowers membership. Component ablations show no monotonic advantage; the full system offers a controllable compromise, not uniformly positive contributions from every LLM decision.

8.3 k sensitivity and transitions

Figures 4/6 show small-dataset settings k=1…10、HOPV/PTC k=1…5. Only curves, not pointwise numerical tables, are supplied; this report does not infer exact values from pixels. Three conclusions are supported: at low k , membership approaches 100%; as k increases, membership falls while diversity and RS rise. Top-k and the first k runs (1-k) show no significant difference in diversity/RS, with differences concentrated in class motifs (p.8; Appendix E). The structural transition is from a few complex, class-specific RHSs to more simple, reusable RHSs. The best k depends on prioritizing class purity versus coverage and synthesizability; no validation-based rule automatically selects k .

8.4 Statistical significance

The only reported significance concerns LLM-judge/expert agreement of 77/108=71% under an independent fair-coin null, p=1.1×10⁻⁵(Appendix D, pp.16–17, Table 7). A recalculated Wilson 95% interval is approximately 62.15%–78.98%. However, repeated comparisons of the same molecules by the same judge, including reversed order, are not independent; the original p-value may be optimistic.

Main Tables 1–2 do not report confidence intervals or significance tests across independent grammar-induction runs. Appendix C argues that 1,000/10,000 generated molecules absorb sampling error. This reduces Monte Carlo error from a fixed grammar, not run-to-run variance from GPT-4o, tree decomposition, tournaments, or trained baselines. Table 4 reports ±without clearly specifying SD, SE, or another quantity, so module differences cannot be judged significant from it.

9. Contributions, reusable designs, and transfer potential

The substantive contribution is not proving GPT-4o understands chemistry, but a reusableneurosymbolic interface pattern: restrict unverifiable model knowledge to local discrete choices while verified algorithms enforce validity. Even poor motif-merging explanations do not defeat triangulation and HRG guarantees that generated structures remain in the grammar's language. This permits more layered auditing than direct SMILES generation.

A second contribution is using natural-language artifacts as auxiliary evidence for candidate structures. Faithfulness remains unproven, but they form a useful expert-review interface: reviewers can replay merging, edge removal, and root selection rather than inspect one opaque score. A third contribution is making the small-data Pareto trade-off among class specificity, coverage, and synthesizability explicit, showing why validity or novelty alone cannot rank AI4Science systems.

Transferable designs include selecting protein domain boundaries while geometric constraints enforce chain validity; ranking local coordination motifs while symmetry checks enforce crystal space groups; and proposing reaction templates while chemistry rules and inventory checks adjudicate synthesis routes. Transfer requires a formally verifiable backbone plus semantic choices that are hard to encode. If validity itself cannot be formalized, putting an LLM in the loop does not automatically create trustworthiness.

10. Related work: problem origins and transferred techniques

10.1 MHG（Kajino, ICML 2019）

Problem addressed: Represent molecules as hypergraphs and encode valence/structure constraints in context-free HRG, enabling a single VAE to achieve 100% validity(MHG PDF pp.1,8, Table 1).Remaining gap: Automatically induced rules are fine-grained and focus on hard constraints, rather than class-specific functional groups or synthesis semantics.FMG's response: Retain MHG's valid generation and clique-tree framework while delegating discrete decomposition choices to an MMFM.Transferred design: FMG's H=(V_H,E_H), HRG tuple, rule application, and valid conversion directly inherit MHG. GPT-4o cannot receive all the credit for validity.

10.2 DEG（Guo et al., ICLR 2022 Oral）

Problem addressed: Optimize graph-grammar construction with a learned policy, balancing distribution matching, synthesis, and diversity using roughly 20 monomer examples and 117 polymer examples (DEG PDF pp.1–3).Remaining gap: The policy's decomposition decisions are opaque and require externally specified optimization metrics.FMG's response: Replace the neural decomposition policy with language-model chemical priors, avoiding a separate decision-model training process for each dataset while retaining natural-language reasons.Transferred design: FMG inherits the three small datasets, DEG as its principal automated-grammar baseline, and the RS/diversity/membership framework. Its +31.6–49.1 pp RS improvements over DEG are therefore the most comparable evidence.

10.3 Random Walks over Interpretable Grammars（Sun et al., ICML 2024 Spotlight）

Problem addressed: Experts specify motifs; molecules become random walks over a grammar design space that unifies generation and property prediction. Expert motifs provide interpretable hierarchy (RW PDF pp.1–3,5).Remaining gap: Motif quality depends on experts, and new chemical classes require repeated costly annotation.FMG's response: Automate expert motif discovery and compare head-to-head with RW on HOPV/PTC.Transferred design: FMG inherits real-world datasets, membership definitions, and the expert-motif baseline/upper-bound argument from RW. HOPV membership of 38% versus RW's 71% shows that automated substitution is not yet equivalent.

10.4 Grammar Prompting（Wang et al., NeurIPS 2023）

Problem addressed: Associate each example with a minimal BNF subgrammar; at inference, predict a grammar and then generate a constrained DSL. This improves few-shot structured generation in semantic parsing, PDDL, and SMILES (paper PDF pp.1–4).Remaining gap: A full preexisting DSL grammar is required; the focus is string syntax, not discovering chemical motifs from molecular graphs.FMG's response: Extend minimal specialized grammars to graphs, letting models participate in induction rather than only selecting known BNF rules.Transferred design: Specialized grammars, rules as intermediate reasoning objects, constrained generation, and reason-then-generate transfer directly into FMG. The difference is that clique/HRG algorithms retain formal correctness.

10.5 Nonlinear technical evolution

                                                  ┌─ SMILES / SELFIES ── CLM / ICL
                         │      Syntax failures, few-shot repetition
Molecular validity ─ MHG/HRG ─┤
  100% validity          ├─ DEG: learned decomposition ─ high RS / opaque decisions
                         │
                         └─ Expert motifs ─ RW: interpretable random walks
                                      │
Few-shot DSLs ─ Grammar Prompting ─────┤
  Specialized grammars                ▼
                              FMG: images + GPT-4o semantic choices
                               │      + formal HRG constraints
                               ├─ Design stories → LLM tournaments
                               └─ Top-k rule pools → specificity/coverage Pareto trade-off

Three shifts drive the evolution: from string validity to hard graph-grammar guarantees; from fixed fine-grained rules to learnable class substructures; then from opaque policies or manual motifs to foundation-model priors. FMG occupies the third transition, replacing inadequate model training with new risks: closed-model drift, narrative faithfulness, and invisible costs.

10.6 Cross-paper comparison

11. Limitations acknowledged by the paper

1. Coverage and diversity: The authors note that complex RHS rules apply narrowly. With roughly 30 or fewer samples, few rules produce low coverage/diversity (printed p.7, discussion after Table 1), consistent with Acrylates diversity of 0.46.
2. Class definitions and k trade-offs: HOPV/PTC membership lacks a strict definition, and k creates a sharp trade-off between membership and {diversity, RS} (pp.7–8; Appendix E). One default k cannot be called optimal across all datasets.
3. Expert intuition: Experts conclude that GPT-4o can miss alternative perspectives when experience, multiple plausible interpretations, or deeper explanations are needed. Difficult tasks still require refinement (Appendix H.7, printed p.52).

12. Independent critique (evidence → implications)

1. [Statistical design] Main tables sample 1,000/10,000 molecules from fixed grammars without repeating the entire GPT-4o induction–tournament process. The claim that large samples absorb error bars (Appendix C) therefore controls molecular sampling error, not method-level stability.
2. [Significance] The judge's 108 comparisons reuse the same molecules and model three times each, including order reversal, violating independent Bernoulli assumptions. Thus, p=1.1e−5 cannot directly establish agreement on new molecules/experts. The Wilson 95% interval for 71% remains approximately 62.2%–79.0%.
3. [Explanation faithfulness] Design stories are summarized after decisions by the same model class, then ranked by similar LLMs; experts assess chemical plausibility. Plausible explanations need not faithfully cause the tree. Causal tests must intervene on stories while holding trees fixed.
4. [External validity] All semantic modules use GPT-4o without a specified snapshot, and no head-to-head comparison with Gemini, open VLMs, or provider versions is given. Results cannot be attributed to the whole MMFM method class; they may be specific to one service model and RDKit rendering style.
5. [Reproduction] The inspected public code places temperature 0, seed 42, and top_p 0 in settings then immediately overwrites it with an empty dictionary. The README also contains the absolute path /home/msun415/... , while full caches and token costs are unpublished. The current repository cannot reproduce randomness and costs in one step. Because the commit postdates the paper, this concerns current release status, not proof that original experiments used empty settings.
6. [Baseline fairness] Training JT-VAE or Hier-VAE from scratch on 11 examples is inherently disadvantaged against FMG's massively pretrained GPT-4o. Data efficiency counts only task-specific samples, ignoring foundation-model pretraining and API resources; it is not total-data or total-compute efficiency.
7. [Metric validity] RS comes from a Retro* proxy, HOPV/PTC membership is loosely defined, and FMG trades +12 pp RS for −33 pp HOPV membership. Table 2 cannot establish more genuinely synthesizable, class-correct photovoltaic materials. Wet-lab validation or at least agreement across planners is required.
8. [Distribution matching] FMG's MOSES FCD is 26.30, 50.58 times CharRNN's 0.52, and SNN is only 0.29. High validity/novelty may reflect departure from the training distribution rather than useful novelty. Deployment must jointly consider out-of-distribution distance and property benefits in its Pareto analysis.

13. Open challenges: actionable head-to-head gaps

Theory

• Explanation faithfulness: Hold clique trees identical and randomly substitute true stories, model-generated counterfactual stories, or no stories. Compare judge rankings, expert preferences, and downstream generation metrics. If stories are certificates, false narratives should be detected without altering formal outputs.
• Rule-complexity bounds: Match rule counts and mean RHS sizes across FMG, DEG, and expert RW, then plot membership–diversity–RS Pareto fronts to separate model knowledge from more complex rules.
• Tests for correlated observations: Use molecule-clustered bootstrap or mixed-effects logistic regression for judge agreement, comparing with the independent coin-flip p-value. Preregister primary endpoints and minimum meaningful differences.

Engineering and applications

• Model drift: Fix 100 molecules and prompts; compare a frozen GPT-4o snapshot, Gemini, and open Qwen-VL, each with ≥10 complete induction runs. Report rule Jaccard similarity, tree-edit distance, API costs, wall-clock time, and variance of all five metrics.
• Budget-matched baselines: Give DEG and FMG equal dollar or GPU-hour budgets, and add RW with two hours of human motif annotation. Compare cost to achieve RS≥70% and membership≥70%, rather than only task-data quantity.
• Wet-lab loop: Have FMG, RW, and DEG propose 20 candidates each for one material class. Blinded chemists screen them, followed by head-to-head evaluation of purchasable precursors, route length, yield, and target properties. Retro* is only a pre-experiment covariate.

Emerging directions

• Open VLMs plus a verifier: Have three models propose each merge and let a SMARTS/reaction-template verifier veto it. Compare erroneous motifs, RS, membership, and cost with one GPT-4o, testing proposer–verifier selection against narrative tournaments.
• Active selection of k： Use held-out class examples or Bayesian multiobjective optimization to select kautomatically versus fixed 1/5/10 values, measuring hypervolume and across-seed stability. The paper supplies curves but no selection rule.
• From 2D to 3D: Represent the same molecule using RDKit 2D images, multiple 3D conformers, or atom-indexed SMILES. Compare grammars on stereochemistry-sensitive tasks to test whether visual benefits arise only from easier highlighting.

14. Recent-work radar (not used as core quantitative evidence)

1. DiffMS（ICML 2025）: generates molecules conditioned on mass spectra, representing observation-driven inverse design. More specific than FMG's class prompts, it does not directly solve interpretable grammar induction.
2. LDMol（ICML 2025）: performs text-to-molecule diffusion in structure-informed latent space, offering a comparison of natural-language control and responsibility for validity.
3. Hierarchical Graph Tokenization（ICML 2025）: uses hierarchical graph tokens for molecule–language alignment. Its learned tokens contrast with FMG's readable productions; compare semantic retrieval and expert explanations on identical data.
4. GenMol（ICML 2025）: builds a drug-discovery generalist using discrete diffusion, offering stronger scaling but weaker formally verifiable rule traces.
5. Offline Model‑based Optimization for Real‑World Molecular Discovery（ICML 2025）: focuses on offline property optimization and distribution shift, complementing FMG's unconditional-generation scope.
6. All‑atom Inverse Protein Folding through Discrete Flow Matching（ICML 2025）: demonstrates discrete generation conditioned on all-atom structures, suggesting that protein applications of FMG cannot stop at 2D motifs.
7. Retrieval‑Augmented Zero‑Shot Enzyme Generation（ICML 2025）: injects substrate knowledge into enzyme generation through retrieval, providing an auditable external-evidence alternative to FMG's parametric chemical knowledge.

15. Conclusion and reading guidance

FMG illustrates a mature architecture for model-assisted science: the model makes semantically rich local choices that are difficult to hand-code, formal machinery ensures validity, and rules plus narratives remain available for human auditing. Its main result is a redistribution of synthesizability and class specificity, not universal dominance. Compared with DEG, small-task RS rises by 31.6–49.1 pp while diversity falls by 8.6%–46.5%; compared with expert RW on HOPV, RS gains 12 pp but membership loses 33 pp.

FMG is best positioned as an expert-facing grammar proposal tool or interactive design assistant, rather than an unreviewed molecular discovery system. Real discovery loops first need variance across complete induction runs, reproduction with open models/frozen snapshots, and independent chemist plus wet-lab validation of RS and membership.

Evidence and generation notes: This report read the 52-page core PMLR PDF and PDFs of MHG, DEG, RW, and Grammar Prompting, and audited public-code commit 6c2e0da(2025-11-11). Candidate numbering and the shuf result can be checked against the TSV in the same directory. All recalculations are simple differences, relative percentages, or Wilson intervals from identified tables; no values were inferred from curve pixels.ml-report-index.md was updated in this run. HTML uses the fixed Warm Editorial Report template and passed its structural validator (0 errors / 0 warnings), plus static responsive, long-link, and wide-table overflow checks. Playwright is installed, but /usr/bin/chromium、/usr/bin/chromium-browser、/opt/pw-browsers and its cache contain no executable Chromium. Required real-browser light/dark/mobile screenshots therefore remain explicitlyincomplete。