SNACK: A Sequential Notation Framework for Probabilistic Graph Generation

The strongest aspect of the paper is its formal grounding. Proposition 1 establishes a true bijection between ordered adjacency matrices and SNACK sequences, which directly solves the many-to-one sequence-to-graph problem that plagues SMILES and SELFIES and makes prior string-based GFlowNet objectives inherently biased. The prefix-decodability property is equally valuable: because every partial SNACK string maps to a well-defined partial graph, the authors can apply grammar, valence, and BFS logit masks during autoregressive decoding, rigorously guaranteeing valid outputs. The complexity analysis in Appendix C is precise, showing that trajectory evaluation drops from $O(N^3)$ for graph-based Transformers to $O(N^2)$ for SNACK.

First, the distribution-learning experiments (Table 2) do not show a compelling advantage over SELFIES or even SMILES on QM9 and MOSES. SNACK (V+B) matches SELFIES on FCD but does not clearly dominate it, and the practical payoff of a more complex encoding scheme is limited when mature alternatives already achieve near-perfect validity and similar downstream metrics. The claim that BFS ordering outperforms Cuthill–McKee (Table 6) contradicts prior work by Diamant et al. and Jang et al., yet the rebuttal offered—dataset dependence and evaluation metrics—is post-hoc and based on a single benchmark comparison; the paper provides no principled reason to prefer BFS in general.

Second, the conditioned-generation success rate (Table 3) is misleading as a comparative metric. SNACK is designed so that any prefix ending in a node token is a valid partial graph, whereas SMILES and SELFIES are not constructed to allow arbitrary extension of internal substructures. Reporting that SMILES terminates immediately is therefore an expected artifact of representation design, not evidence of representational quality. Moreover, the evaluation uses only the 129 smallest MOSES test molecules with 100 random sequences each, a sample too small for robust statistical conclusions. Finally, while the probing analysis (Section 5) reports impressive adjacency reconstruction AUROC (0.9998), it controls only against a random model and SMILES; it does not rule out simple memorization of frequent bond patterns rather than deep structural abstraction.

The evidence supports the technical claims about SNACK’s validity guarantees and GFlowNet compatibility, but key comparisons are incomplete or uneven. For goal-directed learning (Table 4), the graph-based baseline is a 4-layer graph Transformer that recomputes action probabilities at each construction step; SNACK’s advantage in Top-100 reward on albuterol and aripiprazole is confounded by the fact that SNACK amortizes trajectory evaluation into a single forward pass, whereas the graph baseline requires $N+M$ passes. The paper does not isolate the representation effect from the architectural/algorithmic efficiency effect. In the molecular string generation task (Table 2), the authors standardize the LLaMA-style Transformer across methods, which is fair for comparing representations, yet they omit recent graph-based diffusion or flow-matching baselines that currently set the state of the art in molecule generation, limiting the reader’s ability to gauge absolute performance.

Reproducibility is partially strong but missing critical details. The authors provide a public GitHub repository (footnote 1) and clearly specify the LLaMA-based Transformer architecture (6 layers for distribution learning, 4 for goal-directed; Appendix F). However, the main text omits training budgets (number of steps, wall-clock time, GPU types), exact learning rates, and batch sizes, pushing these to Appendix F without explicit page references. The GFlowNet reward functions and conditioning protocols are described only at a high level in the main text, with full derivations relegated to Appendices E and F. The nauty package dependency for automorphism counting is mentioned as efficient but version-specific behavior is not documented. Reproducing the exact BFS masking rules requires careful implementation of Algorithm 1 and the recursive constraints in Appendix A.2, which are non-trivial.