{"id":"5922d32a-f866-475c-a455-85bd4e96f721","arxiv_id":"2607.08207","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":5,"one_line_summary":"Learned committor proxies give accurate Ising nucleation rates via MSMs, while geometric cluster size recovers rates despite failing as a pointwise committor predictor.","lead":"A neural network trained on brute-force committor labels serves as a reaction coordinate for Markov state models of nucleation in the 2D Ising model and recovers accurate rates. The work shows that a simple cluster-size coordinate also yields correct rates despite poor pointwise accuracy, clarifying what collective variables must do for rate calculations.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The manuscript’s strongest claim is an empirical demonstration plus a conceptual distinction: both a high-fidelity learned committor and a low-fidelity geometric cluster size recover brute-force Ising nucleation rates when used as MSM coordinates, so pointwise committor fidelity is not required for rate accuracy provided the coordinate separates the basins. Figure 1 supplies the rate agreement; Figures 2–3 supply the pointwise contrast; saliency maps confirm that p_B-NN attends to physically relevant multi-cluster features. The reader correctly flags basin boundaries and lag-time Markovianity as the softest methodological choices. Those choices are conventional, are applied uniformly to both coordinates, and are already constrained by the implied-timescale plateau and by the observation that p_B = 1 beyond LGCS = 0.5 L^{2}. Because both coordinates still match brute force, residual non-Markovianity or modest boundary misplacement does not appear to drive the headline result. No stronger load-bearing concern (circular training, untested transfer, or hidden free-energy inconsistency) is present. The reader’s ACCEPT / high-confidence verdict is therefore left unchanged; the concrete boundary-shift test is offered only as a useful verification, not as a required fix.","tokens_in":8559,"tokens_out":554,"duration_ms":5770,"concrete_test":"Recompute the LGCS MSM rates of Fig. 1 after shifting the parent boundary by ±1–2 bins around the metastable LGCS peak and the stable boundary by ±0.05 L^{2} around 0.5 L^{2}; if any rate moves outside the reported brute-force error bars, the basin-definition assumption is material.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that basin separation is sufficient for accurate MSM nucleation rates even when a coordinate fails as a pointwise committor—is supported by the direct comparison of p_B-NN and LGCS MSMs against brute-force rates (Fig. 1) and the contrasting pointwise scatter (Figs. 2–3). The reader’s weakest assumption (LGCS-based basin definitions and lag-time selection via the longest implied timescale) is the natural soft spot, yet the paper already reports that both coordinates recover the same brute-force rates across fast/intermediate/slow regimes, that the stable boundary is placed where p_B = 1 for any studied (β,h), and that rates are taken only after the implied-timescale plateau. No internal inconsistency or load-bearing gap that would overturn the claim is evident from the manuscript.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper trains a convolutional neural network (p_B-NN) as a high-accuracy proxy for the committor of magnetisation reversal in the 2D Ising model, using brute-force shooting labels (n=4096) on microstates sampled from nucleating trajectories. Separate MSMs are then built with p_B-NN and with largest geometric cluster size (LGCS) as the reaction coordinate; both recover independent brute-force nucleation rates across fast, intermediate and slow regimes (Fig. 1) and a range of (β,h). Pointwise accuracy is quantified (Figs. 2–3): p_B-NN stays within a ±2.5% band for >95% of states while LGCS (and FK) scatter substantially, yet LGCS still yields correct rates. Saliency maps confirm that p_B-NN attends to clusters and their boundaries. The central claim is that an effective CV for nucleation rates must separate the metastable and stable basins but need not preserve the committor pointwise for every microstate.","tokens_in":8795,"tokens_out":858,"duration_ms":31452,"significance":"The result cleanly separates two requirements that are often conflated in the nucleation literature: pointwise fidelity to the committor versus the ability of a coordinate to support accurate mean-first-passage-time rates. Because both a near-ideal learned committor and a deliberately imperfect geometric size recover the same brute-force rates (and match earlier Brendel et al. values where available), the work supplies concrete evidence that simple cluster-size CVs remain serviceable for rate calculations even when they fail histogram or pointwise tests. Strengths include GPU-enabled ground-truth labels at ±0.01 accuracy, explicit lag-time convergence via the implied-timescale plateau, saliency-based interpretability, and a public data release. The distinction has immediate practical value for the choice of collective variables in rare-event methods for nucleation.","major_comments":[],"minor_comments":[{"comment":"Methods: Basin boundaries are defined via the LGCS peak (parent) and LGCS = 0.5 L^{2} (stable) for both coordinates. While the stable cut is justified by p_B = 1, a short note confirming that pure p_B-based cuts (e.g. 0.01/0.99) leave the p_B-NN rates unchanged would remove any residual hybrid character.","section":null},{"comment":"Methods / Results: Lag times are chosen as the shortest value at which the longest implied timescale plateaus. Including the implied-timescale curves (even in SI) for a few representative (β,h), especially the fast regime where LGCS is slightly worse, would make the Markovianity claim fully transparent.","section":null},{"comment":"Fig. 1 caption and text: The division into regimes A/B/C is clear visually but never stated quantitatively (e.g. by rate decade or free-energy barrier). A one-sentence definition would help readers.","section":null},{"comment":"Fig. 3: The sigmoid mappings used for LGCS and FK are not characterised (parameters or goodness-of-fit). Reporting them, or noting that the scatter is insensitive to the precise sigmoid, would strengthen the pointwise comparison.","section":null},{"comment":"Notation: The symbol appears as p_B-NN, p B-NN and pB-NN in different places; a single consistent form would improve readability.","section":null},{"comment":"Section IV: The broader implications for off-lattice systems with shape fluctuations or polymorphs are asserted rather than argued. A brief caveat that the basin-separation sufficiency has so far been demonstrated only for 2D Ising spin-flip dynamics would keep the claim proportionate.","section":null}],"recommendation":"accept","confidential_remarks":"Solid, carefully executed computational physics paper with public data; fits physics.comp-ph / JCP well. No concerns about novelty disclosure or citation practice. The empty major-comments list reflects that the central claim is already supported by the external rate comparisons; the listed items are polish only."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple: for MSM nucleation rates in 2D Ising, a coordinate only needs to separate the basins cleanly. Pointwise fidelity to the true committor is not required. They show this by training a CNN on brute-force shooting labels (p_B-NN), building MSMs on both that proxy and on largest geometric cluster size, and matching independent brute-force magnetisation-reversal rates across fast, intermediate and slow regimes (Fig. 1). LGCS fails badly as a pointwise predictor (Figs. 2–3) yet still recovers the rates. That contrast is the paper’s real contribution.\n\nWhat is new is not “learning the committor” (Bonati, Huang, Jung et al. already did versions of that). It is using the learned proxy directly as the MSM coordinate for rates, and the explicit side-by-side with LGCS that makes the basin-separation claim concrete. Methods are careful: 4096 shots per label, RMSE limited by label noise, lag times chosen by implied-timescale plateau, rates checked against Brendel et al. where applicable. Saliency maps show the network is looking at clusters and interfaces, not nonsense. Data will be public on acceptance.\n\nSoft spots are minor and already visible. Basin boundaries are defined via LGCS (peak in the metastable distribution; 0.5 L^{2} for the stable side), so there is a mild circularity of definition, though the paper notes the stable boundary sits where p_B = 1 for every (β,h) they study. Free parameters (bin counts, lag, training-set size) are conventional and do not look load-bearing. No code ships, but the description is enough to re-implement. The claim is scoped to rates, not free energies or pathway statistics; they do not over-sell.\n\nThis is for people who build rare-event methods or choose CVs for nucleation. It will not reorganise statistical mechanics, but it gives a practical criterion and a clean worked example. I would send it to referees without hesitation. Worth reading if you care about collective variables for rates; cite it when you need the “basin separation vs pointwise fidelity” distinction.","headline":"Clean Ising demonstration that basin separation, not pointwise committor fidelity, is what MSMs need for nucleation rates; both learned p_B and LGCS recover brute-force rates.","tokens_in":9373,"tokens_out":562,"would_cite":true,"duration_ms":5432,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"An effective nucleation reaction coordinate only needs to separate basins; it need not match the committor pointwise.","keywords":["committor","nucleation rates","Markov state model","Ising model","reaction coordinate","collective variable","geometric cluster size","machine learning"],"falsifier":"Find a thermodynamic condition of the same Ising model at which an MSM on the largest geometric cluster size (or on p_B-NN) yields a nucleation rate that disagrees with an independent brute-force mean first-passage time by more than statistical error.","tokens_in":9433,"feed_emoji":"🧲","tokens_out":550,"duration_ms":5042,"temperature":0.7,"pith_summary":"Finding good low-dimensional reaction coordinates for nucleation is hard. The ideal choice is the committor—the probability a configuration reaches the stable phase before returning to the metastable one—but computing it has long been too expensive for routine use. This paper trains a convolutional neural network on brute-force committor labels for the two-dimensional Ising model, then uses that learned proxy as the coordinate of a Markov state model. The network recovers brute-force magnetisation-reversal rates across a range of temperatures and fields. Surprisingly, the simple largest geometric cluster size does the same, even though it is a poor pointwise predictor of the true committor. The practical claim is therefore clear: for rate calculations it is enough that a coordinate cleanly separates the two basins; it does not have to preserve the committor for every microstate. That distinction matters for how collective variables are chosen in rare-event nucleation simulations more generally.","feed_headline":"Basin separation beats pointwise accuracy for nucleation rates","feed_subtitle":"A neural committor and simple cluster size both recover Ising rates; only basin separation is required.","key_machinery":"p_B-NN, a convolutional neural network trained on brute-force committor labels and used directly as the reaction coordinate of a Markov state model whose rates are obtained from mean first-passage times.","core_discovery":"Markov state models built on a neural-network proxy for the committor recover brute-force nucleation rates for magnetisation reversal in the two-dimensional Ising model across thermodynamic conditions. The largest geometric cluster size recovers the same rates even though it fails as a pointwise committor predictor, showing that reliable basin separation, not pointwise fidelity, is the requirement for accurate rate estimation.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Neural committor recovers Ising nucleation rates via basin separation","Cluster size works for rates despite poor pointwise committor fit","Basin separation not pointwise fidelity drives nucleation rate accuracy","pB-NN Markov models match brute-force Ising nucleation rates","Largest cluster size separates basins enough for accurate rates"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The chosen basin boundaries and the lag times at which the longest implied timescale plateaus are assumed to give Markovian dynamics whose mean first-passage times equal the true nucleation rates.","fun_headline_variants_meta":{"raw":{"variants":["Neural committor recovers Ising nucleation rates via basin separation","Cluster size works for rates despite poor pointwise committor fit","Basin separation not pointwise fidelity drives nucleation rate accuracy","pB-NN Markov models match brute-force Ising nucleation rates","Largest cluster size separates basins enough for accurate rates"]},"model":"grok-4.5","effort":"low","cost_usd":0.003412,"raw_usage":{"total_tokens":1116,"prompt_tokens":725,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":34120000,"prompt_tokens_details":{"text_tokens":725,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":324,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":725,"tokens_out":67,"duration_ms":3403,"temperature":1.0,"reasoning_tokens":324,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T11:18:33.364338+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Find a thermodynamic condition of the same Ising model at which an MSM on the largest geometric cluster size (or on p_B-NN) yields a nucleation rate that disagrees with an independent brute-force mean first-passage time by more than statistical error.","supporting_citations":[],"review_version":1}