{"id":"2766def1-c59f-4f21-affc-9df9531bae75","arxiv_id":"2601.07742","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Phonon fine-tuning, which supervises machine-learned potentials on Hessian columns of the energy, cuts phonon-property errors by ~55% and improves thermal conductivity predictions.","lead":"This paper fine-tunes machine-learned atomistic models by training them to match the curvature of the energy surface (phonon force constants) from DFT, not just energies and forces. This makes predicted vibrational and thermal properties substantially more accurate, cutting errors by about half on standard benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unvalidated zero force/stress labels in Eq. 8 could bias PFT: residual relaxation forces of ~1e-3 eV/Å yield FC errors of ~0.1 eV/Ų at Δ=0.01 Å, comparable to the Hessian MAE gaps in Fig. 2.","rationale":"The central claim is that directly supervising Hessian columns with DFT force constants improves phonon-property prediction. For this to hold, the DFT FC labels and the auxiliary EFS labels in Eq. 8 must be clean. The paper explicitly assumes zero force and stress labels on the phonon supercells but does not quantify residual relaxation forces or the relaxation convergence criteria. This is not an internal inconsistency, but an unvalidated data-quality premise. A quick check against the actual MDR Phonon VASP outputs can settle it. I do not think the 31.6 meV/atom energy shift is load-bearing for the main model because λ_E=0 for Nequix MP PFT, and the co-training loss uses MPtrj energies, not MDR Phonon energies. Single-run benchmarks are a secondary robustness concern, but the improvements are large and replicated on Nequix OAM, so they do not threaten the central mechanism. The missing control (a co-trained EFS-only baseline on displacement data) is mitigated by the no-co-train PFT result, which also improves phonon properties. Thus the zero-label issue is the most load-bearing remaining concern. The stochastic HVP scheme is well validated against full-Hessian training, and the analytical Hessian evaluation is cross-checked against finite-displacement predictions, so those parts of the paper are solid. If the residual-force check passes, the conditional could be upgraded; if it fails, the PFT objective needs correction or the EFS terms need to be masked.","tokens_in":15834,"tokens_out":15658,"duration_ms":170528,"concrete_test":"Parse the VASP vasprun.xml/OUTCAR files for ~100 randomly chosen undisplaced MDR Phonon supercells; compute max/mean residual atomic force norms and stress-tensor components. If max |F| > 1e-3 eV/Å (or equivalently F0/Δ > ~0.03 eV/Ų at Δ=0.01 Å), retrain Nequix MP PFT on a subset with (a) actual F/σ labels from the displacement dataset, and (b) EFS terms masked, then compare Table 1 MAEs and κSRME. A >10% shift in any headline metric would confirm the assumption is load-bearing; negligible residual forces would clear it.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is the zero-force/zero-stress labeling of the phonon supercells in the PFT loss. In Sec. 4.1, the authors state: \"we assume the force and stress labels are zero due to the strict structural relaxation procedure done prior to the phonon calculation.\" This feeds Eq. 8's EFS terms (λ_F=20, λ_σ=5) on every phonon structure. The same assumption underlies Eq. 7: the finite-displacement FCs are computed as -[F(Δ)-F0]/Δ, with F0 treated as zero. If the MDR Phonon relaxation leaves residual forces/stresses above ~1e-3 eV/Å, then (i) the PFT force target is wrong at the equilibrium configuration, and (ii) the FC labels carry a systematic baseline error F0/Δ: at the standard 0.01 Å displacement, F0=1e-3 eV/Å gives 0.1 eV/Ų, larger than the 0.03-0.06 eV/Ų Hessian MAE differences in Fig. 2. The paper never reports residual force/stress norms or the relaxation convergence criterion (EDIFFG/ISIF) used by the MDR Phonon database. Since the headline 55% improvement and the SOTA claim rest on these labels, this needs to be checked, not assumed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes phonon fine-tuning (PFT), a loss that augments standard energy/force/stress (EFS) training by matching the analytical Hessian of an MLIP energy to DFT force constants from finite-displacement phonon calculations. To make this tractable, PFT samples one Hessian column per structure and evaluates the loss with a single Hessian-vector product, giving O(N) training cost. A co-training schedule interleaves upstream EFS batches to limit catastrophic forgetting. On the PBE MDR Phonon benchmark, PFT improves the Nequix MP model by about 55% average MAE across four phonon properties and claims state-of-the-art accuracy among MPtrj-trained models; it also improves thermal-conductivity SRME and preserves Matbench Discovery performance when co-trained. An appendix reports that stochastic HVP training matches full-Hessian training on 64-atom supercells.","tokens_in":16197,"tokens_out":13268,"duration_ms":139189,"significance":"If the underlying label assumptions are validated, this is a practical and scalable way to supervise PES curvature. The stochastic HVP formulation is mathematically clean, and the appendix's full-Hessian comparison is a genuine validation of the approximation. The evaluation is external: held-out DFT phonon calculations, two base models (Nequix MP and OAM), and public benchmarks. The paper also promises code, trained weights, and preprocessed data, which strengthens reproducibility. The co-training scheme is a useful contribution, and the forgetting numbers are encouraging. The main weakness is that the zero force/stress label assumption for phonon structures is stated but not validated, and the dataset energy mismatch is only partially addressed. These issues affect the reliability of the headline numbers but are fixable with additional reporting and targeted experiments.","major_comments":[{"comment":"The zero force/stress label assumption is central and unvalidated. The authors state 'we assume the force and stress labels are zero due to the strict structural relaxation procedure done prior to the phonon calculation,' but they do not report residual force/stress norms or the relaxation convergence criterion used for the MDR Phonon data. With λ_F=20 and λ_σ=5, any residual force of order 1e-3 eV/Å becomes a systematic target error, and Eq. (7) propagates the same residual into the ground-truth force constants as F0/Δ (0.1 eV/Ų at Δ=0.01 Å), which is comparable to the Hessian MAE gaps in Fig. 2. Because the headline 55% and SOTA claims rest on these labels, please report residual statistics and relaxation settings, or recompute with the actual DFT forces from the displacement data, or set λ_F=λ_σ=0 on phonon structures and show the conclusions are unchanged.","section":"Sec. 4.1 / Eq. (8)"}],"minor_comments":[{"comment":"The eSEN-MP row lists only three values for four metrics, leaving the SOTA comparison incomplete. Add the missing value and align the columns.","section":"Table 1"},{"comment":"The caption says 'heat capacity errors,' but the panel plots four different phonon properties. Update the caption to describe the multi-panel layout.","section":"Fig. 2 caption"},{"comment":"The text says the phonon data 'contain[s] the original energy/force/stress calculations at each displacement' and then says it 'does not contain force, or stress labels needed for the PFT loss function.' This is contradictory. Clarify which structures and which labels are actually used in Eq. (8).","section":"Sec. 4.1"},{"comment":"The 31.6 meV/atom energy shift between MDR Phonon and MPtrj is acknowledged. Since PFT sets λ_E=0 (Table A.2), state explicitly that the energy shift does not enter the PFT loss, and comment on whether the large outliers could affect co-training batches.","section":"Sec. A.2"},{"comment":"The expectation notation with E_{b~U,j~U} inside a sum over a,i is easy to misread. Spell out that one column (b,j) is sampled per structure and that the sum over a,i covers the entries of that column.","section":"Eq. (9)"},{"comment":"Consider reporting repeated-seed statistics for the main PFT results; the stochastic column sampling and the random train/test split make seed variability a relevant quantity.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The main gate is the validation of the zero force/stress label assumption. If the authors provide residual force/stress statistics and show that the conclusions are robust to using actual DFT forces or to dropping the EFS terms on phonon structures, I would be happy to support acceptance. No other concerns rise to the level of blocking."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this is a solid, practical methods paper. The authors fine-tune an energy-conserving equivariant MLIP by matching analytically computed Hessian columns to DFT force constants from phonon calculations, using stochastic Hessian-vector products and a simple co-training scheme. It works. On held-out MDR Phonon data they get a 55% average reduction in phonon property error, reach state-of-the-art among MPtrj-trained models, and improve thermal conductivity κSRME from 0.446 to 0.306. The gains are consistent across two different base models, and the ablation showing that direct fine-tuning on displacement data worsens Hessian error is a nice piece of evidence that curvature supervision is doing the real work.\n\nThe genuine novelty is the combination: analytical Hessians for periodic universal MLIPs, stochastic column sampling to make large supercells tractable, and co-training to prevent catastrophic forgetting. The appendix validates the HVP approximation against full-Hessian training on 64-atom systems, with 30× speedup and 90% memory reduction. Code and weights are released. That is reproducible, concrete work.\n\nNow the soft spots. The zero force/stress labels on phonon supercells are an assumption, not a verified fact. The PFT loss injects target force and stress of zero on every phonon structure, and the force-constant labels themselves assume F0=0 in the finite-difference formula. If the MDR Phonon relaxation was loose, residual forces around 1e-3 eV/Å would introduce errors in the force constants on the order of 0.1 eV/Ų at 0.01 Å displacement, comparable to the Hessian MAE gaps in Fig. 2. I don't think this sinks the paper—standard phonon workflows relax tightly, and the test set is genuinely held-out DFT, so the headline improvements are probably real—but it should be checked. The authors should report the relaxation convergence criterion and residual force norms, or better, use the actual forces from the displaced phonon calculations to supervise the EFS terms instead of assuming zero. They have that data. A second, minor issue: all benchmark numbers are single runs with no error bars, and λ_Φ was set to 100 without tuning. The 31.6 meV/atom energy shift between MPtrj and MDR Phonon is acknowledged and reasonably handled, though it muddies the reported energy MAE.\n\nThis paper is for anyone using universal MLIPs for phonon screening or thermal property prediction. It deserves serious peer review—the method is important, the evidence is strong, and the reproducibility raises it above typical MLIP fine-tuning papers. A good referee will ask for residual-force documentation and a sensitivity check on the loss weights, but the central empirical claim is credible. I'd bring it to a reading group and would certainly cite it.","headline":"PFT is a genuinely useful method for supervising PES curvature in universal MLIPs, with strong empirical gains; the main caveat is unvalidated zero-force labels on phonon supercells.","tokens_in":16693,"tokens_out":2229,"would_cite":true,"duration_ms":25003,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Fine-tuning an interatomic potential by matching its energy Hessian to DFT force constants reduces average vibrational-property error by 55 percent.","keywords":["phonon fine-tuning","machine learned interatomic potentials","energy Hessian","force constants","vibrational properties","thermal conductivity","catastrophic forgetting","equivariant neural networks"],"falsifier":"Measure the residual DFT forces on displaced phonon supercells before the zero-force assumption is applied; if those residuals are large and coincide with the materials where PFT fails, the assumption is unsafe. Alternatively, run a controlled experiment where the DFT force constants in the PFT loss are replaced by random values while keeping everything else identical: if phonon property error still drops, the improvement is not caused by Hessian matching.","tokens_in":15715,"feed_emoji":"🔬","tokens_out":6556,"duration_ms":63357,"temperature":0.7,"pith_summary":"This paper argues that the standard way of training machine-learned interatomic potentials—matching energies, forces, and stresses—leaves the curvature of the potential energy surface under-constrained, and that phonon-derived properties suffer as a result. It proposes phonon fine-tuning (PFT), a training objective that directly matches the model's energy Hessian to DFT-computed second-order force constants. On a benchmark of 1,000 held-out materials, PFT reduces average error across maximum phonon frequency, vibrational entropy, Helmholtz free energy, and heat capacity by 55% relative to the base model, and also improves thermal conductivity predictions that depend on third-order derivatives. The method scales to large supercells by stochastically sampling a single Hessian column per structure and computing the loss with one Hessian-vector product, and a co-training schedule keeps the model from forgetting its original training data.","feed_headline":"Hessian matching cuts phonon property error by 55%","feed_subtitle":"Matching the energy Hessian to DFT force constants fixes curvature errors and improves vibrational properties.","key_machinery":"The mechanism is the Hessian of the predicted potential energy, which for a crystal is the same object as the second-order force constant matrix. PFT forms its gradient by sampling one atomic coordinate (one column of the Hessian) per structure in a batch and computing the column via a Hessian-vector product: one forward-mode Jacobian-vector product through a reverse-mode gradient. This makes the fine-tuning loss a weighted sum of the usual energy/force/stress errors plus a force-constant error; in expectation the sampled columns train the full Hessian. A co-training loop interleaves the original upstream energy/force/stress data after each phonon step to mitigate catastrophic forgetting.","core_discovery":"The central claim is that curvature, not just energy and forces, must be explicitly supervised to get vibrational properties right. PFT does this by adding a loss term that compares the analytical Hessian of the predicted energy—the second derivative with respect to pairs of atomic coordinates—with the force constants obtained from finite-displacement DFT phonon calculations. Because only one column of the Hessian is needed per structure in expectation, the extra cost is linear in the number of atoms rather than quadratic. The paper shows that Hessian error tracks phonon property error across existing models, that PFT lowers that error, and that the improvement transfers to thermal conductiv","pith_inferences":["The method could be applied as a universal post-processing step: since the needed labels are force constants that standard DFT phonon workflows already produce, any existing universal interatomic potential could be fine-tuned this way, not just the two base models tested.","The documented energy shift between the phonon data and the pretraining data may be suppressing energy accuracy; explicitly aligning or correcting that shift could improve PFT further.","Uniform random Hessian-column sampling is simple, but symmetry makes many columns redundant; weighting samples by how much they contribute to phonon modes could improve sample efficiency.","Adding third-order force constants directly to the PFT loss is a testable extension that could give a more direct path to thermal conductivity than relying on second-order transfer."],"forward_implications":["If PFT's claims hold, any energy-conserving interatomic potential with automatic differentiation can be improved on phonon properties at a fraction of its original training cost.","The Hessian-error correlation suggests that curvature error, not just energy or force error, is a key bottleneck for vibrational property prediction.","Because PFT also improves thermal conductivity, which depends on third-order force constants, curvature-aware fine-tuning can generalize to anharmonic properties without directly supervising those higher-order derivatives.","Co-training preserves the base model's performance on stability classification, so phonon fine-tuning does not force a trade-off against general-purpose use.","Stochastic Hessian-column sampling makes it feasible to train on supercells large enough for accurate finite-displacement phonon calculations, which were previously impractical for full-Hessian training."],"fun_headline_variants":["Phonon fine-tuning cuts phonon property error by 55%","Supervising Hessians improves MLIP phonons by 55%","Curvature-aware training reduces phonon error 55%","Fine-tune interatomic potentials on force constants","Hessian supervision: 55% better phonon predictions"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing assumption is that the phonon supercells are relaxed tightly enough that force and stress labels can be set to zero; if residual relaxation forces or stresses are sizable, the fine-tuning objective is fitted to biased labels and the Hessian matching is distorted.","fun_headline_variants_meta":{"raw":{"variants":["Phonon fine-tuning cuts phonon property error by 55%","Supervising Hessians improves MLIP phonons by 55%","Curvature-aware training reduces phonon error 55%","Fine-tune interatomic potentials on force constants","Hessian supervision: 55% better phonon predictions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000669,"raw_usage":{"total_tokens":2859,"prompt_tokens":691,"completion_tokens":2168,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":435,"completion_tokens_details":{"reasoning_tokens":2081}},"tokens_in":435,"tokens_out":2168,"duration_ms":15629,"temperature":1.0,"reasoning_tokens":2081,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T10:59:43.519527+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the residual DFT forces on displaced phonon supercells before the zero-force assumption is applied; if those residuals are large and coincide with the materials where PFT fails, the assumption is unsafe. Alternatively, run a controlled experiment where the DFT force constants in the PFT loss are replaced by random values while keeping everything else identical: if phonon property error still drops, the improvement is not caused by Hessian matching.","supporting_citations":[],"review_version":1}