{"id":"d448c539-c0d4-4277-b807-150ba81416bb","arxiv_id":"2509.08418","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Facet trains an E(3)-equivariant interatomic potential on MPTrj with accuracy close to SevenNet and MACE while using under 10% of the training compute, via spline radial filters and an S2-MLP-Mixer node update.","lead":"Facet is a new machine-learning model that predicts crystal energies with accuracy comparable to leading models while using far less computing power for training. Its two tricks are replacing expensive distance filters with simple splines and mixing information on a sphere, which could make materials discovery faster and cheaper.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The only same-split performance baseline (SevenNet-Streamlined) is derived from a checkpoint pretrained on the full MPTrj, so Facet's claimed parity with SevenNet is not yet established by a clean held-out comparison.","rationale":"The paper has real strengths: the Facet architecture is described in detail, the code is public, the spline-filter analysis is supported by an R2>0.99 fit to SevenNet-0's learned filters, and the authors are transparent about the SevenNet leakage. The S2-MLP-Mixer is a sensible middle ground between tensor products and gates. But the headline quantitative claim—comparable performance at under 10% training cost—rests on a comparison whose only same-split baseline is contaminated by pretraining on the full MPTrj. The MACE-MP-0 and EquiformerV2-S rows come from the authors' own splits, so they are not directly comparable to Facet's numbers. SevenNet-0 itself has no held-out test number. That leaves SevenNet-Streamlined as the sole direct comparison, and its 20.1 meV test error is not a trustworthy estimate because the test structures were seen during pretraining. The authors acknowledge this possibility in the Model Performance section, but acknowledging a confound does not remove it from the argument. A from-scratch baseline or a checkpoint pretrained on disjoint data would settle the comparison. The compute-cost comparison is less threatening: even with an unspecified GPU-normalization method, the direction of the hardware difference (RTX 3090 vs A100) makes a 10% claim conservative. Therefore the reader's conditional verdict is appropriate; my concern does not move it, but it identifies the specific experiment needed.","tokens_in":14485,"tokens_out":9198,"duration_ms":82233,"concrete_test":"Obtain or train a from-scratch SevenNet baseline on exactly the same 10:1:1 trajectory split and formation-energy-only objective used for Facet-Small, on the same GPU hardware, and report its single-model test MAE after a comparable training budget. If the from-scratch baseline's test MAE is above Facet-Small's 23.1 meV (ensemble) or 28.6 meV (single), the comparability claim holds or is strengthened; if it is below, Facet is not comparable to SevenNet. A practical alternative is to start from a SevenNet checkpoint pretrained on data disjoint from MPTrj, fine-tune on the identical training split, and evaluate on the identical test split.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is that SevenNet-Streamlined is a valid stand-in for SevenNet-0's held-out error. The only baseline in Table 1 evaluated on the same 10:1:1 trajectory split and the same formation-energy objective as Facet is SevenNet-Streamlined. But that model is produced by modifying and fine-tuning the SevenNet-0 checkpoint, and the authors state that SevenNet-0 was trained on the entire MPTrj without any held-out data. The test structures used to compute the 20.1 meV number were therefore present in the checkpoint's pretraining corpus, so 20.1 meV is not an unbiased estimate of a from-scratch SevenNet's test error. Since Facet-Small's test error (28.6 meV single, 23.1 meV ensemble) is judged against this number, the paper's central performance claim is not actually established. The likely direction of the leakage bias favors Facet—a clean from-scratch baseline would probably score worse than 20.1—but the experiment as reported cannot distinguish 'Facet is competitive with SevenNet' from 'a leaky SevenNet is only 3 meV better.' The compute-normalization issue is a real reporting gap, but it is secondary: correcting it would almost certainly preserve or strengthen the cost advantage.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Facet, an E(3)-equivariant graph neural network architecture for machine-learning interatomic potentials. The main design changes are replacing MLP distance filters with Bessel-spline filters, introducing an S2-MLP-Mixer node self-interaction layer based on spherical grid projection, and making the cutoff radius and message-normalization exponent learnable/tunable. The authors train Facet-Small on the MPTrj dataset using a 10:1:1 trajectory-level split and report formation-energy MAEs of 28.6 meV for a single model and 23.1 meV for a three-model ensemble, claiming accuracy comparable to larger baselines such as SevenNet-0 and MACE-MP-0 with far fewer parameters and less than 10% of their training compute. The paper also reports a relaxation-speed benchmark against MACE and SevenNet, an analysis showing SevenNet-0's filter MLPs are well approximated by splines, and a reduction of SevenNet-0's parameter count by over 25% with negligible accuracy change.","tokens_in":14757,"tokens_out":5844,"duration_ms":53035,"significance":"If the efficiency claims hold, Facet is a practically valuable contribution: it offers a substantially cheaper training path for universal interatomic potentials, and the released code and repeated-seed training curves support reproducibility. The held-out evaluation of Facet itself appears methodologically sound, and the spline-filter analysis is an interesting and credible architectural insight. However, the headline claim of parity with SevenNet is currently underwritten by a baseline that was fine-tuned from a checkpoint pretrained on the entire MPTrj dataset, including the test structures, and by external baseline numbers from different training setups. The significance is therefore conditional: the architecture is promising, but the central comparative claim is not yet established as reported.","major_comments":[{"comment":"The only same-split performance baseline, SevenNet-Streamlined, is produced by modifying and fine-tuning the SevenNet-0 checkpoint, which the authors state was trained on the entire MPTrj dataset with no held-out data. The test structures used to compute the 20.1 meV number were therefore present in the pretraining corpus, so this number is not an unbiased estimate of a from-scratch model's held-out error. Since the paper's central claim that Facet is comparable to SevenNet is judged against this number, the comparison is not established. Please provide a from-scratch baseline trained on the same 10:1:1 trajectory split with the same formation-energy objective, or otherwise present a clean held-out comparison.","section":"Model Performance, Table 1"},{"comment":"The statement that 'all models are trained with the same training set' is inaccurate. EquiformerV2-S (ref. 42) is an OMat24 model, and MACE-MP-0 and SevenNet-0 report results from the original authors' splits and training objectives, which are not the same as Facet's trajectory-level 10:1:1 split. The external rows therefore do not provide a controlled comparison. To support the claim that Facet 'matches leading models,' either retrain the baselines on the same split and objective or clearly restrict the headline comparison to the same-split baselines and label the external rows as context rather than direct competitors.","section":"Table 1 and surrounding text"},{"comment":"The phrase 'All computing costs are mapped to a single GPU' is never defined. The paper does not specify the conversion between A100 and RTX 3090, whether the mapping is based on theoretical peak FLOPs, measured utilization, or wall-clock time, or whether preprocessing, checkpointing, and the ensemble's three training runs are included in the six-day figure. Since the central efficiency claim ('less than 10% of training compute') depends on this accounting, the conversion methodology must be stated explicitly and the per-component costs itemized.","section":"Table 1, Model Performance"}],"minor_comments":[{"comment":"The equation reference in the message-generation paragraph appears as '(??)'; the citation should be completed or removed.","section":"Methods, Message Generation"},{"comment":"The relaxation-timing comparison reports median per-step times but no confidence intervals or per-configuration variability, despite the text noting persistent outliers; please add error bars or a variance measure.","section":"Figure 5"},{"comment":"The claim that the equivariance error is 'less than 1%' should specify the rotation sampling protocol, the number of test configurations, and the dataset used for the measurement.","section":"Methods, S2-MLP-Mixer"},{"comment":"The ct-UAE comparison reports a single run with no uncertainty estimate; please state whether these numbers are averaged over seeds and whether the ensemble variant was also tested.","section":"Facet Learns Informative Element Embeddings From Scratch"},{"comment":"Please clarify the MACE-MP-0 training-cost entry: the text says the model was trained on a cluster of 80 A100 GPUs for 250 epochs, while the table lists '310 days w/ A100'; state whether this is the estimated single-GPU-equivalent time.","section":"Table 1"}],"recommendation":"major_revision","confidential_remarks":"The reader's stress-test concern is well-founded: the SevenNet-Streamlined baseline is contaminated by pretraining on the test split, and the authors themselves concede that residual knowledge may remain. I would not reject, because the held-out Facet results and the architectural ablations are valuable and the flaw is fixable with additional experiments. The main revision must provide a from-scratch same-split baseline and a precise GPU-hour accounting. If those are supplied, the paper would be a solid contribution to efficient MLIP design."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing. The spline-filter result is the most solid piece: fitting an 8-Bessel spline to SevenNet-0's trained MLP distance filters explains over 99% of the variance, which cleanly justifies replacing per-edge filter MLPs with splines. It is checked against a public checkpoint, cheap to reproduce, and likely transfers to other steerable GNNs. Second, the headline claim—comparable accuracy at under 10% of the training cost—is plausible but not yet established, because the only same-split baseline, SevenNet-Streamlined, was fine-tuned from a checkpoint pretrained on the full MPTrj, test structures included. The authors flag this themselves in a Table 1 footnote; that honesty is to their credit, but it means the 20.1 meV number is not an unbiased estimate of a from-scratch SevenNet's test error.\n\nWhat is new and good: the S2-MLP-Mixer node update (project irreps to a spherical grid, apply a channel-wise MLP, project back) is a sensible middle ground between MACE's tensor products and gate nonlinearities, and the head-splitting trick keeps it affordable; they report equivariance error under 1%. The p=0.7 message-normalization analysis is fitted to SevenNet-0's message statistics, not to energy labels, so the circularity burden is genuinely low. Code and dataset are public, training curves are shown; this is a reproducible engineering paper.\n\nSoft spots, in proportion. First, the central comparison: because SevenNet-Streamlined inherits the full-corpus checkpoint, we cannot distinguish 'Facet matches SevenNet' from 'a leaky SevenNet is only 3 meV better.' The bias direction favors Facet—a clean baseline would score worse—so the claim is probably salvageable, but as reported it is a gap. The fix is straightforward: train a from-scratch SevenNet on the same 10:1:1 split, or fine-tune from a checkpoint trained only on the training portion. A referee should ask for this. Second, 'all computing costs are mapped to a single GPU' is a real reporting gap; I agree this is secondary, since two RTX-3090-days versus 90 A100-days is an order of magnitude apart even after generous hardware adjustment, but the conversion should be stated. Third, minor: the 25%-parameter-reduction claim for SevenNet-0 is softer than it looks because the streamlined model's error is only measured on the leaky test set, and the abstract's 'comparable high performance' overreaches until a clean baseline exists.\n\nBottom line: this paper deserves a serious referee. The spline finding is a keeper, the architecture is a reasonable contribution, and the efficiency claim, if confirmed with a clean baseline, matters for anyone who wants to train MLIPs without an A100 cluster. The held-out evaluation of Facet itself is legitimate; the weakness is specifically the baseline comparison. Send it out, with the same-split baseline as the required revision.","headline":"The spline-filter observation is a genuine, transferable finding and the architecture is sound, but the headline accuracy-versus-compute claim rests on a leaky same-split baseline and needs a clean comparison before it convinces.","tokens_in":15315,"tokens_out":7455,"would_cite":true,"duration_ms":58609,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Facet shows that a 270K-parameter equivariant network can match far larger interatomic-potential models in accuracy while training in under 10% of the compute.","keywords":["E(3)-equivariant graph neural networks","interatomic potentials","materials discovery","MPTrj","spherical harmonics","S2-MLP-Mixer","spline distance filters","training efficiency"],"falsifier":"Retrain SevenNet-0 from scratch on the same 10:1:1 trajectory split used for Facet, with the same 25-epoch budget on the same GPU, and measure held-out formation-energy MAE; if it reaches a test MAE at or below Facet-Small's 28.6 meV/atom, the claimed efficiency advantage of the architecture collapses.","tokens_in":14300,"feed_emoji":"⚛️","tokens_out":6317,"duration_ms":54660,"temperature":0.7,"pith_summary":"The paper argues that the high cost of training machine-learning interatomic potentials comes from architectural redundancy, not from the data. Facet removes that redundancy by replacing the expensive MLP that turns interatomic distances into filter weights with an eight-term spline, and by mixing directional node information through an MLP applied on a spherical grid. On the MPTrj dataset, a 270K-parameter Facet model trains in two days on one RTX 3090 and reaches 28.6 meV/atom test MAE; an ensemble of three reaches 23.1 meV/atom. The paper compares this with 90 A100-days for SevenNet-0 and 310 for MACE-MP-0, so the claim is that competitive universal potentials can be trained at a fraction of the usual cost.","feed_headline":"Trains an atomic potential in 2 days, not 90, with comparable accuracy","feed_subtitle":"Facet cuts the price of training a universal potential from months on data-center GPUs to days on one desktop GPU.","key_machinery":"The load-bearing pieces are (1) a spline filter $W(r)$ formed by a linear combination of eight trainable Bessel basis functions, replacing the MLP filter used in NequIP-style equivariant convolution; (2) the S2-MLP-Mixer, which projects irreps to functions on the sphere $S^2$, samples them on an 18x17 grid, applies a standard MLP channel-wise, and projects back into the irrep basis; and (3) message normalization by estimated degree $k(r_{\\max})^{0.7}$ with a trainable cutoff radius $r_{\\max}$. Together these reduce the most expensive parts of message passing while preserving E(3)-equivariance.","core_discovery":"The central discovery is that two expensive components of steerable graph neural network potentials can be replaced or reworked without sacrificing accuracy. First, the MLP that maps interatomic distances to convolution filter weights is effectively a spline: a linear combination of eight Bessel basis functions fits SevenNet-0's learned filters with $R^{2}$ > 0.99, so the MLP mostly wastes parameters and compute. Second, a node-update layer that projects irreps onto a discretized sphere, applies a channel-wise MLP, and projects back offers a middle ground between MACE's costly tensor products and SevenNet's cheaper gate activations. With these changes, Facet-Small reaches 28.6 meV/atom test MAE after 25 epochs with 270K parameters, and the three-model ensemble reaches 23.1 meV/atom, close to SevenNet-Streamlined's 20.7 while using far less training compute. The paper also reports that Facet runs about twice as fast as MACE models on crystal relaxation tasks.","pith_inferences":["If splines can replace MLP filters in SevenNet, the same replacement likely transfers to other steerable potentials whose filters are also MLPs, such as MACE and EquiformerV2, potentially cutting their training costs too.","The S2-MLP-Mixer is a general equivariant nonlinearity that could be dropped into non-atomistic equivariant networks, e.g., point-cloud or molecular models, wherever tensor products are too expensive and gates too weak.","The trainable cutoff radius and the degree-normalization exponent p=0.7 are plausibly reusable as drop-in modifications for other pretrained potentials, though the paper only demonstrates them in models trained with these settings.","A direct same-hardware, same-epoch head-to-head against a from-scratch SevenNet trained on the same held-out split would cleanly separate architecture gains from optimizer, data-split, and hardware-mapping effects."],"forward_implications":["A competitive universal interatomic potential can be trained on a single consumer GPU in about two days rather than months on data-center GPUs.","Existing steerable models can drop over 25% of their parameters by replacing MLP distance filters with splines, with negligible change in accuracy.","Facet's faster inference, about 1.35x faster than SevenNet and 2.35-2.93x faster than MACE variants, directly accelerates crystal-structure-prediction searches that use the potential as a screening function.","Element embeddings learned from scratch outperform pretrained embeddings for this backbone, suggesting that strong architectures do not need external embedding priors.","The same architecture choices should scale to larger models, larger datasets, and additional training objectives such as force prediction."],"supporting_citations":[{"why":"Introduces the equivariant graph convolution and message filter that Facet streamlines.","marker":"[12]"},{"why":"SevenNet is the direct baseline whose checkpoint, parameter efficiency, and training cost Facet is compared against.","marker":"[14]"},{"why":"MACE-MP-0 is the strong tensor-product baseline whose training cost and accuracy anchor the efficiency comparison.","marker":"[13]"},{"why":"EquiformerV2 contributes equivariant layer normalization and the S2 activation idea that Facet extends into a full MLP mixer.","marker":"[37]"},{"why":"Provides the ACE/tensor-product design-space analysis and the normalization scaling discussion behind the k^{0.7} choice.","marker":"[39]"},{"why":"Origin of projecting to the sphere as an equivariant nonlinearity, which the S2-MLP-Mixer builds on.","marker":"[38]"},{"why":"Periodic graph construction used to encode crystals with neighboring unit-cell offsets.","marker":"[30]"},{"why":"The e3nn-jax library used for irreducible representations and Clebsch-Gordan tensor products.","marker":"[52]"}],"fun_headline_variants":["Facet: splines and grid projection cut potential training cost 10x","Training ML potentials 10x faster with splines and equivariant grids","Facet: spline filters and spherical grids match accuracy at 10% compute","Facet: spline-based filters and grid equivariance slash ML potential training cost"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The efficiency claim assumes the reported GPU-days are genuinely comparable, meaning two days on an RTX 3090 can be mapped onto 90 days on an A100, and that SevenNet-Streamlined, fine-tuned from a checkpoint that already trained on all of MPTrj, honestly represents SevenNet-0's error on new structures.","fun_headline_variants_meta":{"raw":{"variants":["Facet: splines and grid projection cut potential training cost 10x","Training ML potentials 10x faster with splines and equivariant grids","Facet: spline filters and spherical grids match accuracy at 10% compute","Facet: spline-based filters and grid equivariance slash ML potential training cost"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000669,"raw_usage":{"total_tokens":3086,"prompt_tokens":1014,"completion_tokens":2072,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":1997}},"tokens_in":630,"tokens_out":2072,"duration_ms":12249,"temperature":1.0,"reasoning_tokens":1997,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:08:39.893124+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Retrain SevenNet-0 from scratch on the same 10:1:1 trajectory split used for Facet, with the same 25-epoch budget on the same GPU, and measure held-out formation-energy MAE; if it reaches a test MAE at or below Facet-Small's 28.6 meV/atom, the claimed efficiency advantage of the architecture collapses.","supporting_citations":[{"cited_title":"Nature Communications13,2453.ISSN: 2041-1723","cited_arxiv_id":null,"evidence_quote":"Introduces the equivariant graph convolution and message filter that Facet streamlines."},{"cited_title":"& Han, S","cited_arxiv_id":null,"evidence_quote":"SevenNet is the direct baseline whose checkpoint, parameter efficiency, and training cost Facet is compared against."},{"cited_title":"& Smidt, T","cited_arxiv_id":null,"evidence_quote":"EquiformerV2 contributes equivariant layer normalization and the S2 activation idea that Facet extends into a full MLP mixer."},{"cited_title":"S., Geiger, M., Köhler, J","cited_arxiv_id":null,"evidence_quote":"Origin of projecting to the sphere as an equivariant nonlinearity, which the S2-MLP-Mixer builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Periodic graph construction used to encode crystals with neighboring unit-cell offsets."}],"review_version":1}