standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.| relation to other work | claim_relations | how this paper stands to another: agrees, contradicts, extends, qualifies |
| claim type | claim_type | the shape of the claim: existence, mechanism, method, critique, prediction, null |
| concept edge | concept_edges | an asserted relation between two concepts, with the sentence asserting it |
| concept | concepts | an idea the paper works with, quoted where the paper uses it |
| content tag | content_tags | a finding, definition, quantity, statistic or variable named in the paper |
| contribution | contribution | what the paper claims to add |
| control | controls | an experiment run to eliminate a rival explanation |
| limitation | limitations | what the paper says its evidence cannot support |
| mechanism | mechanisms | how the reported effect is said to come about |
| method | method | how the paper produced its evidence |
| object of study | object_of_study | what the paper is about — the thing it investigates |
| phenomenon | phenomenon | the effect or regularity under study |
| research question | research_question | the question the paper sets itself |
| sense | senses | a distinct use of a term, quoted where the paper fixes it |
| transfer | transfers | a method or concept carried in from another field |
Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; 1 of 1 relation here carries that mark. The rest are the tagger’s reading of the sentence quoted beside them.
| facet | tag | field | conf. | whose words |
|---|---|---|---|---|
| object_of_study | learning the interatomic potential energy and forces of molecules and materials from first-principles calculations, at a training-set size small enough that the reference calculations are affordable Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | object_of_study | the paper's words | |
| research_question | whether making a network's internal features equivariant rather than invariant changes how much data it needs, and not merely how accurate it is at a fixed data budget Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | research_question | the paper's words | |
| contribution | NequIP - E(3)-equivariant convolutions over geometric tensors giving state-of-the-art accuracy on molecules and materials with up to three orders of magnitude less training data, plus an ablation isolating equivariance as the cause and a learning-curve slope that no other method has Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | contribution | the paper's words | |
| claim_type | method Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_type | the paper's words | |
| phenomenon | sample efficiency in learned interatomic potentials - and the fact that a symmetry built into the representation changes the exponent of the learning curve rather than only its offset Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | phenomenon | the paper's words | |
| method | system-or-tool-building Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: system-or-tool-building | method | the paper's words | |
| mechanisms | learning curves normally follow a power law whose exponent belongs to the data set - methods move the curve up or down and leave its slope alone. Building rotation equivariance into the features changes the slope itself, so the advantage grows with every additional training structure rather than staying constant Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[0] | 0.95 | the tagger's words |
| mechanisms | predicting force vectors directly leaves nothing enforcing that they are the gradient of any energy, so long molecular dynamics runs can drift; taking the forces as the gradient of the predicted potential makes energy conservation a property of the construction rather than something the training has to discover Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: conservation by differentiation | mechanisms[1] | 0.95 | the tagger's words |
| mechanisms | a reported error is the sum of the model's error and the reference calculation's; running one model on two recomputations of the same molecules separates them, and here the energies move while the forces do not, which says the original benchmark's energy noise was the larger term Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[2] | 0.95 | the tagger's words |
| mechanisms | each configuration carries one energy and 3N force components, so M structures are M(3N + 1) labels; a data-efficiency claim counted in structures is counted in a unit that hides how much supervision each one supplies, and the authors raise this before making the claim Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[3] | 0.95 | the tagger's words |
| limitations | the data-efficiency claim is counted in structures, and each structure carries 3N + 1 labels - the authors state the alternative denominator themselves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[0] | 0.95 | the tagger's words |
| limitations | the energy comparison against DeepMD is confounded by there being 3N force targets and one energy target per frame, which the authors expect to favour the larger training set on energies Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[1] | 0.95 | the tagger's words |
| limitations | the DeepMD version compared against is not the smooth one, and the smooth version does not report results on water and ice, so the comparison could not be made Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[2] | 0.95 | the tagger's words |
| limitations | how the many-body character of interactions arises in message-passing potentials has no clear theoretical understanding Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[3] | 0.95 | the tagger's words |
| limitations | long-range interactions are not explicitly included, and how much of them message passing captures is unmeasured Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[4] | 0.95 | the tagger's words |
| limitations | interpretability is an open challenge - classical potentials assign energy to named interaction types and this model does not Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[5] | 0.95 | the tagger's words |
| limitations | the tension is structural: the simple functional form that makes classical force fields interpretable is the same thing that limits their accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[6] | 0.95 | the tagger's words |
| transfers | group representation theory - E(3), tensor rank, parity and spherical harmonics - carried from physics into the design of a network's internal feature space Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[0] | 0.95 | the tagger's words |
| transfers | power-law learning curves and their exponents, carried from statistical learning theory into a claim about what a symmetry does to sample complexity Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[1] | 0.95 | the tagger's words |
| controls | a convergence scan over rotation order l in {0, 1, 2, 3}, where l = 0 is the same network with equivariance switched off Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: every other part of the architecture as the source of the accuracy - depth, cutoff, radial basis and training setup are identical across the scan, so only the tensor rank differs · outcome: held | controls[0] | 0.95 | the tagger's words |
| controls | interactions above l = 0 explicitly turned off to make the network a conventional invariant GNN-IP in a SchNet-style fashion, then run across training-set sizes from 10 to 1000 with identical hyperparameters Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: training budget, capacity or hyperparameter tuning as the explanation of the sample efficiency - the comparison is the same network at every data size · outcome: held | controls[1] | 0.95 | the tagger's words |
| controls | weight- and feature-controlled versions of the same comparison, reported in the supplementary information Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: parameter count as the explanation - a higher-l network has more weights, and without this the ablation would be measuring size rather than symmetry · outcome: held | controls[2] | 0.95 | the tagger's words |
| controls | separate models trained and tested on BOTH the original and the revised MD-17 data sets, with energy and force errors reported for each Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the benchmark's own numerical noise being read as model error - the forces stay put while the energies move, which can only be a property of the reference data · outcome: held | controls[3] | 0.95 | the tagger's words |
| controls | comparison against kernel methods - sGDML and FCHL19/GPR - and not only against other neural networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the small-data claim being tested only against models with the same weakness; kernels are the methods that usually win on small training sets · outcome: held | controls[4] | 0.95 | the tagger's words |
| controls | the trained potential used to run molecular dynamics, with the radial and two angular distribution functions compared against the ab-initio trajectory at the same temperature Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: a low force error being mistaken for correct dynamics - a potential can score well pointwise and still produce the wrong structure when integrated · outcome: held | controls[5] | 0.95 | the tagger's words |
| controls | training exclusively on the 3000 K molten trajectory and evaluating on the 600 K quenched glass Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: memorisation of the training phase - the test structures are a different phase of the same material, which the model never saw · outcome: held | controls[6] | 0.95 | the tagger's words |
| controls | Li diffusivity measured from NequIP-driven MD started from ten different initial velocity draws and compared against the ab-initio value Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: one lucky trajectory - diffusivity from a single run of a superionic conductor is a sample from a distribution, not a number · outcome: held | controls[7] | 0.95 | the tagger's words |
| controls | a published Behler-Parrinello network's force RMSE on the same system quoted against NequIP models trained on 100 and 250 structures Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the data-efficiency comparison resting only on this paper's own baselines · outcome: held | controls[8] | 0.95 | the tagger's words |
| controls | three different weightings of the energy and force terms in the loss function, reported side by side on the water and ice system Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: that the reported accuracy is an artefact of one chosen energy/force weighting in the loss · outcome (stated by the tagger, no quotation): held | controls[9] | 0.95 | the tagger's words |
| concepts | equivariant Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: equivariant | concepts[0] | 0.95 | the paper's words |
| concepts | invariant Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: invariant | concepts[1] | 0.95 | the paper's words |
| concepts | rotation order Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: rotation order | concepts[2] | 0.95 | the paper's words |
| concepts | NequIP Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: NequIP | concepts[3] | 0.95 | the paper's words |
| concepts | interatomic potentials Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: interatomic potentials | concepts[4] | 0.95 | the paper's words |
| concepts | log-log slope Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: log-log slope | concepts[5] | 0.95 | the paper's words |
| concepts | learning curve Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: learning curve | concepts[6] | 0.95 | the paper's words |
| concepts | noise floor Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: noise floor | concepts[7] | 0.95 | the paper's words |
| concepts | MD-17 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: MD-17 | concepts[8] | 0.95 | the paper's words |
| concepts | DeepMD Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: DeepMD | concepts[9] | 0.95 | the paper's words |
| concepts | DimeNet Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: DimeNet | concepts[10] | 0.95 | the paper's words |
| concepts | diffusivity Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: diffusivity | concepts[11] | 0.95 | the paper's words |
| senses | NequIP's MD-17 energy error - ON THE ORIGINAL DATA SET: significantly higher, and the paper attributes the difference to that data set's noise floor rather than to the model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[0] | 0.95 | the tagger's words |
| senses | NequIP's MD-17 energy error - ON THE REVISED DATA SET: significantly lower, and the only version the authors say should be used for comparing methods Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[1] | 0.95 | the tagger's words |
| senses | what raising the rotation order does - CROSSING l = 0 TO l = 1: changes the log-log slope of the learning curve, so the model learns faster from new data Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[2] | 0.95 | the tagger's words |
| senses | what raising the rotation order does - BEYOND l = 1: shifts the curve down without changing its slope, the same thing every other method does to it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[3] | 0.95 | the tagger's words |
| senses | a training set of M structures - COUNTED AS CONFIGURATIONS: M, which is the number the data-efficiency claim is made in Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[4] | 0.95 | the tagger's words |
| senses | a training set of M structures - COUNTED AS LABELS: M(3N + 1), because each structure carries one energy and 3N force components - the authors raise this themselves before claiming efficiency Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[5] | 0.95 | the tagger's words |
| claim_relations | critiques → the belief that deep neural networks require massive training sets - contradicted here by matching or beating existing models with up to three orders of magnitude fewer reference calculations Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[0] | 0.95 | the tagger's words |
| claim_relations | critiques → invariant graph neural network interatomic potentials, whose features are scalars and which therefore discard the directional information equivariant filters can use Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[1] | 0.95 | the tagger's words |
| claim_relations | critiques → direct prediction of atomic force vectors, which is not guaranteed to conserve energy because the forces are not gradients of a potential Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[2] | 0.95 | the tagger's words |
| claim_relations | critiques → the original MD-17 benchmark, whose energy noise floor the authors say is too high for comparing methods - only the revised recomputation should be used Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[3] | 0.95 | the tagger's words |
| claim_relations | qualifies → the empirical rule that learning-curve exponents belong to the data set and methods only shift the curve - broken here by equivariance, and only by crossing l = 0 to 1 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[4] | 0.95 | the tagger's words |
| claim_relations | qualifies → its own DeepMD comparison, which used the non-smooth published version because the smooth one reports no results on water and ice Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[5] | 0.95 | the tagger's words |
| concept_edges | equivariant —distinct-from→ invariant Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: whether the internal features have a direction that rotates with the molecule · the relation itself is separately evidenced · strength of the relation: 0.95 · differs in (stated by the tagger, no quotation): whether the internal features have a direction that rotates with the molecule · the relation stated: this method carries relative position vectors and higher-order tensors where invariant networks carry only distances
Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: 'In contrast' refers to the rotation-invariant GNN-IPs of the previous sentence. also in: equivariant · invariant | concept_edges[0] | 0.95 | the tagger's words |
| content_tags | equivariant networks with l >= 1 outperform the identical network at l = 0 at every training-set size from 10 to 1000 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[0] | 0.95 | the tagger's words |
| content_tags | crossing l = 0 to 1 changes the log-log slope of the learning curve; raising l beyond 1 only shifts it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[1] | 0.95 | the tagger's words |
| content_tags | identical models give lower energy error on revised MD-17 and similar force error, locating the difference in the benchmark's noise floor rather than the method Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[2] | 0.95 | the tagger's words |
| content_tags | With 1000x fewer training data, NequIP beats DeepMD on force error in all four parts of the data set. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[3] | 0.95 | the tagger's words |
| content_tags | Trained only on high-temperature molten data, NequIP reproduces the glass's RDF and both ADFs. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[4] | 0.95 | the tagger's words |
| content_tags | Li diffusivity from NequIP-driven MD is 1.25e-5 cm2/s against 1.37e-5 from ab-initio MD, a 9% relative error Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[5] | 0.95 | the tagger's words |
| content_tags | the method beats kernel approaches such as sGDML and FCHL19/GPR, which normally win on small training sets Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[6] | 0.95 | the tagger's words |
| content_tags | Each training configuration of N atoms supplies 3N + 1 labels. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[7] | 0.95 | the tagger's words |
| content_tags | the exponent of the learning-curve power law - how fast a learning algorithm improves as new data become available, normally fixed across methods for a given data set Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: log-log slope | content_tags.definitions[0] | 0.95 | the tagger's words |
| content_tags | the reference data set's own numerical error, identified here by training identical models on two recomputations of the same molecules and seeing which error moves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: noise floor | content_tags.definitions[1] | 0.95 | the tagger's words |
| content_tags | fewer training structures than the DeepMD comparison on water and ice - 133 against 133,500 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[0] | 0.95 | the tagger's words |
| content_tags | the relative error of the NequIP Li diffusivity against ab-initio MD Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: 9% | content_tags.quantities[1] | 0.95 | the tagger's words |
| content_tags | structures the Behler-Parrinello baseline needed for an RMSE that NequIP matches with 100 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[2] | 0.95 | the tagger's words |
| content_tags | MAE Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: MAE | content_tags.statistics[0] | 0.95 | the tagger's words |
| content_tags | RMSE Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RMSE | content_tags.statistics[1] | 0.95 | the tagger's words |
| content_tags | rotation order Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: rotation order | content_tags.variables[0] | 0.95 | the tagger's words |
| content_tags | log-log slope Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: log-log slope | content_tags.variables[1] | 0.95 | the tagger's words |
Tags that could not be placed in the text:
What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.