phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| 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— “To our surprise, we observe that the equivariant NequIP networks break this pattern. Instead they follow a log-log slope with larger magnitude, meaning that they learn faster as new data become available. An invariant l = 0 NequIP network, however, displays a similar log-log slope to other methods, suggesting that it is indeed the equivariant… | |
| claim-type | method— “While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and… | |
| method — evidence | — “We run a convergence scan on the rotation order l ∈ {0, 1, 2, 3} and find that increasing the tensor rank beyond l = 1 gives a consistent improvement. The significant improvement from l = 0 to l = 1 highlights the crucial role of equivariance in obtaining improved accuracy on this task.” | |
| object of study — evidence | — “One of the limiting factors of neural network interatomic potentials (NN-IPs) is that they typically require large training sets of ab-initio calculations, often including thousands or even millions of reference structures. This computationally expensive process of training data collection has severely limited the adoption of NN-IPs, as it… | |
| research question — evidence | — “In contrast, the method outlined in this work uses relative position vectors rather than simply distances (scalars) together with features comprised of not only scalars, but also higher-order geometric tensors. This makes internal features instead equivariant to rotation and allows for angular information to be used by rotationally… | |
| contribution — evidence | — “The contribution of the present work is the introduction of a deep learning energy-conserving interatomic potential for both molecules and materials built on E(3)-equivariant convolutions over geometric tensors that yields state-of-the-art accuracy, outstanding data-efficiency, and can with high fidelity reproduce structural and kinetic… | |
| transfer | from group theory and physics: group representation theory - E(3), tensor rank, parity and spherical harmonics - carried from physics into the design of a network's internal feature space— “In contrast, the method outlined in this work uses relative position vectors rather than simply distances (scalars) together with features comprised of not only scalars, but also higher-order geometric tensors. This makes internal features instead equivariant to rotation and allows for angular information to be used by rotationally… | transfers[0] |
| transfer | from statistical learning theory: power-law learning curves and their exponents, carried from statistical learning theory into a claim about what a symmetry does to sample complexity— “The exponent of this power-law (or equivalently the slope in log-log space) determines how fast a learning algorithm learns as new data become available. Empirical results have shown that this exponent typically remains fixed across different learning algorithms for a given data set, and different methods only shift the learning curve… | transfers[1] |
| mechanism | a symmetry that changes the exponent, not the offset 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— “To our surprise, we observe that the equivariant NequIP networks break this pattern. Instead they follow a log-log slope with larger magnitude, meaning that they learn faster as new data become available. An invariant l = 0 NequIP network, however, displays a similar log-log slope to other methods, suggesting that it is indeed the equivariant… | mechanisms[0] |
| mechanism | conservation by differentiation 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— “Townshend et al. use the framework of Tensor-Field Networks to directly predict atomic force vectors. The predicted forces are not guaranteed by construction to conserve energy since they are not obtained as gradients of the total potential energy. This may lead to problems in simulations of molecular dynamics over long times. None of these… | mechanisms[1] |
| mechanism | an instrument reading its own reference 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— “Importantly, we train and test separate NequIP models on both the original and the revised MD-17 data set, and find that NequIP obtains significantly lower energy errors on the revised data set, while the force accuracy is similar on the two data sets. In line with previous work, this suggests that the noise floor on the original MD-17 data… | mechanisms[2] |
| mechanism | labels per structure as the hidden denominator 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— “First, it is important to note that each training configuration contains multiple labels: in particular, for a training set of M first-principles calculations with structures consisting of N atoms, the energies and force components together give a total of M(3N + 1) labels.” | mechanisms[3] |
| 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— “While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and… | claim_relations[0] |
| critiques | invariant graph neural network interatomic potentials, whose features are scalars and which therefore discard the directional information equivariant filters can use— “In contrast, the method outlined in this work uses relative position vectors rather than simply distances (scalars) together with features comprised of not only scalars, but also higher-order geometric tensors. This makes internal features instead equivariant to rotation and allows for angular information to be used by rotationally… | claim_relations[1] |
| critiques | direct prediction of atomic force vectors, which is not guaranteed to conserve energy because the forces are not gradients of a potential— “Townshend et al. use the framework of Tensor-Field Networks to directly predict atomic force vectors. The predicted forces are not guaranteed by construction to conserve energy since they are not obtained as gradients of the total potential energy. This may lead to problems in simulations of molecular dynamics over long times. None of these… | claim_relations[2] |
| 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— “Importantly, we train and test separate NequIP models on both the original and the revised MD-17 data set, and find that NequIP obtains significantly lower energy errors on the revised data set, while the force accuracy is similar on the two data sets. In line with previous work, this suggests that the noise floor on the original MD-17 data… | claim_relations[3] |
| 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— “To our surprise, we observe that the equivariant NequIP networks break this pattern. Instead they follow a log-log slope with larger magnitude, meaning that they learn faster as new data become available. An invariant l = 0 NequIP network, however, displays a similar log-log slope to… | claim_relations[4] |
| 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[5] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[0] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[1] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[2] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[3] |
| sense | a training set of M structures - COUNTED AS CONFIGURATIONS: M, which is the number the data-efficiency claim is made in Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[4] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[5] |
| control | a convergence scan over rotation order l in {0, 1, 2, 3}, where l = 0 is the same network with equivariance switched off — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[0] |
| control | 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 — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out training budget, capacity or hyperparameter tuning as the explanation of the sample efficiency - the comparison is the same network at every data size Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[1] |
| control | weight- and feature-controlled versions of the same comparison, reported in the supplementary information — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out parameter count as the explanation - a higher-l network has more weights, and without this the ablation would be measuring size rather than symmetry Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[2] |
| control | separate models trained and tested on BOTH the original and the revised MD-17 data sets, with energy and force errors reported for each — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[3] |
| control | comparison against kernel methods - sGDML and FCHL19/GPR - and not only against other neural networks — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out the small-data claim being tested only against models with the same weakness; kernels are the methods that usually win on small training sets Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[4] |
| control | 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 — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out a low force error being mistaken for correct dynamics - a potential can score well pointwise and still produce the wrong structure when integrated Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[5] |
| control | training exclusively on the 3000 K molten trajectory and evaluating on the 600 K quenched glass — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out memorisation of the training phase - the test structures are a different phase of the same material, which the model never saw Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[6] |
| control | Li diffusivity measured from NequIP-driven MD started from ten different initial velocity draws and compared against the ab-initio value — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out one lucky trajectory - diffusivity from a single run of a superionic conductor is a sample from a distribution, not a number Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[7] |
| control | a published Behler-Parrinello network's force RMSE on the same system quoted against NequIP models trained on 100 and 250 structures — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. — rules out the data-efficiency comparison resting only on this paper's own baselines Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[8] |
| control | three different weightings of the energy and force terms in the loss function, reported side by side on the water and ice system — held — rules out that the reported accuracy is an artefact of one chosen energy/force weighting in the loss Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[9] |
| weight | 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 — 0.95 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[0] |
| weight | invariant graph neural network interatomic potentials, whose features are scalars and which therefore discard the directional information equivariant filters can use — 0.95 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[1] |
| weight | direct prediction of atomic force vectors, which is not guaranteed to conserve energy because the forces are not gradients of a potential — 0.95 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[2] |
| weight | 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 — 0.95 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[3] |
| weight | 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 — 0.9 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[4] |
| weight | its own DeepMD comparison, which used the non-smooth published version because the smooth one reports no results on water and ice — 0.9 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[5] |
| audit | equivariant —distinct-from→ invariant — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[0] |
| differs in (stated by the tagger, no quotation) | equivariant —distinct-from→ invariant — whether the internal features have a direction that rotates with the molecule | concept_edges[0] |
| relation | equivariant —distinct-from→ invariant — this method carries relative position vectors and higher-order tensors where invariant networks carry only distances Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[0] |
| weight | equivariant —distinct-from→ invariant — 0.95 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[0] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[0] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[1] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[2] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[3] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[4] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[5] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[6] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[7] |
| outcome | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[8] |
| outcome (stated by the tagger, no quotation) | control — held Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[9] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| limitation | how the many-body character of interactions arises in message-passing potentials has no clear theoretical understanding Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| limitation | long-range interactions are not explicitly included, and how much of them message passing captures is unmeasured Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| limitation | interpretability is an open challenge - classical potentials assign energy to named interaction types and this model does not Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[2] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[3] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[4] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[5] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[6] |
| finding | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[7] |
| quantity | fewer training structures than the DeepMD comparison on water and ice - 133 against 133,500 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[0] |
| quantity | the relative error of the NequIP Li diffusivity against ab-initio MD Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[1] |
| quantity | structures the Behler-Parrinello baseline needed for an RMSE that NequIP matches with 100 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[2] |
| variable | rotation order Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[0] |
| variable | log-log slope Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[1] |
| definition | log-log slope Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| definition | noise floor Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| concept | equivariant — not defined in this paper's own words; a function whose output transforms the same way its input does under a group action; here the internal features rotate with the molecule instead of being blind to its orientation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[0] |
| concept | invariant — not defined in this paper's own words; a representation built only from distances and angles, unchanged by rotation - what most contemporary interatomic-potential networks use, and the l = 0 setting of this one Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[1] |
| concept | rotation order — not defined in this paper's own words; the maximum tensor rank l the network's features carry; 0 makes it a conventional invariant network and 1, 2, 3 make it equivariant, which is the paper's whole experiment Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[2] |
| concept | NequIP — not defined in this paper's own words; Neural Equivariant Interatomic Potential - the E(3)-equivariant graph network this paper introduces Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[3] |
| concept | interatomic potentials — not defined in this paper's own words; a model of a system's potential energy as a function of atomic positions and species, from which forces follow as gradients Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[4] |
| concept | log-log slope — not defined in this paper's own words; the exponent of the learning curve's power law - how fast error falls as data is added; usually a property of the data set rather than of the method Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[5] |
| concept | learning curve — not defined in this paper's own words; generalization error against training-set size; competing methods normally move it up or down without tilting it Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[6] |
| concept | noise floor — not defined in this paper's own words; the numerical error of the reference calculation itself, below which a model's reported error stops measuring the model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[7] |
| concept | MD-17 — not defined in this paper's own words; the standard small-molecule benchmark for learned potentials, and - in its original version - a data set whose own energy noise the authors say is too high to compare methods on Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[8] |
| concept | DeepMD — not defined in this paper's own words; the neural network potential compared against on water and ice, trained on 133,500 structures against NequIP's 133 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[9] |
| concept | DimeNet — not defined in this paper's own words; an invariant network that adds three-body angular terms, whose features remain scalars - the closest prior art and the clearest contrast Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[10] |
| concept | diffusivity — not defined in this paper's own words; the kinetic property the simulations are validated on, from the slope of the mean square displacement - 1.25e-5 against 1.37e-5 cm2/s from ab-initio MD Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[11] |
| MAE | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| RMSE | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
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.
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