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arxiv: 2605.03964 · v2 · pith:OG7IS5F3new · submitted 2026-05-05 · 💻 cs.LG · physics.chem-ph

Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs

Eszter Varga-Umbrich , Shikha Surana , Paul Duckworth , Jules Tilly , Olivier Peltre , Zachary Weller-Davies This is my paper

Pith reviewed 2026-05-19 16:40 UTC · model grok-4.3

classification 💻 cs.LG physics.chem-ph
keywords active learningmachine learning interatomic potentialspretrained modelsneural tangent kernellatent spacereactive chemistryacquisition functionsMLIPs
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The pith

Pretrained MLIP latent spaces supply acquisition signals that reduce active learning data needs for reactive chemistry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether the internal representations of an already-trained machine learning interatomic potential can directly guide which new quantum calculations to run next during active learning. It extracts two kernels from a pretrained MACE model—one based on the neural tangent kernel and one built from hidden-layer activations—and uses them as acquisition functions on reactive-chemistry benchmarks. These signals select training points that reach target energy and force accuracy with substantially less labeled data than committee disagreement, fixed descriptors, or random selection. A sympathetic reader cares because each quantum label is expensive to compute, so any reliable way to cut the number of labels needed makes it practical to build accurate potentials for complex reactions that were previously out of reach.

Core claim

The central claim is that kernels taken directly from the latent space of a pretrained MACE potential—a finite-width neural tangent kernel and an activation kernel from hidden features—already encode useful acquisition information. On reactive-chemistry benchmarks both kernels outperform fixed-descriptor baselines, committee disagreement, and random acquisition, cutting the data required to reach performance targets by an average of 38 percent for energy error and 28 percent for force error. The same pretrained representations also induce similarity spaces that preserve chemically meaningful structure and give more reliable residual uncertainty estimates than randomly initialised or fixed-2D

What carries the argument

Finite-width neural tangent kernel and activation kernel extracted from the hidden latent features of a pretrained MACE potential, used as acquisition signals in active learning.

If this is right

  • Both kernels outperform fixed-descriptor baselines, committee disagreement, and random acquisition on reactive-chemistry benchmarks.
  • The kernels reduce the data needed to reach targets by an average of 38% for energy error and 28% for force error.
  • Pretrained models induce similarity spaces that preserve chemically meaningful structure.
  • Residual uncertainty estimates from the pretrained kernels are more reliable than those from randomly initialised or fixed-descriptor kernels.
  • Pretraining aligns latent-space geometry with model error, providing a practical signal for MLIP fine-tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same latent-space kernels could be extracted from other pretrained MLIP architectures without retraining, provided their internal representations encode comparable error geometry.
  • This acquisition approach may extend beyond reactive systems to any domain where a strong pretrained model already exists and new labels remain expensive.
  • Combining the kernel signals with lightweight additional heuristics might produce further data savings without reintroducing committee training overhead.

Load-bearing premise

The latent space of a pretrained MLIP already contains the information necessary for effective acquisition without auxiliary uncertainty heads, Bayesian training, fine-tuning, or committee ensembles.

What would settle it

If, on the same reactive-chemistry benchmarks, the NTK or activation-kernel acquisition requires more or equal labeled data than committee disagreement to reach identical energy and force error targets, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.03964 by Eszter Varga-Umbrich, Jules Tilly, Olivier Peltre, Paul Duckworth, Shikha Surana, Zachary Weller-Davies.

Figure 1
Figure 1. Figure 1: Force RMSE (meV Å−1 ) under the natural T1x setting. Each acquisition step adds five structures. The table reports metrics averaged across the natural T1x pools; lower is better for all columns. Among the methods compared here, model-dependent kernels are the strongest acquisition signals: NTK-PV gives the best force AUC and final force error, while Activation-PV gives the best energy AUC. resolution does … view at source ↗
Figure 2
Figure 2. Figure 2: Global kernel matrices on a five-reaction T1x subset. Structures are sorted by reaction family and frame index. The pretrained NTK preserves coarse reaction-family structure while retaining finer variation along reaction paths. Appendix C gives the full global and within-reaction kernel diagnostics for NTK, activations, SOAP, and Tanimoto kernels. 0.0 0.2 0.4 0.6 0.8 1.0 Nominal Coverage 0.0 0.2 0.4 0.6 0.… view at source ↗
Figure 3
Figure 3. Figure 3: Nominal versus empirical coverage, for the selected kernels. Pretrained activation and pretrained NTK show the best calibration among the compared kernels, while random neural kernels and descriptor kernels are less accurate and less well cali￾brated. pretrained NTK gives the lowest expected calibration er￾ror (ECE). Randomly initialised neural kernels are weaker than their pretrained counterparts, and des… view at source ↗
Figure 4
Figure 4. Figure 4: shows the energy and force learning curves for these committee variants on the three T1x candidate pools. The main failure mode is an unstable energy–force trade-off. Energy committees can improve final energy error, but their acquisition scores are not well aligned with force improvement and they give weaker force learning curves than random acquisition. Force committees select structures that are more us… view at source ↗
Figure 4
Figure 4. Figure 4: shows the energy and force learning curves for these committee variants on the three T1x candidate pools. The main failure mode is an unstable energy–force trade-off. Energy committees can improve final energy error, but their acquisition scores are not well aligned with force improvement and they give weaker force learning curves than random acquisition. Force committees select structures that are more us… view at source ↗
Figure 5
Figure 5. Figure 5: Spearman correlation between committee standard deviation and absolute prediction error across active-learning rounds. The weak correlations show that committee disagreement is not a consistently calibrated ranking signal. 15 view at source ↗
Figure 5
Figure 5. Figure 5: Spearman correlation between committee standard deviation and absolute prediction error across active-learning rounds. The weak correlations show that committee disagreement is not a consistently calibrated ranking signal. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Force and energy learning curves across the T1x sets when training from scratch showing similar results to the pretrained case view at source ↗
Figure 6
Figure 6. Figure 6: Force and energy learning curves across the T1x sets when training from scratch showing similar results to the pretrained case [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Global NTK kernel matrices on the T1x subset, with structures ordered by reaction family. The panels compare the random￾initialised MACE NTK with NTK kernels computed after selected active-learning iterations. 17 view at source ↗
Figure 7
Figure 7. Figure 7: Global NTK kernel matrices on the T1x subset, with structures ordered by reaction family. The panels compare the random￾initialised MACE NTK with NTK kernels computed after selected active-learning iterations. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Within-reaction NTK frame-block kernels for the T1x subset after selected active-learning iterations. Each block orders structures by frame index along a reaction pathway. 18 view at source ↗
Figure 8
Figure 8. Figure 8: Within-reaction NTK frame-block kernels for the T1x subset after selected active-learning iterations. Each block orders structures by frame index along a reaction pathway. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Global NTK kernel matrices on the T1x subset, with structures ordered by reaction family. The panels show how an untrained NTK evolves with AL iteration. 19 view at source ↗
Figure 9
Figure 9. Figure 9: Global NTK kernel matrices on the T1x subset, with structures ordered by reaction family. The panels show how an untrained NTK evolves with AL iteration. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Within-reaction scratch NTK frame-block kernels for the T1x subset after selected active-learning iterations. Each block orders structures by frame index along a reaction pathway. 20 view at source ↗
Figure 10
Figure 10. Figure 10: Within-reaction scratch NTK frame-block kernels for the T1x subset after selected active-learning iterations. Each block orders structures by frame index along a reaction pathway. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Global activation-kernel matrices on the T1x subset, with structures ordered by reaction family. The panels compare random￾initialized and active-learning iteration checkpoints using pooled scalar MACE activations. 21 view at source ↗
Figure 11
Figure 11. Figure 11: Global activation-kernel matrices on the T1x subset, with structures ordered by reaction family. The panels compare random￾initialized and active-learning iteration checkpoints using pooled scalar MACE activations. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Within-reaction activation frame-block kernels for the T1x subset after selected active-learning iterations. 22 view at source ↗
Figure 12
Figure 12. Figure 12: Within-reaction activation frame-block kernels for the T1x subset after selected active-learning iterations. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Global srctach activation kernel matrices on the T1x subset, with structures ordered by reaction family. The panels show how an untrained activation kernel evolves with AL iteration. 23 view at source ↗
Figure 13
Figure 13. Figure 13: Global srctach activation kernel matrices on the T1x subset, with structures ordered by reaction family. The panels show how an untrained activation kernel evolves with AL iteration. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Within-reaction scratch activation frame-block kernels for the T1x subset after selected active-learning iterations. 24 view at source ↗
Figure 14
Figure 14. Figure 14: Within-reaction scratch activation frame-block kernels for the T1x subset after selected active-learning iterations. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: SOAP kernel diagnostics on the T1x subset. SOAP captures coarse reaction-family structure using fixed local-geometry descriptors, but many within-reaction similarities remain high. rxn00722 rxn02072 rxn05576 rxn06328 rxn06359 rxn00722 rxn02072 rxn05576 rxn06328 rxn06359 0.2 0.4 0.6 0.8 1.0 Kernel value (a) Tanimoto global kernel 1 2 3 4 5 6 7 8 10 1 2 3 4 5 6 7 8 10 Frame rxn00722 1 2 3 4 5 6 7 8 9 1 2 3 … view at source ↗
Figure 15
Figure 15. Figure 15: SOAP kernel diagnostics on the T1x subset. SOAP captures coarse reaction-family structure using fixed local-geometry descriptors, but many within-reaction similarities remain high. rxn00722 rxn02072 rxn05576 rxn06328 rxn06359 rxn00722 rxn02072 rxn05576 rxn06328 rxn06359 0.2 0.4 0.6 0.8 1.0 Kernel value (a) Tanimoto global kernel 1 2 3 4 5 6 7 8 10 1 2 3 4 5 6 7 8 10 Frame rxn00722 1 2 3 4 5 6 7 8 9 1 2 3 … view at source ↗
Figure 16
Figure 16. Figure 16: Tanimoto kernel diagnostics on the T1x subset. Morgan fingerprints mainly reflect molecular graph identity and are less sensitive to continuous geometry changes along a fixed reaction path and are not able to capture inter reaction similarities. 25 view at source ↗
Figure 16
Figure 16. Figure 16: Tanimoto kernel diagnostics on the T1x subset. Morgan fingerprints mainly reflect molecular graph identity and are less sensitive to continuous geometry changes along a fixed reaction path and are not able to capture inter reaction similarities. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show force RMSE across active-learning rounds. 0 2 4 6 8 10 12 14 16 18 20 50 PMechDB 0 2 4 6 8 10 12 14 16 18 20 100 150 RGD 0 2 4 6 8 10 12 14 16 18 20 20 50 100 T1X Mixed AL Round Force MAE (meV/A) Random Activation LCMD Committee Energy NTK LCMD view at source ↗
Figure 17
Figure 17. Figure 17: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show force RMSE across active-learning rounds. 0 2 4 6 8 10 12 14 16 18 20 50 PMechDB 0 2 4 6 8 10 12 14 16 18 20 100 150 RGD 0 2 4 6 8 10 12 14 16 18 20 20 50 100 T1X Mixed AL Round Force MAE (meV/A) Random Activation LCMD Committee Energy NTK LCMD [PITH_FULL_IMAGE:figures/full_fig_p028_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show force MAE across active-learning rounds. 27 view at source ↗
Figure 18
Figure 18. Figure 18: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show force MAE across active-learning rounds. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show energy RMSE across active-learning rounds. 0 2 4 6 8 10 12 14 16 18 20 15 20 30 PMechDB 0 2 4 6 8 10 12 14 16 18 20 10 15 20 RGD 0 2 4 6 8 10 12 14 16 18 20 2 5 10 20 T1X Mixed AL Round Energy MAE/atom (meV) Random Activation LCMD Committee Energy NTK LCMD view at source ↗
Figure 19
Figure 19. Figure 19: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show energy RMSE across active-learning rounds. 0 2 4 6 8 10 12 14 16 18 20 15 20 30 PMechDB 0 2 4 6 8 10 12 14 16 18 20 10 15 20 RGD 0 2 4 6 8 10 12 14 16 18 20 2 5 10 20 T1X Mixed AL Round Energy MAE/atom (meV) Random Activation LCMD Committee Energy NTK LCMD [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show energy MAE across active-learning rounds. 28 view at source ↗
Figure 20
Figure 20. Figure 20: Additional transferability results on PMechDB, RGD, and T1x Mixed. The curves show energy MAE across active-learning rounds. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
read the original abstract

Training machine learning interatomic potentials (MLIPs) for reactive chemistry is often bottlenecked by the high cost of quantum chemical labels and the scarcity of transition state configurations in candidate pools. Active learning (AL) can mitigate these costs, but its effectiveness hinges on the acquisition rule. We investigate whether the latent space of a pretrained MLIP already contains the information necessary for effective acquisition, eliminating the need for auxiliary uncertainty heads, Bayesian training and fine-tuning, or committee ensembles. We introduce two acquisition signals derived directly from a pretrained MACE potential: a finite-width neural tangent kernel (NTK) and an activation kernel built from hidden latent space features. On reactive-chemistry benchmarks, both kernels consistently outperform fixed-descriptor baselines, committee disagreement, and random acquisition, reducing the data required to reach performance targets by an average of 38% for energy error and 28% for force error. We further show that the pretrained model induces similarity spaces that preserve chemically meaningful structure and provide more reliable residual uncertainty estimates than randomly initialised or fixed-descriptor-based kernels. Our results suggest that pretraining aligns latent-space geometry with model error, yielding a practical and sufficient acquisition signal for reactive MLIP fine-tuning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes deriving acquisition functions for active learning of machine-learning interatomic potentials (MLIPs) directly from the latent representations of a pretrained MACE model, without auxiliary uncertainty heads or ensembles. Two kernels are introduced: a finite-width neural tangent kernel and an activation kernel based on hidden-layer features. On reactive-chemistry benchmarks the kernels are reported to outperform fixed-descriptor baselines, committee disagreement, and random selection, reducing the data volume needed to reach target energy and force errors by average factors of 38 % and 28 %, respectively. The work further claims that the pretrained latent geometry preserves chemically meaningful structure and yields more reliable residual uncertainty estimates than randomly initialized or descriptor-based kernels.

Significance. If the empirical reductions are robust, the result would be practically useful for reactive-chemistry MLIP development by removing the need for Bayesian fine-tuning or committee training during acquisition. The demonstration that a pretrained model’s latent space already aligns with model error supplies a concrete, low-overhead acquisition signal and could influence how pretraining is leveraged in other scientific machine-learning pipelines.

major comments (3)
  1. [§4] §4 (Results), paragraph on data-reduction percentages: the headline claims of 38 % and 28 % average reductions rest on an unspecified procedure for extracting “data required to reach performance targets” from discrete learning curves. Please state whether linear interpolation, log-linear interpolation, or threshold crossing is used, report the exact target error values chosen for each benchmark, and supply the raw per-method data points or a supplementary table so that the percentages can be reproduced.
  2. [§4] §4 and §5 (Experimental protocol): the reported averages appear to derive from single active-learning trajectories per method. Please clarify whether multiple independent runs with different random seeds were performed, and if so, report standard deviations or confidence intervals on the data-reduction figures; otherwise demonstrate that the ordering of methods is stable across at least three seeds.
  3. [§3.2] §3.2 (Kernel definitions): the finite-width NTK is presented as parameter-free, yet its practical evaluation depends on the choice of width scaling and the precise layer at which the kernel is computed. Please confirm that these choices are fixed before seeing any active-learning results and are not tuned on the target benchmarks.
minor comments (2)
  1. [Figure 2] Figure 2 caption: the color scale for the similarity matrices is not labeled with numerical values; adding a color bar would improve readability.
  2. [Table 1] Table 1: the column “Data reduction (%)” should explicitly state the reference baseline against which the percentage is computed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and indicate where revisions will be made to improve reproducibility and clarity.

read point-by-point responses

  1. Referee: [§4] §4 (Results), paragraph on data-reduction percentages: the headline claims of 38 % and 28 % average reductions rest on an unspecified procedure for extracting “data required to reach performance targets” from discrete learning curves. Please state whether linear interpolation, log-linear interpolation, or threshold crossing is used, report the exact target error values chosen for each benchmark, and supply the raw per-method data points or a supplementary table so that the percentages can be reproduced.

    Authors: We agree that the extraction procedure requires explicit documentation for reproducibility. The reported reductions were obtained via linear interpolation between discrete points on the learning curves to identify the label count at which each method first reaches the performance target. We will revise the relevant paragraph in §4 to describe this interpolation method, specify the exact target error values used for each benchmark, and add a supplementary table listing the raw per-method error values at every acquisition step. revision: yes

  2. Referee: [§4] §4 and §5 (Experimental protocol): the reported averages appear to derive from single active-learning trajectories per method. Please clarify whether multiple independent runs with different random seeds were performed, and if so, report standard deviations or confidence intervals on the data-reduction figures; otherwise demonstrate that the ordering of methods is stable across at least three seeds.

    Authors: The averages derive from single active-learning trajectories per method, as repeating full trajectories is computationally expensive for the reactive-chemistry datasets. We have verified in additional checks that the relative ordering of acquisition methods remains consistent across three different random seeds for pool initialization. We will revise §5 to state this explicitly and note the observed stability of the performance ordering. revision: partial

  3. Referee: [§3.2] §3.2 (Kernel definitions): the finite-width NTK is presented as parameter-free, yet its practical evaluation depends on the choice of width scaling and the precise layer at which the kernel is computed. Please confirm that these choices are fixed before seeing any active-learning results and are not tuned on the target benchmarks.

    Authors: The width scaling follows the hidden dimension of the pretrained MACE model, and the kernel is evaluated at the final hidden layer; both choices are taken directly from the model architecture and standard finite-width NTK practice. These settings were fixed before any active-learning experiments on the target benchmarks and were not tuned afterward. We will add an explicit confirmation of this protocol in §3.2. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results on external benchmarks are self-contained

full rationale

The paper evaluates two kernels (NTK and activation kernel) extracted from a pretrained MACE model as acquisition functions for active learning of MLIPs. Performance is measured via direct comparisons against fixed-descriptor baselines, committee disagreement, and random acquisition on reactive-chemistry benchmarks, with data-reduction percentages obtained from observed learning curves. No equations, fitted parameters, or self-citations are shown that define the target quantities in terms of themselves or reduce the reported improvements to the choice of inputs by construction. The central claim rests on external benchmark validation rather than internal redefinition or ansatz smuggling, satisfying the criterion for a self-contained empirical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that pretrained latent spaces encode useful acquisition information and that the chosen benchmarks are representative. No explicit free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Pretrained MLIP latent spaces preserve chemically meaningful structure sufficient for acquisition.
    This premise is invoked to justify using the kernels without additional uncertainty modeling.
  • domain assumption The reactive-chemistry benchmarks used are representative of real-world MLIP training needs.
    Performance claims are conditioned on results from these benchmarks.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

    cs.LG 2026-05 unverdicted novelty 7.0

    Force-aware NTKs and chunked acquisition enable scalable, robust active learning for MLIPs, achieving lowest energy and force errors on OC20 and remaining competitive on other benchmarks.

  2. Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

    cs.LG 2026-05 unverdicted novelty 6.0

    Force-aware Neural Tangent Kernels combined with chunked acquisition provide scalable and distribution-robust active learning for MLIPs, outperforming baselines on OC20 and remaining competitive on other benchmarks.

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