Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive biases. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems, as well as a number of physics-based evaluations (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.
Figures & tables
Figure 1: AllScAIP model design. The simple backbone design enables efficient scaling.
Figure 2: Illustration of the attention operations used in AllScAIP. (a) Neighbor attention. (b) Node attention.
Figure 3: Illustration of the geometric encoding used in AllScAIP. (a) Legendre Angular Encoding (LAE) (b) Euclidean rotary position encoding.
OMol 4M (80 Epochs)
Ablations
Biomol.
Elytes.
Metal Cplx.
Neutral Org.
Total
Size
Thrpt
NeiAtt
LAE
NodeAtt
ERoPE
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
35M
2.279
✓
✓
✓
✓
0.39
5.58
1.27
8.92
2.85
33.53
1.9
13.52
1.47
9.36
7.623
✓
✓
0.5
6.32
1.52
9.81
2.96
34.56
2.22
14.51
1.76
10.21
85M
1.124
✓
✓
✓
✓
0.23
3.51
1.05
6.38
2.45
27.84
1.2
8.93
1.16
6.89
3.333
✓
✓
✓
0.29
4.28
1.17
7.21
2.67
29.79
1.53
10.53
1.22
7.6
Table 2: Component ablations under data and model size scaling . We report Energy / Atom MAE (meV) and Force MAE (meV/Å), lower is better. Each size’s with encoding (Nei Att + LAE + Node Att + ERoPE) configuration is the reference; other rows are colorized relative to that reference ( Green = better , Red = worse ). The Throughput column reports inference speed (ns/day on one H200 with 1000 atoms). We report results for the OMol25 4M split (80 epochs) and the full 102M (10 epochs) 2 2 2 We note that there has been an identified bug in the FAIRChem codebase that made the per atom MAE metric appear to be consistently worse for both AllScAIP and all baselines. We have attached the unnormalized total energy MAE in the Appendix A.4 .
PBC
non-PBC
Rand. Rotation
NVE MD Energy Drift
Model
Training Set
Energy Δ [meV] ↓
Energy Δ [meV] ↓
Cos. Sim. ↑
[meV / atom / ps] ↓
UMA-M-1p1
UMA-459M
2.41×10−2
3.83×10−3
0.9999
1.5×10−3
AllScAIP-md
NA (Random Init)
3.62×10−2
2.49×10−3
0.6827
-
AllScAIP-md
OMol-102M
4.18×10−2
4.73×10−3
0.9999
4.3×10−3
Table 3: Symmetry and Conservation Checks. Extensivity errors for periodic (PBC) and non-periodic (non-PBC) systems, (lower is better), rotational equivariance via force cosine similarity under random rotations (higher is better), and NVE molecular dynamic simulation energy drift on MD22 large molecules (lower is better).
Figure 4: Throughput and Memory vs. System size. Left: Atom-time (number of atoms × ns/day, higher is better) vs. system size. The result is measured on a single H200 141G with graph generation off. We report four model sizes (35M/85M/180M/1B) of AllScAIP, and eSEN baselines. The dotted vertical lines indicate approximately when the O(N2) of the node attention dominates over the O(Nk) of the neighborhood attention, where k is the max number of neighbors. Right: vram usage vs. system size. Dotted horizontal lines indicate the vram size for common GPUs.
Biomol.
Elytes.
Metal Cplx.
Neutral Org.
Total
Dataset
Model
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
All
eSEN-sm-d.
0.67
6.30
1.24
9.41
2.53
33.08
1.23
13.84
1.49
9.92
eSEN-sm-cons.
0.59
4.61
1.01
8.08
2.30
28.86
0.84
11.11
1.27
8.25
eSEN-md-d.
0.34
2.61
0.69
4.40
1.73
19.99
0.59
5.63
0.84
4.76
GemNet-OC
0.15
3.88
0.56
5.98
1.83
25.12
0.86
10.38
0.66
6.52
AllScAIP-sm-ft-cons.
0.22
3.84
0.75
6.01
2.09
26.02
1.00
8.55
0.85
6.61
Table 4: OMol25 validation results. Energy / Atom MAE (meV) and Force MAE (meV/Å) across Biomolecules, Electrolytes, Metal Complexes, and Neutral Organics. AllScAIP variants achieve the lowest overall energy error on both splits, with competitive force errors.
Figure 5: OMol25 energy error vs. efficiency throughput (inference). Energy / Atom MAE (meV, ↓ ) vs. throughput (ns/day, ↑ ) for 35M/85M models with/without encodings; compared with eSEN ( Fu et al., 2025 ) baselines. Conservative models are labeled with a hollow marker. Left: Models trained on OMol25 4M (80 epochs). Right: OMol25 102M (12 epochs). Our models trace the Pareto front at 4M; at 102M the gap between with/without encodings shrinks or flips, indicating these inductive bias may be unnecessary at scale. The larger speed gap between the direct force and conservative AllScAIP models, compared to eSEN, occurs because the differentiable kNN graph construction used in AllScAIP is a newly introduced operation that has not yet been optimized ( Liu et al., 2026 ) .
Energy
Avg.
Ligand pocket
Ligand strain
Conformers
Protonation
Dist. scaling
IE/EA
Spin gap
Model
Cons.
Training Set
Rank
Ixn Energy ↓
Strain Energy ↓
Δ Energy ↓
Δ Energy ↓
Δ Energy ↓
Δ Energy ↓
Δ Energy ↓
AllScAIP-md-d.
OMol-102M
3.43
29.496
4.149
4.985
16.104
10.082
143.035
350.825
AllScAIP-md-cons.
✓
OMol-102M
4.14
50.532
4.103
3.874
17.092
36.145
148.976
317.400
eSEN-md-d.
OMol-102M
4.14
64.246
3.113
3.566
14.988
109.767
145.776
303.883
UMA-M-1p1
✓
UMA-459M
4.86
76.778
2.962
2.532
18.457
138.094
136.386
335.058
UMA-S-1p2
✓
UMA-520M
5.00
66.604
4.365
3.738
18.914
32.174
176.939
246.565
Table 5: Evaluation results across OMol25 test evaluations. Results are reported in energy MAE error [meV] (lower is better). Models are sorted by the average ranking of individual categories, with a lower average ranking indicating better overall performance.
Figure 6: OMol25 distance-scaling evaluation. A group of molecules are uniformly compressed and stretched by a scalar "stretch factor" to probe the long-range ability (x-axis; <1 : compressed, >1 : stretched) and report energy absolute error per atom (meV; ↓ ). AllScAIP-md-cons. stays flat and low across the full range, while eSEN and UMA md-1p1 degrade sharply under stretching, indicating poor long-range capacities. Insets show example geometries at selected factors labeled with dotted lines.
Figure 7: MD Simulations vs. Experimental Density and Enthalpy of Vaporization. NPT MD on 39 different molecular liquids and NVT MD on isolated molecules for 300 ps. Left: predicted vs. experimental densities. Right: predicted vs. experimental enthalpy of vaporization. Top: models trained on OMol25. Bottom: models trained on SPICE (note that SPICE structures, computed at a different DFT level of theory, is also a subset of OMol25). AllScAIP attains lower MAE and higher R2 than MACELES and eSEN on both properties.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 8: Runtime breakdown by component vs. system size. Stacked bars show the percentage of wall-clock inference time spent in each module of AllScAIP on a single H200 (graph construction off), for three model sizes (top: 35M, middle: 85M, bottom: 180M). Colors: Neighbor attention (blue, O(Nk) ), Neighbor FFN (magenta), Node attention (orange, O(N2) ), Node FFN (green), and Input/embeddings (red). At small systems the runtime is dominated by the local block (neighbor attention). As the number of atoms grows into the tens of thousands, the cost of the global node attention increases and eventually becomes the majority of runtime; the crossover happens earlier for larger models.
Figure 9: Throughput vs. System size. Throughput (ns/day, higher is better) is measured on a single H200 141G with graph generation off. Lines show four model sizes (35M/85M/180M/1B) of AllScAIP and eSEN baselines.
Figure 10: OMol25 Prediction Error vs. System Diameter (Å) and Total Charge. Energy / Atom MAE (meV, ↓ , top) and Force MAE (meV/Å, ↓ , bottom) binned by (left) system diameter (Å) and (right) total charge on all of OMol25 validation set. Bars compare AllScAIP-md, UMA-md, and eSEN-md. AllScAIP remains lower and more stable across bins, while eSEN and UMA error grows for large-diameter systems and for high total charge.
Figure 11: Interpreting the All-to-all Node Attention. Example protein pocket with 342 atoms in OMol Validation Set (top-left). Top-right: per-head attention weight in the last node-attention layer as a function of pairwise distance; thin lines = individual heads, thick black = head average. The red dashed line marks the local neighbor cutoff (6 Å). Bottom-left: pairwise distance matrix. Bottom-right: head-averaged attention matrix. Several heads allocate noticeable mass to pairs well beyond the local cutoff, and the attention heatmap shows column "hubs" that attract long-range attention across many rows.
OMol 4M (80 Epochs)
Ablations
Biomol.
Elytes.
Metal Cplx.
Neutral Org.
Total
Size
Thrpt
NeiAtt
LAE
NodeAtt
ERoPE
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
35M
2.279
✓
✓
✓
✓
56.9
5.58
89.3
8.92
166.2
33.53
50.3
13.52
85.2
9.36
7.623
✓
✓
73
6.32
112.3
9.81
174
34.56
58.2
14.51
102.9
10.21
85M
1.124
✓
✓
✓
✓
34.1
3.51
62.2
6.38
139.6
27.84
31.4
8.93
59.7
6.89
3.333
✓
✓
✓
43.6
4.28
70.8
7.21
153.7
29.79
40.5
10.53
68.1
7.6
Appendix
Table 6: Component ablations under data and model size scaling . We report Total Energy MAE (meV) and Force MAE (meV/Å), lower is better. Each size’s with encoding (Nei Att + LAE + Node Att + ERoPE) configuration is the reference; other rows are colorized relative to that reference ( Green = better , Red = worse ). The Throughput column reports inference speed (ns/day on one H200 with 1000 atoms). We report results for the OMol25 4M split (80 epochs) and the full 102M (10 epochs).
Biomol.
Elytes.
Metal Cplx.
Neutral Org.
Total
Dataset
Model
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
E ↓
F ↓
All
eSEN-sm-d.
96.92
6.30
88.20
9.41
145.45
33.08
34.24
13.84
89.34
9.92
eSEN-sm-cons.
86.72
4.61
72.51
8.07
132.71
28.86
22.98
11.11
75.98
8.25
eSEN-md-d.
50.72
2.61
47.37
4.39
97.55
19.99
16.47
5.62
49.21
4.76
GemNet-OC
23.35
3.88
30.73
5.98
103.10
25.12
21.22
10.38
33.85
6.52
AllScAIP-sm-ft-cons.
31.94
3.34
39.70
6.06
123.69
25.94
18.77
8.97
42.48
6.41
Appendix
Table 7: OMol25 validation results. Total Energy MAE (meV) and Force MAE (meV/Å) across Biomolecules, Electrolytes, Metal Complexes, and Neutral Organics.
OC20 (Total Energy)
OMat24
Val ID
Val OOD-Both
Val
Model
Energy
Force
F. Cos.
Energy
Force
F. Cos.
E./Atom
Forces
Stress
F. Cos.
UMA-S
63.6
24.1
0.63
107.0
29.2
0.65
11.3
57.1
2.9
0.98
UMA-M
43.1
15.8
0.73
70.0
19.2
0.75
10.0
47.3
2.7
0.99
UMA-L
32.6
12.0
0.77
49.8
14.5
0.79
9.7
43.5
2.5
0.99
eqV2-S
11
49.2
2.4
0.985
Appendix
Table 8: OC20 validation (Total Energy) and OMat24 validation results.
MACE-L
MACE-M
MACELES-M
EScAIP
eSEN
AllScAIP
Dataset
E
F
E
F
E
F
E
F
E
F
E
F
PubChem
0.88
14.75
0.91
20.57
0.71
17.24
0.53
5.86
0.15
4.21
0.13
3.21
DES370K M.
0.59
6.58
0.63
9.36
0.54
7.65
0.41
3.48
0.13
1.24
0.07
0.97
DES370K D.
0.54
6.62
0.58
9.02
0.47
7.48
0.38
2.18
0.15
2.12
0.06
0.95
Dipeptides
0.42
10.19
0.52
14.27
0.52
11.46
0.31
5.12
0.25
3.68
0.06
1.54
Solvated A.A.
0.98
19.43
1.21
23.26
0.82
18.37
0.61
11.52
0.25
3.68
0.13
4.86
Appendix
Table 9: SPICE test results. Energy / Atom MAE (meV, ↓ ) and Force MAE (meV/Å, ↓ ) across different splits of SPICE. AllScAIP achieve the lowest overall energy and force errors.
Figure 12: Zero-shot MD on MD22: radial distribution h(r) . NVT trajectories with OMol-trained AllScAIP on seven MD22 systems. Curves show h(r) from the simulations compared with PBE + MBD reference runs. Although the reference level differs from OMol, AllScAIP tracks eSEN/UMA in peak locations and overall shape, indicating matched structural statistics.
Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (Materials Representation and Interaction Simulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity O(N), enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.
Yuanchang Zhou, Siyu Hu, Xiangyu Zhang +3
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences · School of Advanced Interdisciplinary Sciences, UCAS
Equivariant machine learning interatomic potentials (MLIPs) have revolutionized atomistic modeling, but accurate treatment of complex materials and molecular systems demands expensive models. This limits simulation length- and time-scales, with tensor products a key computational bottleneck. The recent emergence of foundation-scale MLIPs further exacerbates this challenge. We present Branch Interatomic Potential (BranchIP), a single-model framework for learned adaptive tensor product computation, trained with a novel distillation loss. In our experiments on two systems of physical interest, a heterogeneous catalysis system and a proton-conducting solid acid electrolyte, BranchIP accelerates MLIPs across model sizes by up to 2.4× while reducing memory usage by up to 2.6×. This is achieved while maintaining physical fidelity. Furthermore, the learned adaptive computation provides model interpretability by revealing which interactions demand deeper computation and showing how computational depth relates to chemical complexity and dynamics.
Laura Zichi, Gil Harari, Chuin Wei Tan +6
Harvard University · Robert Bosch LLC Research and Technology Center
Accurate atomistic simulations of materials under electric fields require long-range electrostatics and electrical-response modeling at length scales beyond the reach of conventional first-principles methods. Yet these capabilities remain difficult to reconcile with the scalability of machine-learning interatomic potentials (MLIPs). Strictly local models enable efficient spatial parallelization but neglect long-range interactions, whereas existing electrostatic extensions introduce global dependencies that hinder distributed computation. Here, we overcome this limitation by analytically separating the long-range electrostatic forces and Born effective charges (BECs) into a global electrostatics calculation and strictly local derivatives of learned latent charges. This formulation preserves the spatial decomposability of equivariant MLIPs while enabling distributed evaluation of energies, forces, stresses, and BECs across different boundary conditions. Implemented as DPA4C-LR on the nvalchemi platform, the framework scales to 5.2 million atoms on four GPUs at approximately twice the computational cost of its short-range backbone. Trained on energies and forces, DPA4C-LR accurately infers BECs and reproduces the field-dependent infrared spectra of water. We further demonstrate its capabilities by recovering the characteristic slim polarization hysteresis of relaxor \ce{Pb(Mg_{1/3}Nb_{2/3})O3}, which is obscured by finite-size effects in smaller simulations; predicting a room-temperature field-driven ionic conductivity of 6.8±0.7~mS/cm in amorphous \ce{Li_{0.9}NbO_{0.9}Cl_{4.1}}; and modeling interfacial thermal transport across Si/diamond interfaces with slab-corrected electrostatics. By combining long-range physics, electrical-response inference, and distributed computation, this framework extends predictive atomistic modeling toward device-relevant length scales.
Yicheng Chen, Xiaoyun Yu, Hyejeong Song +5
Department of Materials Science and Engineering, National University of Singapore, Singapore · Department of Physics, National University of Singapore, Singapore