---
kind: concept
slug: machine-learning-interatomic-potential
title: Machine-learning interatomic potential
summary: >-
  A neural network that predicts the energy and the forces on a set of atoms, so a simulation can use it in place of a quantum calculation. Covers local plus global attention for long-range effects, optional geometric encodings, and direct versus energy-conserving forces. Only one paper is covered so far, so no other designs are compared.
tags: [molecular-dynamics, chemistry, attention, interatomic-potential]
papers: ["2603.06567"]
related: [graph-neural-network, self-attention, positional-encoding, equivariance-constraint, euclidean-equivariant-network, molecular-representation-learning, local-global-attention]
status: draft
updated_at: 2026-11-08
---

## Overview

A machine-learning interatomic potential (MLIP) takes the atoms of a system and
returns their energy and the force on each atom. A simulation can then advance
in time using the learned model instead of a quantum calculation at every step
[arxiv:2603.06567 §1]. The hard part is range. A model where each atom sees only
neighbours inside a distance cutoff cannot carry information across long
distances in one step. Explicit long-range physics terms can fill that gap, but
they add modelling and engineering work [arxiv:2603.06567 §1].

The one paper covered here tests a different route: a global attention step over
all atoms of a system, combined with a local neighbourhood step, with an option
to make forces consistent with energy [arxiv:2603.06567 §3.1] [arxiv:2603.06567
§3.3]. Per-atom energies are reduced to one energy per system; the paper does
not state the reduction. Forces come either from a separate output head or from
the negative gradient of the energy [arxiv:2603.06567 §3.3] [arxiv:2603.06567
§3.4].

## Variants

### Local attention plus global all-to-all attention

Each block runs two attention steps. Local attention runs over each atom's fixed
stencil, which holds the atom itself and up to k neighbours, in two directions.
A smooth distance envelope fades far pairs. Global node attention packs all
atoms of one system into one sequence and applies standard multi-head
self-attention, so any two atoms can interact in one step. The local step costs
O(Nk) and the global step O(N²) per system [arxiv:2603.06567 §3.1]. Card:
[AllScAIP](/papers/2603.06567).

### Optional geometric encodings: LAE and ERoPE

Two optional encodings bias attention with geometry. LAE applies to local
attention: real spherical harmonics of the unit edge direction, expanded by
degree, modulate queries and keys before the dot product [arxiv:2603.06567 §3.2].
ERoPE applies to global attention: a bank of log-spaced sinc features of the
pair distance, mixed per head, is added to the attention logit as a bias
[arxiv:2603.06567 §3.2]. Despite the name, ERoPE does not rotate queries and
keys. The paper's own ablations show the encodings cost throughput
[arxiv:2603.06567 tab. 2], and the released code differs from the written form
of ERoPE in several ways (see Paper vs code below).

### Direct forces or energy-conserving forces

A direct model predicts forces with its own head. A conservative model takes the
negative gradient of the predicted energy, so forces and energy agree by
construction [arxiv:2603.06567 §3.3] [arxiv:2603.06567 §3.4]. The paper reports
both on OMol25. On the 102M split the direct medium model gets 0.64 meV/atom
energy and 5.24 meV/Å force, and the conservative one gets 0.67 and 5.78
[arxiv:2603.06567 tab. 4]. Conservative training is slower, because the
gradient path through the differentiable neighbour construction is not yet
optimised [arxiv:2603.06567 fig. 5].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Systems in the 10³–10⁵ atom range, long-range effects matter, plenty of data | Local plus global attention, medium or larger model | Global attention lets distant atoms interact in one step. Its cost grows with the largest system in a batch [arxiv:2603.06567 §5.1] [arxiv:2603.06567 fig. 4]. |
| Throughput is the bottleneck, for example long simulation runs | Drop LAE first | At 1000 atoms the 85M, 4M-split model runs at 1.281 ns/day with LAE and 4.327 ns/day with neighbourhood attention alone [arxiv:2603.06567 tab. 2]. |
| Small model trained on small data (35M, 4M split) | Keep both encodings | Removing both raises energy error from 1.466 to 1.756 meV/atom and force error from 9.357 to 10.213 meV/Å [arxiv:2603.06567 tab. 2]. |
| Medium model trained on 102M samples | Check energy and force separately | Removing both encodings lowers energy error (0.665 to 0.641 meV/atom) but raises force error (5.096 to 5.237 meV/Å) [arxiv:2603.06567 tab. 2]. |
| Forces must match energy by construction | Conservative forces | Accept the small accuracy and speed cost reported above [arxiv:2603.06567 tab. 4] [arxiv:2603.06567 fig. 5]. |
| Small molecules with no long-range effects, or a purely local baseline | Not covered | No purely local comparison is in the covered paper, so this page does not say how much global attention helps there. |

## Implementation sketch

The blocks and the output head, in the order the paper describes them. The
encodings are left out for clarity.

```pseudocode
# One block of a local plus global attention MLIP  [arxiv:2603.06567 §3.3]

def block(nodes, edges, system_index):
    # Each atom attends over its stencil: itself plus up to k neighbours  [§3.1]
    stencil = local_attention(nodes, edges)
    # The self slot becomes the atom's node feature  [§3.3]
    node = stencil[:, 0]
    # Feed-forward on the neighbour slots gives the edge features  [§3.3]
    edge = edge_ffn(stencil[:, 1:])
    # Every atom attends to every other atom of its own system  [§3.1]
    node = global_attention(node, system_index)
    node = node_ffn(node)
    # Put node features back in slot 0 and join the edge features  [§3.3]
    return concat(node[:, None], edge)

def energy_and_forces(atoms, conservative):
    # Run the blocks, then read a per-atom energy  [§3.3]
    nodes, edges = embed(atoms)
    for _ in range(num_blocks):
        stencil = block(nodes, edges, atoms.system_index)
        nodes, edges = stencil[:, 0], stencil[:, 1:]
    per_atom = energy_head(nodes)
    # Sum per system; the paper does not state the reduction  [§3.3]
    energy = scatter_sum(per_atom, by=atoms.system_index)
    if conservative:
        # Forces are the negative gradient of energy  [§3.4]
        return energy, -grad(energy.sum(), atoms.positions)
    # Otherwise a separate head predicts forces  [§3.3]
    return energy, force_head(nodes)
```

## Contradictions

- **Encodings and scale.** The paper's text says the benefit of LAE and ERoPE
  shrinks as data and model size grow [arxiv:2603.06567 §4]. The ablation is
  mixed. At 35M on 102M samples, removing both raises energy error from 0.849
  to 0.971 meV/atom [arxiv:2603.06567 tab. 2]. At 85M on 102M samples, removing
  both lowers energy error [arxiv:2603.06567 tab. 2]. Both sides are cited;
  this page does not resolve them.
- **Distance-scaling claim.** The paper says its model has about 90% lower error
  than the second-best model on the distance-scaling test [arxiv:2603.06567
  §5.3]. The table entries behind that test give a smaller reduction, and the
  90% figure matches a different row [arxiv:2603.06567 tab. 5]. Read the table
  before quoting the claim.
- **Accuracy claims.** The paper says the direct medium model has the best
  overall energy and is competitive on force [arxiv:2603.06567 §5.3]. On the
  same split, the eSEN model has a lower total force error, 4.76 against 5.24
  meV/Å [arxiv:2603.06567 tab. 4]. On SPICE, the paper says its model is lowest
  across splits [arxiv:2603.06567 app. C], but eSEN has lower force error on the
  solvated amino-acid split [arxiv:2603.06567 tab. 9].
- **Epoch count.** The 102M run is 12 epochs in one figure caption and 10 in the
  text and in the ablation caption [arxiv:2603.06567 fig. 5] [arxiv:2603.06567
  §5.3] [arxiv:2603.06567 tab. 2].

## Pitfalls

- **Precision.** The paper says training runs in full fp32 [arxiv:2603.06567
  §5.3]. The released training config enables TF32, so results may differ
  slightly from the paper's numbers.
- **Batch-dependent ERoPE.** The released code's normalisation of the ERoPE bias
  runs over all valid pairs in a padded batch, not per system. One system's
  logits can then change with the other systems in its batch. The paper does not
  describe this [arxiv:2603.06567 §3.2].
- **Unstated settings.** The paper leaves out the ERoPE frequency range, the LAE
  repetition counts and the neighbour count k. Values from the released config
  are defaults, not paper values [arxiv:2603.06567 §3.2].
- **Quadratic global cost.** Plan batches around the largest system, because
  global attention cost follows the largest system, not the total atom count
  [arxiv:2603.06567 §5.1] [arxiv:2603.06567 fig. 4].

## Paper vs code

- **ERoPE form.** The paper gives a linear mix of sinc features added to the
  logit [arxiv:2603.06567 §3.2]. The released code applies softplus, masking and
  a batch-wide normalisation, then a log before adding the bias.
- **LAE in both passes.** The paper describes LAE on local attention in general
  [arxiv:2603.06567 §3.2]. The released code applies it to both the source and
  destination passes.
- **Headline model.** The released medium config turns LAE and ERoPE off. Its
  numbers match the no-encoding row of the ablation [arxiv:2603.06567 tab. 2]
  [arxiv:2603.06567 tab. 4]. This match is inferred from the numbers, not
  stated by the paper.

## Papers

- [AllScAIP](/papers/2603.06567): local plus global all-to-all attention, optional
  LAE and ERoPE encodings, energy-conserving forces, and OMol25 results.