# ASPIRE: Saddle-Point Discovery through Set Prediction and Physical Refinement

arXiv: https://arxiv.org/abs/2610.10969 · HTML: https://mlsanity.com/paper/2610.10969/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 5 of its 43 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [DAB-DETR: Dynamic Anchor Boxes are Better Queries for DETR](https://mlsanity.com/paper/2201.12329/) (2022)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames](https://mlsanity.com/paper/2302.04973/) (2023)
- [ReactionAtlas: Ab origine exploration of chemical reaction networks with machine learning](https://mlsanity.com/paper/2606.30778/) (2026)

## Abstract (arXiv)

Predicting thermally activated diffusion and defect evolution with event-driven models requires identifying atomic rearrangement mechanisms and their activation barriers. Discovering the associated saddle points is a major computational bottleneck: multiple rearrangements may originate from one metastable state, while costly local searches can fail or repeatedly converge to the same saddle. To address this challenge, we introduce ASPIRE (Atomistic Saddle-Point Inference with Refinement for Events), a framework that predicts a set of saddle candidates from a single initial atomic environment and refines them through Dimer searches on the original interatomic potential. The framework's equivariant set predictor, Ev-Quiformer, integrates (i) geometry-conditioned scalar-vector event slots for generating multiple saddle-point proposals and (ii) a decoder that maps each slot to a full atomic displacement field by combining atom, slot, and anchor-relative vectors with invariant coefficients. We also contribute two datasets: (i) BCCFE4VACAV-4000, comprising 4,000 four-vacancy body-centered cubic iron configurations and 65,450 reference events grouped by initial state for set supervision and post-refinement evaluation; and (ii) BCCFE-1TO4VAC, comprising 5,372 configurations with one to four vacancies each. Theoretically, we establish conditions for proposal equivariance. Experimentally, ASPIRE achieves 77.20% reference-event coverage on this benchmark, compared with 75.73% for a conventional Dimer baseline, while requiring approximately half as many Dimer force evaluations. In a timing evaluation on 50 configurations, ASPIRE reduces wall time per configuration from 478.8 s to 176.3 s under the stated hardware settings.