# Fast and Precise Learned Charged-Particle Trajectory Regression at the Large Hadron Collider

arXiv: https://arxiv.org/abs/2609.32479 · HTML: https://mlsanity.com/paper/2609.32479/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [A Bayesian Perspective on Generalization and Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06451/) (2017)
- [On the Generalization Benefit of Noise in Stochastic Gradient Descent](https://mlsanity.com/paper/2006.15081/) (2020)
- [Were RNNs All We Needed?](https://mlsanity.com/paper/2410.01201/) (2024)
- [ColliderML: The First Release of an OpenDataDetector High-Luminosity Physics Benchmark Dataset](https://mlsanity.com/paper/2512.15230/) (2025)

## Abstract (arXiv)

We propose a training recipe that treats charged-particle trajectory parameter regression on high-energy physics detector data as a sequence-modeling task. Kalman filters and linearized least-squares fits have been the classical standard approach for this task: they are optimal estimators for sparsely sampled linear-Gaussian data and are commonly used for trajectory parameter regression (fitting). The classical fitting techniques implemented for this domain reach a final precision of one part in 105 through detailed modeling of detector geometry, material, detection effects and precise numerical integration of the equations of motion through the detector's inhomogeneous magnetic field. With this study, we demonstrate that using a bidirectional gated linear recurrent encoder, one is able to reproduce the full precision of classical track fitting techniques. Using a custom kernel, we also achieve significantly higher throughput during GPU inference, compared to classical fitting software running on similarly priced multi-core CPU servers representing typically employed hardware. Such a speedup would lead to considerable cost savings for the pattern recognition at the Large Hadron Collider. To our knowledge, this is the first end-to-end learned track fit to reach the full precision and, at the same time, offer the opportunity to reduce the computing costs.