# Exploring End-to-end Differentiable Neural Charged Particle Tracking -- A Loss Landscape Perspective

arXiv: https://arxiv.org/abs/2407.13420 · HTML: https://mlsanity.com/paper/2407.13420/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 88 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [Optimizing Rank-based Metrics with Blackbox Differentiation](https://mlsanity.com/paper/1912.03500/) (2019)
- [Linear Connectivity Reveals Generalization Strategies](https://mlsanity.com/paper/2205.12411/) (2022)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)
- [Taxonomizing local versus global structure in neural network loss landscapes](https://mlsanity.com/paper/2107.11228/) (2021)
- [Performance of a Geometric Deep Learning Pipeline for HL-LHC Particle Tracking](https://mlsanity.com/paper/2103.06995/) (2021)
- [Backpropagation through Combinatorial Algorithms: Identity with Projection Works](https://mlsanity.com/paper/2205.15213/) (2022)

## Abstract (arXiv)

Measurement and analysis of high energetic particles for scientific, medical or industrial applications is a complex procedure, requiring the design of sophisticated detector and data processing systems. The development of adaptive and differentiable software pipelines using a combination of conventional and machine learning algorithms is therefore getting ever more important to optimize and operate the system efficiently while maintaining end-to-end (E2E) differentiability. We propose for the application of charged particle tracking an E2E differentiable decision-focused learning scheme using graph neural networks with combinatorial components solving a linear assignment problem for each detector layer. We demonstrate empirically that including differentiable variations of discrete assignment operations allows for efficient network optimization, working better or on par with approaches that lack E2E differentiability. In additional studies, we dive deeper into the optimization process and provide further insights from a loss landscape perspective. We demonstrate that while both methods converge into similar performing, globally well-connected regions, they suffer under substantial predictive instability across initialization and optimization methods, which can have unpredictable consequences on the performance of downstream tasks such as image reconstruction. We also point out a dependency between the interpolation factor of the gradient estimator and the prediction stability of the model, suggesting the choice of sufficiently small values. Given the strong global connectivity of learned solutions and the excellent training performance, we argue that E2E differentiability provides, besides the general availability of gradient information, an important tool for robust particle tracking to mitigate prediction instabilities by favoring solutions that perform well on downstream tasks.