  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.
