# Enhancing the Performance of DeepReach on High-Dimensional Systems through Optimizing Activation Functions

arXiv: https://arxiv.org/abs/2312.17583 · HTML: https://mlsanity.com/paper/2312.17583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2023.

## Built on by (most cited first, 1 of 1)

- [Convergence Guarantees for Neural Network-Based Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2410.02904/) (2024)

## Abstract (arXiv)

With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and safety for dynamical systems and is widely applicable to various tasks and challenges. Traditionally, reachability problems are solved by using grid-based methods, whose computational and memory cost scales exponentially with the dimensionality of the system. To overcome this challenge, DeepReach, a deep learning-based approach that approximately solves high-dimensional reachability problems, is proposed and has shown lots of promise. In this paper, we aim to improve the performance of DeepReach on high-dimensional systems by exploring different choices of activation functions. We first run experiments on a 3D system as a proof of concept. Then we demonstrate the effectiveness of our approach on a 9D multi-vehicle collision problem.