# Autonomous particles

arXiv: https://arxiv.org/abs/2301.10077 · HTML: https://mlsanity.com/paper/2301.10077/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 11 references that are in the map.
- First posted on arXiv 24 Jan 2023.

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

- [The world as a neural network](https://mlsanity.com/paper/2008.01540/) (2020)
- [Decision-Making Technology for Autonomous Vehicles Learning-Based Methods, Applications and Future Outlook](https://mlsanity.com/paper/2107.01110/) (2021)
- [Physics Embedded Neural Network Vehicle Model and Applications in Risk-Aware Autonomous Driving Using Latent Features](https://mlsanity.com/paper/2207.07920/) (2022)
- [Emergent Quantumness in Neural Networks](https://mlsanity.com/paper/2012.05082/) (2020)
- [Towards a theory of quantum gravity from neural networks](https://mlsanity.com/paper/2111.00903/) (2021)

## Built on by (most cited first, 3 of 3)

- [Emergent field theories from neural networks](https://mlsanity.com/paper/2411.08138/) (2024)
- [Covariant Gradient Descent](https://mlsanity.com/paper/2504.05279/) (2025)
- [Molecular Learning Dynamics](https://mlsanity.com/paper/2504.10560/) (2025)

## Abstract (arXiv)

Consider a reinforcement learning problem where an agent has access to a very large amount of information about the environment, but it can only take very few actions to accomplish its task and to maximize its reward. Evidently, the main problem for the agent is to learn a map from a very high-dimensional space (which represents its environment) to a very low-dimensional space (which represents its actions). The high-to-low dimensional map implies that most of the information about the environment is irrelevant for the actions to be taken, and only a small fraction of information is relevant. In this paper we argue that the relevant information need not be learned by brute force (which is the standard approach), but can be identified from the intrinsic symmetries of the system. We analyze in details a reinforcement learning problem of autonomous driving, where the corresponding symmetry is the Galilean symmetry, and argue that the learning task can be accomplished with very few relevant parameters, or, more precisely, invariants. For a numerical demonstration, we show that the autonomous vehicles (which we call autonomous particles since they describe very primitive vehicles) need only four relevant invariants to learn how to drive very well without colliding with other particles. The simple model can be easily generalized to include different types of particles (e.g. for cars, for pedestrians, for buildings, for road signs, etc.) with different types of relevant invariants describing interactions between them. We also argue that there must exist a field theory description of the learning system where autonomous particles would be described by fermionic degrees of freedom and interactions mediated by the relevant invariants would be described by bosonic degrees of freedom.