# Multi-Excitation Projective Simulation with a Many-Body Physics Inspired Inductive Bias

arXiv: https://arxiv.org/abs/2402.10192 · HTML: https://mlsanity.com/paper/2402.10192/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 97 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 28 of 28)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Attention Mechanisms in Computer Vision: A Survey](https://mlsanity.com/paper/2111.07624/) (2021)
- [A Survey of Imitation Learning: Algorithms, Recent Developments, and Challenges](https://mlsanity.com/paper/2309.02473/) (2023)
- [Causal Machine Learning: A Survey and Open Problems](https://mlsanity.com/paper/2206.15475/) (2022)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [A Comprehensive Taxonomy for Explainable Artificial Intelligence: A Systematic Survey of Surveys on Methods and Concepts](https://mlsanity.com/paper/2105.07190/) (2021)
- [Connecting the Dots in Trustworthy Artificial Intelligence: From AI Principles, Ethics, and Key Requirements to Responsible AI Systems and Regulation](https://mlsanity.com/paper/2305.02231/) (2023)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [A Survey on Contextual Multi-armed Bandits](https://mlsanity.com/paper/1508.03326/) (2015)
- [A Review of Adversarial Attack and Defense for Classification Methods](https://mlsanity.com/paper/2111.09961/) (2021)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [A Review of Modularization Techniques in Artificial Neural Networks](https://mlsanity.com/paper/1904.12770/) (2019)
- [Medical Deep Learning -- A systematic Meta-Review](https://mlsanity.com/paper/2010.14881/) (2020)
- [Projective simulation for classical learning agents: a comprehensive investigation](https://mlsanity.com/paper/1305.1578/) (2013)
- [Visual Analytics for Temporal Hypergraph Model Exploration](https://mlsanity.com/paper/2008.07299/) (2020)
- [Neurosymbolic AI and its Taxonomy: a survey](https://mlsanity.com/paper/2305.08876/) (2023)
- [Towards a Survey on Static and Dynamic Hypergraph Visualizations](https://mlsanity.com/paper/2107.13936/) (2021)
- [Optimal foraging strategies can be learned](https://mlsanity.com/paper/2303.06050/) (2023)
- [Towards interpretable quantum machine learning via single-photon quantum walks](https://mlsanity.com/paper/2301.13669/) (2023)
- [On the convergence of projective-simulation-based reinforcement learning in Markov decision processes](https://mlsanity.com/paper/1910.11914/) (2019)
- [Collective defense of honeybee colonies: experimental results and theoretical modeling](https://mlsanity.com/paper/2010.07326/) (2020)
- [Modularity in Deep Learning: A Survey](https://mlsanity.com/paper/2310.01154/) (2023)
- [Benchmarking projective simulation in navigation problems](https://mlsanity.com/paper/1804.08607/) (2018)

## Built on by (most cited first, 2 of 2)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Free Energy Projective Simulation (FEPS): Active inference with interpretability](https://mlsanity.com/paper/2411.14991/) (2024)

## Abstract (arXiv)

With the impressive progress of deep learning, applications relying on machine learning are increasingly being integrated into daily life. However, most deep learning models have an opaque, oracle-like nature making it difficult to interpret and understand their decisions. This problem led to the development of the field known as eXplainable Artificial Intelligence (XAI). One method in this field known as Projective Simulation (PS) models a chain-of-thought as a random walk of a particle on a graph with vertices that have concepts attached to them. While this description has various benefits, including the possibility of quantization, it cannot be naturally used to model thoughts that combine several concepts simultaneously. To overcome this limitation, we introduce Multi-Excitation Projective Simulation (mePS), a generalization that considers a chain-of-thought to be a random walk of several particles on a hypergraph. A definition for a dynamic hypergraph is put forward to describe the agent's training history along with applications to AI and hypergraph visualization. An inductive bias inspired by the remarkably successful few-body interaction models used in quantum many-body physics is formalized for our classical mePS framework and employed to tackle the exponential complexity associated with naive implementations of hypergraphs. We prove that our inductive bias reduces the complexity from exponential to polynomial, with the exponent representing the cutoff on how many particles can interact. We numerically apply our method to two toy environments and a more complex scenario modelling the diagnosis of a broken computer. These environments demonstrate the resource savings provided by an appropriate choice of inductive bias, as well as showcasing aspects of interpretability. A quantum model for mePS is also briefly outlined and some future directions for it are discussed.