Gabriel Béna

Gabriel Béna, Maxence Faldor, Dan F. M. Goodman et al.

Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements have extended cellular automata into continuous domains, raising the question of whether these systems retain the capacity for universal computation. In parallel, neural cellular automata have emerged as a powerful paradigm where rules are learned via gradient descent rather than manually designed. This work explores the potential of neural cellular automata to develop a continuous Universal Cellular Automaton through training by gradient descent. We introduce a cellular automaton model, objective functions and training strategies to guide neural cellular automata toward universal computation in a continuous setting. Our experiments demonstrate the successful training of fundamental computational primitives - such as matrix multiplication and transposition - culminating in the emulation of a neural network solving the MNIST digit classification task directly within the cellular automata state. These results represent a foundational step toward realizing analog general-purpose computers, with implications for understanding universal computation in continuous dynamics and advancing the automated discovery of complex cellular automata behaviors via machine learning.

Vlad C. Andrei, Alexandru P. Drăguţoiu, Gabriel Béna et al.

This paper explores the potential of conversion-based neuromorphic algorithms for highly accurate and energy-efficient single-snapshot multidimensional harmonic retrieval (MHR). By casting the MHR problem as a sparse recovery problem, we devise the currently proposed, deep-unrolling-based Structured Learned Iterative Shrinkage and Thresholding (S-LISTA) algorithm to solve it efficiently using complex-valued convolutional neural networks with complex-valued activations, which are trained using a supervised regression objective. Afterward, a novel method for converting the complex-valued convolutional layers and activations into spiking neural networks (SNNs) is developed. At the heart of this method lies the recently proposed Few Spikes (FS) conversion, which is extended by modifying the neuron model's parameters and internal dynamics to account for the inherent coupling between real and imaginary parts in complex-valued computations. Finally, the converted SNNs are mapped onto the SpiNNaker2 neuromorphic board, and a comparison in terms of estimation accuracy and power efficiency between the original CNNs deployed on an NVIDIA Jetson Xavier and the SNNs is being conducted. The measurement results show that the converted SNNs achieve almost five-fold power efficiency at moderate performance loss compared to the original CNNs.

Gabriel Béna, Dan F. M. Goodman

It has long been believed that the brain is highly modular both in terms of structure and function, although recent evidence has led some to question the extent of both types of modularity. We used artificial neural networks to test the hypothesis that structural modularity is sufficient to guarantee functional specialization, and find that in general, this doesn't necessarily hold. We then systematically tested which features of the environment and network do lead to the emergence of specialization. We used a simple toy environment, task and network, allowing us precise control, and show that in this setup, several distinct measures of specialization give qualitatively similar results. We further find that in this setup (1) specialization can only emerge in environments where features of that environment are meaningfully separable, (2) specialization preferentially emerges when the network is strongly resource-constrained, and (3) these findings are qualitatively similar across the different variations of network architectures that we tested, but that the quantitative relationships depend on the precise architecture. Finally, we show that functional specialization varies dynamically across time, and demonstrate that these dynamics depend on both the timing and bandwidth of information flow in the network. We conclude that a static notion of specialization, based on structural modularity, is likely too simple a framework for understanding intelligence in situations of real-world complexity, from biology to brain-inspired neuromorphic systems. We propose that thoroughly stress testing candidate definitions of functional modularity in simplified scenarios before extending to more complex data, network models and electrophysiological recordings is likely to be a fruitful approach.