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arXiv · 2409.12038

A Unified Framework for Neural Computation and Learning Over Time

Stefano Melacci·Alessandro Betti·Michele Casoni·Tommaso Guidi·Matteo Tiezzi·Marco Gori
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Abstract

This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing works focus on the simplified setting in which the stream has a known finite length or is segmented into smaller sequences, leveraging well-established learning strategies from statistical machine learning. In this paper, the problem of learning over time is rethought from scratch, leveraging tools from optimal control theory, which yield a unifying view of the temporal dynamics of neural computations and learning. Hamiltonian Learning is based on differential equations that: (i) can be integrated without the need of external software solvers; (ii) generalize the well-established notion of gradient-based learning in feed-forward and recurrent networks; (iii) open to novel perspectives. The proposed framework is showcased by experimentally proving how it can recover gradient-based learning, comparing it to out-of-the box optimizers, and describing how it is flexible enough to switch from fully-local to partially/non-local computational schemes, possibly distributed over multiple devices, and BackPropagation without storing activations. Hamiltonian Learning is easy to implement and can help researches approach in a principled and innovative manner the problem of learning over time.

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Stefano Melacci, Alessandro Betti, Michele Casoni, Tommaso Guidi, Matteo Tiezzi, Marco Gori. 2024-09-18. A Unified Framework for Neural Computation and Learning Over Time. https://arxiv.org/abs/2409.12038

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