A Unified Framework for Neural Computation and Learning Over Time
<|reference_start|>A Unified Framework for Neural Computation and Learning Over Time: 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.<|reference_end|>
@article{melacci2024a,
    title={A Unified Framework for Neural Computation and Learning Over Time},
    author={Stefano Melacci, Alessandro Betti, Michele Casoni, Tommaso Guidi,
  Matteo Tiezzi, Marco Gori},
    journal={arXiv preprint arXiv:2409.12038},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12038},
    primaryClass={cs.LG cs.AI}
}