The spectacular results achieved in machine learning, including the recent advances in generative AI, rely on large data collections. On the opposite, intelligent processes in nature arises without the need for such collections, but simply by online processing of the environmental information. In particular, natural learning processes rely on mechanisms where data representation and learning are intertwined in such a way to respect spatiotemporal locality. This paper shows that such a feature arises from a pre-algorithmic view of learning that is inspired by related studies in Theoretical Physics. We show that the algorithmic interpretation of the derived "laws of learning", which takes the structure of Hamiltonian equations, reduces to Backpropagation when the speed of propagation goes to infinity. This opens the doors to machine learning studies based on full on-line information processing that are based the replacement of Backpropagation with the proposed spatiotemporal local algorithm.

翻译：机器学习取得的惊人成果，包括生成式人工智能的最新进展，都依赖于大规模数据集合。而自然界中的智能过程却无需此类集合，仅通过在线处理环境信息即可实现。特别是，自然学习过程依赖于一种机制，其中数据表征与学习相互交织，以尊重时空局部性的方式运作。本文表明，这种特性源于受理论物理学相关研究启发的"前算法化"学习视角。我们证明，所推导出的"学习定律"（其结构呈现哈密顿方程形式）的算法解释，当传播速度趋于无穷时将退化为反向传播算法。这开启了基于全在线信息处理的机器学习研究，其核心是用所提出的时空局部算法替代反向传播算法。