Effective learning in neuronal networks requires the adaptation of individual synapses given their relative contribution to solving a task. However, physical neuronal systems -- whether biological or artificial -- are constrained by spatio-temporal locality. How such networks can perform efficient credit assignment, remains, to a large extent, an open question. In Machine Learning, the answer is almost universally given by the error backpropagation algorithm, through both space (BP) and time (BPTT). However, BP(TT) is well-known to rely on biologically implausible assumptions, in particular with respect to spatiotemporal (non-)locality, while forward-propagation models such as real-time recurrent learning (RTRL) suffer from prohibitive memory constraints. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of BPTT in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, performing an effective spatiotemporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint states necessary for useful parameter updates.

在生物神经网络中实现高效的学习需要对个体突触进行适应性调节，然而，由于时空依赖性的限制，目前对于如何进行高效的信用赋值仍然是一个值得研究的问题。本文提出了一种称为广义潜在均衡（GLE）的计算框架，用于在具有时空连续性神经动力学的物理网络中实现完全本地的时空信用赋值，该框架利用了生物神经元可以根据其膜电位相移其输出速率的能力。

反向传播：超越空间、时间与大脑