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。