Abstract
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.
Abstract (translated)
在神经网络中实现有效的学习需要适应个体突触以解决任务，然而，物理神经网络（无论是生物还是人工）受到时空局部性的约束。如何实现这样的网络高效信用分配，仍然是一个开放性问题。在机器学习中，答案几乎被普遍认为是误差反向传播算法，无论是空间（BP）还是时间（BPTT）。然而，BP（TT）已知依赖于不适用于生物的假设，特别是与时空非局部性有关的假设，而像实时循环学习（RTRL）这样的前馈网络则受到记忆约束的困扰。我们引入了泛化拉格朗日均衡（GLE），一种计算物理、动态神经元网络中完全局部时空间信用分配的计算框架。我们首先定义一个基于神经元局部不匹配的势能，然后通过稳态和参数下降从该势能导出神经元动力学。由此产生的动力学可以解释为在具有连续时间神经元动态和连续活动局部突触的深度皮质网络中，BPTT的生物合理近似。特别是，GLE利用了生物神经元相对于膜电位调整输出率的能力，这对于信息传播的 both 方向 都是至关重要的。对于前馈计算，它实现了将时间连续输入映射到神经元空间，并执行有效的时空间卷积。对于后馈计算，它允许时域反馈信号的时域反演，从而实现有用的参数更新所需的伴随状态近似。
URL
https://arxiv.org/abs/2403.16933
