How physical networks of neurons, bound by spatio-temporal locality constraints, 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 and time. However, this algorithm is well-known to rely on biologically implausible assumptions, in particular with respect to spatio-temporal (non-)locality. Alternative forward-propagation models such as real-time recurrent learning only partially solve the locality problem, but only at the cost of scaling, due to prohibitive storage requirements. 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 backpropagation through space and time in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the morphology of dendritic trees to enable more complex information storage and processing in single neurons, as well as 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, effectively performing a spatio-temporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint variables necessary for useful parameter updates.

翻译：神经元物理网络如何能在受时空局部性约束的条件下实现有效的信用分配，在很大程度上仍是一个未解决的问题。在机器学习领域，答案几乎总是由误差反向传播算法通过空间和时间维度给出。然而，该算法所依赖的生物学假设众所周知是难以实现的，尤其在时空（非）局部性方面。替代性的前向传播模型（如实时循环学习）仅部分解决了局部性问题，但因其巨大的存储需求导致可扩展性受限。我们提出了广义潜在平衡（GLE），这是一个用于在物理的、动态的神经元网络中实现完全局部时空信用分配的计算框架。我们首先基于神经元局部的失配定义了一个能量函数，从中通过平稳性推导出神经元动力学，并通过梯度下降推导出参数动力学。所得动力学可解释为对具有连续时间神经元动态和持续活跃的局部突触可塑性的深度皮层网络中时空反向传播的实时、生物学合理的近似。特别地，GLE利用树突形态实现了单个神经元中更复杂的信息存储与处理，以及生物神经元使其输出率相对于膜电位产生相移的能力——这一特性在信息传播的两个方向上均至关重要。对于前向计算，它能够将时间连续输入映射到神经元空间，实质上执行了时空卷积操作。对于反向计算，它允许反馈信号的时间反转，从而近似得到有效参数更新所需的伴随变量。