Backpropagation through space, time, and the brain

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.

Order from chaos: Interplay of development and learning in recurrent networks of structured neurons

Behavior can be described as a temporal sequence of actions driven by neural activity. To learn complex sequential patterns in neural networks, memories of past activities need to persist on significantly longer timescales than relaxation times of single-neuron activity. While recurrent networks can produce such long transients, training these networks in a biologically plausible way is challenging. One approach has been reservoir computing, where only weights from a recurrent network to a readout are learned. Other models achieve learning of recurrent synaptic weights using propagated errors. However, their biological plausibility typically suffers from issues with locality, resource allocation or parameter scales and tuning. We suggest that many of these issues can be alleviated by considering dendritic information storage and computation. By applying a fully local, always-on plasticity rule we are able to learn complex sequences in a recurrent network comprised of two populations. Importantly, our model is resource-efficient, enabling the learning of complex sequences using only a small number of neurons. We demonstrate these features in a mock-up of birdsong learning, in which our networks first learn a long, non-Markovian sequence that they can then reproduce robustly despite external disturbances.