1 research outputs found
Continual Weight Updates and Convolutional Architectures for Equilibrium Propagation
Equilibrium Propagation (EP) is a biologically inspired alternative algorithm
to backpropagation (BP) for training neural networks. It applies to RNNs fed by
a static input x that settle to a steady state, such as Hopfield networks. EP
is similar to BP in that in the second phase of training, an error signal
propagates backwards in the layers of the network, but contrary to BP, the
learning rule of EP is spatially local. Nonetheless, EP suffers from two major
limitations. On the one hand, due to its formulation in terms of real-time
dynamics, EP entails long simulation times, which limits its applicability to
practical tasks. On the other hand, the biological plausibility of EP is
limited by the fact that its learning rule is not local in time: the synapse
update is performed after the dynamics of the second phase have converged and
requires information of the first phase that is no longer available physically.
Our work addresses these two issues and aims at widening the spectrum of EP
from standard machine learning models to more bio-realistic neural networks.
First, we propose a discrete-time formulation of EP which enables to simplify
equations, speed up training and extend EP to CNNs. Our CNN model achieves the
best performance ever reported on MNIST with EP. Using the same discrete-time
formulation, we introduce Continual Equilibrium Propagation (C-EP): the weights
of the network are adjusted continually in the second phase of training using
local information in space and time. We show that in the limit of slow changes
of synaptic strengths and small nudging, C-EP is equivalent to BPTT (Theorem
1). We numerically demonstrate Theorem 1 and C-EP training on MNIST and
generalize it to the bio-realistic situation of a neural network with
asymmetric connections between neurons