Gatsby Computational Neuroscience Unit, UCL, London, UK
We have recently investigated a new way of conceptualizing the inferential capacities of non-linear recurrent networks in terms of the change in a statistic of the population activity over the time since a stimulus is presented. Evaluating change allows inferences to be fast, relatively insensitive to noise, and, in suitable cases, invariant to irrelevant dimensions of the stimulus. We proved the technique in the context of the bisection task, which is a popular psychophysical testbed for visual hyperacuity, using recurrent weights whose values were determined by hand.
One central observation was that a wide range of structurally different sets of recurrent weights supports near-optimal behaviour. This suggests that a learning algorithm could work well. Here, we show the power of using backpropagation-through-time algorithm (BPTT) to learn weight matrices to solve the task, where we evaluated the change in the location of the centre of mass (in visual space) of the network over the course of one, discrete, iteration. We directly imposed the obvious prior constraint of translation invariance.
BPTT was readily able to find many appropriate sets of recurrent weights that perform near-optimally; different initial conditions lead to different weights. This breadth demonstrates the benefits of an appropriate computational representation of the task. We are presently analyzing how the network performs this inference in a highly non-linear regime, far from equilibrium.