### 51. Learning in the Context of Change-based Inference

R. Moazzezi^{} remo@gatsby.ucl.ac.uk
P. Dayan^{} dayan@gatsby.ucl.ac.uk
^{}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.