NeurIPS

The network topology of neurons in the brain exhibits an abundance of feedback connections, but the computational function of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power achieved through feedback in dynamical systems with fading memory. It implies that many such systems acquire through feedback universal computational capabilities for analog computing with a non-fading memory. In particular, we show that feedback enables such systems to process time-varying input streams in diverse ways according to rules that are implemented through internal states of the dynamical system. In contrast to previous attractor-based computational models for neural networks, these flexible internal states are high-dimensional attractors of the circuit dynamics, that still allow the circuit state to absorb new information from online input streams. In this way one arrives at novel models for working memory, integration of evidence, and reward expectation in cortical circuits. We show that they are applicable to circuits of conductance-based Hodgkin-Huxley (HH) neurons with high levels of noise that reflect experimental data on invivo conditions.

Experimental data show that biological synapses are dynamic, i.e., their weight changes on a short time scale by several hundred percent in dependence of the past input to the synapse. In this article we explore the consequences that this synaptic dynamics entails for the computational power of feedforward neural networks. It turns out that even with just a single hidden layer such networks can approximate a surprisingly large large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Furthermore we show that simple gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses.