Recurrent Linear Threshold Network integrates Sequence Selectivity and Multiplicative Gain Modulation

Selectivity for temporal sequences is important for several visual functions and can be explained by feed-forward mechanisms that combine signals with different temporal delays in a multiplicative or AND-like fashion. Temporal sequence selectivity can also be achieved by recurrent neural networks with asymmetric lateral connections. The dynamics of such recurrent direction-selective neural networks are tractable in the spatial continuum limit. A second important visual function is gain modulation. ``Gain fields‘‘ might play an important role for the implementation of coordinate transformations in the visual cortex . Also, gain control might play a critical role for the realization of attentional modulation which is multiplicative in different cortical areas, e.g. areas V4 and MT . Again, such modulation could be accomplished by mechanisms, like shunting inhibition, that are inherent to individual neurons. Salinas and Abott have shown that, alternatively, multiplicative gain modulation can also be realized by recurrent linear threshold networks with symmetric lateral couplings, which do not contain multiplying neural elements. By quantitative simulations we show that a simple recurrent linear threshold network with asymmetric connections is highly speed-selective, and accomplishes almost perfect multiplicative gain modulation controlled by an additive biasing input. We present also an analytical solution for the nonlinear network dynamics that proves the existence of a stable stimulus-locked pulse travelling pulse solution within a limited regime of stimulus speeds which depends only weakly on the biasing input