The stochastic network dynamics underlying perceptual discrimination

The brain is able to interpret streams of high-dimensional ambiguous information and yield coherent percepts. The mechanisms governing sensory integration have been extensively characterized using time-varying visual stimuli (Britten et al. 1996; Roitman and Shadlen 2002), but some of the basic principles regarding the network dynamics underlying this process remain largely unknown. We captured the basic features of a neural integrator using three canonical one-dimensional models: (1) the Drift Diffusion Model (DDM), (2) the Perfect Integrator (PI) which is a particular case of the DDM where the bounds are set to infinity and (3) the double-well potential (DW) which captures the dynamics of the attractor networks (Wang 2002; Roxin and Ledberg 2008). Although these models has been widely studied (Bogacz et al. 2006; Roxin and Ledberg 2008; Gold and Shadlen 2002), it has been difficult to experimentally discriminate among them because most of the observables measured are only quantitatively different among these models (e.g. psychometric curves). Here we aim to find experimentally measurable quantities that can yield qualitatively different behaviors depending on the nature of the underlying network dynamics. We examined the categorization dynamics of these models in response to fluctuating stimuli of different duration (T). On each time step, stimuli are drawn from a Gaussian distribution N(μ, σ) and the two stimulus categories are defined by μ > 0 and μ < 0. Psychometric curves can therefore be obtained by quantifying the probability of the integrator to yield one category versus μ . We find however that varying σ can reveal more clearly the differences among the different integrators. In the small σ regime, both the DW and the DDM perform transient integration and exhibit a decaying stimulus reverse correlation kernel revealing a primacy effect (Nienborg and Cumming 2009; Wimmer et al. 2015) . In the large σ regime, the integration in the DDM becomes even more transient (i.e. the bound is reached earlier during the stimulus) but in the DW the rate of reversed classifications increases and the kernel changes from monotonically decreasing to monotonically increasing revealing a recency effect. In contrast the PI performs uniform integration and shows a constant kernel for all σ's. The discrimination sensitivity in the PI decreases monotonically as 1/σ just because the two stimulus categories become less separable in the stimulus space. In the DDM the decrease with σ is even more pronounced due to the reduction of the effective integration time (the average time to reach the bound). Unexpectedly however, the sensitivity in the DW shows a non-monotonic behavior with a local maximum for Ts beyond a critical value. This is because, provided there is enough time to reverse the initial classification, the increase in the rate of correcting reversals compensates for the decrease in stimulus separability. Finally, we also found that the three models behave differently with σ when the initial condition of the integrator is offset (e.g. representing that the prior probabilities of the two stimulus categories are uneven): increasing σ decreases the choice bias caused by the offset in the DW model, increases the bias for the DDM model and leaves it unchanged in the PI model. We propose specific ways to test these predictions in a random duration two alternative forced-choice (2AFC) task which could help us pinning down the basic principles of sensory integration dynamics.