Neuronal decision-making with realistic spiking models

The neuronal processes underlying perceptual decision-making have been the focus of numerous studies over the past two decades. In the current standard model [1][2][3] the output of noisy sensory neurons is pooled and integrated by decision neurons. Once the activity of the decision neurons reaches a threshold, the corresponding choice is made. This bottom-up model was recently challenged based on the empirical finding that the time courses of psychophysical kernel (PK) and choice probability (CP) qualitatively differ from each other [4]. It was concluded that the decision-related activity in sensory neurons, at least in part, reflects the decision through a top-down signal, rather than contribute to the decision causally. However, the prediction of the standard bottom-up model about the relationship between the time courses of PKs and CPs crucially depends on the underlying noise model. Our study explores the impact of the time course and correlation structure of neuronal noise on PK and CP for several decision models. For the case of non-leaky integration over the entire stimulus duration, we derive analytical expressions for Gaussian additive noise with arbitrary correlation structure. For comparison, we also investigate biophysically generated responses with a Fano factor that increases with the counting window [5], and alternative decision models (leaky, integration to bound) using numerical simulations. In the case of non-leaky integration over the entire stimulus duration we find that the amplitude of the PK only depends on the overall level of noise, but not its temporal changes. Consequently the PK remains constant regardless of the temporal evolution or correlation structure in the noise. In conjunction with the observed decrease in the amplitude of the PK (e.g. [4]) this supports the conclusion that decreasing PKs are evidence for an integration to a bound model [1][3]. However, we find that the temporal evolution of the CP depends strongly on both the time course of the noise variance and the temporal correlations within the pool of sensory neurons. For instance, a noise variance that increases over time also leads to an increasing CP. The bottom-up account that appears to agree best with the data in [4] combines an increasing variance of the correlated noise (the noise that cannot be eliminated by averaging over many neurons) with an integration-to-bound decision model. This leads to a decreasing PK, as well as a CP that first increases slowly before leveling off and persisting until the end. We do not find qualitatively different results when using biophysically generated or Poisson distributed responses instead of additive Gaussian noise. In summary, we advance the analytical framework for a quantitative comparison of choice probabilities and psychophysical kernels and find that recent data that was taken to be evidence of a top-down component in choice probabilities, may alternatively be accounted for by a bottom-up model when allowing for time-varying correlated noise