The dynamics of vision

We study the dynamics of inhibitory balanced networks at varying (i) the level of symmetry in the synaptic connectivity; and (ii) the variance of the synaptic efficacies (synaptic gain). We find three regimes of activity. For suitably low synaptic gain, regardless of the level of symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits chaotic activity for zero or negative levels of symmetry (i.e., random or antisymmetric). Instead, for positive levels of symmetry, there is multi-stability among a large number of marginally stable fixed points. In this regime, ergodicity is broken and the network exhibits non-exponential relaxational dynamics. We discuss the potential relevance of such a “glassy” phase to explain some features of cortical activity.

The primary visual cortex (V1) processes complex mixtures of orientations to build neural representations of our visual environment. It remains unclear how V1 adapts to the highly volatile distributions of orientations found in natural images. We used naturalistic stimuli and measured the response of V1 neurons to orientation distributions of varying bandwidth. Although broad distributions decreased single neuron tuning, a neurally plausible decoder could robustly retrieve the orientations of stimuli from the population activity at all bandwidths. This decoder demonstrates that V1 population co-encodes orientation and its precision, which enhances population decoding performances. This internal representation is mediated by temporally distinct neural dynamics and supports a precision-weighted description of neuronal message passing in the visual cortex.

We present a recent model [Song et al. 2019] of color perception unifying assimilation and contrast. This model, which relies on the notion of color opponency introduced by Hering, has been tuned to reproduce some nontrivial behaviors of the color shifts observed in experiments. Next, we perform equivariant bifurcation analysis, based on the properties of Wiener-Hopf operators, of this planar model to predict visual hallucinations. Numerical bifurcation analysis on GPU are provided to assess the global stability of the predicted visual hallucinations.