Statistical differences between the adaptive code and the standard sparse code.

(A) Rows correspond to inference tasks: object detection (top), target localization (middle), and orientation estimation (bottom). (B) Distributions of neural responses zt,n for the standard sparse code code optimized for image reconstruction (full, red) and the adaptive code (blue); kurtosis as a measure of sparsness is displayed in inset. (C) Pairwise correlations of 10 example neurons whose activity is modulated by the task (different for each task). Correlations were computed over the entire stimulus trajectory used to generate plots in Fig 4. Upper triangle (red) of correlation matrices corresponds to the full code, bottom triangle (blue) to the adaptive code. (D) Belief-induced response variability in the adaptive code. Neural activation (grayscale proportional to |zn,t|0.5) for 32 example neurons chosen separately for each task, exposed to 1,000 presentations of the same stimulus (orange frame). Response variability at fixed stimulus originates from the fluctuations in the internal belief of the perceptual observer (top part of each panel). Here, these fluctuations are simulated as sinusoidal variations in the probability of environmental state (object detection and orientation estimation tasks; top and bottom row, respectively), or a random walk trajectory of the target for the localization task (middle row). (E) Belief-induced noise correlations in the adaptive code. Left column: correlation matrices of the same 100 neurons computed from responses to stimulus presentations displayed in (D). Right column: scaled singular values of correlation matrices of the adaptive code (blue). We compared this spectrum to the standard sparse coding in which a small amount of independent Gaussian noise is added to each neural activation. The normalized singular spectrum of noise correlations of the sparse code (red) is denser compared to that of the adaptive code.