Figure 1.

Model for neural responses and decoding: (a) tuning curves f(s) showing the mean neural responses to a stimulus s (thin lines), curve from the von Mises functions (thick curves) model with parameters including the preferred stimulus s_k (dots). (b) The relationship of two neurons generalizing to high-dimensional response spaces under varying stimulus s. (c) Linear decoding projects the neural responses, both noise and signal, towards a specific direction w for the estimation of ŝ of the stimulus. (d) The phenomenon of showing neurons having similar tuning has higher correlated fluctuations. Noise correlation coefficients R_ij between distinct neurons i and j are modeled as being proportional on average to the signal correlations Rijsig, with proportionality c₀. (e) Two components to the noise covariance Σ: information-limiting correlations are distinguished; present along the signal direction f′ and therefore show covariance εf′f′^T (front, matrix boxed in red), and the remaining noise with covariance Σ₀ (back, the matrix in the green box). The two types of noise show distinctive structures; apparent in the covariance matrices. The striations in the matrices correspond to the heterogeneous tuning curve amplitudes. Reprinted with permission from the authors of [50].