Neural Information Processing Systems http://nips.cc/

As a result, the brain needs to perform these computations in an approximate manner.

Sensory processing is often characterized as implementing probabilistic inference: networks of neurons compute posterior beliefs over unobserved causes given the sensory inputs. How these beliefs are computed and represented by neural responses is much-debated (Fiser et al. 2010, Pouget et al. 2013). A central debate concerns the question of whether neural responses represent samples of latent variables (Hoyer & Hyvarinnen 2003) or parameters of their distributions (Ma et al. 2006) with efforts being made to distinguish between them (Grabska-Barwinska et al. 2013). A separate debate addresses the question of whether neural responses are proportionally related to the encoded probabilities (Barlow 1969), or proportional to the logarithm of those probabilities (Jazayeri & Movshon 2006, Ma et al. 2006, Beck et al. 2012). Here, we show that these alternatives -- contrary to common assumptions -- are not mutually exclusive and that the very same system can be compatible with all of them. As a central analytical result, we show that modeling neural responses in area V1 as samples from a posterior distribution over latents in a linear Gaussian model of the image implies that those neural responses form a linear Probabilistic Population Code (PPC, Ma et al. 2006). In particular, the posterior distribution over some experimenter-defined variable like orientation is part of the exponential family with sufficient statistics that are linear in the neural sampling-based firing rates.

Recent experiments have demonstrated that humans and animals typically reason probabilistically about their environment. This ability requires a neural code that represents probability distributions and neural circuits that are capable of implementing the operations of probabilistic inference. The proposed probabilistic population coding (PPC) framework provides a statistically efficient neural representation of probability distributions that is both broadly consistent with physiological measurements and capable of implementing some of the basic operations of probabilistic inference in a biologically plausible way. However, these experiments and the corresponding neural models have largely focused on simple (tractable) probabilistic computations such as cue combination, coordinate transformations, and decision making. As a result it remains unclear how to generalize this framework to more complex probabilistic computations.

Sensory processing is often characterized as implementing probabilistic inference: networks of neurons compute posterior beliefs over unobserved causes given the sensory inputs. How these beliefs are computed and represented by neural responses is much-debated (Fiser et al. 2010, Pouget et al. 2013). A central debate concerns the question of whether neural responses represent samples of latent variables (Hoyer & Hyvarinnen 2003) or parameters of their distributions (Ma et al. 2006) with efforts being made to distinguish between them (Grabska-Barwinska et al. 2013). A separate debate addresses the question of whether neural responses are proportionally related to the encoded probabilities (Barlow 1969), or proportional to the logarithm of those probabilities (Jazayeri & Movshon 2006, Ma et al. 2006, Beck et al. 2012). Here, we show that these alternatives -- contrary to common assumptions -- are not mutually exclusive and that the very same system can be compatible with all of them.

Recent experiments have demonstrated that humans and animals typically reason probabilistically about their environment. This ability requires a neural code that represents probability distributions and neural circuits that are capable of implementing the operations of probabilistic inference. The proposed probabilistic population coding (PPC) framework provides a statistically efficient neural representation of probability distributions that is both broadly consistent with physiological measurements and capable of implementing some of the basic operations of probabilistic inference in a biologically plausible way. However, these experiments and the corresponding neural models have largely focused on simple (tractable) probabilistic computations such as cue combination, coordinate transformations, and decision making. As a result it remains unclear how to generalize this framework to more complex probabilistic computations.

Sensory processing is often characterized as implementing probabilistic inference: networks of neurons compute posterior beliefs over unobserved causes given the sensory inputs. How these beliefs are computed and represented by neural responses is much-debated (Fiser et al. 2010, Pouget et al. 2013). A central debate concerns the question of whether neural responses represent samples of latent variables (Hoyer & Hyvarinnen 2003) or parameters of their distributions (Ma et al. 2006) with efforts being made to distinguish between them (Grabska-Barwinska et al. 2013). A separate debate addresses the question of whether neural responses are proportionally related to the encoded probabilities (Barlow 1969), or proportional to the logarithm of those probabilities (Jazayeri & Movshon 2006, Ma et al. 2006, Beck et al. 2012). Here, we show that these alternatives -- contrary to common assumptions -- are not mutually exclusive and that the very same system can be compatible with all of them. As a central analytical result, we show that modeling neural responses in area V1 as samples from a posterior distribution over latents in a linear Gaussian model of the image implies that those neural responses form a linear Probabilistic Population Code (PPC, Ma et al. 2006). In particular, the posterior distribution over some experimenter-defined variable like "orientation" is part of the exponential family with sufficient statistics that are linear in the neural sampling-based firing rates.

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. In this paper we present a method for learning to approximate a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of probabilistic population codes to compute Bayes' rule, and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem, and show how the hidden layer of the neural network develops tuning curves which are consistent with findings in experimental neuroscience.