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.

Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement with physiological experiments. Whereas the OF algorithm can be mapped onto the dynamics and synaptic plasticity in a single-layer neural network, the derived learning rule is nonlocal - the synaptic weight update depends on the activity of neurons other than just pre- and postsynaptic ones - and hence biologically implausible. Here, to overcome this problem, we derive sparse dictionary learning from a novel cost-function - a regularized error of the symmetric factorization of the input's similarity matrix. Our algorithm maps onto a neural network of the same architecture as OF but using only biologically plausible local learning rules. When trained on natural images our network learns Gabor-filter receptive fields and reproduces the correlation among synaptic weights hard-wired in the OF network. Therefore, online symmetric matrix factorization may serve as an algorithmic theory of neural computation.

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. Here we address this short coming by showing that a very general approximate inference algorithm known as Variational Bayesian Expectation Maximization can be implemented within the linear PPC framework. We apply this approach to a generic problem faced by any given layer of cortex, namely the identification of latent causes of complex mixtures of spikes. We identify a formal equivalent between this spike pattern demixing problem and topic models used for document classification, in particular Latent Dirichlet Allocation (LDA). We then construct a neural network implementation of variational inference and learning for LDA that utilizes a linear PPC. This network relies critically on two non-linear operations: divisive normalization and super-linear facilitation, both of which are ubiquitously observed in neural circuits. We also demonstrate how online learning can be achieved using a variation of Hebb’s rule and describe an extesion of this work which allows us to deal with time varying and correlated latent causes.

ABSTRACT A large number of VLSI implementationsof neural networkmodels have been reported. The diversityof these implementations is noteworthy. This paper attempts to put a group of representative VLSI implementations in perspective by comparing and contrasting them. IMPLEMENTATION Changing the way information is represented can be beneficial. For examplea change of representation can make information more compact for storage and transmission.