A Measure of Information Available for Inference

Active inference leads to Bayesian neurophysiology

The neuronal substrates that implement the free-energy principle and ensuing active inference at the neuron and synapse level have not been fully elucidated. This Review considers possible neuronal substrates underlying the principle. First, the foundations of the free-energy principle are introduced, and then its ability to empirically explain various brain functions and psychological and biological phenomena in terms of Bayesian inference is described. Mathematically, the dynamics of neural activity and plasticity that minimise a cost function can be cast as performing Bayesian inference that minimises variational free energy. This equivalence licenses the adoption of the free-energy principle as a universal characterisation of neural networks. Further, the neural network structure itself represents a generative model under which an agent operates. A virtue of this perspective is that it enables the formal association of neural network properties with prior beliefs that regulate inference and learning. The possible neuronal substrates that implement prior beliefs and how to empirically examine the theory are discussed. This perspective renders brain activity explainable, leading to a deeper understanding of the neuronal mechanisms underlying basic psychology and psychiatric disorders in terms of an implicit generative model.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.

Reverse-Engineering Neural Networks to Characterize Their Cost Functions

This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimized by both neural activity and plasticity. We show that such cost functions can be cast as a variational bound on model evidence under an implicit generative model. Using generative models based on partially observed Markov decision processes (POMDP), we show that neural activity and plasticity perform Bayesian inference and learning, respectively, by maximizing model evidence. Using mathematical and numerical analyses, we establish the formal equivalence between neural network cost functions and variational free energy under some prior beliefs about latent states that generate inputs. These prior beliefs are determined by particular constants (e.g., thresholds) that define the cost function. This means that the Bayes optimal encoding of latent or hidden states is achieved when the network's implicit priors match the process that generates its inputs. This equivalence is potentially important because it suggests that any hyperparameter of a neural network can itself be optimized-by minimization with respect to variational free energy. Furthermore, it enables one to characterize a neural network formally, in terms of its prior beliefs.

Information Theory in Neuroscience

This is the Editorial article summarizing the scope and contents of the Special Issue, Information Theory in Neuroscience.

A Comparison of Regularization Techniques in Deep Neural Networks

Artificial neural networks (ANN) have attracted significant attention from researchers because many complex problems can be solved by training them. If enough data are provided during the training process, ANNs are capable of achieving good performance results. However, if training data are not enough, the predefined neural network model suffers from overfitting and underfitting problems. To solve these problems, several regularization techniques have been devised and widely applied to applications and data analysis. However, it is difficult for developers to choose the most suitable scheme for a developing application because there is no information regarding the performance of each scheme. This paper describes comparative research on regularization techniques by evaluating the training and validation errors in a deep neural network model, using a weather dataset. For comparisons, each algorithm was implemented using a recent neural network library of TensorFlow. The experiment results showed that an autoencoder had the worst performance among schemes. When the prediction accuracy was compared, data augmentation and the batch normalization scheme showed better performance than the others.