Classification is one of the major tasks that deep learning is successfully tackling. Categorization is also a fundamental cognitive ability. A well-known perceptual consequence of categorization in humans and other animals, categorical perception, is notably characterized by a within-category compression and a between-category separation: two items, close in input space, are perceived closer if they belong to the same category than if they belong to different categories. Elaborating on experimental and theoretical results in cognitive science, here we study categorical effects in artificial neural networks. We combine a theoretical analysis that makes use of mutual and Fisher information quantities and a series of numerical simulations on networks of increasing complexity. These formal and numerical analyses provide insights into the geometry of the neural representation in deep layers, with expansion of space near category boundaries and contraction far from category boundaries. We investigate categorical representation by using two complementary approaches: one mimics experiments in psychophysics and cognitive neuroscience by means of morphed continua between stimuli of different categories, while the other introduces a categoricality index that, for each layer in the network, quantifies the separability of the categories at the neural population level. We show on both shallow and deep neural networks that category learning automatically induces categorical perception. We further show that the deeper a layer, the stronger the categorical effects. As an outcome of our study, we propose a coherent view of the efficacy of different heuristic practices of the dropout regularization technique. More generally, our view, which finds echoes in the neuroscience literature, insists on the differential impact of noise in any given layer depending on the geometry of the neural representation that is being learned, that is, on how this geometry reflects the structure of the categories.

In experiments on perceptual decision making, individuals learn a categorization task through trial-and-error protocols. We explore the capacity of a decision-making attractor network to learn a categorization task through reward-based, Hebbian-type modifications of the weights incoming from the stimulus encoding layer. For the latter, we assume a standard layer of a large number of stimulus-specific neurons. Within the general framework of Hebbian learning, we have hypothesized that the learning rate is modulated by the reward at each trial. Surprisingly, we find that when the coding layer has been optimized in view of the categorization task, such reward-modulated Hebbian learning (RMHL) fails to extract efficiently the category membership. In previous work, we showed that the attractor neural networks' nonlinear dynamics accounts for behavioral confidence in sequences of decision trials. Taking advantage of these findings, we propose that learning is controlled by confidence, as computed from the neural activity of the decision-making attractor network. Here we show that this confidence-controlled, reward-based Hebbian learning efficiently extracts categorical information from the optimized coding layer. The proposed learning rule is local and, in contrast to RMHL, does not require storing the average rewards obtained on previous trials. In addition, we find that the confidence-controlled learning rule achieves near-optimal performance. In accordance with this result, we show that the learning rule approximates a gradient descent method on a maximizing reward cost function.

In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information-theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in the context of population coding, the mutual information between the activity of a large array of neurons and a stimulus to which the neurons are tuned is naturally related to the Fisher information. In the light of this result, we consider the optimization of the tuning curves parameters in the case of neurons responding to a stimulus represented by an angular variable.

In the context of both sensory coding and signal processing, building factorized codes has been shown to be an efficient strategy. In a wide variety of situations, the signal to be processed is a linear mixture of statistically independent sources. Building a factorized code is then equivalent to performing blind source separation. Thanks to the linear structure of the data, this can be done, in the language of signal processing, by finding an appropriate linear filter, or equivalently, in the language of neural modeling, by using a simple feedforward neural network. In this article, we discuss several aspects of the source separation problem. We give simple conditions on the network output that, if satisfied, guarantee that source separation has been obtained. Then we study adaptive approaches, in particular those based on redundancy reduction and maximization of mutual information. We show how the resulting updating rules are related to the BCM theory of synaptic plasticity. Eventually we briefly discuss extensions to the case of nonlinear mixtures. Through out this article, we take care to put into perspective our work with other studies on source separation and redundancy reduction. In particular we review algebraic solutions, pointing out their simplicity but also their drawbacks.