Deep Boltzmann Machines as Hierarchical Generative Models of Perceptual Inference in the Cortex

Abstract

The mammalian neocortex is integral to all aspects of cognition, in particular perception across all sensory modalities. Whether computational principles can be identified that would explain why the cortex is so versatile and capable of adapting to various inputs is not clear. One well-known hypothesis is that the cortex implements a generative model, actively synthesising internal explanations of the sensory input. This ‘analysis by synthesis’ could be instantiated in the top-down connections in the hierarchy of cortical regions, and allow the cortex to evaluate its internal model and thus learn good representations of sensory input over time. Few computational models however exist that implement these principles. In this thesis, we investigate the deep Boltzmann machine (DBM) as a model of analysis by synthesis in the cortex, and demonstrate how three distinct perceptual phenomena can be interpreted in this light: visual hallucinations, bistable perception, and object-based attention. A common thread is that in all cases, the internally synthesised explanations go beyond, or deviate from, what is in the visual input. The DBM was recently introduced in machine learning, but combines several properties of interest for biological application. It constitutes a hierarchical generative model and carries both the semantics of a connectionist neural network and a probabilistic model. Thus, we can consider neuronal mechanisms but also (approximate) probabilistic inference, which has been proposed to underlie cortical processing, and contribute to the ongoing discussion concerning probabilistic or Bayesian models of cognition. Concretely, making use of the model’s capability to synthesise internal representations of sensory input, we model complex visual hallucinations resulting from loss of vision in Charles Bonnet syndrome.We demonstrate that homeostatic regulation of neuronal firing could be the underlying cause, reproduce various aspects of the syndrome, and examine a role for the neuromodulator acetylcholine. Next, we relate bistable perception to approximate, sampling-based probabilistic inference, and show how neuronal adaptation can be incorporated by providing a biological interpretation for a recently developed sampling algorithm. Finally, we explore how analysis by synthesis could be related to attentional feedback processing, employing the generative aspect of the DBM to implement a form of object-based attention. We thus present a model that uniquely combines several computational principles (sampling, neural processing, unsupervised learning) and is general enough to uniquely address a range of distinct perceptual phenomena. The connection to machine learning ensures theoretical grounding and practical evaluation of the underlying principles. Our results lend further credence to the hypothesis of a generative model in the brain, and promise fruitful interaction between neuroscience and Deep Learning approaches.