Efficient Computation in the Brain

It has been long proposed that the brain should perform computation efficiently to increase the fitness of the organism. However, the validity of this prominent hypothesis remains debated. In this thesis, I investigate how this idea of efficient computation can guide us to understand the operational regimes underlying various cognitive functions, in particular perception and spatial cognition. In the first study, I demonstrate that such idea leads to a well-constrained yet powerful model framework for human perceptual behaviors by assuming the system is efficient both in term of encoding and decoding. This framework, when applying to human visual perception, explains many reported perceptual biases, including the repulsive biases away from prior peak, which are counter-intuitive according to the traditional Bayesian view. This framework also offers a principle way to address the common criticisms of Bayesian models in perception, which argue that Bayesian models are lack of constraints. In the second study, I demonstrate that the idea of efficiency, coupled with a few assumptions, allows us to make quantitative predictions on the functional architecture of the grid cell system in rodents. One such prediction is that the spatial scales of grid modules should follow a geometric progression, importantly, with the scaling factor to be close to the square root of transcendental number e ~1.6. Such zero-parameter predictions closely match the data reported in recent neurophysiological experiments. The theory also makes several other predictions, some of which have been confirmed by the data. This study suggests that achieving efficiency computation may also apply to neural circuits involving a high-level cognition, i.e. representation of space. In the third study, I analytically derive a generic connection between mutual information and Fisher information. This clarifies an important theoretical issue which has been misunderstood in previous neural coding literature. Additionally, it provides some powerful signatures of the Efficient coding hypothesis, which could guide future experimental tests. Together, the results presented in this thesis suggest that achieving efficient computation serves as a basic design principle which generalizes across neural systems processing low-level and high-level cognitive functions