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 largely debated. I have investigated how the idea of efficient computation can guide us to understand the operational regimes underlying various functions of the brain. I will show how this principle can lead to both qualitative and quantitative understanding of the functional organization of neural circuits which process both low-level visual features and higher level cognitive variables, e.g., self-location in space. In particular, I will show that how representations similar to what have been discovered in the brain could emerge as the consequence of processing information or performing specific tasks efficiently. I will also demonstrate that the same principle 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 the prior expectation, which are counter-intuitive according to the traditional Bayesian view. This framework also predicts that two basic psychophysical measures, i.e., perceptual bias and discrimination threshold, should be directly linked via a simple equation - a prediction well supported by a large array of published data. Towards the end, I will describe some recent efforts on developing new statistical/machine learning-based methods to better characterize internal representations of the brain. Importantly, these methods could help tighten the link between experiments and theories.
Collectively, this research points to a venue to unify our understanding of the brain at different levels by leveraging the power of mathematical/statistical tools, experimental techniques and computational principles.
704 Thackeray Hall