Toward a Predictive Theory of Neural Computation: Motion Estimation in the Fly's Visual System

The performance of the nervous system often comes close to the physical limits inherent to its task. Therefore by understanding the structure of specific problems solved by real brains, we can hope to formulate a predictive theory of neural computations. A large class of signal processing problems--such as those solved by the sensory nervous system --are equivalent to the computation of the response to external fields in statistical mechanics. The subject of this dissertation is to use these ideas on a particular example of neural computations: motion estimation in the fly's visual system. A model of the fly's problem is solved by doing perturbation theory in signal-to-noise ratio and by finding the saddle point in the high SNR limit. From this analysis, it is concluded that the fly must adapt to the statistical structure of its environment in order for its motion computation to remain optimal. In particular it should adapt to the rms contrast and to the correlation time of its visual inputs. It is also realized that the structure of the computation must change qualitatively with SNR. These results are compared with experimental data from the literature. New experiments on a motion sensitive neuron in the visual system of the blowfly Calliphora vicina are presented. Their results agree on a qualitative and semi-quantitative level with the theory. In particular, the new idea of adaptation to statistical parameters is clearly demonstrated.