In Neural Computation

Lecture Notes for the MSc/DTC module. The brain is a complex computing machine which has evolved to give the ttest output to a given input. Neural computation has as goal to describe the function of the nervous system in mathematical and computational terms. By analysing or simulating the resulting equations, one can better understand its function, research how changes in parameters would eect the function, and try to mimic the nervous system in hardware or software implementations. Neural Computation is a bit like physics, that has been successful in describing numerous physical phenomena. However, approaches developed in those elds not always work for neural computation, because: 1. Physical systems are best studied in reduced, simplied circumstances, but the nervous system is hard to study in isolation. Neurons require a narrow range of operating conditions (temperature, oxygen, presence of other neurons, ion concentrations, ...) under which they work as they should. These conditions are hard to reproduce outside the body. Secondly, the neurons form a highly interconnected network. The function of the nervous systems depends on this connectivity and interaction, by trying to isolate the components, you are likely to alter the function. 2. It is not clear how much detail one needs to describe the computations in the brain. In these lectures we shall see various description levels. 3. Neural signals and neural connectivity are hard to measure, especially, if disturbance and damage to the nervous system is to be kept minimal. Perhaps Neural Computation has more in common with trying to gure out how a complicated machine, such as a computer or car works. Knowledge of the basic physics helps, but is not sucient. Luckily there are factors which perhaps make understanding the brain easier than understanding an arbitrary complicated machine: 1. There is a high degree of conservation across species. This means that animal studies can be used to gain information about the human brain. Furthermore, study of, say, the visual system might help to understand the auditory system. 2. The nervous system is able to develop by combining on one hand a only limited amount of genetic information and, on the other hand, the input it receives. Therefore it might be possible to nd the organising principles and develop a brain from there. This would be easier than guring out the complete 'wiring diagram'. 3. The nervous system is exible and robust, neurons die everyday. This stands …

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