|M.Sc Thesis||Department of Electrical Engineering|
|Supervisors:||Prof. Meir Ron|
|Prof. Eldar Yonina|
|Full Thesis text|
The selection of appropriate actions in the face of uncertainty is a formidable task faced by any organism attempting to actively survive in a hostile dynamic environment. This task is further exacerbated by the fact that the organism does not have direct access to the environment, but must assess these states through noisy sensors, often representing the world through random spike trains. It is becoming increasingly evident that in many cases organisms employ exact or approximate Bayesian statistical calculations in order to continuously estimate the environmental state, integrate information from multiple sensory modalities, form predictions and choose actions. What is less clear is how these putative computations are implemented by cortical neural networks. Moreover, given that the environment itself is uncertain, it would seem natural to capture this uncertainty by a distribution over states rather than a single state estimator. This full distribution can be later utilized differentially in various contexts. Thus, the effective representation of full probability distributions by neural networks is also an important issue which needs to be resolved.
The problem of hidden state filtering based on multiple noisy spike trains has been receiving increasing attention over the past few years. Much emphasis has been laid on Bayesian approaches, which facilitate the natural incorporation of prior information, and which can often be guaranteed to yield optimal solutions. In this work we examine the case where the hidden state statistics is Markovian, and suggest how a simple recurrent neural network can compute the state distribution in real time. The results of this work suggest a solid theoretical foundation for dynamic neural decoding and computation, and recover many previous results in appropriate limits. In addition, this work goes beyond the basic decoding scheme and provides several extensions - (1) While most of the work to-date deals with the noise introduced by the sensory spike trains, we show how to handle an additional level of noise that is inherent to the perceived stimulus. (2) We show how the framework we suggest can be easily extended to handle two or more input modalities. (3) In order to make the framework more realistic, we extend it to handle history dependent input spike trains. This enables us to model known biophysical phenomena such as refractoriness and adaptation. (4) We extend the framework to make prediction about the world rather than estimating its current state; this is of significant use in a control theoretic setting.