|M.Sc Student||Silbak Jumana|
|Subject||Geometric Analysis of the Dynamic Connectivity of|
Biological and Artifical Neural Networks
|Department||Department of Electrical and Computer Engineering||Supervisors||ASSOCIATE PROF. Ronen Talmon|
|PROF. Ron Meir|
|Full Thesis text|
The analysis of biological and artificial neural networks has gained a lot of interest in the last two decades. Artificial neural networks have become the leading workhorse in a broad range of fields, leading to ground-breaking performance. Biological neural networks have become much more accessible than before thanks to the advanced acquisition technologies allowing researchers to record the activity of thousands of neurons simultaneously.
When a neural network, either biological or artificial, is trained to perform a specific task, the inter-relations between its neurons evolve during the training procedure, calling for the investigation of this dynamic connectivity.
In this work, we take a model-free approach. Our main focus is on the inference and investigation of dynamic connectivity from neuronal activity data observations. Particularly, the data we consider are typically organized in 3D tensors, consisting of the neuronal activity of each neuron over time in multiple experimental trials or repetitions. Our approach largely relies on the particular geometry of symmetric positive-definite (SPD) matrices, which are constructed from the neuronal data observations and are used for the representation of neuronal connectivity.
Our research consists of two main parts. The first part concerns sequential learning in artificial recurrent neural networks (RNNs). When training an RNN to perform multiple tasks sequentially, the network typically suffers from ``catastrophic forgetting'', that is forgetting the previously learned tasks during the learning of a new one. Most prevalent approaches for identifying this phenomenon and devising an appropriate stopping criterion for training the new task assume the full knowledge of the connectivity of the neurons. Conversely, in our work
we address the problem given observations of the activity of the network. We propose to construct appropriate SPD matrices that represent the neuronal connectivity, and then, characterize the catastrophic forgetting systematically by observing the spectral decomposition of the Riemannian geodesic paths between the constructed SPD matrices.
In the second part, we analyze neuronal activity from experiments conducted on awake and behaving rodents, provided by Prof. Jackie Schiller's Lab at The Rappaport Faculty of Medicine and Research Institute, Technion.
Based on the Riemannian geometry of SPD matrices constructed from the data, we propose a new dimensionality reduction method that enables to visually track the dynamic connectivity and to assess it quantitatively. In addition, based on parallel transport on the manifold of SPD matrices, we propose an algorithm to remove batch effects stemming from acquisitions in multiple days or from different animals.