Atilla Botond Kelemen: Chemoaffinity-based development of innate Bayesian priors

BCCN Berlin / Technische Universität Berlin

 

Abstract

Many animals use strong developmental priors to create models of their world that generalise well from sparse data. A recent theoretical study suggests a possible mechanism for genetically encoding structural priors using a chemoaffinity-based wiring rule. Here, connection strengths are determined by the alignment of a presynaptic receptor and a postsynaptic ligand expressed by each neuron.

In this thesis, we extend this framework, investigating whether modifying the expression statistics of chemoaffinity-related receptors and ligands can allow for the encoding of not just structural, but also quantitative/Bayesian priors over the continuous and discrete variables that are defined by the network structure. We analytically determine how gene expression heterogeneity influences the dynamics in both continuous and discrete attractor networks and map these altered dynamics to Bayesian computation.

In continuous attractor networks (CANs), we show that heterogeneities induce a non-flat energy landscape for the movement of the solution bump along the continuous attractor. Under noise, the bump performs Langevin sampling from this landscape, which implements a sampling-based prior. Furthermore, if the external input is a log-likelihood function, it modifies the energy landscape so that the resulting sampling distribution approximates a Bayesian posterior.

In discrete attractor networks, we derive a relationship between the size of the assembly corresponding to each attractor and the geometry of the associated attraction basin. We show how this skewed attraction basin could serve as a Bayesian prior during classification.

In conclusion, this thesis demonstrates how a biologically plausible mechanism could embed approximate Bayesian priors into neural networks.

 

Guests are welcome!

 

Additional information:

Master thesis defense

 

Organized by:

Prof. Henning Sprekeler & Prof. Klaus Obermayer