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Advances in neural architecture search, as well as explainability andinterpretability of connectionist architectures, have been reported in therecent literature. However, our understanding of how to design Bayesian DeepLearning (BDL) hyperparameters, specifically, the depth, width and ensemblesize, for robust function mapping with uncertainty quantification, is stillemerging. This paper attempts to further our understanding by mapping Bayesianconnectionist representations to polynomials of different orders with varyingnoise types and ratios. We examine the noise-contaminated polynomials to searchfor the combination of hyperparameters that can extract the underlyingpolynomial signals while quantifying uncertainties based on the noiseattributes. Specifically, we attempt to study the question that an appropriateneural architecture and ensemble configuration can be found to detect a signalof any n-th order polynomial contaminated with noise having differentdistributions and signal-to-noise (SNR) ratios and varying noise attributes.Our results suggest the possible existence of an optimal network depth as wellas an optimal number of ensembles for prediction skills and uncertaintyquantification, respectively. However, optimality is not discernible for width,even though the performance gain reduces with increasing width at high valuesof width. Our experiments and insights can be directional to understandtheoretical properties of BDL representations and to design practicalsolutions.

Bayesian Deep Learning Hyperparameter Search for Robust Function Mapping to Polynomials with Noise