Representational Structure of Neural Networks Trained on Biased and Out-Of-Distribution Data

Gnyanesh Bangaru, Lalith Bharadwaj Baru, Kiran Chakravarthula

Keywords: Representation analysis, Centered Kernel Alignment, Out-of-Distribution Generalisation, Objective functions, Biased Data, Deep Learning

TL;DR: We analyse how various objective functions perform on standard image classification data, biased data and data with distributional shifts.

Abstract:

Neural networks trained on standard image classification data sets are observed to be less robust to distributional shifts and pertain to certain levels of bias in representations. Thus, it is pertinent to identify the kind of objective function that could correspond to better performance for data with biases and distribution shifts, and how can that objective function be justified to be the apt choice. There is, however, less literature that focuses on the choice of the objective function and its representational structure when trained on such data sets.

In this work, we analyse the performance and the internal representational structure of convolution-based neural networks (eg. ResNets) trained by varying objective functions on biased and out-of-distribution (OOD) data. Specifically, we interpret similarities in representations (using CKA) acquired for distinct objective functions (probabilistic and margin-based) and provide a detailed analysis of the chosen ones. Our analysis reports that representations acquired by ResNets using Softmax Cross-Entropy ($\mathcal{L}_{SCE}$) and Negative Log-Likelihood ($\mathcal{L}_{NLL}$) as objectives are equally competent in providing superior performance and fine representations on OOD and biased data. Subsequently, we interpret that the ResNets are less likely to be robust on cross-data generalization without refined representational similarity.