To grok or not to grok: Disentangling generalization and memorization on corrupted algorithmic datasets

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or understood the underlying rule (or both). Motivated by this challenge, we study an interpretable model where generalizing representations are understood analytically, and are easily distinguishable from the memorizing ones. Namely, we consider two-layer neural networks trained on modular arithmetic tasks where ($\xi \cdot 100\%$) of labels are corrupted (\emph{i.e.} some results of the modular operations in the training set are incorrect). We show that (i) it is possible for the network to memorize the corrupted labels \emph{and} achieve $100\%$ generalization at the same time; (ii) the memorizing neurons can be identified and pruned, lowering the accuracy on corrupted data and improving the accuracy on uncorrupted data; (iii) regularization methods such as weight decay, dropout and BatchNorm force the network to ignore the corrupted data during optimization, and achieve $100\%$ accuracy on the uncorrupted dataset; and (iv) the effect of these regularization methods is (``mechanistically'') interpretable: weight decay and dropout force all the neurons to learn generalizing representations, while BatchNorm de-amplifies the output of memorizing neurons and amplifies the output of the generalizing ones. Finally, we show that in the presence of regularization, the training dynamics involves two consecutive stages: first, the network undergoes the \emph{grokking} dynamics reaching high train \emph{and} test accuracy; second, it unlearns the memorizing representations, where train accuracy suddenly jumps from $100\%$ to $100 (1-\xi)\%$.

Combining Multi-level Contexts of Superpixel using Convolutional Neural Networks to perform Natural Scene Labeling

Modern deep learning algorithms have triggered various image segmentation approaches. However most of them deal with pixel based segmentation. However, superpixels provide a certain degree of contextual information while reducing computation cost. In our approach, we have performed superpixel level semantic segmentation considering 3 various levels as neighbours for semantic contexts. Furthermore, we have enlisted a number of ensemble approaches like max-voting and weighted-average. We have also used the Dempster-Shafer theory of uncertainty to analyze confusion among various classes. Our method has proved to be superior to a number of different modern approaches on the same dataset.