Loss landscape analysis is extremely useful for a deeper understanding of the generalization ability of deep neural network models. In this work, we propose a layerwise loss landscape analysis where the loss surface at every layer is studied independently and also on how each correlates to the overall loss surface. We study the layerwise loss landscape by studying the eigenspectra of the Hessian at each layer. In particular, our results show that the layerwise Hessian geometry is largely similar to the entire Hessian. We also report an interesting phenomenon where the Hessian eigenspectrum of middle layers of the deep neural network are observed to most similar to the overall Hessian eigenspectrum. We also show that the maximum eigenvalue and the trace of the Hessian (both full network and layerwise) reduce as training of the network progresses. We leverage on these observations to propose a new regularizer based on the trace of the layerwise Hessian. Penalizing the trace of the Hessian at every layer indirectly forces Stochastic Gradient Descent to converge to flatter minima, which are shown to have better generalization performance. In particular, we show that such a layerwise regularizer can be leveraged to penalize the middlemost layers alone, which yields promising results. Our empirical studies on well-known deep nets across datasets support the claims of this work.

Active learning algorithms automatically identify the salient and exemplar instances from large amounts of unlabeled data and thus reduce human annotation effort in inducing a classification model. More recently, Batch Mode Active Learning (BMAL) techniques have been proposed, where a batch of data samples is selected simultaneously from an unlabeled set. Most active learning algorithms assume a flat label space, that is, they consider the class labels to be independent. However, in many applications, the set of class labels are organized in a hierarchical tree structure, with the leaf nodes as outputs and the internal nodes as clusters of outputs at multiple levels of granularity. In this paper, we propose a novel BMAL algorithm (BatchRank) for hierarchical classification. The sample selection is posed as an NP-hard integer quadratic programming problem and a convex relaxation (based on linear programming) is derived, whose solution is further improved by an iterative truncated power method. Finally, a deterministic bound is established on the quality of the solution. Our empirical results on several challenging, real-world datasets from multiple domains, corroborate the potential of the proposed framework for real-world hierarchical classification applications.