Softmax classifiers with a very large number of classes naturally occur in many applications such as natural language processing and information retrieval. The calculation of full softmax is costly from the computational and energy perspective. There have been various sampling approaches to overcome this challenge, popularly known as negative sampling (NS). Ideally, NS should sample negative classes from a distribution that is dependent on the input data, the current parameters, and the correct positive class. Unfortunately, due to the dynamically updated parameters and data samples, there is no sampling scheme that is provably adaptive and samples the negative classes efficiently. Therefore, alternative heuristics like random sampling, static frequency-based sampling, or learning-based biased sampling, which primarily trade either the sampling cost or the adaptivity of samples per iteration are adopted. In this paper, we show two classes of distributions where the sampling scheme is truly adaptive and provably generates negative samples in near-constant time. Our implementation in C++ on CPU is significantly superior, both in terms of wall-clock time and accuracy, compared to the most optimized TensorFlow implementations of other popular negative sampling approaches on powerful NVIDIA V100 GPU.

Zero-Shot Learning (ZSL) is a classification task where some classes referred to as unseen classes have no training images. Instead, we only have side information about seen and unseen classes, often in the form of semantic or descriptive attributes. Lack of training images from a set of classes restricts the use of standard classification techniques and losses, including the widespread cross-entropy loss. We introduce a novel Similarity Distribution Matching Network (SDM-Net) which is a standard fully connected neural network architecture with a non-trainable penultimate layer consisting of class attributes. The output layer of SDM-Net consists of both seen and unseen classes. To enable zero-shot learning, during training, we regularize the model such that the predicted distribution of unseen class is close in KL divergence to the distribution of similarities between the correct seen class and all the unseen classes. We evaluate the proposed model on five benchmark datasets for zero-shot learning, AwA1, AwA2, aPY, SUN, and CUB datasets. We show that, despite the simplicity, our approach achieves competitive performance with state-of-the-art methods in Generalized-ZSL setting for all of these datasets.