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In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced…

Neural machine translation (NMT) models are typically trained using a softmax cross-entropy loss where the softmax distribution is compared against smoothed gold labels. In low-resource scenarios, NMT models tend to over-fit because the…

The Softmax bottleneck was first identified in language modeling as a theoretical limit on the expressivity of Softmax-based models. Being one of the most widely-used methods to output probability, Softmax-based models have found a wide…

Softmax is the most commonly used output function for multiclass problems and is widely used in areas such as vision, natural language processing, and recommendation. A softmax model has linear costs in the number of classes which makes it…

In the field of pattern classification, the training of deep learning classifiers is mostly end-to-end learning, and the loss function is the constraint on the final output (posterior probability) of the network, so the existence of Softmax…

SoftMax is a ubiquitous ingredient of modern machine learning algorithms. It maps an input vector onto a probability simplex and reweights the input by concentrating the probability mass at large entries. Yet, as a smooth approximation to…

Contextual representation models have achieved great success in improving various downstream tasks. However, these language-model-based encoders are difficult to train due to the large parameter sizes and high computational complexity. By…

RNN-Transducer has been one of promising architectures for end-to-end automatic speech recognition. Although RNN-Transducer has many advantages including its strong accuracy and streaming-friendly property, its high memory consumption…

To encourage intra-class compactness and inter-class separability among trainable feature vectors, large-margin softmax methods are developed and widely applied in the face recognition community. The introduction of the large-margin concept…

Is the output softmax layer, which is adopted by most language models (LMs), always the best way to compute the next word probability? Given so many attention layers in a modern transformer-based LM, are the pointer networks redundant…

Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Out-of-vocabulary words account for a large proportion of errors in machine translation systems, especially when the system is used on a different domain than the one where it was trained. In order to alleviate the problem, we propose to…

In many scenarios of a language identification task, the user will specify a small set of languages which he/she can speak instead of a large set of all possible languages. We want to model such prior knowledge into the way we train our…

Mixture of Softmaxes (MoS) has been shown to be effective at addressing the expressiveness limitation of Softmax-based models. Despite the known advantage, MoS is practically sealed by its large consumption of memory and computational time…

The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

Despite the effectiveness of recurrent neural network language models, their maximum likelihood estimation suffers from two limitations. It treats all sentences that do not match the ground truth as equally poor, ignoring the structure of…

The use of contrastive loss for representation learning has become prominent in computer vision, and it is now getting attention in Natural Language Processing (NLP). Here, we explore the idea of using a batch-softmax contrastive loss when…

Training neural network language models over large vocabularies is still computationally very costly compared to count-based models such as Kneser-Ney. At the same time, neural language models are gaining popularity for many applications…

Token embeddings play a crucial role in language modeling but, despite this practical relevance, their theoretical understanding remains limited. Our paper addresses the gap by characterizing the structure of embeddings obtained via…

Recent neural network sequence models with softmax classifiers have achieved their best language modeling performance only with very large hidden states and large vocabularies. Even then they struggle to predict rare or unseen words even if…