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Deep neural networks enable real-time monitoring of in-vehicle drivers, facilitating the timely prediction of distractions, fatigue, and potential hazards. This technology is now integral to intelligent transportation systems. Recent…

Softmax GAN is a novel variant of Generative Adversarial Network (GAN). The key idea of Softmax GAN is to replace the classification loss in the original GAN with a softmax cross-entropy loss in the sample space of one single batch. In the…

The merit of Conformal Prediction (CP), as a distribution-free framework for uncertainty quantification, depends on generating prediction sets that are efficient, reflected in small average set sizes, while adaptive, meaning they signal…

Enabling machine learning classifiers to defer their decision to a downstream expert when the expert is more accurate will ensure improved safety and performance. This objective can be achieved with the learning-to-defer framework which…

Noisy labels are ubiquitous in real-world datasets, especially in the large-scale ones derived from crowdsourcing and web searching. It is challenging to train deep neural networks with noisy datasets since the networks are prone to…

Hard-label classification is usually trained with smooth surrogate losses, most prominently softmax cross-entropy. We isolate an asymptotic mechanism by which this mismatch between smooth surrogate and discrete labels produces power-law…

Large language models (LLMs) have made transformed changes for human society. One of the key computation in LLMs is the softmax unit. This operation is important in LLMs because it allows the model to generate a distribution over possible…

The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to…

Softmax is the de facto standard in modern neural networks for language processing when it comes to normalizing logits. However, by producing a dense probability distribution each token in the vocabulary has a nonzero chance of being…

In supervised machine learning, models are typically trained using data with hard labels, i.e., definite assignments of class membership. This traditional approach, however, does not take the inherent uncertainty in these labels into…

Learning with a primary objective, such as softmax cross entropy for classification and sequence generation, has been the norm for training deep neural networks for years. Although being a widely-adopted approach, using cross entropy as the…

This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for…

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and…

A framework is presented for unsupervised learning of representations based on infomax principle for large-scale neural populations. We use an asymptotic approximation to the Shannon's mutual information for a large neural population to…

Singular learning models with non-positive Fisher information matrices include neural networks, reduced-rank regression, Boltzmann machines, normal mixture models, and others. These models have been widely used in the development of…

Deep neural classifiers have recently found tremendous success in data-driven control systems. However, existing models suffer from a trade-off between accuracy and adversarial robustness. This limitation must be overcome in the control of…

Standard softmax self-attention excels in vision tasks but incurs quadratic complexity O(N^2), limiting high-resolution deployment. Linear attention reduces the cost to O(N), yet its compressed state representations can impair modeling…

Adapting a model to perform well on unforeseen data outside its training set is a common problem that continues to motivate new approaches. We demonstrate that application of batch normalization in the output layer, prior to softmax…

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the…

To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs…