Related papers: Smooth Min-Max Monotonic Networks

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…

Mini-batch sub-sampling in neural network training is unavoidable, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. In this study we…

Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound…

Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…

In this paper, we propose Selective Output Smoothing Regularization, a novel regularization method for training the Convolutional Neural Networks (CNNs). Inspired by the diverse effects on training from different samples, Selective Output…

To improve performance in contemporary deep learning, one is interested in scaling up the neural network in terms of both the number and the size of the layers. When ramping up the width of a single layer, graceful scaling of training has…

When training deep neural networks with gradient descent, sharpness often increases -- a phenomenon known as progressive sharpening -- before saturating at the edge of stability. Although commonly observed in practice, the underlying…

We characterize the effectiveness of Sharpness-aware minimization (SAM) under machine unlearning scheme, where unlearning forget signals interferes with learning retain signals. While previous work prove that SAM improves generalization…

Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…

This monograph presents a theoretical background and a broad introduction to the Min-Max Framework for Majorization-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems…

Memristor based neural networks have great potentials in on-chip neuromorphic computing systems due to the fast computation and low-energy consumption. However, the imprecise properties of existing memristor devices generally result in…

Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…

Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…

Sharpness-Aware Minimization (SAM) has emerged as a promising alternative optimizer to stochastic gradient descent (SGD). The originally-proposed motivation behind SAM was to bias neural networks towards flatter minima that are believed to…

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…

A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace $E$ of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an…

Recent investigations into sum-product-max networks (SPMN) that generalize sum-product networks (SPN) offer a data-driven alternative for decision making, which has predominantly relied on handcrafted models. SPMNs computationally represent…