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We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…

The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitative approximation rates for ReLU networks on the class of…

In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…

Modern deep neural networks are powerful predictive tools yet often lack valid inference for causal parameters, such as treatment effects or entire survival curves. While frameworks like Double Machine Learning (DML) and Targeted Maximum…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

Current Vision-Language-Action (VLA) models typically treat the deepest representation of a vision-language backbone as universally optimal for action prediction. However, robotic manipulation is composed of many frequent closed-loop…

Deep neural networks are susceptible to adversarial examples while suffering from incorrect predictions via imperceptible perturbations. Transfer-based attacks create adversarial examples for surrogate models and transfer these examples to…

Applying end-to-end learning to solve complex, interactive, pixel-driven control tasks on a robot is an unsolved problem. Deep Reinforcement Learning algorithms are too slow to achieve performance on a real robot, but their potential has…

Deep neural networks (DNNs) are susceptible to Universal Adversarial Perturbations (UAPs), which are instance agnostic perturbations that can deceive a target model across a wide range of samples. Unlike instance-specific adversarial…

With the development of deep learning, the field of face anti-spoofing (FAS) has witnessed great progress. FAS is usually considered a classification problem, where each class is assumed to contain a single cluster optimized by softmax…

An Undirected Weighted Network (UWN) is commonly found in big data-related applications. Note that such a network's information connected with its nodes, and edges can be expressed as a Symmetric, High-Dimensional and Incomplete (SHDI)…

Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers…

Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional…

Despite dropout's ubiquity in machine learning, its effectiveness as a form of data augmentation remains under-explored. We address two key questions: (i) When is dropout effective as an augmentation strategy? (ii) Is dropout uniquely…

This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…

Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…

We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each…