相关论文: A unified framework for establishing the universal…

Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…

We introduce Universal and Transferable Adversarial Perturbations (UTAP) for pathology foundation models that reveal critical vulnerabilities in their capabilities. Optimized using deep learning, UTAP comprises a fixed and weak noise…

The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that…

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling…

Previous work on the learnability of transformers \textemdash\ focused primarily on examining their ability to approximate specific algorithmic patterns through training \textemdash\ has largely been data-driven, offering only probabilistic…

Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for…

Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete…

The universal approximation property (UAP) of neural networks is fundamental for deep learning, and it is well known that wide neural networks are universal approximators of continuous functions within both the $L^p$ norm and the…

Transformers are deep architectures that define "in-context mappings" which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In this work, we…

Effective feature representation is key to the predictive performance of any algorithm. This paper introduces a meta-procedure, called Non-Euclidean Upgrading (NEU), which learns feature maps that are expressive enough to embed the…

At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…

Conventional hypernetworks are typically engineered around a specific base-model parameterization, so changing the target architecture often entails redesigning the hypernetwork and retraining it from scratch. We introduce the…

Universal Adversarial Perturbations (UAPs) are imperceptible, image-agnostic vectors that cause deep neural networks (DNNs) to misclassify inputs with high probability. In practical attack scenarios, adversarial perturbations may undergo…

Transformers are crucial across many AI fields, such as large language models, computer vision, and reinforcement learning. This prominence stems from the architecture's perceived universality and scalability compared to alternatives. This…

We prove a universal approximation property (UAP) for a class of ODENet and a class of ResNet, which are simplified mathematical models for deep learning systems with skip connections. The UAP can be stated as follows. Let $n$ and $m$ be…

Universal adversarial perturbation (UAP), also known as image-agnostic perturbation, is a fixed perturbation map that can fool the classifier with high probabilities on arbitrary images, making it more practical for attacking deep models in…

Universal domain adaptation (UniDA) aims to transfer knowledge from the source domain to the target domain without any prior knowledge about the label set. The challenge lies in how to determine whether the target samples belong to common…

The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions $\sigma$, then a standard feedforward neural network with one hidden layer is able to approximate any…

Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We…

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem…