Related papers: A Theory of General Difference in Continuous and D…

Automatic differentiation (AD) is a set of techniques that systematically applies the chain rule to compute the gradients of functions without requiring human intervention. Although the fundamentals of this technology were established…

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…

Object detection is a critical task in computer vision, with applications in various domains such as autonomous driving and urban scene monitoring. However, deep learning-based approaches often demand large volumes of annotated data, which…

In Generalized Category Discovery (GCD), we cluster unlabeled samples of known and novel classes, leveraging a training dataset of known classes. A salient challenge arises due to domain shifts between these datasets. To address this, we…

Dynamic graph anomaly detection (DGAD) is critical for many real-world applications but remains challenging due to the scarcity of labeled anomalies. Existing methods are either unsupervised or semi-supervised: unsupervised methods avoid…

The generalization of deep neural networks to unknown domains is a major challenge despite their tremendous progress in recent years. For this reason, the dynamic area of domain generalization (DG) has emerged. In contrast to unsupervised…

In this paper, we focus on Single-Domain Generalized Object Detection (Single-DGOD), aiming to transfer a detector trained on one source domain to multiple unknown domains. Existing methods for Single-DGOD typically rely on discrete data…

While there have been considerable advancements in machine learning driven by extensive datasets, a significant disparity still persists in the availability of data across various sources and populations. This inequality across domains…

This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

Diffusion models are able to produce AI-generated images that are almost indistinguishable from real ones. This raises concerns about their potential misuse and poses substantial challenges for detecting them. Many existing detectors rely…

Transformer-based autoregressive models excel in data generation but are inherently constrained by their reliance on discretized tokens, which limits their ability to represent continuous values with high precision. We analyze the…

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by…

The composition theorems of differential privacy (DP) allow data curators to combine different algorithms to obtain a new algorithm that continues to satisfy DP. However, new granularity notions (i.e., neighborhood definitions), data…

As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…

We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…

Domain generalization is a technique aimed at enabling models to maintain high accuracy when applied to new environments or datasets (unseen domains) that differ from the datasets used in training. Generally, the accuracy of models trained…

This paper presents a generalization for Differential and Integral Calculus. Just as the derivative is the instantaneous angular coefficient of the tangent line to a function, the generalized derivative is the instantaneous parameter value…

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…

Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and…