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

Diffusion models have shown great promise in data generation, yet generating time series data remains challenging due to the need to capture complex temporal dependencies and structural patterns. In this paper, we present \textit{TSGDiff},…

Compositional generalization is a basic mechanism in human language learning, which current neural networks struggle with. A recently proposed Disentangled sequence-to-sequence model (Dangle) shows promising generalization capability by…

Real-world data distributions often shift continuously across multiple latent factors such as time, geography, and socioeconomic contexts. However, existing domain generalization approaches typically treat domains as discrete or as evolving…

We propose a metric for evaluating the generalization ability of deep neural networks trained with mini-batch gradient descent. Our metric, called gradient disparity, is the $\ell_2$ norm distance between the gradient vectors of two…

Although recent advances in machine learning have shown its success to learn from independent and identically distributed (IID) data, it is vulnerable to out-of-distribution (OOD) data in an open world. Domain generalization (DG) deals with…

Typical techniques for sequence classification are designed for well-segmented sequences which have been edited to remove noisy or irrelevant parts. Therefore, such methods cannot be easily applied on noisy sequences expected in real-world…

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy…

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

Difference-in-differences (DID) is a widely used quasi-experimental design for causal inference, traditionally applied to scalar or Euclidean outcomes, while extensions to outcomes residing in non-Euclidean spaces remain limited. Existing…

We establish a calculus of differences for taut endofunctors of the category of sets, analogous to the classical calculus of finite differences for real valued functions. We study how the difference operator interacts with limits and…

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

Machine learning systems generally assume that the training and testing distributions are the same. To this end, a key requirement is to develop models that can generalize to unseen distributions. Domain generalization (DG), i.e.,…

Adaptation to out-of-distribution data is a meta-challenge for all statistical learning algorithms that strongly rely on the i.i.d. assumption. It leads to unavoidable labor costs and confidence crises in realistic applications. For that,…

Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in…

Data-driven deep learning models have enabled tremendous progress in change detection (CD) with the support of pixel-level annotations. However, collecting diverse data and manually annotating them is costly, laborious, and…

Change Detection (CD) enables the identification of alterations between images of the same area captured at different times. However, existing CD methods still struggle to address pseudo changes resulting from domain information differences…

A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with…

Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…

Fine-grained domain generalization (FGDG) is a more challenging task than traditional DG tasks due to its small inter-class variations and relatively large intra-class disparities. When domain distribution changes, the vulnerability of…

Recent works show that speech separation guided diarization (SSGD) is an increasingly promising direction, mainly thanks to the recent progress in speech separation. It performs diarization by first separating the speakers and then applying…