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Deep metric learning (DML) has received much attention in deep learning due to its wide applications in computer vision. Previous studies have focused on designing complicated losses and hard example mining methods, which are mostly…

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…

While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…

Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the…

We show that database schema validation and update processing problems such as view updating, materialized view maintenance, integrity constraint checking, integrity constraint maintenance or condition monitoring can be classified as…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…

Document parsing (DP) transforms unstructured or semi-structured documents into structured, machine-readable representations, enabling downstream applications such as knowledge base construction and retrieval-augmented generation (RAG).…

The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have…

Pre-trained language models (PLMs) have become a prevalent technique in deep learning for code, utilizing a two-stage pre-training and fine-tuning procedure to acquire general knowledge about code and specialize in a variety of downstream…

Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…

Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear equations both with and without coefficients? Constraint variants are…

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being…

Over the past decade, the Gr\"obner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to…

Depth completion is a pivotal challenge in computer vision, aiming at reconstructing the dense depth map from a sparse one, typically with a paired RGB image. Existing learning based models rely on carefully prepared but limited data,…

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Forwarding table verification consists in checking the distributed data-structure resulting from the forwarding tables of a network. A classical concern is the detection of loops. We study this problem in the context of software-defined…

Post-alignment of large language models (LLMs) is critical in improving their utility, safety, and alignment with human intentions. Direct preference optimisation (DPO) has become one of the most widely used algorithms for achieving this…