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Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…

This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…

In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network,…

Recent advances demonstrate that increasing inference-time computation can significantly boost the reasoning capabilities of large language models (LLMs). Although repeated sampling (i.e., generating multiple candidate outputs) is a highly…

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^{-1}$ when $A$ is invertible, which may be traced back to…

Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…

Repeated Sampling (RS) is a simple inference-time algorithm that has been shown to improve model performance on complex tasks. Although it is an effective way of scaling inference time, it often struggles to generate diverse solution…

The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…

Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested…

In an era when the performance of a single compute device plateaus, software must be designed to scale on massively parallel systems for better runtime performance. However, in the context of training deep learning models, the popular…

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

Multimodal Biomedical Image Incremental Learning (MBIIL) is essential for handling diverse tasks and modalities in the biomedical domain, as training separate models for each modality or task significantly increases inference costs.…

Automatic industrial scheduling, aiming at optimizing the sequence of jobs over limited resources, is widely needed in manufacturing industries. However, existing scheduling systems heavily rely on heuristic algorithms, which either…

Summarizing graphs w.r.t. structural features is important to reduce the graph's size and make tasks like indexing, querying, and visualization feasible. Our generic parallel BRS algorithm efficiently summarizes large graphs w.r.t. a custom…

The emerging class of instance-optimized systems has shown potential to achieve high performance by specializing to a specific data and query workloads. Particularly, Machine Learning (ML) techniques have been applied successfully to build…

This paper models the fundamental frequency contours on both Mandarin and Cantonese speech with decision trees and DNNs (deep neural networks). Different kinds of f0 representations and model architectures are tested for decision trees and…

Few-shot learning (FSL) has attracted increasing attention in recent years but remains challenging, due to the intrinsic difficulty in learning to generalize from a few examples. This paper proposes an adaptive margin principle to improve…

This paper presents an inverse reinforcement learning~(IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions…

Conventional recommendation systems (RSs) are typically optimized to enhance performance metrics uniformly across all training samples. This makes it hard for data-driven RSs to cater to a diverse set of users due to the varying properties…

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to…