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Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…

Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…

Process Reward Models (PRMs), which assign fine-grained scores to intermediate reasoning steps within a solution trajectory, have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs). However,…

Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…

Advances in Large Language Models (LLMs) have spurred a wave of LLM library learning systems for mathematical reasoning. These systems aim to learn a reusable library of tools, such as formal Isabelle lemmas or Python programs that are…

Empirical Risk Minimization (ERM) based machine learning algorithms have suffered from weak generalization performance on data obtained from out-of-distribution (OOD). To address this problem, Invariant Risk Minimization (IRM) objective was…

Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…

Large-scale numerical computations make increasing use of low-precision (LP) floating point formats and mixed precision arithmetic, which can be enhanced by the technique of stochastic rounding (SR), that is, rounding an intermediate…

Fine-tuning Large Language Models (LLMs) on consumer-grade GPUs is highly cost-effective, yet constrained by limited GPU memory and slow PCIe interconnects. Pipeline parallelism combined with CPU offloading mitigates these hardware…

We present UniBind, a flexible and efficient approach that learns a unified representation space for seven diverse modalities -- images, text, audio, point cloud, thermal, video, and event data. Existing works, eg., ImageBind, treat the…

Motivated by several applications, we consider the problem of randomly rounding a fractional solution in a matroid (base) polytope to an integral one. We consider the pipage rounding technique and also present a new technique, randomized…

With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as a practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation…

The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the…

The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…

Large Language Models (LLMs) have demonstrated exceptional proficiency in language-related tasks, but their deployment poses significant challenges due to substantial memory and storage requirements. Weight-only quantization has emerged as…

Class-Incremental Learning (CIL) [40] trains classifiers under a strict memory budget: in each incremental phase, learning is done for new data, most of which is abandoned to free space for the next phase. The preserved data are exemplars…

Non-determinism and non-reproducibility present significant challenges in deep learning, leading to inconsistent results across runs and platforms. These issues stem from two origins: random number generation and floating-point computation.…

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a…

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…

We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately…