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Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…
By quantizing network weights and activations to low bitwidth, we can obtain hardware-friendly and energy-efficient networks. However, existing quantization techniques utilizing the straight-through estimator and piecewise constant…
The challenges of solving complex university-level mathematics problems, particularly those from MIT, and Columbia University courses, and selected tasks from the MATH dataset, remain a significant obstacle in the field of artificial…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Standardized math assessments require expensive human pilot studies to establish the difficulty of test items. We investigate the predictive value of open-source large language models (LLMs) for evaluating the difficulty of multiple-choice…
Large Language Models (LLMs) are increasingly deployed in high-stakes financial domains, yet they suffer from specific, reproducible hallucinations when performing arithmetic operations. Current mitigation strategies often treat the model…
This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding…
Translating algorithms from high-level languages like MATLAB to hardware description languages (HDLs) is a resource-intensive but necessary step for deployment on FPGAs and ASICs. While large language models (LLMs) offer a path to…
Matlab is one of the most widely used mathematical computing environments in technical computing. It has an interactive environment which provides high performance computing (HPC) procedures and easy to use. Parallel computing with Matlab…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
Vision-language pre-training like CLIP has shown promising performance on various downstream tasks such as zero-shot image classification and image-text retrieval. Most of the existing CLIP-alike works usually adopt relatively large image…
Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring…
This paper gives a personal assessment of Epoch making advances in Matrix Computations from antiquity and with an eye towards tomorrow. We trace the development of number systems and elementary algebra, and the uses of Gaussian Elimination…
Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…
Recent research in the field of computer vision strongly focuses on deep learning architectures to tackle image processing problems. Deep neural networks are often considered in complex image processing scenarios since traditional computer…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these…