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Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
Intermediate step methodologies like chain of thoughts (COT) have demonstrated effectiveness in enhancing the performance of Large Language Models (LLMs) on code generation. This study explores the utilization of intermediate languages,…
Context: Large Language Models (LLMs) like GPT-5 and LLaMA-405b exhibit advanced code generation abilities, but their deployment demands substantial computation resources and energy. Quantization can reduce memory footprint and hardware…
Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While…
Match-and-copy is a core retrieval primitive used at inference time by large language models to retrieve a matching token from the context then copy its successor. Yet, understanding how this behavior emerges on natural data is challenging…
Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…
General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art vendor libraries tune tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory…
Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter - we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought…
Generative models for source code are an interesting structured prediction problem, requiring to reason about both hard syntactic and semantic constraints as well as about natural, likely programs. We present a novel model for this problem…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
This paper introduces GLLM, an innovative tool that leverages Large Language Models (LLMs) to automatically generate G-code from natural language instructions for Computer Numerical Control (CNC) machining. GLLM addresses the challenges of…
Designing automated market makers (AMMs) for prediction markets on combinatorial securities over large outcome spaces poses significant computational challenges. Prior research has primarily focused on combinatorial prediction markets…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes…
Computational cognitive models, which formalize theories of cognition, enable researchers to quantify cognitive processes and arbitrate between competing theories by fitting models to behavioral data. Traditionally, these models are…
GPTIPS is a free, open source MATLAB based software platform for symbolic data mining (SDM). It uses a multigene variant of the biologically inspired machine learning method of genetic programming (MGGP) as the engine that drives the…
Molecular conformation generation (MCG) is a fundamental and important problem in drug discovery. Many traditional methods have been developed to solve the MCG problem, such as systematic searching, model-building, random searching,…
In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard…
Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…
This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with…