Related papers: ToL: A Tensor of List-Based Unified Computation Mo…

We propose a novel tensor network language model based on the simplest tensor network (i.e., tensor trains), called `Tensor Train Language Model' (TTLM). TTLM represents sentences in an exponential space constructed by the tensor product of…

While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…

Large language models (LLMs) have recently attracted considerable interest for their ability to perform complex reasoning tasks, such as chain-of-thought (CoT) reasoning. However, most of the existing approaches to enhance this ability rely…

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

High-performance deep learning depends on efficient tensor programs. In recent years, automatic tensor program optimization, also known as tensor compilation, has emerged as the primary approach to generating efficient tensor programs.…

A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language…

Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…

I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…

Large language and vision models (LLVMs) have been driven by the generalization power of large language models (LLMs) and the advent of visual instruction tuning. Along with scaling them up directly, these models enable LLVMs to showcase…

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified…

Complex reasoning over tabular data is crucial in real-world data analysis, yet large language models (LLMs) often underperform due to complex queries, noisy data, and limited numerical capabilities. To address these issues, we propose…

Over the past few years, the explosion in sparse tensor algebra workloads has led to a corresponding rise in domain-specific accelerators to service them. Due to the irregularity present in sparse tensors, these accelerators employ a wide…

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…

Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Compositional generalization is an important ability of language models and has many different manifestations. For data-to-text generation, previous research on this ability is limited to a single manifestation called Systematicity and…