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

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…

The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

Modern architectures for high-performance computing and deep learning increasingly incorporate specialized tensor instructions, including tensor cores for matrix multiplication and hardware-optimized copy operations for multi-dimensional…

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

Providing students with detailed and timely grading feedback is essential for self-learning. While existing LLM-based grading systems are promising, most of them rely on one single model, which limits their performance. To address this, we…

This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects. Lambda Prolog achieves its…

Machine learning (ML) is successful in achieving human-level performance in various fields. However, it lacks the ability to explain an outcome due to its black-box nature. While existing explainable ML is promising, almost all of these…

Large language model (LLM) inference has been a prevalent demand in daily life and industries. The large tensor sizes and computing complexities in LLMs have brought challenges to memory, computing, and databus. This paper proposes a…

We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and…

Theory evaluation is a key problem in many areas: machine learning, scientific discovery, inverse engineering, decision making, software engineering, design, human sciences, etc. If we have a set of theories that are able to explain the…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

The approaches that guide Large Language Models (LLMs) to emulate human reasoning during response generation have emerged as an effective method for enabling them to solve complex problems in a step-by-step manner, thereby achieving…

Significant advancements has recently been achieved in the field of multi-modal large language models (MLLMs), demonstrating their remarkable capabilities in understanding and reasoning across diverse tasks. However, these models are often…

Matrix and tensor-guided parametrization for Natural Language Processing (NLP) models is fundamentally useful for the improvement of the model's systematic efficiency. However, the internal links between these two algebra structures and…

With the increasing penetration of renewable energy, traditional physics-based power system operation faces growing challenges in achieving economic efficiency, stability, and robustness. Machine learning (ML) has emerged as a powerful tool…

Chain-of-Thought (CoT) prompting improves reasoning in large language models (LLMs), but its reliance on unstructured text limits interpretability and executability in embodied tasks. Prior work has explored structured CoTs using scene or…

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…