Related papers: Morpho-logic from a Topos Perspective: Application…
Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic…
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning.…
Compositional visual reasoning has emerged as a key research frontier in multimodal AI, aiming to endow machines with the human-like ability to decompose visual scenes, ground intermediate concepts, and perform multi-step logical inference.…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
The association between language and (non-linguistic) thinking ability in humans has long been debated, and recently, neuroscientific evidence of brain activity patterns has been considered. Such a scientific context naturally raises an…
Morphological tasks use large multi-lingual datasets that organize words into inflection tables, which then serve as training and evaluation data for various tasks. However, a closer inspection of these data reveals profound…
The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by…
Multimodal Large Language Models (MLLMs) have demonstrated impressive performance in general vision-language tasks. However, recent studies have exposed critical limitations in their spatial reasoning capabilities. This deficiency in…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We present a framework where neural models develop an AI Mother Tongue, a native symbolic language that simultaneously supports intuitive reasoning, compositional symbol chains, and inherent interpretability. Unlike post-hoc explanation…
Analogical proportions are statements of the form "A is to B as C is to D". They constitute an inference tool that provides a logical framework to address learning, transfer, and explainability concerns and that finds useful applications in…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic…
Multi-modal learning is a fast growing area in artificial intelligence. It tries to help machines understand complex things by combining information from different sources, like images, text, and audio. By using the strengths of each…
Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to…
Despite the practical success of Artificial Intelligence (AI), current neural AI algorithms face two significant issues. First, the decisions made by neural architectures are often prone to bias and brittleness. Second, when a chain of…
Large Language Models (LLMs) excel at many tasks but often falter on complex problems that require structured, multi-step reasoning. We introduce the Diagram of Thought (DoT), a framework that enables a single LLM to build and navigate a…