arXiv Machine Learning
Token Space: A Category Theory Framework for AI Computations
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arXiv AI
Sep 18
Labeled Incidence Structures for Native Transformer Modeling of Text, Knowledge Graphs, and Hypergraphs
arXiv:2609. 20278v1 Announce Type: cross Abstract: Text, knowledge graphs, and hypergraphs all have elements that play distinct roles within relation instances, structure that is lost when data is flattened into token sequences.
arXiv AI
Sep 15
Unraveling the iterative CHAD
arXiv:2505.15002v3 Announce Type: replace-cross Abstract: Combinatory Homomorphic Automatic Differentiation (CHAD) was originally formulated as a semantics-driven source-to-source transformation for...
arXiv AI
Jul 3
Working Paper: Towards a Category-theoretic Comparative Framework for Artificial General Intelligence
arXiv:2603. 28906v4 Announce Type: replace Abstract: AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit.
arXiv AI
Jul 22
From Dependency to Compositionality: A Neurosymbolic Lifting of LLM Outputs via Combinatory Categorial Grammar
arXiv:2607. 18961v1 Announce Type: new Abstract: Large language models (LLMs) generate fluent text by incrementally predicting the next token from a prefix.
arXiv AI
Aug 24
Toward Auto-Research: Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure
The paper proposes a method for automated research‑idea generation that preserves the typed structure of scientific papers by modeling each paper as a small category with typed research entities as objects and asserted relations as morphisms. It introduces a three‑layer algorithm—categorical signature clustering, a functor‑preservation gate, and a six‑axis LLM plausibility judge—to identify cross‑domain analogies that maintain relation chains. Experiments on tens of thousands of papers show the categorical gate filters candidates at a 17:1 ratio while keeping a falsifier rate above 83%, and it logs rejected candidates with detailed rationale.
arXiv AI
Jun 2
AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning
arXiv:2606. 00671v1 Announce Type: new Abstract: We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning.