What question did this study set out to answer?

The aim is to develop a unified framework that explains how large language models achieve structured inference through specific computational mechanisms.

February 19, 2026Open Access

Emergent Reasoning in Large Language Models: Soft Unification, Constraint Mechanisms, and Computational Traversal

Key Points

The aim is to develop a unified framework that explains how large language models achieve structured inference through specific computational mechanisms.
Propose a formal framework for interpreting structured inference in large language models.
Reinterpret the transformer architecture as a dynamical system with unique computation methods.
Identify four structural failure modes affecting reasoning processes within language models.
Establish that reasoning in language models can be framed within a topology-constrained traversal of a learned semantic manifold.
Demonstrate that embeddings allow for the emergence of proto-symbolic behavior through attractor regions.
Differentiate between reasoning traversal and verbalization traversal, highlighting variable fidelity nuances.

Abstract

This paper proposes a unified formal framework for understanding how Large Language Models (LLMs) produce structured inference through topology-constrained traversal within a learned semantic manifold. The Transformer architecture is reinterpreted as a dynamical system whose core computation is a preferred direction function — an instance of local preorder traversal on a constraint manifold — implicitly implemented by attention. Context induces constraint sets; embeddings give rise to conceptual topology; attention performs soft, graded unification analogous to symbolic unification; and trajectories over the manifold follow structured flows that manifest as reasoning. Embedding clusters form proto-symbolic attractor regions — Markov objects with approximate conditional independence boundaries — enabling symbolic-like behavior to emerge from continuous computations. A multi-causal hallucination taxonomy identifies four structural failure modes: sparse constraint regions, wrong-attractor capture, competing attractor interference, and know-generate gaps. A two-process model of chain-of-thought distinguishes reasoning traversal from verbalization traversal, with variable fidelity between them. Version 3 incorporates backflows from the Constraint-Emergence Ontology, including: local preorder traversal as a universal computational primitive; the Constraint Functor formalizing the LLM-physics structural correspondence via category theory; and an empirical correspondence section mapping 28 citations from 2023–2025 mechanistic interpretability, representation geometry, and reasoning faithfulness research to the framework's core claims.

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