Emergence Invariance: From Symbolized Thought to Interface Refinement

Abstract:Language can be viewed as a formalized subset of thought: a consequence-governed symbolic structure projected from wider situated cognition. Large language models trained at scale exhibit compensatory emergence: sparse architectural primitives support in-context learning, multi-step reasoning, tool use, and chain of thought. Yet a language-first probabilistic architecture inherits substantive, substrate, and high-level incompletenesses relative to human cognition. Their coexistence makes an LLM a human-like thought-form generator that reconstructs increasingly human-like reasoning forms from an incomplete substrate. We ask whether emergence can compensate for every missing distinction. We formalize the philosophical premise as the Symbolization--Substructure Thesis and introduce emergence invariance. For a scale-indexed family acting through a shared task interface $\phi$, $\mathcal{R}_s^*=\mathcal{R}_\phi^*+C_s$: scale can reduce the compensation gap $C_s$, while a positive interface floor $\mathcal{R}_\phi^*$ persists. We prove that, under a fixed input law, one interface is universally no less informative exactly when its completed information $\sigma$-field refines the other, and that total compensation occurs exactly when both the interface floor and asymptotic compensation gap vanish. The framework unifies existing results on grounding, memory, position, attention, Bayesian inheritance, scientific abduction, and reasoning control. In a matched DeepSeek V4-Flash API study, thinking improves pointer chasing from $0/16$ to $14/16$ when relevant distinctions are available; exact observational twins remain at their $50\%$ construction floor; and restoring decisive memory moves matched performance from $50\%$ to $100\%$. These results provide initial evidence for the predicted separation between scaling within an interface and refining the interface itself.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2608.01548 [cs.AI]

(or arXiv:2608.01548v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.01548 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.