Path Integral Solution for Dissipative Generative Dynamics

TL;DR

This paper demonstrates that dissipative quantum dynamics with non-local context aggregation can generate coherent language, highlighting the importance of dissipation and non-locality for intelligent behavior in mechanical systems.

Contribution

It introduces a novel framework modeling language generation as dissipative quantum field theory, emphasizing the roles of dissipation and non-locality over conservation laws.

Findings

Dissipative quantum dynamics enable coherent text generation.

Spectral analysis reveals decay, growth, and neutral modes in information flow.

Hamiltonian constraints eliminate dissipative modes, degrading performance.

Abstract

Can purely mechanical systems generate intelligent language? We prove that dissipative quantum dynamics with analytically tractable non-local context aggregation produce coherent text generation, while conservation laws cause fundamental failure. Employing Koopman operators with closed-form path integral propagators, we show irreversible computation fundamentally requires both controlled information dissipation and causal context aggregation. Spectral analysis reveals emergent eigenvalue structure, separating into decay modes (forgetting), growth modes (amplification), and neutral modes (preservation) -- the essential ingredients for directed information flow. Hamiltonian constraints force the elimination of these dissipative modes and degrading performance despite unchanged model capacity. This establishes language generation as dissipative quantum field theory, proving mechanical systems acquire intelligence through the combination of dissipation and non-locality, not through conservation.