Kelly, Matthew (2026) Compression, Dynamics, and Control in Large Language Models: Toward a High-Level Theory. [Preprint]
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Abstract
This paper introduces a trajectory level of explanation for inference-time behaviour in large language models. Existing frameworks (autoregressive conditioning, mechanistic circuit analysis, and quasi-cognitive description) treat generation as a sequence of context-conditioned draws or as circuit execution. None provides the conceptual resources needed to represent directional properties of inference such as regime persistence, transition thresholds, or asymmetric resistance to perturbation. The paper argues that these limitations are not merely empirical but conceptual, and that their persistence indicates the absence of a distinct explanatory level rather than gaps in current knowledge. These limitations motivate the asymmetry coefficient A(M, γ) = Rout (γ)/Rin (γ) as a methodological discriminator between four competing accounts of inference-time behaviour. The existing theoretical and empirical evidence supports the prerequisites for trajectory-level dynamics but does not establish the hypothesis; the asymmetry coefficient is what does the discriminating work. The structure of the test and its result space are developed at a conceptual level, and alignment gating is reframed as trajectory control over a dynamical process rather than as a fixed property of output distributions.
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