Training and Inference Dynamics of PLDR-LLMs: Row-Map Collapse, Renormalization, and Predictive Reduction

The paper introduces exact finite work identities that decompose changes in the absolute energy of the row-centered learned map into parameter contributions, signed interactions, and numerical observation defects, and distinguishes absolute row collapse, relative row concentration, operator stabilization, and predictive accuracy. Prior descriptions of PLDR-LLM training dynamics lacked a finite identity framework that attributes energy changes term by term; this work separates exact identities, conditional dynamical claims, and finite empirical findings. The abstract states the theory comes with proofs, selected formal checks, and compact numerical evidence, i.e., a combination of formal derivation and limited numerical validation.

The paper introduces positive affine blocking to retain restarts at the row-constant face and uses the augmented AdamW state to supply the complete dynamical description; predictive renormalization acts on the complete conditional training law for a single pass over distinct corpus target blocks, retaining optimizer memory, remaining data, schedule, and numerical policy. Optimizer memory, remaining data, schedule, and numerical policy are brought into the renormalization object together, rather than reducing only model parameters or loss. The abstract gives a qualitative description of this construction without concrete numbers or scales.

Experiments reveal observer and optimizer dependence, reject the tested autonomous row-state candidates, and support finite conditional prediction and state-specific operator reduction; independent single-pass families exhibit moving finite fluctuation regions without establishing a thermodynamic critical class. Whether autonomous reduction holds is treated as a testable question: autonomous reductions require closure, and approximate reductions carry successor and emission errors. The abstract describes the experiments as compact numerical evidence and explicitly rejects only the tested candidates, not a general conclusion.

The paper specifies assumptions needed to transfer scaling laws to inference, including conditional symmetry, head limits, covariance flows, and readout error budgets. The preconditions for extrapolating scaling laws to inference are made explicit rather than assumed to hold automatically. This is a theoretical statement of conditions; the abstract gives no corresponding experimental scale.

The work targets the specific PLDR-LLM family; its exact identities and conditional dynamical claims apply to the row-centered learned map and to a single pass over distinct corpus target blocks. Predictive renormalization retains optimizer memory, remaining data, schedule, and numerical policy, so it suits settings that need a complete conditional training-law description. For researchers analyzing sources of training energy change, distinguishing row collapse from row concentration, or testing whether autonomous reduction closes, the framework offers an operational decomposition and criteria; transferring scaling laws to inference requires the stated assumptions of conditional symmetry, head limits, covariance flows, and readout error budgets to hold.

The abstract gives no model scale, dataset, training steps, or concrete numbers, so the strength of finite conditional prediction and state-specific operator reduction can only be judged qualitatively; which autonomous row-state candidates were rejected and by what criteria is not spelled out; the gap between the moving finite fluctuation regions of independent single-pass families and a thermodynamic critical class needs the fluctuation analysis in the body to assess; and while proofs and selected formal checks are mentioned, the abstract does not say which propositions were machine-verified and which were derived by hand.