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Coherence Mechanisms for Provable Self-Improvement

NeurIPS 2026 · Large language models › Agents, code and math · approach: Inductive and abstract reasoning evaluation · 0 citations (OpenAlex)

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Theoretical framework showing that Bregman projection onto coherence sets (invariance-constrained models) provably improves a baseline model toward an ideal model, with extensions to non-realizable, empirical, and relaxed settings, plus characterization and rigidity results; no experiments reported in the provided text.

Problem

Self-improvement of language models and intelligent systems lacks formal guarantees; existing heuristics do not provide provable monotonic improvement.

Approach

Define coherence as invariance of model outputs under task-preserving input transformations (an involution Phi), and treat self-improvement as Bregman projection of the baseline model onto the coherent set, which provably reduces expected Bregman divergence to an ideal coherent model; two-step projection equals direct projection for common divergences, and a characterization theorem argues coheren

Key results

• Direct Bregman projection onto the coherent set satisfies E[B_F(pi* || hat pi)] <= E[B_F(pi* || pi0)] - E[B_F(hat pi || pi0)], giving monotonic improvement.
• Under strong convexity, improvement is lower bounded by (mu/2) * gamma_0 / 4 style incoherence term; the empirical-sample guarantee carries a 6*epsilon_m estimation error term.
• Two-step projection equals direct projection for Euclidean, KL, and separable/quadratic generators.

Limitations

• No empirical experiments in the provided text; the abstract's experimental section is commented out.
• Assumes Phi is an involution (or finite orbit) and a known task-preserving invariance mapping.
• Improvement guarantees rely on realizability or closeness of pi* to the coherent set; universal improvement only under restrictive conditions.

Experimental setup

Metrics: expected Bregman divergence KL divergence improvement bound

Baselines: self-consistency data augmentation via paraphrasing self-instruction RLAIF

Builds on: Bregman divergences Legendre functions self-consistency Pythagorean theorem for Bregman projections

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