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Oct 16

ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation

Inference-time control steers a pretrained generative model towards a target distribution without retraining. We study tilted targets π_0propto G_0,p_0, where p_0 is the sampler output distribution and G_0 is an evaluable reweighting function. Existing approaches rely on sequential annealing with sequential Monte Carlo (SMC) or parallel annealing with replica exchange (RE). Sequential control is exact but needs large particle populations, whereas no exact parallel control method exists: existing RE corrections approximate an intractable time reversal and are biased. We propose Exact Non-equilibrium COntrol with Replica Exchange (ENCORE), the first exact parallel control method. Each replica stores its generation trajectory, so the upward move is a truncation and the intractable time reversal is never simulated. We prove target invariance and show that the resulting dynamics are those of non-equilibrium replica exchange with the exact time reversal as forward proposal. Under regularity conditions, our diffusion analysis shows that both sequential and parallel control become unstable under refinement of the time discretisation without guidance, whereas guided proposals remain stable and yield diagnostics for tuning the schedule and the computational budget. Across synthetic targets, Boltzmann sampling of biomolecules, and image generation, ENCORE achieves competitive accuracy and diversity, remains robust to sampler perturbations, and applies to distilled samplers where existing RE corrections are unavailable.

  • 4 authors
·
Sep 30

Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition

A core goal of efficient reasoning is to improve the accuracy-efficiency frontier. However, jointly improving reasoning accuracy and inference efficiency can be challenging, as the two objectives can favor different reasoning behaviors. Independently post-trained models already offer distinct strengths in accuracy and efficiency. We introduce Lightning Weave, a post-training framework that extracts and composes these independently learned capabilities in a single student through on-policy distillation. Each acquired capability is represented by the policy shift from the model before post-training to the resulting specialist. Lightning Weave combines aligned log-ratio shifts at shared student token states and uses Tilted-Target DOPD to convert the cached signals into a stable learning target. Each anchor pair scores the cached trajectories once, enabling subsequent student training without serving multiple live anchor models concurrently. Across diverse student models and benchmarks in mathematics and code, Lightning Weave substantially improves upon the base students and achieves a state-of-the-art accuracy-efficiency frontier. On Qwen3.5-4B, it raises HMMT 2025 accuracy from 59.2% to 64.0% with 10.7% fewer response tokens, and LiveCodeBench v5 accuracy from 41.7% to 54.2% with 9.6% fewer response tokens. Adjusting the relative strengths of the anchor signals yields a strong empirical accuracy-efficiency Pareto frontier. These results establish Lightning Weave as a new practical route to efficient reasoning through capability composition. Code will be released soon.

  • 3 authors
·
Sep 12 2