PACED: Distillation and Self-Distillation at the Frontier of Student Competence

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight $w(p) = p^α(1 - p)^β$ derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel $w(p) = p^α(1-p)^β$ is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only $O(δ^2)$. (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

PACED: Distillation at the Frontier of Student Competence

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight $w(p) = p^α(1 - p)^β$ derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel $w(p) = p^α(1-p)^β$ is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only $O(δ^2)$. (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

On-Policy Self-Distillation for Reasoning Compression

Reasoning models think out loud, but much of what they say is noise. We introduce OPSDC (On-Policy Self-Distillation for Reasoning Compression), a method that teaches models to reason more concisely by distilling their own concise behavior back into themselves. The entire approach reduces to one idea: condition the same model on a "be concise" instruction to obtain teacher logits, and minimize per-token reverse KL on the student's own rollouts. No ground-truth answers, no token budgets, no difficulty estimators. Just self-distillation. Yet this simplicity belies surprising sophistication: OPSDC automatically compresses easy problems aggressively while preserving the deliberation needed for hard ones. On Qwen3-8B and Qwen3-14B, we achieve 57-59% token reduction on MATH-500 while improving accuracy by 9-16 points absolute. On AIME 2024, the 14B model gains 10 points with 41% compression. The secret? Much of what reasoning models produce is not just redundant-it is actively harmful, compounding errors with every unnecessary token.

Overconfident Errors Need Stronger Correction: Asymmetric Confidence Penalties for Reinforcement Learning

Reinforcement Learning with Verifiable Rewards (RLVR) has become the leading paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard RLVR algorithms suffer from a well-documented pathology: while they improve Pass@1 accuracy through sharpened sampling, they simultaneously narrow the model's reasoning boundary and reduce generation diversity. We identify a root cause that existing methods overlook: the uniform penalization of errors. Current approaches -- whether data-filtering methods that select prompts by difficulty, or advantage normalization schemes -- treat all incorrect rollouts within a group identically. We show that this uniformity allows overconfident errors (incorrect reasoning paths that the RL process has spuriously reinforced) to persist and monopolize probability mass, ultimately suppressing valid exploratory trajectories. To address this, we propose the Asymmetric Confidence-aware Error Penalty (ACE). ACE introduces a per-rollout confidence shift metric, c_i = log(pi_theta(y_i|x) / pi_ref(y_i|x)), to dynamically modulate negative advantages. Theoretically, we demonstrate that ACE's gradient can be decomposed into the gradient of a selective regularizer restricted to overconfident errors, plus a well-characterized residual that partially moderates the regularizer's strength. We conduct extensive experiments fine-tuning Qwen2.5-Math-7B, Qwen3-8B-Base, and Llama-3.1-8B-Instruct on the DAPO-Math-17K dataset using GRPO and DAPO within the VERL framework. Evaluated on MATH-500 and AIME 2025, ACE composes seamlessly with existing methods and consistently improves the full Pass@k spectrum across all three model families and benchmarks.

An Extendible, Graph-Neural-Network-Based Approach for Accurate Force Field Development of Large Flexible Organic Molecules

An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accuracy beyond density functional theory is often needed to describe the intermolecular interactions, while most correlated wavefunction (CW) methods are prohibitively expensive for large molecules. Therefore, it posts a great challenge to develop an extendible ab initio force field for large flexible organic molecules at CW level of accuracy. In this work, we face this challenge by combining the physics-driven nonbonding potential with a data-driven subgraph neural network bonding model (named sGNN). Tests on polyethylene glycol polymer chains show that our strategy is highly accurate and robust for molecules of different sizes. Therefore, we can develop the force field from small molecular fragments (with sizes easily accessible to CW methods) and safely transfer it to large polymers, thus opening a new path to the next-generation organic force fields.