Offline preference optimization aligns reasoning models from fixed chosen--rejected pairs, yet standard methods apply gradient updates from every pair regardless of its training value under the current policy. We argue that this uniform treatment is wasteful and potentially harmful. From the perspective of gradient utility, we show that a pair's contribution depends jointly on informativeness and stability. Pair utility drifts as the policy evolves, high-gradient samples can coincide with high-curvature regions, leading to noisy and destabilizing updates, and the most effective supervision comes from stable confident errors where the model is reliably wrong yet curvature remains low. These findings motivate SAGE (Stability-Aware Gradient Efficiency), which maintains difficulty-stratified candidate pools refreshed during training and selects pairs within each pool by a forward-pass signal-to-curvature score. Only pairs with high current utility receive gradient computation; the rest are excluded from backpropagation. On mathematical reasoning benchmarks across multiple model scales, SAGE outperforms full-data and size-matched baselines while producing substantially smoother optimization trajectories.
Existing reasoning data curation pipelines score whole samples, treating every intermediate step as equally valuable. In reality, steps within a trace contribute very unevenly, and selecting reasoning data well requires assessing them individually. We present GRACE, a gradient-aligned curation method that views each reasoning trace as a sequence of optimization events and scores every step by two complementary signals: its alignment with the answer-oriented gradient direction, and its consistency with the preceding reasoning trajectory. Step-level scores are aggregated into a sample-level value for subset selection, using only the model's internal optimization signals and no external reward models or step annotations. To make this scalable, GRACE introduces a representation-level gradient proxy that estimates step-level alignment from token-level upstream signals in a single forward pass. Post-training Qwen3-VL-2B-Instruct on MMathCoT-1M, GRACE reaches 108.8% of the full-data performance with 20% of the data and retains 100.2% with only 5%, with subsets that transfer effectively across model backbones.
Preference optimization has become a central paradigm for aligning large language models with human feedback. Direct Preference Optimization (DPO) simplifies reinforcement learning from human feedback by directly optimizing pairwise preferences, removing the need for reward modeling and policy optimization. However, recent work shows that DPO exhibits a squeezing effect, where negative gradients applied to rejected responses concentrate probability mass on high-confidence predictions while suppressing alternative responses. This phenomenon arises even in simple softmax models and can lead to systematic probability collapse during training. We introduce Gradient-Gated Preference Optimization (Gate-DPO), a method that stabilizes training by modulating rejected gradients according to the model's probability geometry. When updates target extremely low-probability responses, the gate attenuates harmful gradients while preserving standard optimization behavior. Gate-DPO addresses this optimization pathology without modifying the underlying preference objective and is complementary to existing methods such as extended SFT, IPO, and Cal-DPO. Experiments across multiple architectures and preference datasets show that Gate-DPO consistently reduces squeezing and improves chosen-response likelihood. Mass-dynamics analysis further reveals healthier optimization behavior, with improved preferred responses and reduced suppression of the overall distribution. Notably, smaller gated models can exhibit stronger chosen-response improvements than larger ungated models, suggesting that controlling gradient dynamics, rather than scale alone, is key to stable and efficient alignment.
Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.