SALT: When More Rollouts Don't Help in Group-Based Policy Optimization and How to Make Them Matter

Reinforcement learning with verifiable rewards (RLVR) often adopts GRPO-style group-relative updates, sampling multiple rollouts per prompt to construct normalized learning signals. However, merely increasing the number of rollouts does not reliably strengthen learning: under GRPO-style group normalization, per-rollout policy-gradient features can concentrate into a low-rank, signed geometry, causing substantial cancellation during aggregation and weakening the effective update. We address this failure mode with SALT, a Subspace-Adaptive geometry pLug-in componenT that uses sample-wise gradient geometry to reweight the coefficients of group-relative updates. SALT estimates a dominant shared subspace from the mini-batch Gram geometry, decomposes group-relative coefficients into shared and residual channels, and adaptively amplifies the residual channel when signed cancellation is severe. Across diverse reasoning-oriented RLVR benchmarks and model scales, SALT improves effective update geometry and performance without modifying the reward model or the rollout sampling procedure

PDF-HR: Pose Distance Fields for Humanoid Robots

Pose and motion priors play a crucial role in humanoid robotics. Although such priors have been widely studied in human motion recovery (HMR) domain with a range of models, their adoption for humanoid robots remains limited, largely due to the scarcity of high-quality humanoid motion data. In this work, we introduce Pose Distance Fields for Humanoid Robots (PDF-HR), a lightweight prior that represents the robot pose distribution as a continuous and differentiable manifold. Given an arbitrary pose, PDF-HR predicts its distance to a large corpus of retargeted robot poses, yielding a smooth measure of pose plausibility that is well suited for optimization and control. PDF-HR can be integrated as a reward shaping term, a regularizer, or a standalone plausibility scorer across diverse pipelines. We evaluate PDF-HR on various humanoid tasks, including single-trajectory motion tracking, general motion tracking, style-based motion mimicry, and general motion retargeting. Experiments show that this plug-and-play prior consistently and substantially strengthens strong baselines. Code and models will be released.

SPICE: Submodular Penalized Information-Conflict Selection for Efficient Large Language Model Training

Information-based data selection for instruction tuning is compelling: maximizing the log-determinant of the Fisher information yields a monotone submodular objective, enabling greedy algorithms to achieve a $(1-1/e)$ approximation under a cardinality budget. In practice, however, we identify alleviating gradient conflicts, misalignment between per-sample gradients, is a key factor that slows down the decay of marginal log-determinant information gains, thereby preventing significant loss of information. We formalize this via an $\varepsilon$-decomposition that quantifies the deviation from ideal submodularity as a function of conflict statistics, yielding data-dependent approximation factors that tighten as conflicts diminish. Guided by this analysis, we propose SPICE, a conflict-aware selector that maximizes information while penalizing misalignment, and that supports early stopping and proxy models for efficiency. Empirically, SPICE selects subsets with higher log-determinant information than original criteria, and these informational gains translate into performance improvements: across 8 benchmarks with LLaMA2-7B and Qwen2-7B, SPICE uses only 10% of the data, yet matches or exceeds 6 methods including full-data tuning. This achieves performance improvements with substantially lower training cost.