Group Adaptive Clipping Policy Optimization

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

XClipGS: Exact Half-Space Clipping for Medical Volume Gaussian Splatting

Gaussian-splatting proxies enable interactive rendering of volumetric medical scans, but a clipping plane exposes anatomy not constrained by external-view training and intersects primitives that conventional splatting can only keep or drop whole. We present XClipGS (eXact Clipping), which treats these as two separate problems: the render-time clip operator and supervision of the hidden interior. Under the local affine model used by EWA splatting, the ray integral of a half-space-restricted Gaussian factorizes exactly into its ordinary 2D footprint and a conditional Gaussian CDF whose argument is affine in pixel coordinates. The resulting closed-form per-pixel operator introduces no learned clipping parameters or auxiliary network and remains differentiable with respect to the primitive and plane. We use multi-distance reference views with varied clipping-plane axes and offsets to supervise the interior through the same operator. We also introduce a paired clipped/unclipped cut-face protocol with difference-referenced cut error (CDE) and culled-side leakage (Leak), because global image metrics dilute errors near the plane. On eight CT and MRI volumes with plane offsets not used for training, XClipGS attains the highest PSNR on every volume (33.56 versus 32.34 dB for ClipGS) while rendering at over 650 FPS, far above real time, versus 278 FPS. On voxel-axis cut-face views, it raises average band SSIM from 0.809 to 0.860 and leaks roughly 40 times less. Without retraining, it also achieves the best average across all four metrics on arbitrary-normal planes; on a fixed interior, it matches RaRa's face fidelity with about 16 times less leakage. Project page: https://gaozhongpai.github.io/XClipGS/

High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence

We study first-order methods for smooth objectives satisfying the Polyak-Łojasiewicz (PL) condition when gradient samples are generated by an exogenous Markov chain. In the light-tailed setting, prior uniform-in-time high-probability bounds for ordinary Stochastic Gradient Descent (SGD) under a standard growth envelope scale as $\widetilde{O}(t_{mix}^2/k)$, leaving a gap with the $\widetilde{O}(t_{mix}/k)$ expectation bounds. We close this gap using a lag-blocking argument to establish a uniform high-probability guarantee with a leading stochastic term of $\widetilde{O}(t_{mix}/(k+K_0))$ under geometric mixing. We prove this linear dependence on the mixing time is optimal via a matching $Ω(σ^2 t_{mix}/k)$ lower bound on a quadratic objective driven by a persistent two-state chain. We then extend this framework to heavy-tailed Markovian gradients satisfying a stationary finite-$p$-moment condition, $p \in (1,2]$. We design an all-samples clipped block method that uses every Markov transition while mitigating Markovian bias. Under a transition budget $T$, this algorithm achieves a high-probability stochastic error of $\widetilde{O}(σ_p^2(t_{mix}/T)^{2(p-1)/p})$. We establish a matching lower bound by reducing PL optimization to heavy-tailed mean estimation for a sticky Markov chain. Ultimately, this work tightly characterizes the optimal polynomial dependence on mixing time for light-tailed PL-SGD, and the optimal heavy-tail exponent and effective-sample-size dependence in the robust regime.

Clipping the Price of Adaptivity at the Tail

Adaptive stochastic convex optimization (SCO) methods face a fundamental ``price of adaptivity'' barrier: under the standard set of assumptions, they cannot efficiently adapt to large uncertainty in both the initial distance to optimality and the Lipschitz constant. We circumvent this barrier by requiring a small amount of additional structure common to many learning problems. Specifically, we assume that the objective decomposes into a model and a loss function, enabling us to intervene by modifying the model's output before it passes to the loss function. Under this assumption, we design a method that clips the learned model output in tail events where it deviates too much from the output of a fixed reference model. Our method matches the optimal bounds for known-parameter SCO up to logarithmic factors in the uncertainty in the distance and Lipschitz parameters, thus efficiently adapting to large uncertainty in both.

Clipping Bottleneck: Stabilizing RLVR via Stochastic Recovery of Near-Boundary Signals

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a central paradigm for scaling LLM reasoning, yet its optimization often suffers from training instability and suboptimal convergence. Through a systematic dissection of clipping-based GRPO-style objectives, we identify the rigid clipping decision induced by hard clipping as a key practical bottleneck in the studied RLVR setups. Specifically, our analysis suggests that informative signals can lie in the near-boundary region just beyond the clipping threshold, and are therefore discarded by the standard hard-clipping rule. Notably, once this bottleneck is precisely identified, even simple stochastic perturbations at the boundary can recover meaningful performance gains. Building on this finding, we propose Near-boundary Stochastic Rescue (NSR), a minimal, plug-and-play modification that stochastically retains these slightly out-of-bound tokens to recover lost signals. While NSR, via stochastic sampling, can be interpreted as inducing an implicit gradient decay in expectation, our ablations reveal that its stochastic, boundary-local rescue mechanism is consistently more effective than deterministic gradient decay. Validated by extensive experiments across model sizes from 7B to 30B and both dense and MoE architectures, as a plug-and-play solution, NSR substantially improves training stability and delivers consistent gains over strong baselines such as DAPO and GSPO.