BandPO: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for LLM Reinforcement Learning

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce Band-constrained Policy Optimization (BandPO). BandPO replaces canonical clipping with Band, a unified theoretical operator that projects trust regions defined by f-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse.

E2-Capsule Neural Networks for Facial Expression Recognition Using AU-Aware Attention

Capsule neural network is a new and popular technique in deep learning. However, the traditional capsule neural network does not extract features sufficiently before the dynamic routing between the capsules. In this paper, the one Double Enhanced Capsule Neural Network (E2-Capsnet) that uses AU-aware attention for facial expression recognition (FER) is proposed. The E2-Capsnet takes advantage of dynamic routing between the capsules, and has two enhancement modules which are beneficial for FER. The first enhancement module is the convolutional neural network with AU-aware attention, which can help focus on the active areas of the expression. The second enhancement module is the capsule neural network with multiple convolutional layers, which enhances the ability of the feature representation. Finally, squashing function is used to classify the facial expression. We demonstrate the effectiveness of E2-Capsnet on the two public benchmark datasets, RAF-DB and EmotioNet. The experimental results show that our E2-Capsnet is superior to the state-of-the-art methods. Our implementation will be publicly available online.