Entropy Regularizing Activation: Boosting Continuous Control, Large Language Models, and Image Classification with Activation as Entropy Constraints

We propose ERA, a new paradigm for entropy-constrained policy via output activation. It guarantees minimum sampling entropy by transforming the outputs of the last layer. Our approach demonstrates broad effectiveness across different domains: 1) for large language models~(LLMs), boosting the AIME 2025 score for Qwen2.5-Math-7B by 37.4%; 2) for continuous control reinforcement learning agents, improving performance by more than 30% over strong baselines such as SAC on the challenging HumanoidBench; 3) for image classification, enhancing ImageNet top-1 accuracy by 0.69% for ResNet-50. These gains are achieved with a computational overhead of less than 7%. Our work validates output activation as a powerful tool for entropy control, opening a new direction for designing simpler and more robust algorithms.