Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

Primary sclerosing cholangitis (PSC) is a rare disease wherein altered bile acid metabolism contributes to sustained liver injury. This paper introduces REMEDI, a framework that captures bile acid dynamics and the body's adaptive response during PSC progression that can assist in exploring treatments. REMEDI merges a differential equation (DE)-based mechanistic model that describes bile acid metabolism with reinforcement learning (RL) to emulate the body's adaptations to PSC continuously. An objective of adaptation is to maintain homeostasis by regulating enzymes involved in bile acid metabolism. These enzymes correspond to the parameters of the DEs. REMEDI leverages RL to approximate adaptations in PSC, treating homeostasis as a reward signal and the adjustment of the DE parameters as the corresponding actions. On real-world data, REMEDI generated bile acid dynamics and parameter adjustments consistent with published findings. Also, our results support discussions in the literature that early administration of drugs that suppress bile acid synthesis may be effective in PSC treatment.