Longitudinal Value Modeling: Training of Quantitative Value for Token Level Modeling
A token serves as the basic unit of calculation in modern automation models, and the length of production directly influences both the cost of consideration and the performance of the consideration. Despite its importance, existing methods lack refined length models, working primarily at the sequence level. In this paper, we present the Length Value Model (LenVM), a token-level framework that models the length of the remaining generation at each encoding step. By modeling duration as a valuation problem and assigning a negative infinite reward to each token produced, LenVM predicts a finite, discounted return that acts as a monotone proxy over the remaining generation horizon. This architecture provides annotated, dense, unbiased, and scalable monitoring. Experiments on LLMs and VLMs show that LenVM provides the most efficient signal processing time. In the LIFEBench accurate height matching function, using LenVM on the 7B model improves the height score from 30.9 to 64.8, outperforming the boundary closed source models. In addition, LenVM enables continuous control of the trade-off between performance and efficiency. For GSM8K on a budget of 200 tokens, LenVM maintains an accuracy of 63 percent compared to 6 percent of the base token budget. It also accurately predicts the total production length from the fast boundary. Finally, LenVM's token-level values provide an interpretable view of generational dynamics, revealing how certain tokens shift logic in short or long regimes. The results show that LenVM supports a wide range of applications, including length control, projection, and definition of variable generation. They suggest that generation length can be effectively measured as a token value signal, highlighting the potential of LenVM as a general length modeling framework and as a direct value signal that may support future RL training.
- † University of California, Santa Barbara
- ‡ Carnegie Mellon University
- § LMSYS Org
- University of Wisconsin-Madison
