Fractional reasoning in LLMS: a new way of controlling the inference depth

What is included in this article:

The limits of calculating the current test time LLM strategies. Introduction of fractional reasoning (FR) As a framework without training, without automobile model. Latent state manipulation techniques Using reasoning prompts and an adjustable scale. Distribution advantages based on width and depth Demonstrated through GSM8K, Math500 and GPQA. Evaluation results showing the superiority of the FR over the best of N and the majority of votes. Analysis of the behavior of the FR Through different models, including Deepseek-R1.

Introduction: challenges in uniform reasoning during inference

The LLMs have shown improvements in various fields, the calculation of the test time playing a crucial role in their performance. This approach improves reasoning during inference by allocating additional calculation resources, such as the generation of several candidate responses and the most appropriate selection, or refine the responses in an iterative manner by self-reflection. However, the current testing time calculation strategies deal with all the problems uniformly, applying the same depth of reasoning, regardless of the difficulty or structure of the request. In reality, the reasoning needs are very variable, and reasoning with a sub-reflection or reflection can lead to degraded responses or unnecessary calculation costs. Therefore, LLMs must be able to dynamically adjust their depth of reasoning or their level of reflection.

Previous work: management control and latent representation

Existing research has explored various methods to improve LLM reasoning by scaling up time and control of the latent state. The technique of the chain of thoughts (COT) guides models to break down complex problems into intermediate steps to improve the performance of reasoning. The results reward models (Orms) and processes reward models (PRMS) assess the responses generated according to the accuracy or quality of internal reasoning. In addition, the engineering methods of the representation use direction vectors in LLM latent spaces for a controlled generation, while methods such as vectors in context (ICV) extract the latent vectors of demonstrations to internal management states at the time of inference, and finetuning representation (REF) learns low -rank interventions.

The proposed framework: fractional reasoning for adaptive inference

Researchers from the University of Stanford have proposed a fractional reasoning (FR), a framework without training and model of cars to improve the calculation of the test time thanks to an adaptive reasoning control. Fr adjusts the behavior of the reasoning by directly modifying the internal representations of the model, in extraction of the latent lag shift induced by inputs promoting reasoning such as bed or reflection prompts, and by applying this offset again with a factor of scaling. This allows models to adjust the depth of reasoning during inference without modifying the input text or requiring fine adjustment. The FR supports and improves two key forms of testing time testing: (a) the width-based scaling, like the best of N and the majority, and (b) depth-based scale, such as self-reflection.

Benchmarking: performance gains on reasoning tasks

Fr is evaluated on three benchmarks which require reasoning in several steps: GSM8K, Math500 and GPQA. The evaluation uses sets of tests for GSM8K and Math500 when using the diamond division for GPQA. The main experiments use two models for adjusting the Open Source Competitive: QWEN2.5-7B-ISTRUCT and LLAMA-3.1-8B-ISTRUCT, which both demonstrate solid reasoning capacities and give access to the latent state representations required by the proposed method. FR surpasses standard test calculation methods on all benchmarks and models, showing that it can strongly improve performance. Adjusting the influence of prompts allows a broader exploration of the solution space, increasing the effectiveness of traditional test calculation methods.

Agnostic behavior and generality of the fractional reasoning model

The researchers also analyzed the FR to understand its behavioral dynamics, its generality between models and other measures. The analysis reveals that the increase in the scaling parameter leads to longer outputs with a reasoning in several more detailed steps, confirming the behavior of the bou model the framework predictable and continuously. The FR remains effective even when applied to models specialized in reasoning such as Deepseek-R1-Distill-Qwen-7b, improving precision compared to the basic lines inviting standard and showing its generality in LLM for general and specialized use. Performance scaling analysis shows improvements consistent with an increasing number of generations, and FR shows higher accuracy in most sampling budgets compared to the majority voting reference base.

Conclusion: towards a more dynamic and more efficient LLM inference

In conclusion, researchers from the University of Stanford have introduced a fractional reasoning (FR), a framework without training and model of cars which improves the calculation of the test time by the adaptive control of the behavior of the reasoning in the LLM. It offers a general and interpretable approach for a more precise and more effective allowance of the calculation effort during inference, overcoming the limitation of the application of uniform reasoning in the strategies for calculating the current test time. However, the framework currently depends on the predefined reasoning departments and lack of automatic selection of scaling factors, indicating future research guidelines to adaptive policies for fully dynamic inference.

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