Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.

Large language models demonstrate impressive reasoning abilities but struggle to provide personalized content due to their lack of individual user preference information.Existing methods, such as in-context learning and parameter-efficient fine-tuning, fall short in capturing the complexity of human preferences, especially given the small, personal datasets individuals possess.In this paper, we propose a novel approach utilizing small parameter models as preference agents to generate natural language rules that guide a larger, pre-trained model, enabling efficient personalization.Our method involves a small, local "steering wheel" model that directs the outputs of a much larger foundation model, producing content tailored to an individual's preferences while leveraging the extensive knowledge and capabilities of the large model.Importantly, this personalization is achieved without the need to fine-tune the large model.Experimental results demonstrate that our technique significantly outperforms baseline personalization methods.By allowing foundation models to adapt to individual preferences in a data and compute-efficient manner, our approach paves the way for highly personalized language model applications.