Despite the remarkable successes of Large Language Models (LLMs), the underlying Transformer architecture has inherent limitations in handling complex reasoning tasks. Chain-of-Thought (CoT) prompting has emerged as a practical workaround, but most CoT-based methods rely on a single generic prompt like “think step by step,” with no task-specific adaptation. These approaches expect the model to discover an effective reasoning path on its own, forcing it to search through a vast prompt space. In contrast, many work has explored task-specific prompt designs to boost performance. However, these designs are typically developed through trial and error, lacking a theoretical ground. As a result, prompt engineering remains largely ad hoc and unguided.In this paper, we provide a theoretical framework that explains why some prompts succeed while others fail. We show that prompts function as selectors, extracting specific task-relevant information from the model’s full hidden state during CoT reasoning. Each prompt defines a unique trajectory through the answer space, and the choice of this trajectory is crucial for task performance and future navigation in the answer space.We analyze the complexity of finding optimal prompts and the size of the prompt space for a given task. Our theory reveals principles behind effective prompt design and shows that naive CoT—using model-self-guided prompt like “think step by step” —can severely hinder performance. Showing that optimal prompt search can lead to over a 50% improvement on reasoning tasks through experiments, our work provide a theoretical foundation for prompt engineering.

In this work, we utilize Large Language Models (LLMs) for a novel use case: constructing Performance Predictors (PP) that estimate the performance of specific deep neural network architectures on downstream tasks. We create PP prompts for LLMs, comprising (i) role descriptions, (ii) instructions for the LLM, (iii) hyperparameter definitions, and (iv) demonstrations presenting sample architectures with efficiency metrics and ‘training from scratch’ performance. In machine translation (MT) tasks, GPT-4 with our PP prompts (LLM-PP) achieves a SoTA mean absolute error and a slight degradation in rank correlation coefficient compared to baseline predictors. Additionally, we demonstrate that predictions from LLM-PP can be distilled to a compact regression model (LLM-Distill-PP), which surprisingly retains much of the performance of LLM-PP. This presents a cost-effective alternative for resource-intensive performance estimation. Specifically, for Neural Architecture Search (NAS), we introduce a Hybrid-Search algorithm (HS-NAS) employing LLM-Distill-PP for the initial search stages and reverting to the baseline predictor later. HS-NAS performs similarly to SoTA NAS, reducing search hours by approximately 50%, and in some cases, improving latency, GFLOPs, and model size. The code can be found at: https://github.com/UBC-NLP/llmas.