LLMs are highly sensitive to prompt design, but handcrafting effective prompts is difficult and often requires intricate crafting of few-shot examples. We propose a fast automatic prompt construction algorithm that augments human instructions by generating a small set of few shot examples. Our method iteratively replaces/drops/keeps few-shot examples using Monte Carlo Shapley estimation of example utility. For faster execution, we use aggressive subsampling and a replay buffer for faster evaluations. Our method can be run using different compute time budgets. Under a limited budget, it outperforms prior automatic prompting methods on text simplification and mathematical reasoning (GSM8K, DeepMath, Math500), while achieving second-best results on classification and summarization and third-best on MedQA. With an extended, yet still modest budget, PIAST sets a new state of the art among automatic prompting methods on classification, simplification, GSM8K, DeepMath, and Math500. Overall, our results suggest that optimizing in-context examples, rather than exhaustively searching over instruction rewrites is the dominant lever for fast and data-efficient prompt engineering. We will release code and data upon acceptance.

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.