First is Not Really Better Than Last: Evaluating Layer Choice and Aggregation Strategies in Language Model Data Influence Estimation

Identifying how training samples influence/impact Large Language Model (LLM) decision-making is essential for effectively interpreting model decisions and auditing large-scale datasets. Current training sample influence estimation methods (also known as influence functions) undertake this goal by utilizing information flow through the model via its first-order and higher-order gradient terms. However, owing to the large model sizes of today consisting of billions of parameters, these influence computations are often restricted to some subset of model layers to ensure computational feasibility. Prior seminal work by Yeh et al. (2022) in assessing which layers are best suited for computing language data influence concluded that the first (embedding) layers are the most informative for this purpose, using a hypothesis based on influence scores canceling out (i.e., the cancellation effect). In this work, we propose theoretical and empirical evidence demonstrating how the cancellation effect is unreliable, and that middle attention layers are better estimators for influence. Furthermore, we address the broader challenge of aggregating influence scores across layers, and showcase how alternatives to standard averaging (such as ranking and vote-based methods) can lead to significantly improved performance. Finally, we propose better methods for evaluating influence score efficacy in LLMs without undertaking model retraining, and propose a new metric known as the Noise Detection Rate (NDR) that exhibits strong predictive capability compared to the cancellation effect. Through extensive experiments across LLMs of varying types and scales, we concretely determine that the first (layers) are not necessarily better than the last (layers) for LLM influence estimation, contrasting with prior knowledge in the field.