Title: Correcting Influence: Unboxing LLM Outputs with Orthogonal Latent Spaces
Primary area: interpretability and explainable AI
Keywords: Influence Functions, Sparse Autoencoder, Interpretability, LLM

Abstract: A critical step for reliable large language models (LLMs) use in healthcare is to at-
tribute predictions to their training data, akin to a medical case study. This requires
token-level precision: pinpointing not just which training examples influence a de-
cision, but which tokens within them are responsible. While influence functions
offer a principled framework for this, prior work is restricted to autoregressive
settings and relies on an implicit assumption of token independence, rendering
their identified influences unreliable. We introduce a flexible framework that in-
fers token-level influence through a latent mediation approach for general predic-
tion tasks. Our method attaches sparse autoencoders to any layer of a pretrained
LLM to learn a basis of approximately independent latent features. Unlike prior
methods where influence decomposes additively across tokens, influence com-
puted over latent features is inherently non-decomposable. To address this, we
introduce a novel method using Jacobian-vector products. Token-level influence
is obtained by propagating latent attributions back to the input space via token
activation patterns. We scale our approach using efficient inverse-Hessian ap-
proximations. Experiments on medical benchmarks show our approach identifies
sparse, interpretable sets of tokens that jointly influence predictions. Our frame-
work enhances trust and enables model auditing, generalizing to any high-stakes
domain requiring transparent and accountable decisions