Select or Project? Evaluating Lower-dimensional Vectors for LLM Training Data Explanations

2026-01-23

AI Summary

This study addresses the high computational cost of gradient-based explanation methods for large language models, which stems from their extremely high dimensionality, and the lack of systematic evaluation and theoretical grounding for existing dimensionality reduction strategies. The authors construct a new benchmark to systematically compare the performance and efficiency of structure-informed component selection against full-gradient projection in training data influence attribution tasks. They propose and validate an architecture-aware greedy component selection method that significantly reduces computational overhead while preserving high explanation fidelity. Experimental results demonstrate that the selected subset of critical components outperforms both full-gradient and random projection approaches in training data retrieval tasks, achieving superior accuracy and efficiency.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Gradient-based methods for instance-based explanation for large language models (LLMs) are hindered by the immense dimensionality of model gradients. In practice, influence estimation is restricted to a subset of model parameters to make computation tractable, but this subset is often chosen ad hoc and rarely justified by systematic evaluation. This paper investigates if it is better to create low-dimensional representations by selecting a small, architecturally informed subset of model components or by projecting the full gradients into a lower-dimensional space. Using a novel benchmark, we show that a greedily selected subset of components captures the information about training data influence needed for a retrieval task more effectively than either the full gradient or random projection. We further find that this approach is more computationally efficient than random projection, demonstrating that targeted component selection is a practical strategy for making instance-based explanations of large models more computationally feasible.

Problem

• large language models
• instance-based explanation
• gradient dimensionality
• influence estimation
• computational tractability

Innovation

• gradient-based explanation
• component selection
• low-dimensional representation
• training data influence
• large language models