Abstract
Influence functions estimate how individual training examples affect the behavior of large language models (LLMs). Analyzing how training data influence different behaviors of an LLM involves repeated influence computation. Reusing stored training gradients reduces the computational cost, but storing full gradients is prohibitively expensive at LLM scale. We study how to compress these gradients while preserving influence estimates for future queries that are unknown at storage time. Through a worst-case analysis, we characterize the optimal fixed-dimensional linear representation and propose eigenbasis-corrected one-bit gradient projection (EOGP) to approximate it at scale. Specifically, EOGP uses EK-FAC to reduce gradient dimensionality, then applies PCA within the retained subspace to learn compression directions from the training gradients. We then apply one-bit quantization to the resulting coordinates, allowing more coordinates to be retained within a fixed storage budget. On GPT-2, EOGP predicts retraining outcomes more accurately than the evaluated compression baselines while using one-sixteenth of their per-example storage. On OLMo 2 SFT models from 1B to 32B parameters, EOGP remains competitive with the baselines allocated over 100 times as much storage per example.
Keywords
Publication details
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- Open access
- Green open access
Cite this article
APA 7
Heo, J., Rosser, J., & Kim, D. (2026). Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection. https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection
MLA 9
Heo, Jaeseung, et al. "Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection." https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection.
Chicago (author–date)
Heo, Jaeseung, J Rosser, and Dongwoo Kim. 2026. "Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection." https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection.
Harvard
Heo, J., Rosser, J. and Kim, D. (2026) 'Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection', Available at: https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection.
Vancouver
Heo J, Rosser J, Kim D. Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection. https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection
IEEE
J. Heo, J. Rosser, and D. Kim, "Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection," https://omanscience.com/en/articles/scaling-influence-functions-in-llms-through-eigenbasis-corrected-one-bit-gradient-projection.