Training data attribution stalls on large models because it stores every projected gradient, so LoRIF keeps only low-rank factors
AspireAI community · arXiv (cs.LG)
Influence-function methods for training data attribution are theoretically grounded but scale badly: storing and loading projected per-example gradients for every training example makes query latency I/O bound, and the inverse Hessian approximation costs O(D squared) memory. LoRIF stores rank-c factors of the projected gradients instead, cutting storage and query I/O from O(D) to O(c times square root of D) per layer per sample, and uses truncated SVD with the Woodbury identity to approximate the inverse Hessian in an r-dimensional subspace, reducing memory from O(D squared) to O(D times r). On models from 0.1B to 70B parameters trained on datasets with millions of examples, it reports up to 20 times storage reduction.
Read the story and explore more from the AspireAI community.
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.