Factor Augmented High-Dimensional SGD
Authors: Shubo Li, Yuefeng Han, Xiufan Yu
Summary
arXiv:2605. 19291v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning.
Relevance
Read next because Factor Augmented High-Dimensional SGD overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)", experiment "Follow-up to #354: cascading chunk-binding — does A→B, B→C, C→D propagate the full chain on a recipient trained only to emit A?". Matching terms: under, line, rate, full, factor, stage. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.19291v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations in high-dimensional learning tasks. Unlike standard two-stage dimension reduction approaches that rely on offline representation learning and full data storage, a key novelty of FSGD is that it operates purely on streaming data, making it scalable to large-scale and high-dimensional problems. Furthermore, we establish the first theoretical framework that explicitly incorporates latent factor estimation error into the analysis of SGD, and provide moment convergence in $\ell^s$ norm under decaying step sizes and mini-batch updates. Our results provide a new foundation for employing SGD reliably and scalably in high-dimensional machine learning systems.