SGD Convergence under Stepsize Shrinkage in Low-Precision Training

• URL: http://arxiv.org/abs/2508.07142v2
• Date: Sun, 24 Aug 2025 09:22:59 GMT
• Title: SGD Convergence under Stepsize Shrinkage in Low-Precision Training
• Authors: Vincent-Daniel Yun,
• Abstract summary: quantizing gradient shrinkage introduces magnitude shrinkage, which can change how gradient descent converges.<n>We show that this shrinkage affect the usual stepsize ( mu_k q_k ) with an effective stepsize ( mu_k q_k )<n>We prove that low-precision SGD still converges, but at a slower pace set by ( q_min ) and with a higher steady error level due to quantization effects.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Low-precision training has become crucial for reducing the computational and memory costs of large-scale deep learning. However, quantizing gradients introduces magnitude shrinkage, which can change how stochastic gradient descent (SGD) converges. In this study, we explore SGD convergence under a gradient shrinkage model, where each stochastic gradient is scaled by a factor \( q_k \in (0,1] \). We show that this shrinkage affect the usual stepsize \( \mu_k \) with an effective stepsize \( \mu_k q_k \), slowing convergence when \( q_{\min} < 1 \). With typical smoothness and bounded-variance assumptions, we prove that low-precision SGD still converges, but at a slower pace set by \( q_{\min} \), and with a higher steady error level due to quantization effects. We analyze theoretically how lower numerical precision slows training by treating it as gradient shrinkage within the standard SGD convergence setup.

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