SoftServe: A Scalable Quasi-Newton Method for Deep Learning

Problem

The paper addresses the limitations of traditional Quasi-Newton methods in deep learning, particularly due to the non-convex nature of loss landscapes and the enormous parameter sizes involved. These factors hinder the practical application of such methods, which are known for their efficiency in optimization tasks. The work is presented as a preprint, indicating it has not yet undergone peer review.

Method

The authors propose a novel optimization algorithm named SoftServe. This method derives curvature estimates from the variational objective outlined by Berglund et al. (2025). SoftServe includes both diagonal and Kronecker-factored variants to enhance scalability and efficiency. A key technical contribution is the implementation of a stable coupled Newton-Schulz iteration, which replaces traditional matrix decompositions with GPU-friendly matrix multiplications. This design choice aims to leverage modern hardware capabilities, making the method more applicable to large-scale deep learning tasks.

Results

SoftServe demonstrates lower loss values compared to established optimization algorithms such as Adam, Muon, and SOAP. However, the paper does not provide specific numerical scores for these comparisons, limiting the ability to quantify the performance improvements.

Limitations

The authors do not report any limitations in their work. However, the absence of specific quantitative results regarding loss values compared to baselines may be seen as a limitation for practitioners seeking to evaluate the method's effectiveness rigorously.

Why it matters

The introduction of SoftServe has significant implications for the optimization landscape in deep learning. By addressing the challenges posed by non-convexity and large parameter spaces, this method could facilitate more efficient training of complex models, potentially leading to advancements in various applications of deep learning. The scalable nature of SoftServe may also encourage further exploration of quasi-Newton methods in high-dimensional optimization problems.