Skip to content

Fast Differentiable SVD on GPU via Polar Decomposition

Sep 2026 · 0 citations · 52 references
Mathematics Computer Science

Abstract

We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration. We show that this approach enables up to a $2\times$ speedup compared to standard implementations. Furthermore, we derive a numerically stable backward pass for the polar decomposition and leverage it to obtain a fully differentiable SVD. Our methods are released as open-source implementations in both PyTorch and JAX: https://github.com/fallnlove/cans_svd.

View source

Similar papers

#machine learning Review Open access Oct 2014

Software development in startup companies: A systematic mapping study

The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.

Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al. · 394 citations · ⚡54

Diffusion models as plug-and-play priors

The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.

Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al. · 316 citations · ⚡15

Trajectory Balance: Improved Credit Assignment in GFlowNets

It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequenc...

Esmeralda S. Whitammer, Moksh Jain, Emmanuel Bengio et al. · 302 citations · ⚡60

KTO: Model Alignment as Prospect Theoretic Optimization

This work proposes a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, and suggests that the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.

Kawin Ethayarajh, Winnie Xu, Niklas Muennighoff et al. · 195 citations · ⚡28
#machine learning Review Open access Jun 2014

Why Early-Stage Software Startups Fail: A Behavioral Framework

This state-of-practice investigation was performed using a literature review followed by a multiple-case study approach and presents how inconsistency between managerial strategies and execution can lead to failure by means of a behavioral framework.

Carmine Giardino, Xiaofeng Wang, P. Abrahamsson · 175 citations · ⚡19

TabICLv2: A better, faster, scalable, and open tabular foundation model

TabICLv2 is introduced, a new state-of-the-art foundation model for regression and classification built on three pillars: a novel synthetic data generation engine designed for high pretraining diversity, various architectural innovations, and optimized pretraining protocols, notably replacing AdamW with the Muon optimi...

Jingang Qu, David Holzmüller, G. Varoquaux et al. · 159 citations · ⚡44

Related blog posts

Microsoft Research Blog Oct 12, 2026

Simulating student learning for better AI tutoring

StudentSim is a research system for evaluating and improving AI tutoring tools before they are tested with learners. It models how individuals may engage with tutors, giving feedback to improve tutor performance across subjects like chess, writing, and mathematics. The post Simulating student learning for better AI tutoring appeared first on Microsoft Research.

MIT News · Artificial Intelligence Oct 7, 2026

Discovering the value of humanistic inquiry

Students in MIT’s Concourse program delve deeply into the human condition, debate challenging questions, and learn to develop judgment about issues that can’t be quantified.

We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.