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Researcher profile

Aaron Defazio

Aaron Defazio contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer Visioneess.IVmath.OCArtificial Intelligence

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Published work

7 published item(s)

preprint2026arXiv

ScheduleFree+: Scaling Learning-Rate-Free & Schedule-Free Learning to Large Language Models

Schedule-Free Learning has shown promise as a practical anytime training method for machine learning, showing success across dozens of standard benchmark problems. However, strong performance for LLM training has only been demonstrated at small scales. We identify a number of fixes necessary to scale up Schedule-Free Learning to larger batch sizes and model sizes, and present a learning-rate-free and schedule-free method (ScheduleFree+) for training large language models which greatly outperforms Warmup-Stable-Decay (WSD) schedules. We also demonstrate that Schedule-Free Learning is most effective for long duration training, and at 1000 tokens per parameter, it outperforms SOTA schedules by 31%. Schedule-Free Learning provides a theoretical foundation for the use of model averaging and checkpoint merging during pretraining.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Grad-GradaGrad? A Non-Monotone Adaptive Stochastic Gradient Method

The classical AdaGrad method adapts the learning rate by dividing by the square root of a sum of squared gradients. Because this sum on the denominator is increasing, the method can only decrease step sizes over time, and requires a learning rate scaling hyper-parameter to be carefully tuned. To overcome this restriction, we introduce GradaGrad, a method in the same family that naturally grows or shrinks the learning rate based on a different accumulation in the denominator, one that can both increase and decrease. We show that it obeys a similar convergence rate as AdaGrad and demonstrate its non-monotone adaptation capability with experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Almost sure convergence rates for Stochastic Gradient Descent and Stochastic Heavy Ball

We study stochastic gradient descent (SGD) and the stochastic heavy ball method (SHB, otherwise known as the momentum method) for the general stochastic approximation problem. For SGD, in the convex and smooth setting, we provide the first \emph{almost sure} asymptotic convergence \emph{rates} for a weighted average of the iterates . More precisely, we show that the convergence rate of the function values is arbitrarily close to $o(1/\sqrt{k})$, and is exactly $o(1/k)$ in the so-called overparametrized case. We show that these results still hold when using stochastic line search and stochastic Polyak stepsizes, thereby giving the first proof of convergence of these methods in the non-overparametrized regime. Using a substantially different analysis, we show that these rates hold for SHB as well, but at the last iterate. This distinction is important because it is the last iterate of SGD and SHB which is used in practice. We also show that the last iterate of SHB converges to a minimizer \emph{almost surely}. Additionally, we prove that the function values of the deterministic HB converge at a $o(1/k)$ rate, which is faster than the previously known $O(1/k)$. Finally, in the nonconvex setting, we prove similar rates on the lowest gradient norm along the trajectory of SGD.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Beyond Folklore: A Scaling Calculus for the Design and Initialization of ReLU Networks

We propose a system for calculating a "scaling constant" for layers and weights of neural networks. We relate this scaling constant to two important quantities that relate to the optimizability of neural networks, and argue that a network that is "preconditioned" via scaling, in the sense that all weights have the same scaling constant, will be easier to train. This scaling calculus results in a number of consequences, among them the fact that the geometric mean of the fan-in and fan-out, rather than the fan-in, fan-out, or arithmetic mean, should be used for the initialization of the variance of weights in a neural network. Our system allows for the off-line design & engineering of ReLU neural networks, potentially replacing blind experimentation.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

End-to-End Variational Networks for Accelerated MRI Reconstruction

The slow acquisition speed of magnetic resonance imaging (MRI) has led to the development of two complementary methods: acquiring multiple views of the anatomy simultaneously (parallel imaging) and acquiring fewer samples than necessary for traditional signal processing methods (compressed sensing). While the combination of these methods has the potential to allow much faster scan times, reconstruction from such undersampled multi-coil data has remained an open problem. In this paper, we present a new approach to this problem that extends previously proposed variational methods by learning fully end-to-end. Our method obtains new state-of-the-art results on the fastMRI dataset for both brain and knee MRIs.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction

Magnetic Resonance Image (MRI) acquisition is an inherently slow process which has spurred the development of two different acceleration methods: acquiring multiple correlated samples simultaneously (parallel imaging) and acquiring fewer samples than necessary for traditional signal processing methods (compressed sensing). Both methods provide complementary approaches to accelerating the speed of MRI acquisition. In this paper, we present a novel method to integrate traditional parallel imaging methods into deep neural networks that is able to generate high quality reconstructions even for high acceleration factors. The proposed method, called GrappaNet, performs progressive reconstruction by first mapping the reconstruction problem to a simpler one that can be solved by a traditional parallel imaging methods using a neural network, followed by an application of a parallel imaging method, and finally fine-tuning the output with another neural network. The entire network can be trained end-to-end. We present experimental results on the recently released fastMRI dataset and show that GrappaNet can generate higher quality reconstructions than competing methods for both $4\times$ and $8\times$ acceleration.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Offset Sampling Improves Deep Learning based Accelerated MRI Reconstructions by Exploiting Symmetry

Deep learning approaches to accelerated MRI take a matrix of sampled Fourier-space lines as input and produce a spatial image as output. In this work we show that by careful choice of the offset used in the sampling procedure, the symmetries in k-space can be better exploited, producing higher quality reconstructions than given by standard equally-spaced samples or randomized samples motivated by compressed sensing.

0 citations0 reviewsNo code linkedOpen access