Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
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On the convergence of adam and beyond
15 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.
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2026 15representative citing papers
High-resolution interferometric imaging of eight post-AGB circumbinary discs reveals diverse inner-rim substructures including azimuthal brightness enhancements and arc-like features not explained by inclination alone.
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VISTA adaptively tunes consistency thresholds in decentralized SGD so that the system converges asymptotically like standard SGD even when adversaries dominate the worker pool.
New optimizer uses auxiliary loss to imitate low-order Hessian information, replacing gradient squares in Adam-like training with convergence guarantee and some experimental gains.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
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New adaptive decentralized algorithms select stepsizes from local curvature estimates derived from a Lyapunov function, delivering sublinear convergence for convex problems and linear rates for strongly convex ones.
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Unsupervised denoising methods improve faint-source detection in astronomical images from HST and CFHT, with better performance when models are initialized on similar-domain data.
Two machine-learned potentials for protonated oxalate agree closely on vibrational energies, IR spectra, and hydrogen tunneling splittings despite using different regression techniques.
Compressed Gluon variants using unbiased/contraction compressors and SARAH-style variance reduction achieve convergence guarantees and lower communication costs in federated learning under layer-wise smoothness.
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Fidelity of Machine Learned Potentials: Quantitative Assessment for Protonated Oxalate
Two machine-learned potentials for protonated oxalate agree closely on vibrational energies, IR spectra, and hydrogen tunneling splittings despite using different regression techniques.