• Corpus ID: 211171365

# The Geometry of Sign Gradient Descent

@article{Balles2020TheGO,
title={The Geometry of Sign Gradient Descent},
author={Lukas Balles and Fabian Pedregosa and Nicolas Le Roux},
journal={ArXiv},
year={2020},
volume={abs/2002.08056}
}
• Published 19 February 2020
• Computer Science
• ArXiv
Sign-based optimization methods have become popular in machine learning due to their favorable communication cost in distributed optimization and their surprisingly good performance in neural network training. Furthermore, they are closely connected to so-called adaptive gradient methods like Adam. Recent works on signSGD have used a non-standard "separable smoothness" assumption, whereas some older works study sign gradient descent as steepest descent with respect to the $\ell_\infty$-norm. In…
7 Citations

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## References

SHOWING 1-10 OF 34 REFERENCES

### signSGD: compressed optimisation for non-convex problems

• Computer Science
ICML
• 2018
SignSGD can get the best of both worlds: compressed gradients and SGD-level convergence rate, and the momentum counterpart of signSGD is able to match the accuracy and convergence speed of Adam on deep Imagenet models.

### Adam: A Method for Stochastic Optimization

• Computer Science
ICLR
• 2015
This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.

### Entropy-SGD: Biasing Gradient Descent Into Wide Valleys

• Computer Science
ICLR
• 2017
This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape and compares favorably to state-of-the-art techniques in terms of generalization error and training time.

### On Stochastic Sign Descent Methods

• Computer Science
• 2019
This paper performs a general analysis of sign-based methods for non-convex optimization and assures exponentially fast variance reduction with respect to number of nodes, maintaining 1-bit compression in both directions and using small mini-batch sizes.

• Computer Science
ICLR
• 2020
It is shown that gradient smoothness, a concept central to the analysis of first-order optimization algorithms that is often assumed to be a constant, demonstrates significant variability along the training trajectory of deep neural networks, and positively correlates with the gradient norm, and contrary to standard assumptions in the literature.

### Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition

• Computer Science, Mathematics
ECML/PKDD
• 2016
This work shows that this much-older Polyak-Lojasiewicz (PL) inequality is actually weaker than the main conditions that have been explored to show linear convergence rates without strong convexity over the last 25 years, leading to simple proofs of linear convergence of these methods.

### Beyond Convexity: Stochastic Quasi-Convex Optimization

• Computer Science
NIPS
• 2015
This paper analyzes a stochastic version of NGD and proves its convergence to a global minimum for a wider class of functions: it requires the functions to be quasi-convex and locally-Lipschitz.

### BLOCK-NORMALIZED GRADIENT METHOD: AN EMPIRICAL STUDY FOR TRAINING DEEP NEURAL NETWORK

• Computer Science
• 2018
The normalized gradient methods having constant step size with occasionally decay, such as SGD with momentum, have better performance in the deep convolution neural networks, while those with adaptive step sizes perform better in recurrent neural networks.

### Stochastic Spectral Descent for Discrete Graphical Models

• Computer Science
IEEE Journal of Selected Topics in Signal Processing
• 2016
A new, largely tuning-free algorithm that derives novel majorization bounds based on the Schatten- ∞ norm and demonstrates empirically that this algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.

### Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization

• Computer Science
SDM
• 2020
New empirical observations and theoretical results on both the optimization dynamics and generalization behavior of SGD for deep nets based on the Hessian of the training loss and associated quantities are presented.