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cite.bib
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@inproceedings{shi2017tnvnn,
author={Shi, Shaohuai and Xu, Pengfei and Chu, Xiaowen},
booktitle={2017 IEEE 23rd International Conference on Parallel and Distributed Systems (ICPADS)},
title={Supervised Learning Based Algorithm Selection for Deep Neural Networks},
year={2017},
volume={},
number={},
pages={344-351},
keywords={Graphics processing units;Kernel;Artificial neural networks;Machine learning;Libraries;Machine learning algorithms;Linear Algebra;Matrix Multiplication;Transpose;GPU;Deep Neural Networks},
doi={10.1109/ICPADS.2017.00053}}
@Manual{bokeh,
title = {Bokeh: Python library for interactive visualization},
author = {{Bokeh Development Team}},
year = {2024},
url = {https://bokeh.org/},
}
@article{paraver,
author = {Computadors, Departament and Pillet, Vincent and Labarta, Jesús and Cortes, Toni and Girona, Sergi},
year = {1995},
month = {03},
pages = {},
title = {PARAVER: A tool to visualize and analyze parallel code},
volume = {44},
journal = {WoTUG-18}
}
@article{grynbaum2023times,
title={The times sues openai and microsoft over ai use of copyrighted work},
author={Grynbaum, Michael M and Mac, Ryan},
journal={The New York Times},
volume={27},
year={2023}
}
@misc{parmar2024nemotron4,
title={Nemotron-4 15B Technical Report},
author={Jupinder Parmar and Shrimai Prabhumoye and Joseph Jennings and Mostofa Patwary and Sandeep Subramanian and Dan Su and Chen Zhu and Deepak Narayanan and Aastha Jhunjhunwala and Ayush Dattagupta and Vibhu Jawa and Jiwei Liu and Ameya Mahabaleshwarkar and Osvald Nitski and Annika Brundyn and James Maki and Miguel Martinez and Jiaxuan You and John Kamalu and Patrick LeGresley and Denys Fridman and Jared Casper and Ashwath Aithal and Oleksii Kuchaiev and Mohammad Shoeybi and Jonathan Cohen and Bryan Catanzaro},
year={2024},
eprint={2402.16819},
archivePrefix={arXiv},
primaryClass={cs.CL}
}
@misc{pytorch-profiler,
author = {Meta},
title = {PyTorch Profiler},
year = {},
publisher = {},
journal = {},
howpublished = {\url{https://pytorch.org/tutorials/recipes/recipes/profiler_recipe.html}},
commit = {}
}
@article{jumpshot,
author = {Omer Zaki and Ewing Lusk and William Gropp and Deborah Swider},
title ={Toward Scalable Performance Visualization with Jumpshot},
journal = {The International Journal of High Performance Computing Applications},
volume = {13},
number = {3},
pages = {277-288},
year = {1999},
doi = {10.1177/109434209901300310},
URL = {
https://doi.org/10.1177/109434209901300310
},
eprint = {
https://doi.org/10.1177/109434209901300310
}
}
@software{omnitrace,
title = {Omnitrace: Application Profiling, Tracing, and Analysis},
author = {AMD Research},
year = {},
journal = {GitHub repository},
publisher = {GitHub},
howpublished = {\url{https://github.com/AMDResearch/omnitrace}}
}
@software{hta,
title = {Holistic Trace Analysis (HTA): A library to analyze PyTorch traces},
author = {Meta Research},
year = {},
journal = {GitHub repository},
publisher = {GitHub},
howpublished = {\url{https://github.com/facebookresearch/HolisticTraceAnalysis}}
}
@article{lamport,
author = {Lamport, Leslie},
title = {Time, clocks, and the ordering of events in a distributed system},
year = {1978},
issue_date = {July 1978},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {21},
number = {7},
issn = {0001-0782},
url = {https://doi.org/10.1145/359545.359563},
doi = {10.1145/359545.359563},
abstract = {The concept of one event happening before another in a distributed system is examined, and is shown to define a partial ordering of the events. A distributed algorithm is given for synchronizing a system of logical clocks which can be used to totally order the events. The use of the total ordering is illustrated with a method for solving synchronization problems. The algorithm is then specialized for synchronizing physical clocks, and a bound is derived on how far out of synchrony the clocks can become.},
journal = {Commun. ACM},
month = {jul},
pages = {558–565},
numpages = {8},
keywords = {multiprocess systems, distributed systems, computer networks, clock synchronization}
}
@ARTICLE{lateness,
author={Isaacs, Katherine E. and Gamblin, Todd and Bhatele, Abhinav and Schulz, Martin and Hamann, Bernd and Bremer, Peer-Timo},
journal={IEEE Transactions on Parallel and Distributed Systems},
title={Ordering Traces Logically to Identify Lateness in Message Passing Programs},
year={2016},
volume={27},
number={3},
pages={829-840},
keywords={Visualization;Partitioning algorithms;Merging;Message passing;Delays;Trace analysis;performance;Trace analysis;performance},
doi={10.1109/TPDS.2015.2417531}}
@inproceedings{trace-vis-task-dependencies,
author = {Haugen, Blake and Richmond, Stephen and Kurzak, Jakub and Steed, Chad A. and Dongarra, Jack},
title = {Visualizing execution traces with task dependencies},
year = {2015},
isbn = {9781450340137},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/2835238.2835240},
doi = {10.1145/2835238.2835240},
abstract = {Task-based scheduling has emerged as one method to reduce the complexity of parallel computing. When using task-based schedulers, developers must frame their computation as a series of tasks with various data dependencies. The scheduler can take these tasks, along with their input and output dependencies, and schedule the task in parallel across a node or cluster. While these schedulers simplify the process of parallel software development, they can obfuscate the performance characteristics of the execution of an algorithm.The execution trace has been used for many years to give developers a visual representation of how their computations are performed. These methods can be employed to visualize when and where each of the tasks in a task-based algorithm is scheduled. In addition, the task dependencies can be used to create a directed acyclic graph (DAG) that can also be visualized to demonstrate the dependencies of the various tasks that make up a workload. The work presented here aims to combine these two data sets and extend execution trace visualization to better suit task-based workloads.This paper presents a brief description of task-based schedulers and the performance data they produce. It will then describe an interactive extension to the current trace visualization methods that combines the trace and DAG data sets. This new tool allows users to gain a greater understanding of how their tasks are scheduled. It also provides a simplified way for developers to evaluate and debug the performance of their scheduler.},
booktitle = {Proceedings of the 2nd Workshop on Visual Performance Analysis},
articleno = {2},
numpages = {8},
keywords = {task-based scheduling, execution trace, data movement, DAG},
location = {Austin, Texas},
series = {VPA '15}
}
@misc{litgpt-2023,
author = {{Lightning AI}},
title = {LitGPT},
howpublished = {\url{https://github.com/Lightning-AI/litgpt}},
year = {2023},
}
@InProceedings{rabenseifneroptimization2004,
author="Rabenseifner, Rolf",
editor="Bubak, Marian
and van Albada, Geert Dick
and Sloot, Peter M. A.
and Dongarra, Jack",
title="Optimization of Collective Reduction Operations",
booktitle="Computational Science - ICCS 2004",
year="2004",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="1--9",
abstract="A 5-year-profiling in production mode at the University of Stuttgart has shown that more than 40{\%} of the execution time of Message Passing Interface (MPI) routines is spent in the collective communication routines MPI{\_}Allreduce and MPI{\_}Reduce. Although MPI implementations are now available for about 10 years and all vendors are committed to this Message Passing Interface standard, the vendors' and publicly available reduction algorithms could be accelerated with new algorithms by a factor between 3 (IBM, sum) and 100 (Cray T3E, maxloc) for long vectors. This paper presents five algorithms optimized for different choices of vector size and number of processes. The focus is on bandwidth dominated protocols for power-of-two and non-power-of-two number of processes, optimizing the load balance in communication and computation.",
isbn="978-3-540-24685-5"
}
@InProceedings{thakurimproving2003,
author="Thakur, Rajeev
and Gropp, William D.",
editor="Dongarra, Jack
and Laforenza, Domenico
and Orlando, Salvatore",
title="Improving the Performance of Collective Operations in MPICH",
booktitle="Recent Advances in Parallel Virtual Machine and Message Passing Interface",
year="2003",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="257--267",
abstract="We report on our work on improving the performance of collective operations in MPICH on clusters connected by switched networks. For each collective operation, we use multiple algorithms depending on the message size, with the goal of minimizing latency for short messages and minimizing bandwidth usage for long messages. Although we have implemented new algorithms for all MPI collective operations, because of limited space we describe only the algorithms for allgather, broadcast, reduce-scatter, and reduce. We present performance results using the SKaMPI benchmark on a Myrinet-connected Linux cluster and an IBM SP. In all cases, the new algorithms significantly outperform the old algorithms used in MPICH on the Myrinet cluster, and, in many cases, they outperform the algorithms used in IBM's MPI on the SP.",
isbn="978-3-540-39924-7"
}
@Inproceedings{Zhang2023,
author = {Zhen Zhang and Shuai Zheng and Yida Wang and Justin Chiu and George Karypis and Trishul Chilimbi and Mu Li and Xin Jin},
title = {MiCS: Near linear scaling for training gigantic model on public cloud},
year = {2023},
url = {https://www.amazon.science/publications/mics-near-linear-scaling-for-training-gigantic-model-on-public-cloud},
booktitle = {VLDB 2023},
}
@inproceedings{wang2024zero,
title={Ze{RO}++: Extremely Efficient Collective Communication for Large Model Training},
author={Guanhua Wang and Heyang Qin and Sam Ade Jacobs and Xiaoxia Wu and Connor Holmes and Zhewei Yao and Samyam Rajbhandari and Olatunji Ruwase and Feng Yan and Lei Yang and Yuxiong He},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=gx2BT0a9MQ}
}
@inproceedings{black-etal-2022-gpt,
title = "{GPT}-{N}eo{X}-20{B}: An Open-Source Autoregressive Language Model",
author = "Black, Sidney and
Biderman, Stella and
Hallahan, Eric and
Anthony, Quentin and
Gao, Leo and
Golding, Laurence and
He, Horace and
Leahy, Connor and
McDonell, Kyle and
Phang, Jason and
Pieler, Michael and
Prashanth, Usvsn Sai and
Purohit, Shivanshu and
Reynolds, Laria and
Tow, Jonathan and
Wang, Ben and
Weinbach, Samuel",
editor = "Fan, Angela and
Ilic, Suzana and
Wolf, Thomas and
Gall{\'e}, Matthias",
booktitle = "Proceedings of BigScience Episode {\#}5 -- Workshop on Challenges {\&} Perspectives in Creating Large Language Models",
month = may,
year = "2022",
address = "virtual+Dublin",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2022.bigscience-1.9",
doi = "10.18653/v1/2022.bigscience-1.9",
pages = "95--136",
}
@misc{luo2019adaptive,
title={Adaptive Gradient Methods with Dynamic Bound of Learning Rate},
author={Liangchen Luo and Yuanhao Xiong and Yan Liu and Xu Sun},
year={2019},
eprint={1902.09843},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{keskar2017improving,
title={Improving Generalization Performance by Switching from Adam to SGD},
author={Nitish Shirish Keskar and Richard Socher},
year={2017},
eprint={1712.07628},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@article{zhuang2020adabelief,
title={AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients},
author={Zhuang, Juntang and Tang, Tommy and Ding, Yifan and Tatikonda, Sekhar C and Dvornek, Nicha and Papademetris, Xenophon and Duncan, James},
journal={Advances in Neural Information Processing Systems},
volume={33},
year={2020}
}
@misc{he2016identity,
title={Identity Mappings in Deep Residual Networks},
author={Kaiming He and Xiangyu Zhang and Shaoqing Ren and Jian Sun},
year={2016},
eprint={1603.05027},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
@InProceedings{tang2021skfac,
author = {Tang, Zedong and Jiang, Fenlong and Gong, Maoguo and Li, Hao and Wu, Yue and Yu, Fan and Wang, Zidong and Wang, Min},
title = {SKFAC: Training Neural Networks With Faster Kronecker-Factored Approximate Curvature},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2021},
pages = {13479-13487}
}
@inproceedings{
zhang2023eva,
title={Eva: Practical Second-order Optimization with Kronecker-vectorized Approximation},
author={Lin Zhang and Shaohuai Shi and Bo Li},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=_Mic8V96Voy}
}
@misc{wang2017stochastic,
title={Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization},
author={Xiao Wang and Shiqian Ma and Donald Goldfarb and Wei Liu},
year={2017},
eprint={1607.01231},
archivePrefix={arXiv},
primaryClass={math.OC}
}
@misc{bollapragada2018progressive,
title={A Progressive Batching L-BFGS Method for Machine Learning},
author={Raghu Bollapragada and Dheevatsa Mudigere and Jorge Nocedal and Hao-Jun Michael Shi and Ping Tak Peter Tang},
year={2018},
eprint={1802.05374},
archivePrefix={arXiv},
primaryClass={math.OC}
}
@misc{berahas2016multibatch,
title={A Multi-Batch L-BFGS Method for Machine Learning},
author={Albert S. Berahas and Jorge Nocedal and Martin Takáč},
year={2016},
eprint={1605.06049},
archivePrefix={arXiv},
primaryClass={math.OC}
}
@misc{erdogdu2015convergence,
title={Convergence rates of sub-sampled Newton methods},
author={Murat A. Erdogdu and Andrea Montanari},
year={2015},
eprint={1508.02810},
archivePrefix={arXiv},
primaryClass={stat.ML}
}
@misc{perlmutter,
author = {NERSC},
title = {Perlmutter System Architecture},
year = {},
publisher = {},
journal = {},
howpublished = {\url{https://docs.nersc.gov/systems/perlmutter/architecture/}},
commit = {}
}
@inproceedings{heo2021adamp,
title={AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights},
author={Heo, Byeongho and Chun, Sanghyuk and Oh, Seong Joon and Han, Dongyoon and Yun, Sangdoo and Kim, Gyuwan and Uh, Youngjung and Ha, Jung-Woo},
year={2021},
booktitle={International Conference on Learning Representations (ICLR)},
}
@software{torchvision2016,
title = {TorchVision: PyTorch's Computer Vision library},
author = {TorchVision maintainers and contributors},
year = 2016,
journal = {GitHub repository},
publisher = {GitHub},
howpublished = {\url{https://github.com/pytorch/vision}}
}
@misc{mozaffari2023mkor,
title={MKOR: Momentum-Enabled Kronecker-Factor-Based Optimizer Using Rank-1 Updates},
author={Mohammad Mozaffari and Sikan Li and Zhao Zhang and Maryam Mehri Dehnavi},
year={2023},
eprint={2306.01685},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{shi2023distributed,
title={A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale},
author={Hao-Jun Michael Shi and Tsung-Hsien Lee and Shintaro Iwasaki and Jose Gallego-Posada and Zhijing Li and Kaushik Rangadurai and Dheevatsa Mudigere and Michael Rabbat},
year={2023},
eprint={2309.06497},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{shi2021accelerating,
title={Accelerating Distributed K-FAC with Smart Parallelism of Computing and Communication Tasks},
author={Shaohuai Shi and Lin Zhang and Bo Li},
year={2021},
eprint={2107.06533},
archivePrefix={arXiv},
primaryClass={cs.DC}
}
@inproceedings{ueno2020rich,
author = {Ueno, Yuichiro and Osawa, Kazuki and Tsuji, Yohei and Naruse, Akira and Yokota, Rio},
title = {Rich Information is Affordable: A Systematic Performance Analysis of Second-Order Optimization Using K-FAC},
year = {2020},
isbn = {9781450379984},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3394486.3403265},
doi = {10.1145/3394486.3403265},
abstract = {Rich information matrices from first and second-order derivatives have many potential applications in both theoretical and practical problems in deep learning. However, computing these information matrices is extremely expensive and this enormous cost is currently limiting its application to important problems regarding generalization, hyperparameter tuning, and optimization of deep neural networks. One of the most challenging use cases of information matrices is their use as a preconditioner for the optimizers, since the information matrices need to be updated every step. In this work, we conduct a step-by-step performance analysis when computing the Fisher information matrix during training of ResNet-50 on ImageNet, and show that the overhead can be reduced to the same amount as the cost of performing a single SGD step. We also show that the resulting Fisher preconditioned optimizer can converge in 1/3 the number of epochs compared to SGD, while achieving the same Top-1 validation accuracy. This is the first work to achieve such accuracy with K-FAC while reducing the training time to match that of SGD.},
booktitle = {Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
pages = {2145–2153},
numpages = {9},
keywords = {distributed training, information matrix, performance optimization},
location = {Virtual Event, CA, USA},
series = {KDD '20}
}
@misc{osawa2020scalable,
title={Scalable and Practical Natural Gradient for Large-Scale Deep Learning},
author={Kazuki Osawa and Yohei Tsuji and Yuichiro Ueno and Akira Naruse and Chuan-Sheng Foo and Rio Yokota},
year={2020},
eprint={2002.06015},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{osawa2019largescale,
title={Large-Scale Distributed Second-Order Optimization Using Kronecker-Factored Approximate Curvature for Deep Convolutional Neural Networks},
author={Kazuki Osawa and Yohei Tsuji and Yuichiro Ueno and Akira Naruse and Rio Yokota and Satoshi Matsuoka},
year={2019},
eprint={1811.12019},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@inproceedings{pauloski-2020-kfac,
author = {Pauloski, J. Gregory and Zhang, Zhao and Huang, Lei and Xu, Weijia and Foster, Ian T.},
title = {Convolutional {N}eural {N}etwork {T}raining with {D}istributed {K}-{FAC}},
year = {2020},
isbn = {9781728199986},
publisher = {IEEE Press},
booktitle = {Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis},
articleno = {94},
numpages = {14},
location = {Atlanta, Georgia},
series = {SC '20},
doi = {10.5555/3433701.3433826}
}
@inproceedings{pauloski-kaisa-2021,
doi = {10.1145/3458817.3476152},
url = {https://doi.org/10.1145%2F3458817.3476152},
year = 2021,
month = {nov},
publisher = {{ACM}
},
author = {J. Gregory Pauloski and Qi Huang and Lei Huang and Shivaram Venkataraman and Kyle Chard and Ian Foster and Zhao Zhang},
title = {{KAISA}},
booktitle = {Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis}
}
@InProceedings{agarwal-ggt-2019,
title = {Efficient Full-Matrix Adaptive Regularization},
author = {Agarwal, Naman and Bullins, Brian and Chen, Xinyi and Hazan, Elad and Singh, Karan and Zhang, Cyril and Zhang, Yi},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {102--110},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/agarwal19b/agarwal19b.pdf},
url = {https://proceedings.mlr.press/v97/agarwal19b.html},
abstract = {Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in <em>non-convex</em> optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show improved iteration-wise convergence rates across synthetic tasks and standard deep learning benchmarks, and that the more carefully-preconditioned steps sometimes lead to a better solution.}
}
@inproceedings{hessian-free-rnn,
author = {Martens, James and Sutskever, Ilya},
title = {Learning Recurrent Neural Networks with Hessian-Free Optimization},
year = {2011},
isbn = {9781450306195},
publisher = {Omnipress},
address = {Madison, WI, USA},
abstract = {In this work we resolve the long-outstanding problem of how to effectively train recurrent neural networks (RNNs) on complex and difficult sequence modeling problems which may contain long-term data dependencies. Utilizing recent advances in the Hessian-free optimization approach (Martens, 2010), together with a novel damping scheme, we successfully train RNNs on two sets of challenging problems. First, a collection of pathological synthetic datasets which are known to be impossible for standard optimization approaches (due to their extremely long-term dependencies), and second, on three natural and highly complex real-world sequence datasets where we find that our method significantly outperforms the previous state-of-the-art method for training neural sequence models: the Long Short-term Memory approach of Hochreiter and Schmidhuber (1997). Additionally, we offer a new interpretation of the generalized Gauss-Newton matrix of Schraudolph (2002) which is used within the HF approach of Martens.},
booktitle = {Proceedings of the 28th International Conference on International Conference on Machine Learning},
pages = {1033–1040},
numpages = {8},
location = {Bellevue, Washington, USA},
series = {ICML'11}
}
@misc{grosse2016kfacconvolution,
title={A Kronecker-factored approximate Fisher matrix for convolution layers},
author={Roger Grosse and James Martens},
year={2016},
eprint={1602.01407},
archivePrefix={arXiv},
primaryClass={stat.ML}
}
@misc{zhu2019anisotropic,
title={The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Sharp Minima and Regularization Effects},
author={Zhanxing Zhu and Jingfeng Wu and Bing Yu and Lei Wu and Jinwen Ma},
year={2019},
eprint={1803.00195},
archivePrefix={arXiv},
primaryClass={stat.ML}
}
@misc{sagun2018empirical,
title={Empirical Analysis of the Hessian of Over-Parametrized Neural Networks},
author={Levent Sagun and Utku Evci and V. Ugur Guney and Yann Dauphin and Leon Bottou},
year={2018},
eprint={1706.04454},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{jastrzebski2018factors,
title={Three Factors Influencing Minima in SGD},
author={Stanislaw Jastrzebski and Zachary Kenton and Devansh Arpit and Nicolas Ballas and Asja Fischer and Yoshua Bengio and Amos Storkey},
year={2018},
eprint={1711.04623},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@article{duchi:jmlr2011,
author = {John Duchi and Elad Hazan and Yoram Singer},
title = {Adaptive Subgradient Methods for Online Learning and Stochastic Optimization},
journal = {Journal of Machine Learning Research},
year = {2011},
volume = {12},
number = {61},
pages = {2121--2159},
url = {http://jmlr.org/papers/v12/duchi11a.html}
}
@article{martens:jmlr2020,
author = {Martens, James},
title = {New Insights and Perspectives on the Natural Gradient Method},
year = {2020},
issue_date = {January 2020},
publisher = {JMLR.org},
volume = {21},
number = {1},
issn = {1532-4435},
abstract = {Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically analyze this method and its properties, and show how it can be viewed as a type of 2nd-order optimization method, with the Fisher information matrix acting as a substitute for the Hessian. In many important cases, the Fisher information matrix is shown to be equivalent to the Generalized Gauss-Newton matrix, which both approximates the Hessian, but also has certain properties that favor its use over the Hessian. This perspective turns out to have significant implications for the design of a practical and robust natural gradient optimizer, as it motivates the use of techniques like trust regions and Tikhonov regularization. Additionally, we make a series of contributions to the understanding of natural gradient and 2nd-order methods, including: a thorough analysis of the convergence speed of stochastic natural gradient descent (and more general stochastic 2nd-order methods) as applied to convex quadratics, a critical examination of the oft-used "empirical" approximation of the Fisher matrix, and an analysis of the (approximate) parameterization invariance property possessed by natural gradient methods (which we show also holds for certain other curvature matrices, but notably not the Hessian).},
journal = {J. Mach. Learn. Res.},
month = {jan},
articleno = {146},
numpages = {76},
keywords = {neural networks, convergence rate, parameterization invariance, natural gradient methods, 2nd-order optimization}
}
@inproceedings{kunstner:neurips2019,
author = {Kunstner, Frederik and Hennig, Philipp and Balles, Lukas},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Limitations of the empirical Fisher approximation for natural gradient descent},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/46a558d97954d0692411c861cf78ef79-Paper.pdf},
volume = {32},
year = {2019}
}
@inproceedings{tonga,
author = {Roux, Nicolas and Manzagol, Pierre-antoine and Bengio, Yoshua},
booktitle = {Advances in Neural Information Processing Systems},
editor = {J. Platt and D. Koller and Y. Singer and S. Roweis},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Topmoumoute Online Natural Gradient Algorithm},
url = {https://proceedings.neurips.cc/paper_files/paper/2007/file/9f61408e3afb633e50cdf1b20de6f466-Paper.pdf},
volume = {20},
year = {2007}
}
@inproceedings{Desjardins:nips2015,
author = {Desjardins, Guillaume and Simonyan, Karen and Pascanu, Razvan and kavukcuoglu, koray},
booktitle = {Advances in Neural Information Processing Systems},
editor = {C. Cortes and N. Lawrence and D. Lee and M. Sugiyama and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Natural Neural Networks},
url = {https://proceedings.neurips.cc/paper_files/paper/2015/file/2de5d16682c3c35007e4e92982f1a2ba-Paper.pdf},
volume = {28},
year = {2015}
}
@article{Park2000AdaptiveNG,
title={Adaptive natural gradient learning algorithms for various stochastic models},
author={Hyeyoung Park and Shun‐ichi Amari and Kenji Fukumizu},
journal={Neural networks : the official journal of the International Neural Network Society},
year={2000},
volume={13 7},
pages={
755-64
},
url={https://api.semanticscholar.org/CorpusID:6471036}
}
@article{ngd-og,
author = {Amari, Shun-ichi},
title = "{Natural Gradient Works Efficiently in Learning}",
journal = {Neural Computation},
volume = {10},
number = {2},
pages = {251-276},
year = {1998},
month = {02},
abstract = "{When a parameter space has a certain underlying structure, the ordinary gradient of a function does not represent its steepest direction, but the natural gradient does. Information geometry is used for calculating the natural gradients in the parameter space of perceptrons, the space of matrices (for blind source separation), and the space of linear dynamical systems (for blind source deconvolution). The dynamical behavior of natural gradient online learning is analyzed and is proved to be Fisher efficient, implying that it has asymptotically the same performance as the optimal batch estimation of parameters. This suggests that the plateau phenomenon, which appears in the backpropagation learning algorithm of multilayer perceptrons, might disappear or might not be so serious when the natural gradient is used. An adaptive method of updating the learning rate is proposed and analyzed.}",
issn = {0899-7667},
doi = {10.1162/089976698300017746},
url = {https://doi.org/10.1162/089976698300017746},
eprint = {https://direct.mit.edu/neco/article-pdf/10/2/251/813415/089976698300017746.pdf},
}
@InProceedings{botev-practical-17,
title = {Practical {G}auss-{N}ewton Optimisation for Deep Learning},
author = {Aleksandar Botev and Hippolyt Ritter and David Barber},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {557--565},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/botev17a/botev17a.pdf},
url = {https://proceedings.mlr.press/v70/botev17a.html},
abstract = {We present an efficient block-diagonal approximation to the Gauss-Newton matrix for feedforward neural networks. Our resulting algorithm is competitive against state-of-the-art first-order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for which hyperparameter tuning of the optimisation parameters is often a laborious process, our approach can provide good performance even when used with default settings. A side result of our work is that for piecewise linear transfer functions, the network objective function can have no differentiable local maxima, which may partially explain why such transfer functions facilitate effective optimisation.}
}
@InProceedings{krylov-subspace-descent,
title = {Krylov Subspace Descent for Deep Learning},
author = {Vinyals, Oriol and Povey, Daniel},
booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
pages = {1261--1268},
year = {2012},
editor = {Lawrence, Neil D. and Girolami, Mark},
volume = {22},
series = {Proceedings of Machine Learning Research},
address = {La Palma, Canary Islands},
month = {21--23 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v22/vinyals12/vinyals12.pdf},
url = {https://proceedings.mlr.press/v22/vinyals12.html},
abstract = {In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data samples to optimize over this subspace. As with the Hessian Free (HF) method of Martens (2010), the Hessian matrix is never explicitly constructed, and is computed using a subset of data. In practice, as in HF, we typically use a positive definite substitute for the Hessian matrix such as the Gauss-Newton matrix. We investigate the effectiveness of our proposed method on deep neural networks, and compare its performance to widely used methods such as stochastic gradient descent, conjugate gradient descent and L-BFGS, and also to HF. Our method leads to faster convergence than either L-BFGS or HF, and generally performs better than either of them in cross-validation accuracy. It is also simpler and more general than HF, as it does not require a positive semidefinite approximation of the Hessian matrix to work well nor the setting of a damping parameter. The chief drawback versus HF is the need for memory to store a basis for the Krylov subspace.}
}
@inproceedings{hessian-free-optimization,
added-at = {2011-07-08T14:11:15.000+0200},
author = {Martens, James},
biburl = {https://www.bibsonomy.org/bibtex/2af0029f21446a26c04f2e4650ec1fbf1/gromgull},
booktitle = {ICML},
editor = {Fürnkranz, Johannes and Joachims, Thorsten},
ee = {http://www.icml2010.org/papers/458.pdf},
interhash = {1d6577ca73270732c2cc1e3c2cce6cdb},
intrahash = {af0029f21446a26c04f2e4650ec1fbf1},
keywords = {machinelearning neural-networks optimisation recurrent-neural-networks},
pages = {735-742},
publisher = {Omnipress},
timestamp = {2011-07-08T14:11:15.000+0200},
title = {Deep learning via Hessian-free optimization.},
url = {http://dblp.uni-trier.de/db/conf/icml/icml2010.html#Martens10},
year = 2010
}
@article{schraudolphGGN,
author = {Schraudolph, Nicol N.},
title = {Fast Curvature Matrix-Vector Products for Second-Order Gradient Descent},
year = {2002},
issue_date = {July 2002},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
volume = {14},
number = {7},
issn = {0899-7667},
url = {https://doi.org/10.1162/08997660260028683},
doi = {10.1162/08997660260028683},
abstract = {We propose a generic method for iteratively approximating various second-order gradient steps--Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient--in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this approach. Since both were originally derived by very different routes, this offers fresh insight into their operation, resulting in further improvements to SMD.},
journal = {Neural Comput.},
month = {jul},
pages = {1723–1738},
numpages = {16}
}
@inproceedings{loshchilov2017sgdr,
title={{SGDR}: Stochastic Gradient Descent with Warm Restarts},
author={Ilya Loshchilov and Frank Hutter},
booktitle={International Conference on Learning Representations},
year={2017},
url={https://openreview.net/forum?id=Skq89Scxx}
}
@misc{grafting,
title={Disentangling Adaptive Gradient Methods from Learning Rates},
author={Naman Agarwal and Rohan Anil and Elad Hazan and Tomer Koren and Cyril Zhang},
year={2020},
eprint={2002.11803},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@inproceedings{adapative-optimizer-bad-sgd-good,
author = {Wilson, Ashia C and Roelofs, Rebecca and Stern, Mitchell and Srebro, Nati and Recht, Benjamin},
booktitle = {Advances in Neural Information Processing Systems},
editor = {I. Guyon and U. Von Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {The Marginal Value of Adaptive Gradient Methods in Machine Learning},
url = {https://proceedings.neurips.cc/paper_files/paper/2017/file/81b3833e2504647f9d794f7d7b9bf341-Paper.pdf},
volume = {30},
year = {2017}
}
@inproceedings{dense-net,
added-at = {2018-09-04T11:33:01.000+0200},
author = {Huang, Gao and Liu, Zhuang and van der Maaten, Laurens and Weinberger, Kilian Q.},
biburl = {https://www.bibsonomy.org/bibtex/24ea2e82bd87f8102b9f1f14a98b4dc53/nosebrain},
booktitle = {CVPR},
ee = {http://doi.ieeecomputersociety.org/10.1109/CVPR.2017.243},
interhash = {39c8ce8d8104d4c557d508eb421fb90c},
intrahash = {4ea2e82bd87f8102b9f1f14a98b4dc53},
isbn = {978-1-5386-0457-1},
keywords = {classification densenet image},
pages = {2261-2269},
publisher = {IEEE Computer Society},
timestamp = {2018-09-04T11:41:32.000+0200},
title = {Densely Connected Convolutional Networks},
url = {http://dblp.uni-trier.de/db/conf/cvpr/cvpr2017.html#HuangLMW17},
year = 2017
}
@incollection{ssd,
doi = {10.1007/978-3-319-46448-0_2},
url = {https://doi.org/10.1007%2F978-3-319-46448-0_2},
year = 2016,
publisher = {Springer International Publishing},
pages = {21--37},
author = {Wei Liu and Dragomir Anguelov and Dumitru Erhan and Christian Szegedy and Scott Reed and Cheng-Yang Fu and Alexander C. Berg},
title = {{SSD}: Single Shot {MultiBox} Detector},
booktitle = {Computer Vision {\textendash} {ECCV} 2016}
}
@incollection{alexnet,
added-at = {2016-11-14T12:05:24.000+0100},
author = {Krizhevsky, Alex and Sutskever, Ilya and Hinton, Geoffrey E.},
biburl = {https://www.bibsonomy.org/bibtex/2886c491fe45049fee3c9660df30bb5c4/albinzehe},
booktitle = {Advances in Neural Information Processing Systems 25},
editor = {Pereira, F. and Burges, C. J. C. and Bottou, L. and Weinberger, K. Q.},
interhash = {74bbb5dea5afb1b088bd10e317f1f0d2},
intrahash = {886c491fe45049fee3c9660df30bb5c4},
keywords = {cnn deeplearning ma-zehe neuralnet},
pages = {1097--1105},
publisher = {Curran Associates, Inc.},
timestamp = {2016-11-14T12:05:24.000+0100},
title = {ImageNet Classification with Deep Convolutional Neural Networks},
url = {http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf},
year = 2012
}
@article{sgd-nesterov,
title={A method for solving the convex programming problem with convergence rate $\mathcal{O}(1/k^2)$},
author={Yurii Nesterov},
journal={Proceedings of the USSR Academy of Sciences},
year={1983},
volume={269},
pages={543-547},
url={https://api.semanticscholar.org/CorpusID:145918791}
}
@article{sgd-momentum,
title = {Some methods of speeding up the convergence of iteration methods},
journal = {USSR Computational Mathematics and Mathematical Physics},
volume = {4},
number = {5},
pages = {1-17},
year = {1964},
issn = {0041-5553},
doi = {https://doi.org/10.1016/0041-5553(64)90137-5},
url = {https://www.sciencedirect.com/science/article/pii/0041555364901375},
author = {B.T. Polyak},
abstract = {For the solution of the functional equation P (x) = 0 (1) (where P is an operator, usually linear, from B into B, and B is a Banach space) iteration methods are generally used. These consist of the construction of a series x0, …, xn, …, which converges to the solution (see, for example [1]). Continuous analogues of these methods are also known, in which a trajectory x(t), 0 ⩽ t ⩽ ∞ is constructed, which satisfies the ordinary differential equation in B and is such that x(t) approaches the solution of (1) as t → ∞ (see [2]). We shall call the method a k-step method if for the construction of each successive iteration xn+1 we use k previous iterations xn, …, xn−k+1. The same term will also be used for continuous methods if x(t) satisfies a differential equation of the k-th order or k-th degree. Iteration methods which are more widely used are one-step (e.g. methods of successive approximations). They are generally simple from the calculation point of view but often converge very slowly. This is confirmed both by the evaluation of the speed of convergence and by calculation in practice (for more details see below). Therefore the question of the rate of convergence is most important. Some multistep methods, which we shall consider further, which are only slightly more complicated than the corresponding one-step methods, make it possible to speed up the convergence substantially. Note that all the methods mentioned below are applicable also to the problem of minimizing the differentiable functional (x) in Hilbert space, so long as this problem reduces to the solution of the equation grad (x) = 0.}
}
@article{sgd,
author = {Herbert Robbins and Sutton Monro},
title = {{A Stochastic Approximation Method}},
volume = {22},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {400 -- 407},
year = {1951},
doi = {10.1214/aoms/1177729586},
URL = {https://doi.org/10.1214/aoms/1177729586}
}
@inproceedings{mask-rcnn,
added-at = {2021-07-07T12:16:11.000+0200},
author = {He, Kaiming and Gkioxari, Georgia and Doll{\'{a}}r, Piotr and Girshick, Ross B.},
bibsource = {dblp computer science bibliography, https://dblp.org},
biburl = {https://www.bibsonomy.org/bibtex/2d2deec4bb1449a5f55dcc9086b669e37/pkoch},
booktitle = {{IEEE} International Conference on Computer Vision, {ICCV} 2017, Venice, Italy, October 22-29, 2017},
doi = {10.1109/ICCV.2017.322},
interhash = {3743d2a88223517f9adc496b9ad099bc},
intrahash = {d2deec4bb1449a5f55dcc9086b669e37},
keywords = {instance mask mask-rcnn segmentation},
pages = {2980--2988},
publisher = {{IEEE} Computer Society},
timestamp = {2021-07-07T12:16:11.000+0200},
title = {Mask {R-CNN}},
url = {https://doi.org/10.1109/ICCV.2017.322},
year = 2017
}
@article{iyer2020wideminima,
title={Wide-minima Density Hypothesis and the Explore-Exploit Learning Rate Schedule},
author={Iyer, Nikhil and Thejas, V and Kwatra, Nipun and Ramjee, Ramachandran and Sivathanu, Muthian},
journal={arXiv preprint arXiv:2003.03977},
year={2020}
}
@misc{mscoco,
title={Microsoft COCO: Common Objects in Context},
author={Tsung-Yi Lin and Michael Maire and Serge Belongie and Lubomir Bourdev and Ross Girshick and James Hays and Pietro Perona and Deva Ramanan and C. Lawrence Zitnick and Piotr Dollár},
year={2015},
eprint={1405.0312},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
@misc{deeplabv3,
title={Rethinking Atrous Convolution for Semantic Image Segmentation},
author={Liang-Chieh Chen and George Papandreou and Florian Schroff and Hartwig Adam},
year={2017},
eprint={1706.05587},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
@inproceedings{faster_rcnn,
author = {Ren, Shaoqing and He, Kaiming and Girshick, Ross and Sun, Jian},
booktitle = {Advances in Neural Information Processing Systems},
editor = {C. Cortes and N. Lawrence and D. Lee and M. Sugiyama and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks},
url = {https://proceedings.neurips.cc/paper_files/paper/2015/file/14bfa6bb14875e45bba028a21ed38046-Paper.pdf},
volume = {28},
year = {2015}
}
@misc{shampoo-scalable,
title={Scalable Second Order Optimization for Deep Learning},
author={Rohan Anil and Vineet Gupta and Tomer Koren and Kevin Regan and Yoram Singer},
year={2021},
eprint={2002.09018},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@InProceedings{shampoo-icml,
title = {Shampoo: Preconditioned Stochastic Tensor Optimization},
author = {Gupta, Vineet and Koren, Tomer and Singer, Yoram},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {1842--1850},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/gupta18a/gupta18a.pdf},
url = {https://proceedings.mlr.press/v80/gupta18a.html},
abstract = {Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Surprisingly, although it involves a more complex update rule, Shampoo’s runtime per step is comparable in practice to that of simple gradient methods such as SGD, AdaGrad, and Adam.}
}
@article{alpa,
author = {Lianmin Zheng and
Zhuohan Li and
Hao Zhang and
Yonghao Zhuang and
Zhifeng Chen and
Yanping Huang and
Yida Wang and
Yuanzhong Xu and
Danyang Zhuo and
Joseph E. Gonzalez and
Ion Stoica},
title = {Alpa: Automating Inter- and Intra-Operator Parallelism for Distributed
Deep Learning},
journal = {CoRR},
volume = {abs/2201.12023},
year = {2022},
eprinttype = {arXiv},
eprint = {2201.12023},
}
@misc{jangda2022breaking,
title={Breaking the Computation and Communication Abstraction Barrier in Distributed Machine Learning Workloads},
author={Abhinav Jangda and Jun Huang and Guodong Liu and Amir Hossein Nodehi Sabet and Saeed Maleki and Youshan Miao and Madanlal Musuvathi and Todd Mytkowicz and Olli Sarikivi},
year={2022},
eprint={2105.05720},
archivePrefix={arXiv},
primaryClass={cs.DC}
}
@misc{afhq-dataset,
title={StarGAN v2: Diverse Image Synthesis for Multiple Domains},
author={Yunjey Choi and Youngjung Uh and Jaejun Yoo and Jung-Woo Ha},
year={2020},
eprint={1912.01865},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
@article{object-detection-survey,
doi = {10.1109/access.2019.2939201},
url = {https://doi.org/10.1109%2Faccess.2019.2939201},
year = 2019,
publisher = {Institute of Electrical and Electronics Engineers ({IEEE})},
volume = {7},
pages = {128837--128868},
author = {Licheng Jiao and Fan Zhang and Fang Liu and Shuyuan Yang and Lingling Li and Zhixi Feng and Rong Qu},
title = {A Survey of Deep Learning-Based Object Detection},
journal = {{IEEE} Access}
}
@ARTICLE{image-segmentation-survey,
author={Minaee, Shervin and Boykov, Yuri and Porikli, Fatih and Plaza, Antonio and Kehtarnavaz, Nasser and Terzopoulos, Demetri},
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
title={Image Segmentation Using Deep Learning: A Survey},
year={2022},
volume={44},
number={7},
pages={3523-3542},
doi={10.1109/TPAMI.2021.3059968}}
@misc{group-norm,
title={Group Normalization},
author={Yuxin Wu and Kaiming He},
year={2018},
eprint={1803.08494},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
@misc{improved-diffusion,
title={Improved Denoising Diffusion Probabilistic Models},
author={Alex Nichol and Prafulla Dhariwal},
year={2021},
eprint={2102.09672},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@article{ring-all-reduce,
author = {Patarasuk, Pitch and Yuan, Xin},
title = {Bandwidth Optimal All-Reduce Algorithms for Clusters of Workstations},
year = {2009},
issue_date = {February, 2009},
publisher = {Academic Press, Inc.},
address = {USA},
volume = {69},
number = {2},
issn = {0743-7315},
url = {https://doi.org/10.1016/j.jpdc.2008.09.002},
doi = {10.1016/j.jpdc.2008.09.002},
abstract = {We consider an efficient realization of the all-reduce operation with large data sizes in cluster environments, under the assumption that the reduce operator is associative and commutative. We derive a tight lower bound of the amount of data that must be communicated in order to complete this operation and propose a ring-based algorithm that only requires tree connectivity to achieve bandwidth optimality. Unlike the widely used butterfly-like all-reduce algorithm that incurs network contention in SMP/multi-core clusters, the proposed algorithm can achieve contention-free communication in almost all contemporary clusters, including SMP/multi-core clusters and Ethernet switched clusters with multiple switches. We demonstrate that the proposed algorithm is more efficient than other algorithms on clusters with different nodal architectures and networking technologies when the data size is sufficiently large.},
journal = {J. Parallel Distrib. Comput.},
month = {feb},
pages = {117–124},
numpages = {8},
keywords = {Collective communication, All-reduce, Tree topology, Cluster of workstations}
}