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Equality Saturation for Tensor Graph Superoptimization [article]

Yichen Yang, Phitchaya Mangpo Phothilimtha, Yisu Remy Wang, Max Willsey, Sudip Roy, Jacques Pienaar
2021 arXiv   pre-print
This paper presents a novel technique for tensor graph superoptimization that employs equality saturation to apply all possible substitutions at once.  ...  However, we observe that existing approaches for tensor graph superoptimization both in production and research frameworks apply substitutions in a sequential manner.  ...  ACKNOWLEDGMENTS We thank Zhihao Jia, Martin Maas, Hyeontaek Lim, and the anonymous reviewers for their insightful and helpful comments.  ... 
arXiv:2101.01332v2 fatcat:3axztui5mjcxtpxrv3z7laqegy

Metatheory.jl: Fast and Elegant Algebraic Computation in Julia with Extensible Equality Saturation

Alessandro Cheli
2021 Journal of Open Source Software  
(Rackauckas & Foster, 2021) , Taine Zhao for developing MLStyle (Zhao, 2021) and MatchCore (Zhao & Carlsson, 2020) , and Philip Zucker for his original idea of implementing E-Graphs in Julia (Zucker  ...  Acknowledgements We acknowledge Max Willsey and contributors for their work on the original egg library , Christopher Rackauckas and Christopher Foster for their efforts in developing RuntimeGeneratedFunctions  ...  In Yang et al. (2021) , the authors used egg to superoptimize tensor signal flow graphs describing neural networks.  ... 
doi:10.21105/joss.03078 fatcat:5nw6ru2virbbvkmmv6k6fq4lva

Future Directions for Optimizing Compilers [article]

Nuno P. Lopes, John Regehr
2018 arXiv   pre-print
Acknowledgments The authors would like to thank Dan Gohman and members of the Utah PL reading group for their valuable feedback on drafts of this paper.  ...  Equality saturation: a new approach to optimization. Logical Methods in Computer Science, ( ), . .  ...  This strategy, however, only works within InstCombine; a more comprehensive approach such as equality saturation [ ] will be needed to solve coordination problems across passes.  ... 
arXiv:1809.02161v1 fatcat:hwn23mp7rza4dfgnygdcmu64ri

egg: Fast and Extensible Equality Saturation [article]

Max Willsey, Chandrakana Nandi, Yisu Remy Wang, Oliver Flatt, Zachary Tatlock, Pavel Panchekha
2020 arXiv   pre-print
Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven  ...  This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation.  ...  ACKNOWLEDGMENTS Thanks to our anonymous paper and artifact reviewers for their feedback. Special thanks to our shepherd Simon Peyton Jones, Leonardo de Moura, and many members of the PLSE group.  ... 
arXiv:2004.03082v3 fatcat:jqqec6vamnaejcl2fqw3tq2nyy

Automap: Towards Ergonomic Automated Parallelism for ML Models [article]

Michael Schaarschmidt and Dominik Grewe and Dimitrios Vytiniotis and Adam Paszke and Georg Stefan Schmid and Tamara Norman and James Molloy and Jonathan Godwin and Norman Alexander Rink and Vinod Nair and Dan Belov
2021 arXiv   pre-print
The rapid rise in demand for training large neural network architectures has brought into focus the need for partitioning strategies, for example by using data, model, or pipeline parallelism.  ...  Through a combination of inductive tactics and search in a platform-independent partitioning IR, automap can recover expert partitioning strategies such as Megatron sharding for transformer layers.  ...  Equality saturation for tensor graph superoptimization. In A. Smola, A. Di- makis, and I. Stoica, editors, Proceedings of Machine Learning and Systems, volume 3, pages 255–268, 2021.  ... 
arXiv:2112.02958v1 fatcat:tlda37oxgjeezggohojvh4sdni

Statistical models of fracture

Mikko J. Alava, Phani K. V. V. Nukala, Stefano Zapperi
2006 Advances in Physics  
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics.  ...  Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.  ...  eventual saturation.  ... 
doi:10.1080/00018730300741518 fatcat:lci2ujifsngcdgjjgzneknxm7y