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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.11202">arXiv:2401.11202</a> <span> [<a href="https://arxiv.org/pdf/2401.11202">pdf</a>, <a href="https://arxiv.org/format/2401.11202">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Distributed, Parallel, and Cluster Computing">cs.DC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Programming Languages">cs.PL</span> </div> </div> <p class="title is-5 mathjax"> PartIR: Composing SPMD Partitioning Strategies for Machine Learning </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Alabed%2C+S">Sami Alabed</a>, <a href="/search/cs?searchtype=author&query=Belov%2C+D">Daniel Belov</a>, <a href="/search/cs?searchtype=author&query=Chrzaszcz%2C+B">Bart Chrzaszcz</a>, <a href="/search/cs?searchtype=author&query=Franco%2C+J">Juliana Franco</a>, <a href="/search/cs?searchtype=author&query=Grewe%2C+D">Dominik Grewe</a>, <a href="/search/cs?searchtype=author&query=Maclaurin%2C+D">Dougal Maclaurin</a>, <a href="/search/cs?searchtype=author&query=Molloy%2C+J">James Molloy</a>, <a href="/search/cs?searchtype=author&query=Natan%2C+T">Tom Natan</a>, <a href="/search/cs?searchtype=author&query=Norman%2C+T">Tamara Norman</a>, <a href="/search/cs?searchtype=author&query=Pan%2C+X">Xiaoyue Pan</a>, <a href="/search/cs?searchtype=author&query=Paszke%2C+A">Adam Paszke</a>, <a href="/search/cs?searchtype=author&query=Rink%2C+N+A">Norman A. Rink</a>, <a href="/search/cs?searchtype=author&query=Schaarschmidt%2C+M">Michael Schaarschmidt</a>, <a href="/search/cs?searchtype=author&query=Sitdikov%2C+T">Timur Sitdikov</a>, <a href="/search/cs?searchtype=author&query=Swietlik%2C+A">Agnieszka Swietlik</a>, <a href="/search/cs?searchtype=author&query=Vytiniotis%2C+D">Dimitrios Vytiniotis</a>, <a href="/search/cs?searchtype=author&query=Wee%2C+J">Joel Wee</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.11202v4-abstract-short" style="display: inline;"> Training of modern large neural networks (NN) requires a combination of parallelization strategies encompassing data, model, or optimizer sharding. When strategies increase in complexity, it becomes necessary for partitioning tools to be 1) expressive, allowing the composition of simpler strategies, and 2) predictable to estimate performance analytically. We present PartIR, our design for a NN par… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.11202v4-abstract-full').style.display = 'inline'; document.getElementById('2401.11202v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.11202v4-abstract-full" style="display: none;"> Training of modern large neural networks (NN) requires a combination of parallelization strategies encompassing data, model, or optimizer sharding. When strategies increase in complexity, it becomes necessary for partitioning tools to be 1) expressive, allowing the composition of simpler strategies, and 2) predictable to estimate performance analytically. We present PartIR, our design for a NN partitioning system. PartIR is focused on an incremental approach to rewriting and is hardware-and-runtime agnostic. We present a simple but powerful API for composing sharding strategies and a simulator to validate them. The process is driven by high-level programmer-issued partitioning tactics, which can be both manual and automatic. Importantly, the tactics are specified separately from the model code, making them easy to change. We evaluate PartIR on several different models to demonstrate its predictability, expressibility, and ability to reach peak performance.. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.11202v4-abstract-full').style.display = 'none'; document.getElementById('2401.11202v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.07692">arXiv:2103.07692</a> <span> [<a href="https://arxiv.org/pdf/2103.07692">pdf</a>, <a href="https://arxiv.org/ps/2103.07692">ps</a>, <a href="https://arxiv.org/format/2103.07692">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computational Complexity">cs.CC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> </div> <p class="title is-5 mathjax"> The complexity of multilayer $d$-dimensional circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Sitdikov%2C+T+R">T. R. Sitdikov</a>, <a href="/search/cs?searchtype=author&query=Kalachev%2C+G+V">G. V. Kalachev</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.07692v1-abstract-short" style="display: inline;"> In this paper we research a model of multilayer circuits with a single logical layer. We consider $位$-separable graphs as a support for circuits. We establish the Shannon function lower bound $\max \bigl(\frac{2^n}{n}, \frac{2^n (1 - 位)}{\log k} \bigr)$ for this type of circuits where $k$ is the number of layers. For $d$-dimensional graphs, which are $位$-separable for $位= \frac{d - 1}{d}$, this gi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.07692v1-abstract-full').style.display = 'inline'; document.getElementById('2103.07692v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.07692v1-abstract-full" style="display: none;"> In this paper we research a model of multilayer circuits with a single logical layer. We consider $位$-separable graphs as a support for circuits. We establish the Shannon function lower bound $\max \bigl(\frac{2^n}{n}, \frac{2^n (1 - 位)}{\log k} \bigr)$ for this type of circuits where $k$ is the number of layers. For $d$-dimensional graphs, which are $位$-separable for $位= \frac{d - 1}{d}$, this gives the Shannon function lower bound $\frac{2^n}{\min(n, d \log k)}$. For multidimensional rectangular circuits the proved lower bound asymptotically matches to the upper bound. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.07692v1-abstract-full').style.display = 'none'; document.getElementById('2103.07692v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a 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