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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/2408.00118">arXiv:2408.00118</a> <span> [<a href="https://arxiv.org/pdf/2408.00118">pdf</a>, <a href="https://arxiv.org/format/2408.00118">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Gemma 2: Improving Open Language Models at a Practical Size </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gemma+Team"> Gemma Team</a>, <a href="/search/cs?searchtype=author&query=Riviere%2C+M">Morgane Riviere</a>, <a href="/search/cs?searchtype=author&query=Pathak%2C+S">Shreya Pathak</a>, <a href="/search/cs?searchtype=author&query=Sessa%2C+P+G">Pier Giuseppe Sessa</a>, <a href="/search/cs?searchtype=author&query=Hardin%2C+C">Cassidy Hardin</a>, <a href="/search/cs?searchtype=author&query=Bhupatiraju%2C+S">Surya Bhupatiraju</a>, <a href="/search/cs?searchtype=author&query=Hussenot%2C+L">L茅onard Hussenot</a>, <a href="/search/cs?searchtype=author&query=Mesnard%2C+T">Thomas Mesnard</a>, <a href="/search/cs?searchtype=author&query=Shahriari%2C+B">Bobak Shahriari</a>, <a href="/search/cs?searchtype=author&query=Ram%C3%A9%2C+A">Alexandre Ram茅</a>, <a href="/search/cs?searchtype=author&query=Ferret%2C+J">Johan Ferret</a>, <a href="/search/cs?searchtype=author&query=Liu%2C+P">Peter Liu</a>, <a href="/search/cs?searchtype=author&query=Tafti%2C+P">Pouya Tafti</a>, <a href="/search/cs?searchtype=author&query=Friesen%2C+A">Abe Friesen</a>, <a href="/search/cs?searchtype=author&query=Casbon%2C+M">Michelle Casbon</a>, <a href="/search/cs?searchtype=author&query=Ramos%2C+S">Sabela Ramos</a>, <a href="/search/cs?searchtype=author&query=Kumar%2C+R">Ravin Kumar</a>, <a href="/search/cs?searchtype=author&query=Lan%2C+C+L">Charline Le Lan</a>, <a href="/search/cs?searchtype=author&query=Jerome%2C+S">Sammy Jerome</a>, <a href="/search/cs?searchtype=author&query=Tsitsulin%2C+A">Anton Tsitsulin</a>, <a href="/search/cs?searchtype=author&query=Vieillard%2C+N">Nino Vieillard</a>, <a href="/search/cs?searchtype=author&query=Stanczyk%2C+P">Piotr Stanczyk</a>, <a href="/search/cs?searchtype=author&query=Girgin%2C+S">Sertan Girgin</a>, <a href="/search/cs?searchtype=author&query=Momchev%2C+N">Nikola Momchev</a>, <a href="/search/cs?searchtype=author&query=Hoffman%2C+M">Matt Hoffman</a> , et al. (173 additional authors not shown) </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="2408.00118v3-abstract-short" style="display: inline;"> In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We al… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00118v3-abstract-full').style.display = 'inline'; document.getElementById('2408.00118v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.00118v3-abstract-full" style="display: none;"> In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00118v3-abstract-full').style.display = 'none'; document.getElementById('2408.00118v3-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> 2 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.07839">arXiv:2404.07839</a> <span> [<a href="https://arxiv.org/pdf/2404.07839">pdf</a>, <a href="https://arxiv.org/format/2404.07839">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="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> </div> </div> <p class="title is-5 mathjax"> RecurrentGemma: Moving Past Transformers for Efficient Open Language Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Botev%2C+A">Aleksandar Botev</a>, <a href="/search/cs?searchtype=author&query=De%2C+S">Soham De</a>, <a href="/search/cs?searchtype=author&query=Smith%2C+S+L">Samuel L Smith</a>, <a href="/search/cs?searchtype=author&query=Fernando%2C+A">Anushan Fernando</a>, <a href="/search/cs?searchtype=author&query=Muraru%2C+G">George-Cristian Muraru</a>, <a href="/search/cs?searchtype=author&query=Haroun%2C+R">Ruba Haroun</a>, <a href="/search/cs?searchtype=author&query=Berrada%2C+L">Leonard Berrada</a>, <a href="/search/cs?searchtype=author&query=Pascanu%2C+R">Razvan Pascanu</a>, <a href="/search/cs?searchtype=author&query=Sessa%2C+P+G">Pier Giuseppe Sessa</a>, <a href="/search/cs?searchtype=author&query=Dadashi%2C+R">Robert Dadashi</a>, <a href="/search/cs?searchtype=author&query=Hussenot%2C+L">L茅onard Hussenot</a>, <a href="/search/cs?searchtype=author&query=Ferret%2C+J">Johan Ferret</a>, <a href="/search/cs?searchtype=author&query=Girgin%2C+S">Sertan Girgin</a>, <a href="/search/cs?searchtype=author&query=Bachem%2C+O">Olivier Bachem</a>, <a href="/search/cs?searchtype=author&query=Andreev%2C+A">Alek Andreev</a>, <a href="/search/cs?searchtype=author&query=Kenealy%2C+K">Kathleen Kenealy</a>, <a href="/search/cs?searchtype=author&query=Mesnard%2C+T">Thomas Mesnard</a>, <a href="/search/cs?searchtype=author&query=Hardin%2C+C">Cassidy Hardin</a>, <a href="/search/cs?searchtype=author&query=Bhupatiraju%2C+S">Surya Bhupatiraju</a>, <a href="/search/cs?searchtype=author&query=Pathak%2C+S">Shreya Pathak</a>, <a href="/search/cs?searchtype=author&query=Sifre%2C+L">Laurent Sifre</a>, <a href="/search/cs?searchtype=author&query=Rivi%C3%A8re%2C+M">Morgane Rivi猫re</a>, <a href="/search/cs?searchtype=author&query=Kale%2C+M+S">Mihir Sanjay Kale</a>, <a href="/search/cs?searchtype=author&query=Love%2C+J">Juliette Love</a>, <a href="/search/cs?searchtype=author&query=Tafti%2C+P">Pouya Tafti</a> , et al. (37 additional authors not shown) </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="2404.07839v2-abstract-short" style="display: inline;"> We introduce RecurrentGemma, a family of open language models which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide two sizes of models, containing 2B and 9B parameters, and provide pre-tr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.07839v2-abstract-full').style.display = 'inline'; document.getElementById('2404.07839v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.07839v2-abstract-full" style="display: none;"> We introduce RecurrentGemma, a family of open language models which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide two sizes of models, containing 2B and 9B parameters, and provide pre-trained and instruction tuned variants for both. Our models achieve comparable performance to similarly-sized Gemma baselines despite being trained on fewer tokens. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.07839v2-abstract-full').style.display = 'none'; document.getElementById('2404.07839v2-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> 28 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.08295">arXiv:2403.08295</a> <span> [<a href="https://arxiv.org/pdf/2403.08295">pdf</a>, <a href="https://arxiv.org/format/2403.08295">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Gemma: Open Models Based on Gemini Research and Technology </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gemma+Team"> Gemma Team</a>, <a href="/search/cs?searchtype=author&query=Mesnard%2C+T">Thomas Mesnard</a>, <a href="/search/cs?searchtype=author&query=Hardin%2C+C">Cassidy Hardin</a>, <a href="/search/cs?searchtype=author&query=Dadashi%2C+R">Robert Dadashi</a>, <a href="/search/cs?searchtype=author&query=Bhupatiraju%2C+S">Surya Bhupatiraju</a>, <a href="/search/cs?searchtype=author&query=Pathak%2C+S">Shreya Pathak</a>, <a href="/search/cs?searchtype=author&query=Sifre%2C+L">Laurent Sifre</a>, <a href="/search/cs?searchtype=author&query=Rivi%C3%A8re%2C+M">Morgane Rivi猫re</a>, <a href="/search/cs?searchtype=author&query=Kale%2C+M+S">Mihir Sanjay Kale</a>, <a href="/search/cs?searchtype=author&query=Love%2C+J">Juliette Love</a>, <a href="/search/cs?searchtype=author&query=Tafti%2C+P">Pouya Tafti</a>, <a href="/search/cs?searchtype=author&query=Hussenot%2C+L">L茅onard Hussenot</a>, <a href="/search/cs?searchtype=author&query=Sessa%2C+P+G">Pier Giuseppe Sessa</a>, <a href="/search/cs?searchtype=author&query=Chowdhery%2C+A">Aakanksha Chowdhery</a>, <a href="/search/cs?searchtype=author&query=Roberts%2C+A">Adam Roberts</a>, <a href="/search/cs?searchtype=author&query=Barua%2C+A">Aditya Barua</a>, <a href="/search/cs?searchtype=author&query=Botev%2C+A">Alex Botev</a>, <a href="/search/cs?searchtype=author&query=Castro-Ros%2C+A">Alex Castro-Ros</a>, <a href="/search/cs?searchtype=author&query=Slone%2C+A">Ambrose Slone</a>, <a href="/search/cs?searchtype=author&query=H%C3%A9liou%2C+A">Am茅lie H茅liou</a>, <a href="/search/cs?searchtype=author&query=Tacchetti%2C+A">Andrea Tacchetti</a>, <a href="/search/cs?searchtype=author&query=Bulanova%2C+A">Anna Bulanova</a>, <a href="/search/cs?searchtype=author&query=Paterson%2C+A">Antonia Paterson</a>, <a href="/search/cs?searchtype=author&query=Tsai%2C+B">Beth Tsai</a>, <a href="/search/cs?searchtype=author&query=Shahriari%2C+B">Bobak Shahriari</a> , et al. (83 additional authors not shown) </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="2403.08295v4-abstract-short" style="display: inline;"> This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Ge… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.08295v4-abstract-full').style.display = 'inline'; document.getElementById('2403.08295v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.08295v4-abstract-full" style="display: none;"> This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of 18 text-based tasks, and we present comprehensive evaluations of safety and responsibility aspects of the models, alongside a detailed description of model development. We believe the responsible release of LLMs is critical for improving the safety of frontier models, and for enabling the next wave of LLM innovations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.08295v4-abstract-full').style.display = 'none'; document.getElementById('2403.08295v4-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> 16 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.11805">arXiv:2312.11805</a> <span> [<a href="https://arxiv.org/pdf/2312.11805">pdf</a>, <a href="https://arxiv.org/format/2312.11805">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Gemini: A Family of Highly Capable Multimodal Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gemini+Team"> Gemini Team</a>, <a href="/search/cs?searchtype=author&query=Anil%2C+R">Rohan Anil</a>, <a href="/search/cs?searchtype=author&query=Borgeaud%2C+S">Sebastian Borgeaud</a>, <a href="/search/cs?searchtype=author&query=Alayrac%2C+J">Jean-Baptiste Alayrac</a>, <a href="/search/cs?searchtype=author&query=Yu%2C+J">Jiahui Yu</a>, <a href="/search/cs?searchtype=author&query=Soricut%2C+R">Radu Soricut</a>, <a href="/search/cs?searchtype=author&query=Schalkwyk%2C+J">Johan Schalkwyk</a>, <a href="/search/cs?searchtype=author&query=Dai%2C+A+M">Andrew M. Dai</a>, <a href="/search/cs?searchtype=author&query=Hauth%2C+A">Anja Hauth</a>, <a href="/search/cs?searchtype=author&query=Millican%2C+K">Katie Millican</a>, <a href="/search/cs?searchtype=author&query=Silver%2C+D">David Silver</a>, <a href="/search/cs?searchtype=author&query=Johnson%2C+M">Melvin Johnson</a>, <a href="/search/cs?searchtype=author&query=Antonoglou%2C+I">Ioannis Antonoglou</a>, <a href="/search/cs?searchtype=author&query=Schrittwieser%2C+J">Julian Schrittwieser</a>, <a href="/search/cs?searchtype=author&query=Glaese%2C+A">Amelia Glaese</a>, <a href="/search/cs?searchtype=author&query=Chen%2C+J">Jilin Chen</a>, <a href="/search/cs?searchtype=author&query=Pitler%2C+E">Emily Pitler</a>, <a href="/search/cs?searchtype=author&query=Lillicrap%2C+T">Timothy Lillicrap</a>, <a href="/search/cs?searchtype=author&query=Lazaridou%2C+A">Angeliki Lazaridou</a>, <a href="/search/cs?searchtype=author&query=Firat%2C+O">Orhan Firat</a>, <a href="/search/cs?searchtype=author&query=Molloy%2C+J">James Molloy</a>, <a href="/search/cs?searchtype=author&query=Isard%2C+M">Michael Isard</a>, <a href="/search/cs?searchtype=author&query=Barham%2C+P+R">Paul R. Barham</a>, <a href="/search/cs?searchtype=author&query=Hennigan%2C+T">Tom Hennigan</a>, <a href="/search/cs?searchtype=author&query=Lee%2C+B">Benjamin Lee</a> , et al. (1325 additional authors not shown) </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="2312.11805v4-abstract-short" style="display: inline;"> This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.11805v4-abstract-full').style.display = 'inline'; document.getElementById('2312.11805v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.11805v4-abstract-full" style="display: none;"> This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.11805v4-abstract-full').style.display = 'none'; document.getElementById('2312.11805v4-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> 17 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.05586">arXiv:2011.05586</a> <span> [<a href="https://arxiv.org/pdf/2011.05586">pdf</a>, <a href="https://arxiv.org/format/2011.05586">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Strict Enforcement of Conservation Laws and Invertibility in CNN-Based Super Resolution for Scientific Datasets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Geiss%2C+A">Andrew Geiss</a>, <a href="/search/cs?searchtype=author&query=Hardin%2C+J+C">Joseph C. Hardin</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="2011.05586v2-abstract-short" style="display: inline;"> Recently, deep Convolutional Neural Networks (CNNs) have revolutionized image super-resolution (SR), dramatically outperforming past methods for enhancing image resolution. They could be a boon for the many scientific fields that involve image or gridded datasets: satellite remote sensing, radar meteorology, medical imaging, numerical modeling etc. Unfortunately, while SR-CNNs produce visually com… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.05586v2-abstract-full').style.display = 'inline'; document.getElementById('2011.05586v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.05586v2-abstract-full" style="display: none;"> Recently, deep Convolutional Neural Networks (CNNs) have revolutionized image super-resolution (SR), dramatically outperforming past methods for enhancing image resolution. They could be a boon for the many scientific fields that involve image or gridded datasets: satellite remote sensing, radar meteorology, medical imaging, numerical modeling etc. Unfortunately, while SR-CNNs produce visually compelling outputs, they may break physical conservation laws when applied to scientific datasets. Here, a method for ``Downsampling Enforcement" in SR-CNNs is proposed. A differentiable operator is derived that, when applied as the final transfer function of a CNN, ensures the high resolution outputs exactly reproduce the low resolution inputs under 2D-average downsampling while improving performance of the SR schemes. The method is demonstrated across seven modern CNN-based SR schemes on several benchmark image datasets, and applications to weather radar, satellite imager, and climate model data are also shown. The approach improves training time and performance while ensuring physical consistency between the super-resolved and low resolution data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.05586v2-abstract-full').style.display = 'none'; document.getElementById('2011.05586v2-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> 26 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68T07; 94A08 <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> I.4.3; I.4.4 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/cs/0511097">arXiv:cs/0511097</a> <span> [<a href="https://arxiv.org/pdf/cs/0511097">pdf</a>, <a href="https://arxiv.org/ps/cs/0511097">ps</a>, <a href="https://arxiv.org/format/cs/0511097">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Logic in Computer Science">cs.LO</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2168/LMCS-1(3:4)2005">10.2168/LMCS-1(3:4)2005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Modularizing the Elimination of r=0 in Kleene Algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Hardin%2C+C">Christopher Hardin</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="cs/0511097v3-abstract-short" style="display: inline;"> Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of <i>elimination of hypotheses</i>, which is useful because the equational theory of Kleene algebra is decidable while the universal Horn theory is not. We show that hypot… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('cs/0511097v3-abstract-full').style.display = 'inline'; document.getElementById('cs/0511097v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="cs/0511097v3-abstract-full" style="display: none;"> Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of <i>elimination of hypotheses</i>, which is useful because the equational theory of Kleene algebra is decidable while the universal Horn theory is not. We show that hypotheses of the form r = 0 can still be eliminated in the presence of other hypotheses. This lets us extend any technique for eliminating hypotheses to include hypotheses of the form r = 0. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('cs/0511097v3-abstract-full').style.display = 'none'; document.getElementById('cs/0511097v3-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> 16 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 November, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.3.1 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Logical Methods in Computer Science, Volume 1, Issue 3 (December 21, 2005) lmcs:2264 </p> </li> </ol> <div 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