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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&amp;query=Gemma+Team"> Gemma Team</a>, <a href="/search/cs?searchtype=author&amp;query=Riviere%2C+M">Morgane Riviere</a>, <a href="/search/cs?searchtype=author&amp;query=Pathak%2C+S">Shreya Pathak</a>, <a href="/search/cs?searchtype=author&amp;query=Sessa%2C+P+G">Pier Giuseppe Sessa</a>, <a href="/search/cs?searchtype=author&amp;query=Hardin%2C+C">Cassidy Hardin</a>, <a href="/search/cs?searchtype=author&amp;query=Bhupatiraju%2C+S">Surya Bhupatiraju</a>, <a href="/search/cs?searchtype=author&amp;query=Hussenot%2C+L">L茅onard Hussenot</a>, <a href="/search/cs?searchtype=author&amp;query=Mesnard%2C+T">Thomas Mesnard</a>, <a href="/search/cs?searchtype=author&amp;query=Shahriari%2C+B">Bobak Shahriari</a>, <a href="/search/cs?searchtype=author&amp;query=Ram%C3%A9%2C+A">Alexandre Ram茅</a>, <a href="/search/cs?searchtype=author&amp;query=Ferret%2C+J">Johan Ferret</a>, <a href="/search/cs?searchtype=author&amp;query=Liu%2C+P">Peter Liu</a>, <a href="/search/cs?searchtype=author&amp;query=Tafti%2C+P">Pouya Tafti</a>, <a href="/search/cs?searchtype=author&amp;query=Friesen%2C+A">Abe Friesen</a>, <a href="/search/cs?searchtype=author&amp;query=Casbon%2C+M">Michelle Casbon</a>, <a href="/search/cs?searchtype=author&amp;query=Ramos%2C+S">Sabela Ramos</a>, <a href="/search/cs?searchtype=author&amp;query=Kumar%2C+R">Ravin Kumar</a>, <a href="/search/cs?searchtype=author&amp;query=Lan%2C+C+L">Charline Le Lan</a>, <a href="/search/cs?searchtype=author&amp;query=Jerome%2C+S">Sammy Jerome</a>, <a href="/search/cs?searchtype=author&amp;query=Tsitsulin%2C+A">Anton Tsitsulin</a>, <a href="/search/cs?searchtype=author&amp;query=Vieillard%2C+N">Nino Vieillard</a>, <a href="/search/cs?searchtype=author&amp;query=Stanczyk%2C+P">Piotr Stanczyk</a>, <a href="/search/cs?searchtype=author&amp;query=Girgin%2C+S">Sertan Girgin</a>, <a href="/search/cs?searchtype=author&amp;query=Momchev%2C+N">Nikola Momchev</a>, <a href="/search/cs?searchtype=author&amp;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&hellip; <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';">&#9661; 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';">&#9651; 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/2403.12324">arXiv:2403.12324</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/2403.12324">pdf</a>, <a href="https://arxiv.org/ps/2403.12324">ps</a>, <a href="https://arxiv.org/format/2403.12324">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Towards a Theory of Pragmatic Information </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&amp;query=Weinberger%2C+E+D">Edward D. Weinberger</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="2403.12324v5-abstract-short" style="display: inline;"> Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a rigorously justifiable, quantitative definition of ``pragmatic information&#39;&#39;, the amount of meaning in a message relevant to a particular decision. We posit that such a message updates a random variable, $蠅$, that informs the decision. The pragmatic information of a single message is t&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.12324v5-abstract-full').style.display = 'inline'; document.getElementById('2403.12324v5-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.12324v5-abstract-full" style="display: none;"> Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a rigorously justifiable, quantitative definition of ``pragmatic information&#39;&#39;, the amount of meaning in a message relevant to a particular decision. We posit that such a message updates a random variable, $蠅$, that informs the decision. The pragmatic information of a single message is then defined as the Kulbach-Leibler divergence between the apriori and aposteriori probabilities of $蠅$; the pragmatic information of a message ensemble is the expected value of the pragmatic information of the ensemble&#39;s component messages. We justify these definitions by proving that the pragmatic information of a single message is the expected difference between the shortest binary encoding of $蠅$ under the a priori and a posteriori distributions, and that the average of the pragmatic values of individual messages, when sampled a large number of times from the ensemble, approaches its expected value. Pragmatic information is non-negative and additive for independent decisions and ``pragmatically independent&#39;&#39; messages. Also, pragmatic information is the information analogue of free energy: just as free energy quantifies the part of a system&#39;s total energy available to do useful work, so pragmatic information quantifies the information actually used in making a decision. We sketch 3 applications: the single play of a slot machine, a.k.a. a ``one armed bandit&#39;&#39;, with an unknown payout probability; a characterization of the rate of biological evolution in the so-called ``quasi-species&#39;&#39; model; and a reformulation of the efficient market hypothesis of finance. We note the importance of the computational capacity of the receiver in each case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.12324v5-abstract-full').style.display = 'none'; document.getElementById('2403.12324v5-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </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">15 pages, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> H.1.1 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.11656">arXiv:2101.11656</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/2101.11656">pdf</a>, <a href="https://arxiv.org/format/2101.11656">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantitative Methods">q-bio.QM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> </div> </div> <p class="title is-5 mathjax"> G-MIND: An End-to-End Multimodal Imaging-Genetics Framework for Biomarker Identification and Disease Classification </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&amp;query=Ghosal%2C+S">Sayan Ghosal</a>, <a href="/search/cs?searchtype=author&amp;query=Chen%2C+Q">Qiang Chen</a>, <a href="/search/cs?searchtype=author&amp;query=Pergola%2C+G">Giulio Pergola</a>, <a href="/search/cs?searchtype=author&amp;query=Goldman%2C+A+L">Aaron L. Goldman</a>, <a href="/search/cs?searchtype=author&amp;query=Ulrich%2C+W">William Ulrich</a>, <a href="/search/cs?searchtype=author&amp;query=Berman%2C+K+F">Karen F. Berman</a>, <a href="/search/cs?searchtype=author&amp;query=Blasi%2C+G">Giuseppe Blasi</a>, <a href="/search/cs?searchtype=author&amp;query=Fazio%2C+L">Leonardo Fazio</a>, <a href="/search/cs?searchtype=author&amp;query=Rampino%2C+A">Antonio Rampino</a>, <a href="/search/cs?searchtype=author&amp;query=Bertolino%2C+A">Alessandro Bertolino</a>, <a href="/search/cs?searchtype=author&amp;query=Weinberger%2C+D+R">Daniel R. Weinberger</a>, <a href="/search/cs?searchtype=author&amp;query=Mattay%2C+V+S">Venkata S. Mattay</a>, <a href="/search/cs?searchtype=author&amp;query=Venkataraman%2C+A">Archana Venkataraman</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="2101.11656v1-abstract-short" style="display: inline;"> We propose a novel deep neural network architecture to integrate imaging and genetics data, as guided by diagnosis, that provides interpretable biomarkers. Our model consists of an encoder, a decoder and a classifier. The encoder learns a non-linear subspace shared between the input data modalities. The classifier and the decoder act as regularizers to ensure that the low-dimensional encoding capt&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.11656v1-abstract-full').style.display = 'inline'; document.getElementById('2101.11656v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.11656v1-abstract-full" style="display: none;"> We propose a novel deep neural network architecture to integrate imaging and genetics data, as guided by diagnosis, that provides interpretable biomarkers. Our model consists of an encoder, a decoder and a classifier. The encoder learns a non-linear subspace shared between the input data modalities. The classifier and the decoder act as regularizers to ensure that the low-dimensional encoding captures predictive differences between patients and controls. We use a learnable dropout layer to extract interpretable biomarkers from the data, and our unique training strategy can easily accommodate missing data modalities across subjects. We have evaluated our model on a population study of schizophrenia that includes two functional MRI (fMRI) paradigms and Single Nucleotide Polymorphism (SNP) data. Using 10-fold cross validation, we demonstrate that our model achieves better classification accuracy than baseline methods, and that this performance generalizes to a second dataset collected at a different site. In an exploratory analysis we further show that the biomarkers identified by our model are closely associated with the well-documented deficits in schizophrenia. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.11656v1-abstract-full').style.display = 'none'; document.getElementById('2101.11656v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1711.01134">arXiv:1711.01134</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1711.01134">pdf</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Accountability of AI Under the Law: The Role of Explanation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&amp;query=Doshi-Velez%2C+F">Finale Doshi-Velez</a>, <a href="/search/cs?searchtype=author&amp;query=Kortz%2C+M">Mason Kortz</a>, <a href="/search/cs?searchtype=author&amp;query=Budish%2C+R">Ryan Budish</a>, <a href="/search/cs?searchtype=author&amp;query=Bavitz%2C+C">Chris Bavitz</a>, <a href="/search/cs?searchtype=author&amp;query=Gershman%2C+S">Sam Gershman</a>, <a href="/search/cs?searchtype=author&amp;query=O%27Brien%2C+D">David O&#39;Brien</a>, <a href="/search/cs?searchtype=author&amp;query=Scott%2C+K">Kate Scott</a>, <a href="/search/cs?searchtype=author&amp;query=Schieber%2C+S">Stuart Schieber</a>, <a href="/search/cs?searchtype=author&amp;query=Waldo%2C+J">James Waldo</a>, <a href="/search/cs?searchtype=author&amp;query=Weinberger%2C+D">David Weinberger</a>, <a href="/search/cs?searchtype=author&amp;query=Weller%2C+A">Adrian Weller</a>, <a href="/search/cs?searchtype=author&amp;query=Wood%2C+A">Alexandra Wood</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="1711.01134v3-abstract-short" style="display: inline;"> The ubiquity of systems using artificial intelligence or &#34;AI&#34; has brought increasing attention to how those systems should be regulated. The choice of how to regulate AI systems will require care. AI systems have the potential to synthesize large amounts of data, allowing for greater levels of personalization and precision than ever before---applications range from clinical decision support to aut&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.01134v3-abstract-full').style.display = 'inline'; document.getElementById('1711.01134v3-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1711.01134v3-abstract-full" style="display: none;"> The ubiquity of systems using artificial intelligence or &#34;AI&#34; has brought increasing attention to how those systems should be regulated. The choice of how to regulate AI systems will require care. AI systems have the potential to synthesize large amounts of data, allowing for greater levels of personalization and precision than ever before---applications range from clinical decision support to autonomous driving and predictive policing. That said, there exist legitimate concerns about the intentional and unintentional negative consequences of AI systems. There are many ways to hold AI systems accountable. In this work, we focus on one: explanation. Questions about a legal right to explanation from AI systems was recently debated in the EU General Data Protection Regulation, and thus thinking carefully about when and how explanation from AI systems might improve accountability is timely. In this work, we review contexts in which explanation is currently required under the law, and then list the technical considerations that must be considered if we desired AI systems that could provide kinds of explanations that are currently required of humans. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.01134v3-abstract-full').style.display = 'none'; document.getElementById('1711.01134v3-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.2243">arXiv:0903.2243</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/0903.2243">pdf</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Portfolio Management">q-fin.PM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Trading and Market Microstructure">q-fin.TR</span> </div> </div> <p class="title is-5 mathjax"> Pragmatic Information Rates, Generalizations of the Kelly Criterion, and Financial Market Efficiency </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&amp;query=Weinberger%2C+E+D">Edward D. Weinberger</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="0903.2243v4-abstract-short" style="display: inline;"> This paper is part of an ongoing investigation of &#34;pragmatic information&#34;, defined in Weinberger (2002) as &#34;the amount of information actually used in making a decision&#34;. Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon&#39;s theory, we begin the paper by defining a pragmatic information rate, showing that all of the rele&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.2243v4-abstract-full').style.display = 'inline'; document.getElementById('0903.2243v4-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.2243v4-abstract-full" style="display: none;"> This paper is part of an ongoing investigation of &#34;pragmatic information&#34;, defined in Weinberger (2002) as &#34;the amount of information actually used in making a decision&#34;. Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon&#39;s theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races. If the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor&#39;s winnings is bounded by the pragmatic information of the messages. A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the &#34;tradable past&#34; with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon&#39;s Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors&#39; willful ignorance degrade the information processing capabilities of the market. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.2243v4-abstract-full').style.display = 'none'; document.getElementById('0903.2243v4-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 September, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </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">Revised to clarify the text</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 94A17; 91G80 </p> </li> </ol> <div class="is-hidden-tablet"> <!-- feedback for mobile only --> <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>&nbsp;&nbsp;</span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary"> <!-- MetaColumn 1 --> <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div> <!-- end MetaColumn 1 --> <!-- MetaColumn 2 --> <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div> <!-- end MetaColumn 2 --> </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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