{"id":382863,"date":"2021-12-18T11:00:03","date_gmt":"2021-12-18T08:00:03","guid":{"rendered":"https:\/\/en.buradabiliyorum.com\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/"},"modified":"2021-12-18T11:00:03","modified_gmt":"2021-12-18T08:00:03","slug":"sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition","status":"publish","type":"post","link":"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/","title":{"rendered":"#Sure, DeepMind\u2019s AI is impressive, but can it guide human intuition?"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a26ea1d08904\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #dd3333;color:#dd3333\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #dd3333;color:#dd3333\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a26ea1d08904\" checked aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/#A_framework_for_mathematical_discovery_with_machine_learning\" >A framework for mathematical discovery with machine learning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/#Knots_and_representations\" >Knots and representations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/#Reactions_to_DeepMinds_math_AI\" >Reactions to DeepMind\u2019s math AI<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/#Reasons_to_be_skeptical\" >Reasons to be skeptical<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/buradabiliyorum.com\/en\/sure-deepminds-ai-is-impressive-but-can-it-guide-human-intuition\/#Deep_learning_and_intuition\" >Deep learning and intuition<\/a><\/li><\/ul><\/nav><\/div>\n<p>&#8220;<strong>#Sure, DeepMind\u2019s AI is impressive, but can it guide human intuition?<\/strong>&#8221;<\/p>\n<div><em>This article is part of our <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/tag\/ai-research-papers\/\">reviews of AI research papers<\/a>, a <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/watch-movies-tv-seriess\/\" data-internallinksmanager029f6b8e52c=\"8\" title=\"Watch Movies &amp; TV Series\" target=\"_blank\" rel=\"noopener\">series<\/a> of posts that explore the latest findings in artificial intelligence.<\/em><\/p>\n<p>Deep learning can help discover mathematical relations that evade human scientists, a recent paper by researchers at DeepMind shows. Like many things coming from the Alphabet-owned artificial intelligence lab, the paper, which is titled \u201c<a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.nature.com\/articles\/s41586-021-04086-x\">Advancing mathematics by guiding human intuition with AI<\/a>,\u201d has received much attention from <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/sciencee\/\" data-internallinksmanager029f6b8e52c=\"5\" title=\"Science\" target=\"_blank\" rel=\"noopener\">science<\/a> and tech <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/social-mediaa\/\" data-internallinksmanager029f6b8e52c=\"1\" title=\"Social Media\" target=\"_blank\" rel=\"noopener\">media<\/a>.<\/p>\n<p>Some mathematicians and computer scientists have lauded DeepMind\u2019s efforts and the findings in the paper as breakthroughs. Others are more skeptical and believe that the use of deep learning in mathematics might have been overstated in the paper and its coverage in popular press.<\/p>\n<p>The results are nonetheless fascinating and can expand the toolbox of scientists in discovering and proving mathematical theorems.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"A_framework_for_mathematical_discovery_with_machine_learning\"><\/span>A framework for mathematical discovery with machine learning<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In their paper, the scientists at DeepMind suggest that AI can be used to \u201cassist in the discovery of theorems and conjectures at the forefront of mathematical research.\u201d They propose a \u201cframework for augmenting the standard mathematician\u2019s toolkit with powerful pattern recognition and interpretation methods from machine learning.\u201d<\/p>\n<figure class=\"post-image post-mediaBleed aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"size-featured_img wp-image-1376391 js-lazy\" alt=\"Framework for using machine learning in mathematical discovery (by DeepMind)\" width=\"796\" height=\"259\" sizes=\"auto, (max-width: 796px) 100vw, 796px\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-796x259.jpeg\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-796x259.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-280x91.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-270x88.jpeg 270w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-540x176.jpeg 540w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind.jpeg 1392w\"\/><figcaption><a rel=\"nofollow noopener\" target=\"_blank\" href=\"#\" data-url=\"https:\/\/twitter.com\/intent\/tweet?url=https%3A%2F%2Feditorial.thenextweb.com%2Fneural%2F2021%2F12%2F18%2Fdeepminds-ai-impressive-can-it-guide-human-intuition-syndication%2F&amp;via=thenextweb&amp;related=thenextweb&amp;text=Check out this picture on: Framework for using machine learning in mathematical discovery. DeepMind\" data-title=\"Share Framework for using machine learning in mathematical discovery. DeepMind on Twitter\" data-width=\"685\" data-height=\"500\" class=\"post-image-share popitup\" title=\"Share Framework for using machine learning in mathematical discovery. DeepMind on Twitter\"><i class=\"icon icon--inline icon--twitter--dark\"\/><\/a>Framework for using machine learning in mathematical discovery. DeepMind<\/figcaption><noscript><img decoding=\"async\" loading=\"lazy\" class=\"size-featured_img wp-image-1376391\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-796x259.jpeg\" alt=\"Framework for using machine learning in mathematical discovery (by DeepMind)\" width=\"796\" height=\"259\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-796x259.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-280x91.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-270x88.jpeg 270w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind-540x176.jpeg 540w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Framework-for-using-machine-learning-in-mathematical-discovery-by-DeepMind.jpeg 1392w\"\/><\/noscript><\/figure>\n<p>Mathematicians start by making a hypothesis about the relation between two mathematical objects. To verify the hypothesis, they use computer programs to generate data for both types of objects. Next, a <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/unsupervised-learning-vs-supervised-learning\">supervised machine learning<\/a> model algorithm crunches the numbers and tries to tune its parameters that map one type of object to the other.<\/p>\n<p>\u201cThe key contributions of machine learning in this regression process are the broad set of possible nonlinear functions that can be learned given a sufficient amount of data,\u201d the researchers write.<\/p>\n<p>If the trained model performs better than random guessing, then it might indicate that there is indeed a discoverable relation between the two mathematical objects. Using various machine learning techniques, the researchers can find the data points that are more relevant to the problem, reform their hypothesis, generate new data, and train new models. By repeating these steps, they can narrow down the set of plausible conjectures and speed their way toward a final solution.<\/p>\n<p>DeepMind\u2019s scientists describe the framework as a \u201ctest bed for intuition\u201d that can quickly verify \u201cwhether an intuition about the relationship between two quantities may be worth pursuing\u201d and provide guidance as to how they may be related.<\/p>\n<p>Using this framework, the DeepMind researchers used deep learning to reach \u201ctwo fundamental new discoveries, one in topology and another in representation theory.\u201d<\/p>\n<p>An interesting aspect of the work was that it did not require the <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/ai-research-neural-networks-compute-costs\">huge amount of compute power<\/a> that has become a mainstay of DeepMind\u2019s research. According to the paper, the deep learning models used in both discoveries can be trained \u201cwithin several hours on a machine with a single graphics processing unit.\u201d<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Knots_and_representations\"><\/span>Knots and representations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><figure class=\"post-image post-mediaBleed aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376392 js-lazy\" alt=\"knots-deep-learning-deepmind\" width=\"570\" height=\"356\" sizes=\"auto, (max-width: 570px) 100vw, 570px\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-796x497.jpeg\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-796x497.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-280x175.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-216x135.jpeg 216w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-432x270.jpeg 432w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind.jpeg 1392w\"\/><noscript><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376392\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-796x497.jpeg\" alt=\"knots-deep-learning-deepmind\" width=\"570\" height=\"356\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-796x497.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-280x175.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-216x135.jpeg 216w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind-432x270.jpeg 432w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/knots-deep-learning-deepmind.jpeg 1392w\"\/><\/noscript><\/figure>\n<p>Knots are closed loops in dimensional space that can be defined in various ways. They become more complex as the number of their crossings grows. The researchers wanted to see whether they could use machine learning to discover a m<a href=\"https:\/\/buradabiliyorum.com\/en\/category\/download-scripts-themes-apps\/\" data-internallinksmanager029f6b8e52c=\"9\" title=\"Download Scripts &amp; Themes &amp; Apps\" target=\"_blank\" rel=\"noopener\">app<\/a>ing between algebraic invariants and hyperbolic invariants, two fundamentally different ways of defining knots.<\/p>\n<p>\u201cOur hypothesis was that there exists an undiscovered relationship between the hyperbolic and algebraic invariants of a knot,\u201d the researchers write.<\/p>\n<p>Using the SnapPy software package, the researchers generated the \u201csignature,\u201d an algebraic invariant, and 12 promising hyperbolic invariants for 1.7 million knots with up to 16 crossings.<\/p>\n<p>Next, they created a fully connected, <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/deep-learning-explainer\">feed-forward neural network<\/a> with three hidden layers, each having 300 units. They trained the deep learning model to map the values of the hyperbolic invariants to the signature. Their initial model was able to predict the signature with 78 percent accuracy. Further analysis brought them to a smaller set of parameters in the hyperbolic invariants that were predictive of the signature. The researchers refined their conjecture, generated new data, retrained their models, and reached a final theorem.<\/p>\n<p>The researchers describe the theorem as \u201cone of the first results that connect the algebraic and geometric invariants of knots and has various interesting applications.\u201d<\/p>\n<p>\u201cWe expect that this newly discovered relationship between natural slope and signature will have many other applications in low-dimensional topology. It is surprising that a simple yet profound connection such as this has been overlooked in an area that has been extensively studied,\u201d the researchers write.<\/p>\n<figure class=\"post-image post-mediaBleed aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376393 js-lazy\" alt=\"deep-learning-graph-representation\" width=\"592\" height=\"370\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-796x497.jpeg\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-796x497.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-280x175.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-216x135.jpeg 216w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-432x270.jpeg 432w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation.jpeg 1392w\"\/><noscript><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376393\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-796x497.jpeg\" alt=\"deep-learning-graph-representation\" width=\"592\" height=\"370\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-796x497.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-280x175.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-216x135.jpeg 216w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation-432x270.jpeg 432w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/deep-learning-graph-representation.jpeg 1392w\"\/><\/noscript><\/figure>\n<p>The second result in the paper is also a mapping of two different views of symmetries, a problem that is much more complicated than knots.<\/p>\n<p>In this case, they used a type of <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/what-is-graph-neural-network\">graph neural network (GNN)<\/a> to find relations between Bruhat interval graph and the Kazhdan-Lusztig (KL) polynomial. One of the benefits of GNNs is that they can compute and learn graphs that are very large and hard to manage for the unaided mind. The deep learning model takes the interval graph as input and tries to predict the corresponding KL polynomial.<\/p>\n<p>Again, by generating data, training DL models, and readjusting the process, the scientists were able to formulate a provable conjecture.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Reactions_to_DeepMinds_math_AI\"><\/span>Reactions to DeepMind\u2019s math AI<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Speaking about DeepMind\u2019s discovery in knot theory, Mark Brittenham, a knot theorist at the University of Nebraska\u2013Lincoln told <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.nature.com\/articles\/d41586-021-03593-1\"><em>Nature<\/em><\/a>, \u201cThe fact that the authors have proven that these invariants are related, and in a remarkably direct way, shows us that there is something very fundamental that we in the field have yet to fully understand.\u201d Brittenham added that, in comparison to other efforts to apply machine learning to knots, DeepMind\u2019s technique is novel in its ability to discover surprising connections.<\/p>\n<p>Adam Zsolt Wagner, a mathematician at Tel Aviv University, Israel, who also spoke to Nature, said that the methods presented by DeepMind could prove valuable for certain kinds of problems.<\/p>\n<p>Wagner, who has experience in applying machine learning to mathematics, said, \u201cWithout this tool, the mathematician might waste weeks or months trying to prove a formula or theorem that would ultimately turn out to be false.\u201d But he also added that it is unclear how broad its impact will be.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Reasons_to_be_skeptical\"><\/span>Reasons to be skeptical<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><figure class=\"post-image post-mediaBleed aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376394 js-lazy\" alt=\"neural-networks-deep-learning-stochastic-gradient-descent\" width=\"627\" height=\"418\" sizes=\"auto, (max-width: 627px) 100vw, 627px\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-796x531.jpeg\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-796x531.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-280x187.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-203x135.jpeg 203w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-405x270.jpeg 405w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent.jpeg 1392w\"\/><noscript><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376394\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-796x531.jpeg\" alt=\"neural-networks-deep-learning-stochastic-gradient-descent\" width=\"627\" height=\"418\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-796x531.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-280x187.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-203x135.jpeg 203w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent-405x270.jpeg 405w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/neural-networks-deep-learning-stochastic-gradient-descent.jpeg 1392w\"\/><\/noscript><\/figure>\n<p>Following the publication of DeepMind\u2019s work in Nature, Ernest Davis, Computer Science Professor at New York University, <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/arxiv.org\/abs\/2112.04324\">published a paper of his own<\/a>, which raises some important questions about DeepMind\u2019s framing of the results and the limits of applying deep learning to mathematics in <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/general\/\" data-internallinksmanager029f6b8e52c=\"3\" title=\"General\" target=\"_blank\" rel=\"noopener\">general<\/a>.<\/p>\n<p>On the first result presented in DeepMind\u2019s paper, Davis observes that knot theory is not the kind of problem where deep learning typically outshines other machine learning or statistical methods.<\/p>\n<p>\u201cDL\u2019s strength is in cases like vision or text where each instance (image or text) has a large number of low-level input features, it is hard to reliably identify high-level features, and the function relating the input features to the answer is, as far as anyone can tell, immensely complex, with no small subset of the input features being at all determinative,\u201d Davis writes.<\/p>\n<p>The knot problem had only twelve input features, of which only three turned out to be relevant. And the mathematical relation between the input features and target variable was simple.<\/p>\n<p>\u201cIt is hard to see why a neural network with 200,000 parameters would be the method of choice; simple, conventional statistical methods or a support vector machine would be more suitable,\u201d Davis writes.<\/p>\n<p>In the second project, the role of deep learning was much more relevant, Davis notes. \u201cUnlike the knot theory project, which used a generic DL architecture, the neural network was carefully designed to fit deep mathematical knowledge about the problem. Moreover, the DL worked much better, with something like 1\/40th the error rate, on pre-processed data than on the original data,\u201d he writes.<\/p>\n<p>On the one hand, the results cut against criticism pertaining that it is hard to incorporate domain knowledge into deep learning, Davis notes. \u201cOn the other hand, enthusiasts for DL have often praised DL as a \u2018plug-and-play\u2019 learning methodology that can be thrown at raw data for whatever problem comes to hand; this cuts against that praise,\u201d he writes.<\/p>\n<p>Davis also notes that the success of applying deep learning to these tasks may depend critically on the way the training data is generated and the way that the mathematical structures are encoded. This suggests that the framework might be applicable to a narrow class of mathematical problems.<\/p>\n<p>\u201cFinding the best way to generate and encode data involves a mixture of theory, experience, art, and experimentation. The burden of all this lies on the human expert,\u201d he writes. \u201cDeep learning can be a powerful tool, but it is not always a robust one.\u201d<\/p>\n<p>Davis warns that in the current climate of hype surrounding deep learning, \u201cthere is a perverse incentive to focus the role of the DL in this research, not just for the ML specialists from DeepMind, but even for the mathematicians.\u201d<\/p>\n<p>Davis concludes that, as used in the paper, deep learning is best viewed as \u201canother analytic tool in the toolbox of experimental mathematics rather than as a fundamentally new approach to mathematics.\u201d<\/p>\n<p>It is worth noting that the authors of the original paper have also pointed out some of the limits of their framework, including that \u201cit requires the ability to generate large datasets of the representations of objects and for the patterns to be detectable in examples that are calculable. Further, in some domains the functions of interest may be difficult to learn in this paradigm.\u201d<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Deep_learning_and_intuition\"><\/span>Deep learning and intuition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><figure class=\"post-image post-mediaBleed aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376395 js-lazy\" alt=\"human-mind-thoughts\" width=\"613\" height=\"406\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-796x527.jpeg\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-796x527.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-280x185.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-204x135.jpeg 204w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-408x270.jpeg 408w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts.jpeg 1392w\"\/><noscript><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1376395\" src=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-796x527.jpeg\" alt=\"human-mind-thoughts\" width=\"613\" height=\"406\" srcset=\"https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-796x527.jpeg 796w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-280x185.jpeg 280w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-204x135.jpeg 204w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts-408x270.jpeg 408w, https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/human-mind-thoughts.jpeg 1392w\"\/><\/noscript><\/figure>\n<p>One of the topics of controversy is the paper\u2019s claim that deep learning is \u201cguiding intuition.\u201d Davis describes this claim as a \u201cseriously inaccurate description of the assistance that mathematicians have gained, or can hope to gain, from this use of DL systems.\u201d<\/p>\n<p>Intuition is <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/myth-of-artificial-intelligence-erik-larson\">one of the key differentiators<\/a> between human and artificial intelligence. It is the ability to make decisions that are better than random guesses and can direct you in the right direction most of the time. As the history of AI has so far shown, intuition is not captured in countless predefined rules or patterns found in vast amounts of data.<\/p>\n<p>\u201cIn the mathematical setting, the word \u2018intuitive\u2019 means that a concept or a proof can be grounded in a person\u2019s deep-seated sense of familiar domains such as numerosity, space, time, or motion, or in some other way \u2018makes sense\u2019 or \u2018seems right\u2019 in a way that does not involve explicit calculation or step-by-step reasoning,\u201d Davis writes.<\/p>\n<p>While obtaining an intuitive grasp of mathematical concepts often requires working through multiple specific examples, it is not a work of statistical correlations, Davis argues. In other words, you don\u2019t gain intuitions by running millions of examples and observing the percent of times certain patterns recur.<\/p>\n<p>This means that it was not the deep learning models that provided the scientists with an intuitive understanding of the concepts they defined, the theorems they proved, and the conjectures they put forward.<\/p>\n<p>Writes Davis, \u201cWhat the DL did was to give them some advice as to which features of the problem seemed to be important and which seemed unimportant. That is not to be sneezed at, but it should not be exaggerated.\u201d<\/p>\n<p><em>This article was originally published by Ben Dickson on<span>\u00a0<\/span><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/\">TechTalks<\/a>, a publication that examines trends in <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/technology\/\" data-internallinksmanager029f6b8e52c=\"4\" title=\"Technology\" target=\"_blank\" rel=\"noopener\">technology<\/a>, how they affect the way we live and do business, and the problems they solve. But we also discuss the evil side of technology, the darker implications of new tech, and what we need to look out for. You can read the original article <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/bdtechtalks.com\/news\/deepminds-machine-learning-mathematics\">here<\/a>.<\/em><\/p>\n<\/div>\n<p><script async src=\"\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script><\/p>\n<blockquote><p><strong><span style=\"color: #ff6600;\">If you liked the article, do not forget to share it with your friends. Follow us on\u00a0<span style=\"color: #ff0000;\"><a style=\"color: #ff0000;\" href=\"https:\/\/news.google.com\/publications\/CAAqBwgKMLG0nwswvr63Aw\" target=\"_blank\" rel=\"nofollow noopener noreferrer\">Google News<\/a><\/span>\u00a0too, click on the star and choose us from your favorites.<\/span><\/strong><\/p><\/blockquote>\n<blockquote>\n<p style=\"text-align: center;\">For forums sites go to <span style=\"color: #ff9900;\"><a style=\"color: #ff9900;\" href=\"https:\/\/forum.buradabiliyorum.com\/\" target=\"_blank\" rel=\"noopener\">Forum.BuradaBiliyorum.Com<\/a><\/span><\/strong>\n<\/p><\/blockquote>\n<blockquote>\n<p style=\"text-align: center;\"><strong>If you want to read more like this article, you can visit our <span style=\"color: #ff9900;\"><a style=\"color: #ff9900;\" href=\"https:\/\/en.buradabiliyorum.com\/technology\/\" target=\"_blank\" rel=\"noopener\">Technology category.<\/a><\/span><\/strong><\/p>\n<\/blockquote>\n<p><span style=\"color: black;\"><a style=\"color: #ff9900;\" href=\"https:\/\/thenextweb.com\/news\/deepminds-ai-impressive-can-it-guide-human-intuition-syndication\" target=\"_blank\" rel=\"noopener\">Source<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;#Sure, DeepMind\u2019s AI is impressive, but can it guide human intuition?&#8221; This article is part of our reviews of AI research papers, a series of posts that explore the latest findings in artificial intelligence. Deep learning can help discover mathematical relations that evade human scientists, a recent paper by researchers at DeepMind shows. Like many&#8230;<\/p>\n","protected":false},"author":1,"featured_media":382864,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img-cdn.tnwcdn.com\/image\/neural?filter_last=1&fit=1280,640&url=https:\/\/cdn0.tnwcdn.com\/wp-content\/blogs.dir\/1\/files\/2021\/12\/Untitled-3.jpg&signature=107dcf61f785ba39f0b1a80dccb68d4e","fifu_image_alt":"","footnotes":""},"categories":[18],"tags":[],"class_list":["post-382863","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-technology"],"_links":{"self":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts\/382863","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/comments?post=382863"}],"version-history":[{"count":0,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts\/382863\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/media\/382864"}],"wp:attachment":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/media?parent=382863"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/categories?post=382863"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/tags?post=382863"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}