The Computer Scientist Who Builds Big Pictures From Small Details

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Article</title><path fill="currentColor" d="M2.1 0h45.8v50L25.5 37.5 2.1 50V0z"></path></svg> <div class='h6t uppercase kern ml1 mv0 theme__text'> Read Later </div> </button> <div class='q-tooltip hidden force-mobile-placement w-32 ml-n16 -top-10'> <div class='q-tooltip-content'> <div class='q-tooltip-arrow -bottom-3'></div> <div class='q-tooltip-inner py-1 pl-1' role='tooltip'> <div class='h6t relative z1 uppercase kern--w mx025'> <span class='small no-wrap'>Read Later</span> </div> </div> </div> </div> </div> </li> </ul> <div class='nav__local__progress absolute fit-b fit-l fit-r z1 theme__accent'> <span class='block' style='transform: translateX(-100%);' data-role='content-progress-bar'></span> </div> </div> </div> <div id='postBody' class='theme__background-background theme__text'> <section class='post__title__wrapper relative '> <section class='outer fill-h relative outer--content '> <div class='mha container--s'> <div class='header-spacer'></div> <div class='post__title pv1 scale1 mha'> <div class='scale0'> <div class='mb1 pb025 mt0 h6t post__title__kicker '> <a class="kicker theme__accent theme__text-hover uppercase" href="/tag/qa/">Q&A</a> </div> <h1 class='post__title__title mv025 noe theme__text' >The Computer Scientist Who Builds Big Pictures From Small Details</h1> <div class='post__title__author-date h5 mt1'> <div class='byline relative flex flex-items-start merriweather mv025 mr1 gray3 h6t theme__text-hover'> <em class='byline__by gray4 mr075'>By </em> <a href='https://www.quantamagazine.org/authors/john-pavlus/'> <span class='byline__author uppercase kern light small'>John Pavlus</span> </a> </div> <p class="h6 mv1 pv025 o6"><em>October 7, 2024</em></p> </div> <div class='post__title__meta flex flex-wrap flex-items-start'> <div class='post__title__excerpt wysiwyg p italic mb1 mt025 pr2 o4 theme__text ' > To better understand how machines learn, Lenka Zdeborová treats them like physical materials. </div> <div class='post__title__actions h5 mt025 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class="mb-6 w-full s:mb-4" alt="Lenka Zdeborová in a tan sweater stands outside in a large pavilion" decoding="async" fetchpriority="high" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-1720x968.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-520x293.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-768x432.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-1536x864.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Lede-2048x1152.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-large justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>Lenka Zdeborová studies how the physics of matter can help model the behavior of machine learning algorithms.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <h2 class='screen-reader-text'>Introduction</h2> <div class='post__wrapper scale0 show-dropcap'> <div class='mha container--m'> <div class='post__content relative flex flex-items-start flex-justify-between'> <aside class='post__sidebar hide flex flex-justify-center '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' href='https://www.quantamagazine.org/authors/john-pavlus/'> <div class='sidebar__author__avatar mha mb1'> <div class='image mx0 relative image--circle '> <div class='image__inner absolute fit-x is-loaded'> <img width="1500" height="1500" src="https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1.jpg" class="absolute fit-x fill-h fill-v mxa" alt="" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1.jpg 1500w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-520x520.jpg 520w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-768x768.jpg 768w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-160x160.jpg 160w" sizes="(max-width: 1500px) 100vw, 1500px" /> </div> </div> </div> <div class='h3t mv05'> <span class='screen-reader-text'>By </span>John Pavlus </div> <p class="o8 theme__text h5 mt05 mb1"><em>Contributing Writer</em></p> </a> </div> <hr class='mb075 o1'> <p class="h6 mv1 pv025 o6"><em>October 7, 2024</em></p> </div> <form action='https://www.quantamagazine.org/the-computer-scientist-who-builds-big-pictures-from-small-details-20241007' method='get' class='sidebar__actions'> <hr class='mt075 mb1 o1'> <input type='hidden' id='print' name='print' value='1' /> <button type="submit" class='h6 pangram uppercase mv05 pb1 bold kern flex flex-items-center flex-justify-between sidebar__print transition--color theme__accent-hover'> <small>View PDF/Print Mode</small> <svg class="icon-l theme__accent ml05" viewbox="0 0 50 50" enable-background="new 0 0 50 50"><path fill="currentColor" d="M39.9,27.5h4.9v22.4H0.1V5.1h22.4V10H5v35h35V27.5z M49.8,0.1h-2.4h-1H33.8V5h7.6L20.7,25.8l3.4,3.4L45,8.4v7.7h4.9V2.6L49.8,0.1z"></path></svg> </button> </form> <div class='mt1 pt05 sidebar__tag-wrap'> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/artificial-intelligence'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>artificial intelligence</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/computer-science'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>computer science</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/machine-learning'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>machine learning</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/natural-language-processing'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>natural language processing</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/neural-networks'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>neural networks</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/physics'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>physics</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/qa'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>Q&A</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative theme__accent w-full' href='/topics'> <span class='absolute fit-x theme__text-background 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novel. A character in Asimov’s “Foundation” series invents a mathematical method for predicting the path of an entire civilization by averaging out the haphazard behavior of billions of individuals. The concept gave her a “mesmerizing feeling,” Zdeborová recalls — one that returned when she later encountered a method that she could actually apply to make sense of huge numbers of unpredictable elements.</p> <p>“I realized, ‘Oh my God, Asimov was just describing statistical physics,’” she said, referring to a discipline that describes the big-picture properties of matter by using the rules that apply to individual molecules. As a physics master’s student at Charles University in Prague, she reveled in its predictive power. Then, while she was pursuing her doctorate, Zdeborová’s adviser showed her <a href="https://www.science.org/doi/abs/10.1126/science.1073287">a paper</a> that applied the techniques of statistical physics to theoretical computer science — the mathematical study of computation and how algorithms behave. The familiar feeling returned with a vengeance.</p> <p>“I was completely mesmerized by that paper,” Zdeborová said. “I had always had this impression that to do computer science, you had to be a hacker and know everything about Linux. I realized that theoretical computer science was as fascinating as theoretical physics, and I said, ‘OK — this is what I want to do.’”</p> <p>Zdeborová now leads the <a href="https://www.epfl.ch/labs/spoc/">Statistical Physics of Computation Laboratory</a> at the Swiss Federal Institute of Technology Lausanne. Her work currently focuses on how the physics of phase transitions in matter — such as water freezing into ice — can help model the behavior of algorithms, especially those used in machine learning.</p> </div> </div> </div> </section> <aside class='post__sidebar hide flex flex-justify-center theme__anchors--solid '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='h3t mt0'> Share this article </div> <div data-id='social-links'> <div class='social-links social-links--share flex flex-justify-between'> <a href='http://www.facebook.com/sharer.php?u=https://www.quantamagazine.org/the-computer-scientist-who-builds-big-pictures-from-small-details-20241007/' class='social-links__link flex flex-items-center relative' target="_blank" > <div class='icon-button inline-block relative pointer theme__accent-hover-child'> <div class='absolute fit-x mxa o2 hover--opaque theme__text'> </div> <svg class="absolute fit-x mxa theme__text" viewbox="0 0 50 50" 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items-center justify-center flex-col max-w-img-inline py-0 px-16 s:px-0 l:px-16 '> <div class='w-full flex justify-center max-w-mod-inline image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1 s:px-5'> <img width="1829" height="2560" src="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-scaled.webp" class="mb-6 w-full s:mb-4 vertical" alt="Lenka Zdeborová sits outside on a sculpture of the letters EPFL in red" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-scaled.webp 1829w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-1229x1720.webp 1229w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-371x520.webp 371w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-768x1075.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-1097x1536.webp 1097w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Logo-1463x2048.webp 1463w" sizes="(max-width: 1829px) 100vw, 1829px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='s:pt-0 s:px-5 s:pb-6 s:w-full-minus-25'> <div class='w-full my-0 mx-auto max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>Zdeborová leads the Statistical Physics of Computation Laboratory at the Swiss Federal Institute of Technology Lausanne, or EPFL.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h '> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p><em>Quanta</em> spoke with Zdeborová about the similarities between water and algorithms, using physics to understand large language models, and chasing unreasonable scientific goals. The interview has been condensed and edited for clarity.</p> <h3><strong>Your work crosses disciplinary boundaries, so do you think of yourself as a physicist, a computer scientist or a mathematician?</strong></h3> <p>I would say all of the above. The problems I’m interested in are mostly in computer science and machine learning. But in theoretical computer science, everything should be formally proven, down to the last detail. With machine learning today, that’s just not happening anymore — it’s so complicated.</p> <p>So from an approach perspective, I feel like a theoretical physicist because, just like in physics, you can seek to explain phenomena with theories that are still mathematically rigorous, even if they may not have formal mathematical proofs.</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-large py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-large m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2560" height="1658" src="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-scaled.webp" class="mb-6 w-full s:mb-4" alt="Lenka Zdeborová pulls on pieces of a giant sculpture made of metal rods" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-1720x1114.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-520x337.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-768x497.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-1536x995.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Sculpture-2048x1326.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-large justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>The EPFL campus features many works of art. Here, Zdeborová interacts with <em>Big Bang</em> by Etienne Krähenbühl.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <h3><strong>How does statistical physics help you understand computer science?</strong></h3> <p>What is usually taught to students about theoretical computer science is to focus on the worst case — instances of a problem that make it too hard to compute. That’s how the field started; that’s where we have beautiful results. But there’s a difference between the worst case and the typical case. Machine learning is a clear example of that. So even with very high-dimensional data — like medical imaging with millions of pixels, where we want to detect certain markers for disease — the relevant instances of the problem are often not as computationally hard as the worst ones.</p> <p>This is where statistical physics kicks in, because that is historically the field of science that dealt with these high-dimensional problems. When you want to describe the behavior of many molecules interacting at once, statistical physics brings up probability distributions. These are mathematical objects that, in a very similar form, appear in computer science when describing how bits of data interact when a given algorithm is executed. It’s just that statistical physics got started a century ago, when computer science didn’t even exist. Luckily, by the time I did my Ph.D. in the 2000s, the disciplines were realizing how much they had in common.</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-inline py-0 px-16 s:px-0 l:px-16 '> <div class='w-full flex justify-center max-w-mod-inline image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1 s:px-5'> <img width="1890" height="2560" src="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-scaled.webp" class="mb-6 w-full s:mb-4 vertical" alt="Lenka Zdeborová in a tan sweater looks down, behind an out of focus bookshelf" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-scaled.webp 1890w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-1270x1720.webp 1270w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-384x520.webp 384w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-768x1040.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-1134x1536.webp 1134w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-Looking_down-1512x2048.webp 1512w" sizes="(max-width: 1890px) 100vw, 1890px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='s:pt-0 s:px-5 s:pb-6 s:w-full-minus-25'> <div class='w-full my-0 mx-auto max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>For Zdeborová, algorithms can behave just as mysteriously as molecules. “How do we derive that water will freeze at zero degrees Celsius?” she asked. “That’s not at all obvious!”</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h '> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <h3><strong>What do they have in common?</strong></h3> <p>In both cases, extracting the macroscopic behavior of a system from a microscopic description is difficult.</p> <p>Even though Newton’s laws and quantum mechanics can give you a really detailed description of how water molecules interact, how do we derive that water will freeze at zero degrees Celsius? That’s not at all obvious! Even in the 1940s it was not figured out. And there are still <a href="https://www.quantamagazine.org/the-enduring-mystery-of-how-water-freezes-20240617/">many questions</a> about phase transitions in water, especially at high pressure.</p> <p>Similarly, in computer science, there are very simple-to-define problems with relatively simple algorithms, where we don’t know under what conditions they will work. In my Ph.D. thesis, we studied the problem of graph coloring, which a 5-year-old kid can understand. You have points, and some are connected with edges, which creates a graph. You want to color each point with one of three colors. And if two points are connected, they can’t have the same color. So can you color the graph or not?</p> <p>For any given algorithm to solve this problem, you could understand it, even code it, and it would run. But what if I asked, “Can you tell me when this algorithm will work, and when it won’t?” For most algorithms, we don’t know. And that’s kind of the overall status in theoretical computer science: Even for a simple problem like that, when we start asking natural questions about the behavior of algorithms, we often don’t have the answers.</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-full py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-full m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2560" height="1366" src="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-scaled.webp" class="mb-6 w-full s:mb-4" alt="Lenka Zdeborová uses a laptop on a desk with colorful artwork on the wall behind her" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-1720x918.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-520x278.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-768x410.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-1536x820.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-AtDesk-2048x1093.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-16 s:p-0'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-full justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>With her interdisciplinary work, Zdeborová considers herself a physicist, computer scientist and mathematician.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <h3><strong>If it’s so hard to fully understand algorithms, how can phase transitions help?</strong></h3> <p>The phase transitions we study are not literally physical, like water turning into ice. But they are analogous in that you have a sharp, sudden change in the behavior [of the system] under certain conditions. In the case of neural networks, one of the first transitions to be characterized was in how learning efficiency depends on the amount of training data.</p> <p>You take a given neural network that learns from high-dimensional data — like images with millions of pixels — and then analyze, in certain simplified settings, how many training samples you need for the network to learn a function to a certain level of precision. You get a phase transition in the very sense we’re talking about, a sudden change in the optimal performance for that system. And these conditions tell you something about how hard or easy the learning will be, and whether it makes sense to look for better algorithms.</p> <h3><strong>Has this approach helped you learn anything new about these complicated systems?</strong></h3> <p>In recent work, we did <a href="https://arxiv.org/abs/2402.03902">find a phase transition</a> in the performance of a simplified version of a large language model, but what was also interesting was the nature of the two phases on either side of the transition.</p> <p>In physics, there are certain quantities in the mathematical description of a phase transition that we call order parameters. They allow you to understand what the phase transition is actually about. This allowed us to understand that magnetism is about atoms aligning: In one phase, the overall alignment is big, and in the other (nonmagnetic) phase, there is no alignment.</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-regular py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-regular m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2000" height="1413" src="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp.webp" class="mb-6 w-full s:mb-4" alt="Closeup of Lenka Zdeborová in a tan sweater" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp.webp 2000w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp-1720x1215.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp-520x367.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp-768x543.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/10/LenkaZdeborova-cr.SamuelRubio-CloseUp-1536x1085.webp 1536w" sizes="(max-width: 2000px) 100vw, 2000px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full l:max-w-mod-inline'> <section class='p-0 m:py-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:m-0 l:p-0 max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>By learning enough about simple machine learning systems, Zdeborová hopes to help decode their overarching rules.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h '> <p>Samuel Rubio for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>That’s the beautiful thing that appeared in our mathematical description of the language models. There were two order parameters, each with a precise meaning. One determined if the learning that happens relies a lot on the position of the words in the sentence. The other order parameter was specifically about the meaning of each word, the semantics.</p> <p>And when we looked at the phase transition, we found that below a certain threshold of training examples, only the position mattered — not the semantics. And if we had more examples above that threshold, it was only the semantics that mattered. So, in a sense, it’s a new type of phase transition between positional and semantic learning that we could characterize in a simplified language model. To me, this is a baby step toward understanding <a href="https://www.quantamagazine.org/the-unpredictable-abilities-emerging-from-large-ai-models-20230316/">emergent properties</a> in large language models, like suddenly being able to do arithmetic, answer questions in Greek, or things like that.</p> <h3><strong>Where do you think enough of these baby steps could lead you?</strong></h3> <div class="related-list"> <aside class="post__aside mb2 relative hide-on-print post__aside--right"> <h2 class="mv0 h5 bold uppercase kern">Related:</h2> <hr class="mt1 o2"> <ol class="post__aside__list theme__anchors--none pt05"> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/does-ai-know-what-an-apple-is-she-aims-to-find-out-20240425/"> <span class="' . $span_class . '">Does AI Know What an Apple Is? She Aims to Find Out.</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/a-close-up-view-reveals-the-melting-point-of-an-infinite-graph-20231218/"> <span class="' . $span_class . '">A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/complexity-theorys-50-year-journey-to-the-limits-of-knowledge-20230817/"> <span class="' . $span_class . '">Complexity Theory’s 50-Year Journey to the Limits of Knowledge</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/the-unpredictable-abilities-emerging-from-large-ai-models-20230316/"> <span class="' . $span_class . '">The Unpredictable Abilities Emerging From Large AI Models</span> </a> </h3> </li> </ol> </aside> </div> <p>The analogy I really like is to thermodynamics. When we had the steam engine in the 18th century, it gave rise to the Industrial Revolution: railways and companies and many things running on the steam engine, all without understanding thermodynamics. That came decades later, and it was inspired by wanting to understand the steam engine. From that, a lot of other physics emerged.</p> <p>This is probably a completely unreasonable goal, but you know, somebody has to come up with the thermodynamics of machine learning. I would love to be that person. If it’s not me and it’s somebody else, that’s also great. But I will definitely push toward that goal.</p> </div> </div> </div> </section> </div> <div class='pv2'></div> <div class='post__footer'> <div class='mha container--m'> <div class='flex flex-wrap flex-items-stretch'> <div class='post__footer__col fill-h pv2 flex flex-items-center flex-justify-center'> <section class='outer'> <aside class='post__sidebar hide flex flex-justify-center post__sidebar--footer'> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' href='https://www.quantamagazine.org/authors/john-pavlus/'> <div class='sidebar__author__avatar mha mb1'> <div class='image mx0 relative image--circle '> <div class='image__inner absolute fit-x is-loaded'> <img width="1500" height="1500" src="https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1.jpg" class="absolute fit-x fill-h fill-v mxa" alt="" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1.jpg 1500w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-520x520.jpg 520w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-768x768.jpg 768w, https://www.quantamagazine.org/wp-content/uploads/2017/04/John_Pavlus1-160x160.jpg 160w" sizes="(max-width: 1500px) 100vw, 1500px" /> </div> </div> </div> <div class='h3t mv05'> <span class='screen-reader-text'>By </span>John Pavlus </div> <p class="o8 theme__text h5 mt05 mb1"><em>Contributing Writer</em></p> </a> </div> <hr class='mb075 o1'> <p class="h6 mv1 pv025 o6"><em>October 7, 2024</em></p> </div> <form action='https://www.quantamagazine.org/the-computer-scientist-who-builds-big-pictures-from-small-details-20241007' method='get' class='sidebar__actions'> <hr class='mt075 mb1 o1'> <input type='hidden' id='print' name='print' value='1' /> <button type="submit" class='h6 pangram uppercase mv05 pb1 bold kern flex 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