Médaille d'or 2025 : Stéphane Mallat, bâtisseur de ponts mathématiques et informatiques

Transcription

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When I was about ten years old, I would spend hours drawing furniture plans that I dreamed of building. I would draw the geometry of the boards, I would calculate their size. And the next day, typically, I would move on to cutting them. I loved that back-and-forth between free imagination through drawing and the making of a piece of furniture that could actually be useful.
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And I now realize that this pleasure has really remained at the heart of my research.

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I am a researcher and professor at the Collège de France and at the École normale supérieure, and I work on mathematics applied to information processing—in other words, today on neural networks and artificial intelligence.
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The challenge is to try to understand the mathematical principles that govern the performance of these algorithms, which are increasingly present in our everyday lives.
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Mathematics is not an esoteric language, detached from the world. It defines abstractions that capture the essence of problems that come from the real world. And that then makes it possible to compute, to prove things, before coming back to applications.
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It is, in a way, on this bridge between concrete questions and mathematical abstractions that I approached wavelet theory.

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I did my PhD at the University of Pennsylvania in Philadelphia, where my advisor, Ruzena Bajcsy, was a true pioneer of computer vision. She suggested that I study how images evolve as you gradually increase their resolution.
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I connected that to the work of Yves Meyer. He had constructed the first orthogonal wavelets. To improve them, we needed to better understand their underlying mathematical properties.
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Yves Meyer had built a basis that seemed miraculous. While he was giving prestigious talks in Chicago, I, as a PhD student, got in touch with him. That fits perfectly with both intellectual boldness and Stéphane's natural ease. And they worked together to translate Stéphane's intuition into a mathematical framework, which became multiresolution analysis.
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In return, this theory allowed me to introduce a fast algorithm to decompose and synthesize data using wavelets.

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An audio wavelet looks like a musical note that is well localized in time, with a specific frequency pitch. And I realized that in an image, wavelets correspond more to the smallest details that make it possible to increase the resolution of images.
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In other words, where the image is uniform, there is no wavelet—just like silence in music. And in this way, we obtain a representation that makes it possible to synthesize an image with far fewer wavelets than pixels.
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This has had many applications, for example, the JPEG 2000 image compression standard, and in many other areas of signal processing and even physics.

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I returned to France as a professor at École Polytechnique. And with my students, we built dictionaries of what are called "bandlets," which describe the geometry of edges in images.
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That is when a somewhat naive dream was born: to try to push a theorem all the way to a consumer product. And that was the beginning of the startup Let It Wave in 2001.
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High-definition television was arriving, and with it, flat screens. This raised enormous display and image-quality problems on these TV sets. To address this, we needed to develop microprocessors and sell them to companies like Samsung, LG, and Sony, who would integrate them into their chips.
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In a year and a half, we built a reputation that made us a reference in the quality of image-processing systems embedded on microprocessors.
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Stéphane is both a true mathematician and a true engineer. He has the ability to arrive at technical solutions and create simple, elegant, efficient, and fast algorithms that stand up to real-world testing.
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Once again, this adventure was a constant back-and-forth between mathematics, computer science, and very concrete problems.
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After seven years, I still only dreamed of one thing: to return to research. I even wondered whether, at 45, it wasn't ultimately too late to set off in a different direction.
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But I think it is probably in these moments of uncertainty that we are the most creative, when we step away from our somewhat rigid trajectories.

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In 2012, we were already starting to see artificial intelligence and neural networks achieve unexpected and amazing results. We urgently had to tackle the mathematical foundations to understand how and why it works.
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This is the new major endeavor that Stéphane took on by studying the work of Yann Le Cun and others on deep neural networks.
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I realized that their performance was as spectacular as it was poorly understood. Stéphane presents his view of the field and, above all, the tools he brings to the table to build the foundations of artificial intelligence—always with a level of excellence that is inspiring.
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Stéphane is, in my view, as much a great mathematician as a great computer scientist. In that sense, he is a true scientific leader who has opened paths that are now widely followed.

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Regulating and adapting to the explosion of artificial intelligence is truly a major societal challenge. I think it starts at school. Adapting will probably involve education that encourages this back-and-forth between knowledge, critical thinking, and experimenting with the world—something AI does not have.
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Becoming a researcher first requires finding your path. For that, you need to let in chance events and serendipitous encounters. Keep a form of naivety, quite simply.
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It is also about working with a community, a team. For me, it was my students who contributed fundamentally to all the results that were achieved.
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It is a path that is much more winding than planning a career, but it more often leads us down the path of passion.
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The role of the CNRS is very important in this completely global scientific vision across disciplines.
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The Gold Medal was a big surprise for me at first and deeply moving because it was the recognition of a community. And it's the first time a medal has been awarded in applied mathematics.