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Intelligence Begins with Memory: From Reflexes to Attention
Why associative memory is the oldest mechanism of intelligence—and still its computational core. By Tomaso Poggio & John Gabrieli Buchet Modern AI systems—transformers, diffusion models, large language models—appear astonishingly sophisticated. Yet beneath their apparent complexity lies a very simple and ancient idea: Store associations between patterns, and retrieve them by similarity. This is associative memory.
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Most Real Numbers Do Not Exist (And Why That Matters for Intelligence)
The most useful mathematical objects are the ones that aren’t real at all. By Tomaso Poggio We think of numbers as the foundation of science. We measure positions, voltages, masses, probabilities, and temperatures using quantities that—at least in theory—take values in the continuum of real numbers. This continuous line underpins classical mathematics and physics. But
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The Second Pillar: Genericity
Why learning works at all—and why not all functions are learnable By Tomaso Poggio & Pierfrancesco Beneventano In our last post, we explored the first pillar of intelligence: Sparse Compositionality. It explains the structure of the functions we want to learn: they must be sparse, hierarchical, and built from simple reusable components. Sparse compositionality tells
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The First Principle: Nature Builds with LEGO Bricks
Why can we understand a complex world? Because it is not a random mess — it is a hierarchy of reusable parts By Tomaso Poggio & Daniel Mitropolsky In our last post, we argued that modern AI resembles the period between Volta and Maxwell: we can build remarkable systems, but we do not yet have
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The Missing Foundations of Intelligence
Modern AI works, but we don’t know why. Here is a proposal for the fundamental principles that explain it. By Tomaso Poggio & John Gabrieli Buchet We are living through the fastest expansion of technological capability in human history. Every month, a new AI system appears that writes code, analyzes genomes, composes music, translates languages,
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![Brains, Minds, and Machines [book epilogue]](https://poggio-lab.mit.edu/files/2025/11/poggio-book-cover-215x300.jpg)
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Brains, Minds, and Machines [book epilogue]
The book Brains, Minds and Machines—originally published in Italian, going to appear in English published by MIT Press—has two authors: Marco Magrini and Tomaso Poggio. One is accustomed to working and creating with the signs of the alphabet; the other with the signs of mathematics. Since the mathematician among us has personally witnessed the evolution of artificial intelligence over the past fifty years—and therefore has stories worth telling—the closing pages have been written, quite naturally, in the first person. This epilogue reflects not only two complementary ways of seeing the world, but also the intersection of narrative and theory that…
