Topic: GPT-2

David Persson presents Polar Express, a method for polar decomposition and the matrix sign function motivated by the Muon neural-network optimizer. It uses matrix multiplications suited to GPUs and adapts each polynomial update through a minimax problem to reduce worst-case error. The talk covers convergence, finite-precision implementation in bfloat16 and validation-loss improvements when training GPT-2 on FineWeb data. This is an in-person PACM IDeAS seminar at Princeton.

Robert Gower introduces Polar Express for the polar decomposition and matrix sign function, motivated by Muon neural-network training. Using only matrix-matrix products makes the method suited to high-throughput GPUs. Each iteration adapts its polynomial update through minimax optimization, building on Chen and Chow and Nakatsukasa and Freund. Worst-case error minimization gives rapid initial and asymptotic convergence. The talk addresses finite-precision implementation in bfloat16 and reports improved validation loss when training GPT-2 on one billion FineWeb tokens across several learning ra

Analogical reasoning –learning about new things by relating it to previous knowledge– lies at the heart of human intelligence and creativity and forms the core of educational practice. Children start creating and using analogies early on, making incredible progress moving from associative processes to successful analogical reasoning. For example, if we ask a four-year-old “Horse belongs to stable like chicken belongs to …?” they may use association and reply “egg”, whereas older children will likely give the intended relational response “chicken coop” (or other term to refer to a chicken’s hom