PeopleofSuperintelligence

Researcher

Noah Amsel

Noah Amsel is a computer science PhD student at NYU's Courant Institute who brings approximation theory and numerical linear algebra to the training of neural networks. As an undergraduate at Yale he worked on neural stack networks, and he then spent time as a research engineer at Reservoir Labs before starting his PhD under Joan Bruna and Chris Musco in 2022. In 2025, he coauthored The Polar Express with David Persson, Christopher Musco and Robert Gower, a method for computing the polar decomposition inside the Muon optimizer, and ICLR gave the paper an Outstanding Paper Honorable Mention in 2026. In August 2026, he posted Dion3, a faster revision of Muon built with John Langford, Tri Dao and others, and he continues as a fifth-year PhD student at NYU.

Badges

Timeline

  1. By 2019

    Neural stacks at Yale

    He studies as an undergraduate at Yale, where he works with Bob Frank in the CLAY lab and is advised by Dan Spielman. He is a coauthor of two BlackboxNLP workshop papers on stack-augmented neural networks: 'Context-Free Transductions with Neural Stacks' in 2018 and 'Finding Hierarchical Structure in Neural Stacks Using Unsupervised Parsing' in 2019.

  2. By 2021

    Research engineer at Reservoir Labs

    He works as a research engineer at Reservoir Labs (now Qualcomm), modeling congestion control in communication networks. His papers on bottleneck structures in data networks appear at INDIS in 2020 and at ACM SIGCOMM in 2021.

  3. September 2022

    Starting a PhD at NYU

    He joins Joan Bruna's group at NYU in September 2022 as a computer science PhD student, co-advised by Chris Musco. An NSF Graduate Research Fellowship supports his degree.

  4. December 2024–April 2025

    Matrix functions and attention theory

    In December 2024, he publishes 'Nearly Optimal Approximation of Matrix Functions by the Lanczos Method' at NeurIPS with Tyler Chen, Anne Greenbaum, Cameron Musco and Christopher Musco, and the paper is a spotlight. In April 2025, he publishes 'Quality over Quantity in Attention Layers: When Adding More Heads Hurts' at ICLR with Gilad Yehudai and Joan Bruna, which proves that the rank of attention has a dramatic effect on its representational capacity.

  5. May 2025

    The Polar Express preprint

    In May 2025, he posts The Polar Express on arXiv with David Persson, Christopher Musco and Robert M. Gower. The method computes the polar decomposition used in the Muon optimizer with matrix-matrix multiplications only, solves a minimax problem to adapt the update rule at each iteration, and supplies optimal coefficients that become a core component of Muon.

  6. 2026

    An ICLR honorable mention

    ICLR 2026 gives The Polar Express an Outstanding Paper Honorable Mention. Entries in the nanoGPT speedrun training contest use the method, and he says Microsoft Research and larger frontier-scale language models use it too.

  7. August 2026

    Dion3 for Muon

    In August 2026, he posts Dion3: Full-Stack Orthogonal Updates on arXiv with John Langford, Tri Dao and others. The revision of Muon combines a Gram Newton-Schulz algorithm, kernels that exploit symmetry and a row-selection update rule, and it matches or improves Muon's loss while cutting optimizer step time by up to 6x. He has also worked with John Langford at Microsoft Research on optimization algorithms for pretraining.

  8. As of October 2026

    PhD student at NYU Courant

    He is a fifth-year computer science PhD student at NYU's Courant Institute, advised by Joan Bruna and Chris Musco. His research themes are linear algebra, approximation theory and deep learning, and he helps organize the ML-NYC speaker series at the Flatiron Institute.

Career

  1. Until 2021Reservoir LabsResearch Engineer

Education

  1. Yale University
  2. Courant Institute of Mathematical SciencesPhD

From the biography.

  1. The median h-index is 48 at universities and 14 at frontier AI labsIncludes New York University. The median h-index is 48 at universities and 14 at frontier AI labs. We compare publishing careers, recent citations, dual appointments and job moves across 2,420 university researchers and 308 frontier-lab researchers.
  2. The Massachusetts Institute of Technology trained or employed 44 of the 187 AI major-prize winners, more than any other universityIncludes New York University. The Massachusetts Institute of Technology trained or employed 44 of the 187 AI major-prize winners, more than any other university. We compare doctorate and 5+ year employment links, career timing and current workplaces for 187 major-prize and 1,111 best-paper winners.
  3. 84% of people shaping AI with recorded undergraduate and doctoral schools changed institutions for their doctorateIncludes Yale University. 84% of people shaping AI with recorded undergraduate and doctoral schools changed institutions for their doctorate. Across 2,116 people with both an undergraduate degree and a doctorate recorded, we trace which undergraduate schools feed which doctoral programs, how often students stay at the same school, and how paths differ by birth-country region.
  4. Companies supply the most prior-work hires at 7 of the 9 frontier AI labsIncludes New York University. Our estimates of the organizations where 550 people worked directly before joining 9 frontier AI labs across 620 career transitions, comparing the main feeder organizations per lab.

Colleagues

People named in this biography, and people with dated positions at the same organization in the same years.

Sources and credits

Photo: We have no published photo of Noah Amsel yet. Send us a free-licensed photo.

  1. Noah Amsel noahamsel.github.io. Checked 22 October 2026.
  2. Publications | Noah Amsel noahamsel.github.io. Checked 22 October 2026.
  3. Group :: Joan Bruna cims.nyu.edu. Checked 22 October 2026.
  4. The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm arxiv.org. Checked 22 October 2026.
  5. Announcing the ICLR 2026 Outstanding Papers – ICLR Blog blog.iclr.cc. Checked 22 October 2026.
  6. Noah Amsel, Professor David Persson, and Professor Christopher Musco Receive ICLR 2026 Outstanding Paper Honorable Mention cims.nyu.edu. Checked 22 October 2026.
  7. How Flatiron Institute Mathematicians Helped Make AI More Efficient – Simons Foundation simonsfoundation.org. Checked 22 October 2026.
  8. Dion3: Full-Stack Orthogonal Updates arxiv.org. Checked 22 October 2026.