Nicholas Krämer
@pnkraemer
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Probabilistic numerics, state-space models, differentiable linear algebra, and of course a healthy dose of figure-making.
Copenhagen
Joined March 2020
Ever thought about using matrix-exp's or log-det's in large-scale ML (think PDEs/GGN matrices with >1M rows)? I have, and maybe you have, too—but gradients? That's where it gets tricky. Not anymore! We have a #NeurIPS2024 spotlight: "Gradients of Functions of Large Matrices."🧵
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Poster session happening *today* at 4:30 local time. *East* Exhibit Hall. Poster #3511. Looking forward to presenting this work! See you there? 🙂.
🛩️ On my way to #NeurIPS2024 and excited to chat about (ML applications of) linear algebra, differentiable programming, and probabilistic numerics! . Feel free to DM if you’d like to meet up, hang out, and/or discuss any of these topics 😊.
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🛩️ On my way to #NeurIPS2024 and excited to chat about (ML applications of) linear algebra, differentiable programming, and probabilistic numerics! . Feel free to DM if you’d like to meet up, hang out, and/or discuss any of these topics 😊.
Ever thought about using matrix-exp's or log-det's in large-scale ML (think PDEs/GGN matrices with >1M rows)? I have, and maybe you have, too—but gradients? That's where it gets tricky. Not anymore! We have a #NeurIPS2024 spotlight: "Gradients of Functions of Large Matrices."🧵
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RT @fedebergamin: Heading to Vancouver for NeurIPS to present our paper “On Conditional Diffusion Models for PDE Simulation”. I'll be toget….
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⭐️To add to the above, here are the links to #Matfree: ⭐️. ➡️ Experiments: ➡️ Github: ➡️ Online docs: Try it out, leave a star if you like Matfree, and let us know what you think! 😊.
github.com
Matrix-free linear algebra in JAX. Contribute to pnkraemer/matfree development by creating an account on GitHub.
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What's next? Try it out! *pip install matfree* or read the full paper here: This is joint work with @pablorenoz, Hrittik Roy, and Søren Hauberg. Let's talk matrix-free linear algebra and differentiable programming at #NeurIPS2024! See you in Vancouver!
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The result: A matrix-free algorithm for reverse-differentiating (aaaaa)all the matrix functions, eliminating complicated, problem-specific workarounds. Our #JAX code competes with the SotA on tasks like PDEs, GPs, and Laplace-approximated vision transformers (~4M params).
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Our solution: deriving and solving previously unknown adjoint systems for the Lanczos and Arnoldi iterations—two absolute workhorses for numerical matrix functions. (Don't worry too much about the details; we have packaged this all into a #JAX library).
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Why it matters: Matrix functions are essential in probabilistic & scientific ML, but traditional methods become too expensive as matrices grow. Matrix-free algorithms help, but there's a big gap in reverse-mode autodiff of matrix-free linear algebra beyond linear systems solvers.
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RT @DynamicsSIAM: "A tutorial on automatic differentiation with complex numbers" (by Nicholas Krämer):
arxiv.org
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in...
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RT @stefanhsommer: Score matching for bridges can be learned without time-reversal w/ @thelibbybaker @MoritzSchauer….
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RT @jeha_paul: Excited to share that our paper on reducing variance in diffusion models with control variates is published at the SPIGM @ic….
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RT @pablorenoz: We’ll be presenting our work in poster session 5 (#1214, Thursday 10:45) @ #NeurIPS2023 — Come to chat with us if you want….
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RT @runame_: How can Kronecker-Factored Approximate Curvature (K-FAC) be generalised to modern deep learning architectures like transformer….
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RT @sigmabayesian: On my way 🚨✈️🚨 to NOLA. I'll be presenting our work on scalable implicit VI on Wed from 5pm (#1313). I am also looking f….
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RT @fedebergamin: On my way to #NeurIPS23 for the first time. I’ll be there presenting our work "Riemannian Laplace approximations for Baye….
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RT @VectorInst: Did you know Vector’s new Postdoc Fellow @akristiadi7 moved all the way from Tübingen, Germany to Toronto this past month?….
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RT @stefanhsommer: Stochastic bunnies and stochastic spheres: A function space perspective on stochastic shape evolution @thelibbybaker @Th….
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Apply now! Registration closes tonight. #ProbNumSchool.
#ProbNumSchool information!. Almost all spots are filled. Next Friday, 20th of January, we will admit the final batch of applicants to the #ProbNumSchool. (End of the day, German time.) If you apply afterwards, we will place you on a waiting list. (Thread continues 👇).
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So hurry up and get one of the last spots! Apply here ( and come to Tübingen next March to learn about probabilistic numerics and meet a whole bunch of amazing people. We look forward to having you!.
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