Rob Nowak
@rdnowak
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Director of the Center for the Advancement of Progress
Ho-Chunk land
Joined April 2009
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3D attractor set of recurrent ReLU network (courtesy of Dave Nowak)
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Here’s my take on the “mathematical foundations” of machine learning and AI. These course notes cover the basics of statistical learning theory, optimization, and functional analysis.
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My dad (86 years old today!) is really into fractals and art. He’s sitting in on my ML course on neural nets etc, and he decided to start experimenting with fractal images generated using ReLU nonlinearities.
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What kinds of functions do deep neural networks learn? Now we know!
Our paper presents a new representer theorem for deep ReLU networks and provides theoretical insights into weight decay, sparsity, skip connections, and low-rank weight matrices.
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Rahul Parhi and I wrote a tutorial style article to explain modern theory of deep learning and neural function spaces via elementary signal/image processing concepts (Fourier transform, Radon transform, L1 regularization, sparsity)
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What kinds of functions do neural networks learn? I gave a lecture on the topic at the Joint Statistical Meetings (JSM) this week. Slides are online here:
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I am immensely honored to be named the Grace Wahba Professor of Data Science. Grace has been a tremendous inspiration and guiding force throughout my entire career.
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1/4 Interesting facts concerning neural network depth (and activation functions): Finite-width, single hidden-layer neural networks cannot approximate continuous functions
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Video is now available for my recent lecture on “What kinds of functions do neural networks learn?”
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New paper on label-efficient supervised finetuning of LLMs.
We address the expensive prompt annotation cost by humans/proprietary LLMs, saving as much as 50% on FLAN V2.
Paper:
Work led by:
@jifan_zhang
@cloudwaysX
@BhattGantavya
@arnaved
1/
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We are pleased to announce plans for a special issue of Signal Processing Magazine focused on the mathematics of deep learning:
We look forward to your submissions!
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A wonderful, must-read article summarizing Grace Wahba’s amazing contributions to statistics and machine learning.
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Congratulations to
@yinglun122
, who successfully defended his PhD thesis "Interactive ML: From Theory to Scale". He'll be starting at UC-Riverside as an Assistant Prof this summer!
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We are hiring in Electrical and Computer Engineering or Industrial and Systems Engineering as part of a campus-wide cluster initiative to expand and broaden expertise in the foundations of data science at UW-Madison!
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The Institute for Foundations of Data Science (IFDS) workshop on Statistical Approaches to Understanding Modern ML Methods will be held in Madison, August 2-4. Fantastic line up of speakers. More info and registration at .
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Here is another one using a leaky ReLU recurrent net: x(n) = C(1) + C(2)*min(x(n-1),0)+(C(2)+C(3))*max(x(n-1),0) + C(4)*min(x(n-2),0)+(C(4)+C(5))*max(x(n-2),0) + C(6)*min(x(n-3),0)+(C(6)+C(7))*max(x(n-3),0)
C = [-0.3948 -0.0697 -0.1657 -0.2916 0.7402 0.8650 0.0673]
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Mike Jordan gives an excellent short interview about AI
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Donna Shalala, Roland Chin, and me, circa 1989. I believe that neural networks were involved in this meeting.
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Hop on the LabelTrain🚂 ()
Excited to have LabelBench published in the new DMLR journal. We study label efficient fine-tuning for foundation models using blends of active and semi-supervised learning. More info: 1/
Introducing our framework and benchmarks for label-efficient learning.
Evaluations of large pretrained models, Semi-SL and active learning have mostly stayed isolated. LabelBench combines all these mutually beneficial techniques to examine the best possible label-efficiency 1/
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For several years,
@stochasticlalit
,
@kgjamieson
, and I have been helping the
@NewYorker
crowdsource the rating of the cartoon caption contest
#NewYorkerCartoons
. We have millions of ratings for thousands of cartoon captions, all here . An NLP goldmine!
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UW–Madison to Continue Fundamental Data Science Research with Phase II Award from NSF – Wisconsin Institute for Discovery
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I can’t believe they let him put up a giant new X installation on the UW Madison campus
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1/4 This amazing success of
#AlphaFold
on the “protein folding problem” takes my mind back to my first success with neural networks. It was the early 1990s and I was a summer research intern at GE Medical Systems.
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Two exciting tenure-track positions in ECE at UW-Madison. The first position is in the broadly defined area of foundations of Machine Learning and AI: . The second position is in Artificial Intelligence (AI) and Medical Imaging:
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3/4 Rahul Parhi has a nice blog post summarizing this intriguing fact
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Some new representer theory for neural nets. [2006.05626] Neural Networks, Ridge Splines, and TV Regularization in the Radon Domain
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I am very happy and pleased to share this announcement of the IMS Grace Wahba Award and Lecture. Grace has been so inspiring to me, I cannot put it into words... what a fitting tribute to one of the greats in our field!
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All my favorite topics appear in the "Roadmap of Mathematics of Deep Learning."
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Using synthetic data to train generative models can lead to insane results! Interesting new work from Rice U:
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4/4 Here is a formal statement of the theorem due to Maiorov and Pinkus.
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Charles Lee Isbell Jr. named UW-Madison provost via
@uwmadison
Wow! This is huge. I'm absolutely thrilled.
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We are holding an in-person-only MAD NeurIPS poster session and reception here in Madison this afternoon! Fantastic line up of papers/posters!
**Bonus** some of these cool papers will not appear at
#NeurIPS2021
.
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My sailing adventure didn’t go as planned. Winds went from 6kts to 20 just like that. Some how managed to get the laser onto dry land without injury.
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2/4 However, there is a class of finite-width, two hidden-layer neural networks that can approximate any continuous function in d-dimensions to arbitrary accuracy. This class is based on a special construction of a universal activation function that is analytic and increasing.
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Yes. Madison is pretty awesome in Winter!
Caught the lights changing on the Wisconsin Capitol during our first snowstorm. ❄️
#MadisonWI
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Visit for more information and to submit your application by the December 12, 2022 deadline.
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Madison found as the best place to live in the U.S., according to Livability. I rate this as totally true!
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Sorry I’m not in NOLA, but please check out cool new work from the brilliant Yinglun Zhu (who happens to be on the job market). Yinglun presents provably good and computationally efficient algorithms for active deep learning
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The IFDS is holding a data sci summer school here in Madison, July 26-30th, with an all-star cast of speakers including
@DimitrisPapail
@SebastienBubeck
@cecileane
@kgjamieson
@karlrohe
@WangMiaoyan
. Registration and more information here:
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Don’t miss the workshop on the Theory of Overparameterized Machine Learning!
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@roydanroy
The more pertinent question is this: What kinds of functions do neural networks learn when fit to data? Answers could help us understand the nature of extrapolations made by trained neural networks. Classical universal approximation theorems don't help with this sort of question
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@SenatorBaldwin
Honestly, I would be impressed if some of our representatives stepped aside and refused to be vaccinated until all our healthcare workers and seniors are vaccinated.
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