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On the Geometry of Deep Learning
Randall Balestriero, Ahmed Imtiaz Humayun, Richard G. Baraniuk
Notices of the American Mathematical Society
April 2025

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in multiple dimensions). In particular, we overview work over the past decade on understanding certain geometrical properties of a deep network’s affine spline mapping, in particular how it tessellates its input space. The affine spline connection and geometrical viewpoint provide a powerful portal through which to view, analyze, and improve the inner workings of deep networks.

Arxiv version

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Richard Baraniuk, Rice University's C. Sidney Burrus Professor of Electrical and Computer Engineering and founder and director of OpenStax and SafeInsights, has been named the recipient of the 2025 IEEE Jack S. Kilby Signal Processing Medal.

The medal, presented annually since 1995, is given for outstanding achievements in signal processing. Baraniuk was specifically cited for his "contributions to multiscale and sparse signal processing."  The medal will be presented at the IEEE VIC Summit & Honors Gala in Tokyo in April 2025.

Rice Engineering News story | Rice News story | IEEE News story

 

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Three DSP group papers have been accepted by The 2024 Conference on Empirical Methods in Natural Language Processing (EMNLP) Findings 2024 in Miami, Florida:

  1. MalAlgoQA: A Pedagogical Approach for Evaluating Counterfactual Reasoning Abilities by Naiming Liu, Shashank Sonkar, MyCo Le, and Richard G. Baraniuk
  2. Pedagogical Alignment of Large Language Models by Shashank Sonkar, Kangqi Ni, Sapana Chaudhary, and Richard G. Baraniuk
  3. The Student Data Paradox: Examining the Regressive Side Effects of Training LLMs for Personalized Learning by Shashank Sonkar, Naiming Liu, and Richard G. Baraniuk

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To help organize the growing literature on AI self-consuming feedback loops, we have launched a "Self-Consuming AI Resources" archive at dsp.rice.edu/ai-loops.

In the 2000s, the Rice DSP group managed a similar archive for the field of compressive sensing, and it grew to several thousand papers that were used by a large community of researchers. We're hoping that this archive can be similarly useful.

We are currently in the process of refining the materials on the page. We would greatly appreciate it if you would recommend missing or new literature. There is also a ton of missing media coverage, and we are slowly working toward gathering it all.

Email us at selfconsumingAI@gmail.com to add your latest work or that of others in this fast-moving area!

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Self-Improving Diffusion Models with Synthetic Data

Sina Alemohammad, Ahmed Imtiaz Humayun, Richard Baraniuk
Rice University
Shruti Agarwal, John Collomosse
Adobe Research

arxiv.org/abs/2408.16333, 30 August 2024

Abstract: The artificial intelligence (AI) world is running out of real data for training increasingly large generative models, resulting in accelerating pressure to train on synthetic data.
Unfortunately, training new generative models with synthetic data from current or past generation models creates an autophagous (self-consuming) loop that degrades the quality and/or diversity of the synthetic data in what has been termed model autophagy disorder (MAD) and model collapse. Current thinking around model autophagy recommends that synthetic data is to be avoided for model training lest the system deteriorate into MADness.
In this paper, we take a different tack that treats synthetic data differently from real data.
Self-IMproving diffusion models with Synthetic data (SIMS) is a new training concept for diffusion models that uses self-synthesized data to provide negative guidance during the generation process to steer a model's generative process away from the non-ideal synthetic data manifold and towards the real data distribution. We demonstrate that SIMS is capable of self-improvement; it establishes new records based on the Fréchet inception distance (FID) metric for CIFAR-10 and ImageNet-64 generation and achieves competitive results on FFHQ-64 and ImageNet-512. Moreover, SIMS is, to the best of our knowledge, the first prophylactic generative AI algorithm that can be iteratively trained on self-generated synthetic data without going MAD. As a bonus, SIMS can adjust a diffusion model's synthetic data distribution to match any desired in-domain target distribution to help mitigate biases and ensure fairness.

The figure above illustrates that SIMS simultaneously improves diffusion modeling and synthesis performance while acting as a prophylactic against Model Autophagy Disorder (MAD). First row: Samples from a base diffusion model (EDM2-S) trained on 1.28M real images from the ImageNet-512 dataset (Fréchet inception distance, FID = 2.56). Second row: Samples from the base model after fine-tuning with 1.5M images synthesized from the base model, which degrades synthesis performance and pushes the model towards MADness (model collapse) (FID = 6.07). Third row: Samples from the base model after applying SIMS using the same self-generated synthetic data as in the second row (FID = 1.73).

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Google's integration of its Gemini AI tool suite with OpenStax launched today.

"Starting today, Gemini can pull information from academic textbooks with OpenStax, an educational nonprofit initiative of Rice University. Let’s say you’re taking an economics class and need help with new concepts — just ask questions like "@OpenStax explain the concept of supply and demand." In seconds, you’ll get a clear, concise explanation complete with links to relevant textbook content."