Exploring the Spline Theory of Neural Networks

Professor Randall Balestriero joins us to discuss neural network geometry, spline theory, and emerging phenomena in deep learning, based on research presented at ICML. Topics include the delayed emergence of adversarial robustness in neural networks ("grokking"), geometric interpretations of neural networks via spline theory, and challenges in reconstruction learning. We also cover geometric analysis of Large Language Models (LLMs) for toxicity detection and the relationship between intrinsic dimensionality and model control in RLHF.

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Randall Balestriero

https://x.com/randall_balestr

https://randallbalestriero.github.io/

Show notes and transcript: https://www.dropbox.com/scl/fi/3lufge4upq5gy0ug75j4a/RANDALLSHOW.pdf?rlkey=nbemgpa0jhawt1e86rx7372e4&dl=0

TOC:

- Introduction

- 00:00:00: Introduction

- Neural Network Geometry and Spline Theory

- 00:01:41: Neural Network Geometry and Spline Theory

- 00:07:41: Deep Networks Always Grok

- 00:11:39: Grokking and Adversarial Robustness

- 00:16:09: Double Descent and Catastrophic Forgetting

- Reconstruction Learning

- 00:18:49: Reconstruction Learning

- 00:24:15: Frequency Bias in Neural Networks

- Geometric Analysis of Neural Networks

- 00:29:02: Geometric Analysis of Neural Networks

- 00:34:41: Adversarial Examples and Region Concentration

- LLM Safety and Geometric Analysis

- 00:40:05: LLM Safety and Geometric Analysis

- 00:46:11: Toxicity Detection in LLMs

- 00:52:24: Intrinsic Dimensionality and Model Control

- 00:58:07: RLHF and High-Dimensional Spaces

- Conclusion

- 01:02:13: Neural Tangent Kernel

- 01:08:07: Conclusion

REFS:

[00:01:35] Humayun – Deep network geometry & input space partitioning

https://arxiv.org/html/2408.04809v1

[00:03:55] Balestriero & Paris – Linking deep networks to adaptive spline operators

https://proceedings.mlr.press/v80/balestriero18b/balestriero18b.pdf

[00:13:55] Song et al. – Gradient-based white-box adversarial attacks

https://arxiv.org/abs/2012.14965

[00:16:05] Humayun, Balestriero & Baraniuk – Grokking phenomenon & emergent robustness

https://arxiv.org/abs/2402.15555

[00:18:25] Humayun – Training dynamics & double descent via linear region evolution

https://arxiv.org/abs/2310.12977

[00:20:15] Balestriero – Power diagram partitions in DNN decision boundaries

https://arxiv.org/abs/1905.08443

[00:23:00] Frankle & Carbin – Lottery Ticket Hypothesis for network pruning

https://arxiv.org/abs/1803.03635

[00:24:00] Belkin et al. – Double descent phenomenon in modern ML

https://arxiv.org/abs/1812.11118

[00:25:55] Balestriero et al. – Batch normalization’s regularization effects

https://arxiv.org/pdf/2209.14778

[00:29:35] EU – EU AI Act 2024 with compute restrictions

https://www.lw.com/admin/upload/SiteAttachments/EU-AI-Act-Navigating-a-Brave-New-World.pdf

[00:39:30] Humayun, Balestriero & Baraniuk – SplineCam: Visualizing deep network geometry

https://openaccess.thecvf.com/content/CVPR2023/papers/Humayun_SplineCam_Exact_Visualization_and_Characterization_of_Deep_Network_Geometry_and_CVPR_2023_paper.pdf

[00:40:40] Carlini – Trade-offs between adversarial robustness and accuracy

https://arxiv.org/pdf/2407.20099

[00:44:55] Balestriero & LeCun – Limitations of reconstruction-based learning methods

https://openreview.net/forum?id=ez7w0Ss4g9

(truncated, see shownotes PDF)