Neural Networks Are Elastic Origami! [Prof. Randall Balestriero]

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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Show notes and transcript: https://www.dropbox.com/scl/fi/3lufge...

TOC:
[00:00:00] Introduction

1. Neural Network Geometry and Spline Theory
[00:01:41] 1.1 Neural Network Geometry and Spline Theory
[00:07:41] 1.2 Deep Networks Always Grok
[00:11:39] 1.3 Grokking and Adversarial Robustness
[00:16:09] 1.4 Double Descent and Catastrophic Forgetting

2. Reconstruction Learning
[00:18:49] 2.1 Reconstruction Learning
[00:24:15] 2.2 Frequency Bias in Neural Networks

3. Geometric Analysis of Neural Networks
[00:29:02] 3.1 Geometric Analysis of Neural Networks
[00:34:41] 3.2 Adversarial Examples and Region Concentration

4. LLM Safety and Geometric Analysis
[00:40:05] 4.1 LLM Safety and Geometric Analysis
[00:46:11] 4.2 Toxicity Detection in LLMs
[00:52:24] 4.3 Intrinsic Dimensionality and Model Control
[00:58:07] 4.4 RLHF and High-Dimensional Spaces

5. Conclusion
[01:02:13] 5.1 Neural Tangent Kernel
[01:08:07] 5.2 Conclusion

REFS:
[00:01:35] Balestriero/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/bal...

[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/SiteA...

[00:39:30] Humayun, Balestriero & Baraniuk – SplineCam: Visualizing deep network geometry
https://openaccess.thecvf.com/content...

[00:40:40] Carlini – Trade-offs between adversarial robustness and accuracy
https://arxiv.org/abs/1902.06705

[00:44:55] Balestriero & LeCun – Limitations of reconstruction-based learning methods
https://raw.githubusercontent.com/mlr...

[00:47:20] Balestriero & LeCun – Spectral analysis of neural network learning
https://proceedings.neurips.cc/paper_...

[00:49:45] He et al. – MAE: Masked Autoencoders for self-supervised learning
https://arxiv.org/abs/2111.06377

[00:54:50] Balestriero et al. – Geometric analysis of LLM layers for toxicity detection
https://arxiv.org/abs/2309.12312

[00:59:35] Balestriero et al. – Superior toxicity detection via geometric features
https://arxiv.org/html/2312.01648v2

[01:04:45] UofT ML – Self-attention control & context length effects
https://arxiv.org/abs/2310.04444

[01:11:55] Roberts – Foundations of deep learning theory
https://arxiv.org/abs/2106.10165

[01:15:40] Balestriero & Cha – Kolmogorov GAM Networks via spline partition theory
https://arxiv.org/pdf/2501.00704

[01:16:40] Various – Graph Kolmogorov-Arnold Networks (GKAN) extension
https://www.nature.com/articles/s4159...