mlsanityData to 7 Oct 2026

Lyapunov Exponents for Diversity in Differentiable Games

arXiv 2112.14570 ↗First posted 24 Dec 2021cs.GT cs.LG cs.MAcited by 8

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Abstract (arXiv)

Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function), where it branches at saddles - easy-to-find bifurcation points. We generalize this idea to non-conservative, multi-agent gradient systems by proposing a method - denoted Generalized Ridge Rider (GRR) - for finding arbitrary bifurcation points. We give theoretical motivation for our method by leveraging machinery from the field of dynamical systems. We construct novel toy problems where we can visualize new phenomena while giving insight into high-dimensional problems of interest. Finally, we empirically evaluate our method by finding diverse solutions in the iterated prisoners' dilemma and relevant machine learning problems including generative adversarial networks.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 62 of its 122 references that are in the map. First posted on arXiv 24 Dec 2021.

Builds on

62 of 122 references.

References · 62

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38 more
  1. 2017Adversarial Examples: Attacks and Defenses for Deep Learningcited by 350
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50 most cited of 62 All 62 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 1; 2024: 1; 2025: 1; 2026: 1.

8 papers.

  1. 2022Task Discovery: Finding the Tasks that Neural Networks Generalize oncited by 9
  2. 2022Domain Adversarial Training: A Game Perspectivecited by 7
  3. 2024JacNet: Learning Functions with Structured Jacobianscited by 7
  4. 2022Neural Payoff Machines: Predicting Fair and Stable Payoff Allocations Among Team Memberscited by 6
  5. 2022Task Selection for AutoML System Evaluationcited by 6
  6. 2025Score Distillation Sampling for Audio: Source Separation, Synthesis, and Beyondcited by 5
  7. 2026Motion Attribution for Video Generationcited by 4
  8. 2023Using Cooperative Game Theory to Prune Neural Networkscited by 1