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Recent work suggests that certain neural network architectures -- particularly recurrent neural networks (RNNs) and implicit neural networks (INNs) -- are capable of logical extrapolation.
Detecting strange attractors in turbulence
Takens, F. 2006 · 1979
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Scaling Laws for Neural Language Models
Kaplan, J.; McCandlish, S.; Henighan, T.; Brown, T. B.; Chess, B.; Child, R.; Gray, S.; Radford, A.; Wu, J.; and Amodei, D. 2020 · 2001
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Algebraic Topology
Hatcher, A. 2002 · 2002
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Topological Analysis of Recurrent Systems
De Silva, V.; Skraba, P.; and Vejdemo-Johansson, M. 2012 · 2012
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Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
Perea, J. A.; and Harer, J. 2015 · 2015
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A User’s Guide to Topological Data Analysis
Munch, E. 2017 · 2017
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Dehghani, M.; Gouws, S.; Vinyals, O.; Uszkoreit, J.; and Kaiser, Ł. 2018 · 2018
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(Quasi)Periodicity Quantification in Video Data, Using Topology
Tralie, C. J.; and Perea, J. A. 2018 · 2018
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Deep Equilibrium Models
Bai, S.; Kolter, J. Z.; and Koltun, V. 2019 · 2019
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Multiscale Deep Equilibrium Models
Bai, S.; Koltun, V.; and Kolter, J. Z. 2020 · 2020
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Monotone operator equilibrium networks
Winston, E.; and Kolter, J. Z. 2020 · 2020
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Measuring robustness in deep learning based compressive sensing
Darestani, M. Z.; Chaudhari, A. S.; and Heckel, R. 2021 · 2021
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Implicit Deep Learning
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Deep Equilibrium Architectures for Inverse Problems in Imaging
Gilton, D.; Ongie, G.; and Willett, R. 2021 · 2021
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Feasibility-based fixed point networks
Heaton, H.; Wu Fung, S.; Gibali, A.; and Yin, W. 2021 · 2021
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Representation Matters: Assessing the Importance of Subgroup Allocations in Training Data
Rolf, E.; Worledge, T. T.; Recht, B.; and Jordan, M. 2021 · 2021
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The Evolution of Out-of-Distribution Robustness Throughout Fine-Tuning
Andreassen, A. J.; Bahri, Y.; Neyshabur, B.; and Roelofs, R. 2022 · 2022
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Path Independent Equilibrium Models Can Better Exploit Test-Time Computation
Anil, C.; Pokle, A.; Liang, K.; Treutlein, J.; Wu, Y.; Bai, S.; Kolter, J. Z.; and Grosse, R. B. 2022 · 2022
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Deep equilibrium optical flow estimation
Bai, S.; Geng, Z.; Savani, Y.; and Kolter, J. Z. 2022 · 2022
JFB: Jacobian-Free Backpropagation for Implicit Networks
Wu Fung, S.; Heaton, H.; Li, Q.; McKenzie, D.; Osher, S.; and Yin, W. 2022 · 2022
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Learning to Optimize: Where Deep Learning Meets Optimization and Inverse Problems
Yin, W.; McKenzie, D.; and Fung, S. W. 2022 · 2022
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Explainable AI via learning to optimize
Heaton, H.; and Wu Fung, S. 2023 · 2023
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Algorithm Design for Learned Algorithms
Schwarzschild, A.; McLeish, S. M.; Bansal, A.; Diaz, G.; Stein, A.; Chandnani, A.; Saha, A.; Baraniuk, R.; Tran-Thanh, L.; Geiping, J.; et al. 2023 · 2023
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A Generalization Bound for a Family of Implicit Networks
Fung, S. W.; and Berkels, B. 2024 · 2024
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Deep learning for accelerated and robust MRI reconstruction
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End-to-end Algorithm Synthesis with Recurrent Networks: Extrapolation without Overthinking
Bansal, A.; Schwarzschild, A.; Borgnia, E.; Emam, Z.; Huang, F.; Goldblum, M.; and Goldstein, T. 2022 · 2022
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Goal Misgeneralization in Deep Reinforcement Learning
Langosco, L. L. D.; Koch, J.; Sharkey, L. D.; Pfau, J.; and Krueger, D. 2022 · 2022
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Online deep equilibrium learning for regularization by denoising
Liu, J.; Xu, X.; Gan, W.; Kamilov, U.; et al. 2022 · 2022
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SHINE: SHaring the INverse Estimate from the forward pass for bi-level optimization and implicit models
Ramzi, Z.; Mannel, F.; Bai, S.; Starck, J.-L.; Ciuciu, P.; and Moreau, T. 2022 · 2022
Cited alongside, same era.
Goal Misgeneralization: Why Correct Specifications Aren’t Enough For Correct Goals
Shah, R.; Varma, V.; Kumar, R.; Phuong, M.; Krakovna, V.; Uesato, J.; and Kenton, Z. 2022 · 2022
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The clrs algorithmic reasoning benchmark
Veličković, P.; Badia, A. P.; Budden, D.; Pascanu, R.; Banino, A.; Dashevskiy, M.; Hadsell, R.; and Blundell, C. 2022 · 2022
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Heckel, R.; Jacob, M.; Chaudhari, A.; Perlman, O.; and Shimron, E. 2024 · 2024
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Three-Operator Splitting for Learning to Predict Equilibria in Convex Games
McKenzie, D.; Heaton, H.; Li, Q.; Wu Fung, S.; Osher, S.; and Yin, W. 2024 · 2024
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Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting
McKenzie, D.; Wu Fung, S.; and Heaton, H. 2024 · 2024
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Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
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The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems
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Learning to Reason with LLMs
OpenAI. 2024 · 2025
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