Fetching the paper…
Reading the bibliography…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps.
G. Zames, “On the input-output stability of time-varying nonlinear feedback systems part one: Conditions derived using concepts of loop gain, conicity, and positivity,” IEEE Transactions on Automatic Control , vol. 11, no. 2, pp. 228–238, 1966
1966
Earlier work this paper cites.
C. A. Desoer and M. Vidyasagar, Feedback systems: input-output properties . SIAM, 1975, vol. 55
1975
Earlier work this paper cites.
J. L. Elman, “Finding structure in time,” Cognitive science , vol. 14, no. 2, pp. 179–211, 1990
1990
Earlier work this paper cites.
Y. Bengio, P. Simard, and P. Frasconi, “Learning long-term dependencies with gradient descent is difficult,” IEEE transactions on neural networks , vol. 5, no. 2, pp. 157–166, 1994
1994
Earlier work this paper cites.
S. Hochreiter and J. Schmidhuber, “Long Short-Term Memory,” Neural computation , vol. 9, pp. 1735–1780, 1997
1997
Earlier work this paper cites.
W. Lohmiller and J.-J. E. Slotine, “On contraction analysis for non-linear systems,” Automatica , vol. 34, pp. 683–696, 1998
1998
Earlier work this paper cites.
Y.-C. Chu and K. Glover, “Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities,” IEEE Transactions on Automatic Control , vol. 44, pp. 471–483, Mar. 1999
1999
Earlier work this paper cites.
A. Pinkus, “Approximation theory of the mlp model in neural networks,” Acta numerica , vol. 8, no. 1, pp. 143–195, 1999
1999
Earlier work this paper cites.
E. Kaszkurewicz and A. Bhaya, Matrix Diagonal Stability in Systems and Computation . Birkhäuser Basel, 2000
2000
Earlier work this paper cites.
N. E. Barabanov and D. V. Prokhorov, “Stability analysis of discrete-time recurrent neural networks,” IEEE Transactions on Neural Networks , vol. 13, no. 2, pp. 292–303, Mar. 2002
2002
Cited alongside, same era.
S. L. Lacy and D. S. Bernstein, “Subspace identification with guaranteed stability using constrained optimization,” IEEE Transactions on automatic control , vol. 48, no. 7, pp. 1259–1263, 2003
2003
Cited alongside, same era.
D. N. Miller and R. A. De Callafon, “Subspace identification with eigenvalue constraints,” Automatica , vol. 49, no. 8, pp. 2468–2473, 2013
2013
Cited alongside, same era.
I. Goodfellow, Y. Bengio, and A. Courville, Deep learning . MIT press, 2016
2016
Cited alongside, same era.
P. L. Bartlett, D. J. Foster, and M. J. Telgarsky, “Spectrally-normalized margin bounds for neural networks,” in Advances in Neural Information Processing Systems , 2017, pp. 6240–6249
J. Umenberger, J. Wågberg, I. R. Manchester, and T. B. Schön, “Maximum likelihood identification of stable linear dynamical systems,” Automatica , vol. 96, pp. 280–292, 2018
2018
Later among the works it cites.
J. Umenberger and I. R. Manchester, “Specialized interior-point algorithm for stable nonlinear system identification,” IEEE Transactions on Automatic Control , vol. 64, no. 6, pp. 2442–2456, 2018
2018
Later among the works it cites.
2019
Later among the works it cites.
H. Qian and M. N. Wegman, “L2-nonexpansive neural networks,” International Conference on Learning Representations (ICLR) , 2019
2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2017
Cited alongside, same era.
M. M. Tobenkin, I. R. Manchester, and A. Megretski, “Convex parameterizations and fidelity bounds for nonlinear identification and reduced-order modelling,” IEEE Transactions on Automatic Control , vol. 62, no. 7, pp. 3679–3686, 2017
2017
Cited alongside, same era.
J. Umlauft, A. Lederer, and S. Hirche, “Learning stable gaussian process state space models,” in 2017 American Control Conference (ACC) . IEEE, 2017, pp. 1499–1504
2017
Cited alongside, same era.
D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” International Conference for Learning Representations (ICLR) , Jan. 2017
2017
Cited alongside, same era.
T. Huster, C.-Y. J. Chiang, and R. Chadha, “Limitations of the lipschitz constant as a defense against adversarial examples,” in Joint European Conference on Machine Learning and Knowledge Discovery in Databases . Springer, 2018, pp. 16–29
2018
Cited alongside, same era.
J. Z. Kolter and G. Manek, “Learning stable deep dynamics models,” in Advances in Neural Information Processing Systems 32 . Curran Associates, Inc., 2019, pp. 11 128–11 136
2019
Later among the works it cites.
J. Miller and M. Hardt, “Stable recurrent models,” In Proceedings of International Conference on Learning Representations 2019 , 2019
2019
Later among the works it cites.
M. Fazlyab, A. Robey, H. Hassani, M. Morari, and G. Pappas, “Efficient and accurate estimation of lipschitz constants for deep neural networks,” in Advances in Neural Information Processing Systems , 2019, pp. 11 423–11 434
2019
Later among the works it cites.
M. Cheng, J. Yi, P.-Y. Chen, H. Zhang, and C.-J. Hsieh, “Seq2sick: Evaluating the robustness of sequence-to-sequence models with adversarial examples.” in Association for the Advancement of Artificial Intelligence , 2020, pp. 3601–3608
2020
Closest in time.
M. Revay and I. R. Manchester, “Contracting implicit recurrent neural networks: Stable models with improved trainability,” Learning for Dynamics and Control (L4DC) , 2020
2020
Closest in time.