Multistability is necessary for temporal horizon generalization in POMDPs, sufficient in simple tasks along with transient dynamics in complex ones, while monostable parallelizable RNNs like SSMs and gated linear RNNs fail by construction.
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Feedback linearization is achieved for hyperbolic PDEs with Volterra nonlinearities via a transport-adapted Chen-Fliess series that eliminates kernel PDEs in the controller design.
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On the Importance of Multistability for Horizon Generalization in Reinforcement Learning
Multistability is necessary for temporal horizon generalization in POMDPs, sufficient in simple tasks along with transient dynamics in complex ones, while monostable parallelizable RNNs like SSMs and gated linear RNNs fail by construction.
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Feedback Linearization of Hyperbolic PDEs with Volterra Nonlinearities
Feedback linearization is achieved for hyperbolic PDEs with Volterra nonlinearities via a transport-adapted Chen-Fliess series that eliminates kernel PDEs in the controller design.