arXiv:2606. 10596v1 Announce Type: cross Abstract: This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.
This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization.
arXiv:2607. 27924v1 Announce Type: new Abstract: In the physical world we inhabit, space and time are fundamentally continuous.
In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world.
arXiv:2608. 06595v1 Announce Type: cross Abstract: Neural networks applied to sequential decision-making tasks typically rely on latent representations of environment states.
arXiv:2606. 14284v1 Announce Type: cross Abstract: Time series prototype learning is fundamentally challenged by observational ambiguity.
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.