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arXiv:2609.38524v1 Announce Type: new Abstract: We consider estimating the one-step-ahead conditional distribution of a multivariate stochastic process. Many existing approaches rely on assumptions s...
arXiv:2610. 08816v1 Announce Type: new Abstract: Long-range temporal dependence poses a resource question for sequence models: for a specified predictive-memory law, how much state, context, or dynamical criticality is required in order to forecast accurately?
arXiv:2609.08740v1 Announce Type: new Abstract: In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynam...
arXiv:2608. 13621v1 Announce Type: new Abstract: A hidden Markov model (HMM) combines three roles: inference of a hidden-state belief from observations, propagation through a Markov transition, and emission back to observation space.
The paper investigates whether compression explains why over‑parameterized neural networks generalize, using the minimum description length (MDL) principle. It introduces prequential regret, a computable metric from the training trajectory, and shows that in the nearly interpolating regime it upper‑bounds the description length of the trained parameters, leading to a high‑probability generalization bound in the PAC‑MDL setting. The study also connects MDL with the algorithm‑level information bottleneck by bounding encoder‑complexity correction with MDL parameter description length, and demonstrates that prequential regret correlates strongly (Pearson > 0.9) with generalization error on CIFAR‑10 and CIFAR‑100.
The paper shows that a memory state that reproduces every current prediction can still fail to learn from subsequent observations. It characterizes when a fixed‑dimensional continuous recurrent state exists for exact cumulative learning and attention, proving that for smooth convex residual losses the state exists only when the loss is polynomial. The work further quantifies the dimensionality required for various loss functions, demonstrates unbounded requirements for nonpolynomial losses, and analyzes specific cases such as ridge regression and kernel attention.