The paper investigates observability in neural state‑space models, particularly the Mamba architecture, using tools from ordinary differential equations and control theory. It introduces several strategies—based on eigenvalues, roots of unity, permutations, Fourier transforms, and Vandermonde matrices—to enforce observability in high‑dimensional, learnable hidden states while maintaining computational efficiency. The authors also present a shared‑parameter construction for Mamba and a training algorithm that satisfies a Robbins‑Monro condition, contrasting it with classical procedures that fail to meet contraction requirements.
arXiv:2608. 08003v1 Announce Type: cross Abstract: As machine learned models increase in complexity and expressive power, features of simpler models, such as interpretability and control over the shape of the modeled function are lost.
The paper investigates how many linear samples are needed to learn Lipschitz operators under Gaussian measures. It establishes both lower and upper bounds on the Hermite polynomial approximation error and shows that the minimal worst‑case error cannot converge algebraically with the number of samples. However, if the covariance operator of the Gaussian measure decays rapidly, convergence rates arbitrarily close to any algebraic rate can be achieved.
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
arXiv:2607. 02050v1 Announce Type: new Abstract: Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction.
arXiv:2609.38786v1 Announce Type: new Abstract: Differentiable learning typically assumes that the scalar objective evaluated in the forward pass and the gradient supplied to the optimizer in the bac...
arXiv:2608.22636v1 Announce Type: cross Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...
Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning.
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
arXiv:2607. 06472v1 Announce Type: cross Abstract: Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations?
arXiv:2608. 10172v1 Announce Type: new Abstract: Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it.
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
arXiv:2507.19290v2 Announce Type: replace-cross Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-...