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Introduces Cluster-Weighted EDMD, a data-driven method that jointly learns a partition and per-cluster Koopman operators via expectation-maximization, improving prediction accuracy over standard EDMD on classical dynamical systems.
This paper applies dynamical systems analysis to interpret latent chain-of-thought reasoning in models like CODI and COCONUT, revealing structured dynamics with stable and unstable classes.
Introduces Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems from noisy measurements, combining a weak formulation with kernel ridge regression to filter noise and improve accuracy. The method outperforms baseline methods on chaotic benchmarks up to 64 dimensions and 15,000-dimensional real-world fluid data.
Proposes a hierarchical Bayesian framework for meta-learning in dynamical systems from multiple sparse, noisy datasets, using gradient-based MCMC with an embedded ODE solver for efficient posterior inference of shared and dataset-specific parameters.
This paper analyzes why machine learning, particularly neural networks, remains opaque in its learning process by framing it as a complex dynamical system, identifying three key properties that contribute to learning opacity, and arguing that some sources may be irreducible.
This paper introduces attention-free latent memory and dynamic re-encoding to improve long-horizon predictions in Koopman autoencoders, reducing error accumulation on benchmark dynamical systems.
This paper argues that time series modeling should incorporate a dynamical systems perspective to improve understanding and prediction of complex temporal data.
Mathematicians have extended the classic 1992 proof about card shuffling to less precise shuffles, showing that a 'cutoff phenomenon' still occurs even with uneven deck splits.
Physics-conforming Latent Twins is a framework for learning latent surrogate solution operators that enforce physical principles such as conservation laws and dissipative inequalities by design, using a constraint-transfer approach and structure-preserving latent dynamics.
Proposes a spectral learning method for stochastic nonlinear dynamical systems using deep feature spaces and an operator-based latent state-space model, demonstrating stable performance in forecasting and filtering tasks.
This paper presents a memory–stability–expressivity trilemma for trainable dissipative oscillator networks, showing that damping governs all three and limits trainability, with experimental validation on a 20-oscillator network confirming the theoretical bounds.
This paper develops a dynamical framework to analyze how AI-assisted optimization can either reduce or enhance exploratory adaptation, depending on the system's initial adaptive responsiveness, leading to possible metastable trapping or exploration-collapse dynamics.
LFNO is a unified neural operator framework that integrates Laplace and Fourier transforms to decompose system dynamics into transient and steady-state components, significantly outperforming existing operators on ODE and PDE benchmarks.
Proposes the Mamba-Assisted Closure (MAC) framework, a Mamba-based sequence model for non-Markovian closure in reduced-order modeling of high-dimensional dynamical systems, outperforming GRU-based and Markovian methods on Burgers' equation and Lorenz '96 systems.
DeepMDMD combines deep learning with algebraic constraints to learn compact, dynamically coherent Koopman operator representations that enforce the product rule as an exact constraint. The method outperforms geometric approaches on high-dimensional chaotic and fluid dynamics problems, reducing spectral pollution and enabling stable long-term forecasting.
This paper introduces the Gauge-Fixed Ordinal Network (GON), a temporal convolutional model that assigns consistent predictability scores across different dynamical systems by fixing the gauge freedom of ordinal scoring. The method transfers better than training from scratch on held-out systems, with zero-shot scores retaining ordinal structure at the stochastic boundary.
ChaosBench-Logic v2 is a large-scale benchmark of 40,886 questions over 165 dynamical systems that evaluates LLMs' logical reasoning abilities, revealing near-random performance on regime transition reasoning and systematic failure modes even in frontier models.
This paper proposes a structural and dynamical framework for modeling cognitive processes using iterative state transformations and semantic equivalence, integrating dynamical systems, category theory, and feedback mechanisms to model cognition as a process evolving toward stable interpretations.
This paper proposes Human-Centered Learning Mechanics (HCLM), a dynamical and information-theoretic framework for studying open and controlled learning systems. It formalizes entropy regularization through effective information force, derives convergence and generalization results, and provides a conditional interpretation of scaling-law behavior.
Equilibrium Reasoners (EqR) introduce a novel framework for scalable reasoning by learning task-conditioned attractors in latent dynamical systems, achieving over 99% accuracy on Sudoku-Extreme by unrolling up to 40,000 layers.