liquid latent dynamics

To address the cyclic dependency problem arising from the coupling of latent states and nonlinear dynamics in time-series modeling, this paper proposes LaNoLem: a method that models the system as a time-varying dynamical process in a latent space and decouples latent-state inference from dynamics learning via an alternating minimization algorithm. It introduces a fully automated, human-in-the-loop-free complexity regularization criterion to enable adaptive control of model capacity. By jointly optimizing latent-state representation, nonlinear differential equation learning, and dynamics estimation, LaNoLem achieves state-of-the-art accuracy in dynamical system identification. Moreover, it significantly outperforms existing methods on multi-step long-horizon forecasting tasks—particularly for systems exhibiting intricate hidden mechanisms and long-range temporal dependencies.

This work addresses the poor generalization in continuous-time series modeling caused by entanglement between dynamic evolution and static factors. We propose a novel neural ODE–Energy-Based Model (EBM) joint framework: a neural ODE implicitly models the continuous-time latent dynamics, while a learnable EBM prior is explicitly embedded into the latent space—marking the first integration of such priors to disentangle dynamic states from static factors. Coupled with a neural emission model and MCMC-based approximate inference, the framework enables end-to-end maximum-likelihood training. Evaluated on oscillatory systems, video frame sequences, and real-world MuJoCo dynamics data, our method significantly outperforms existing approaches. Notably, it achieves superior long-horizon prediction performance under unseen dynamical parameters, demonstrating strong out-of-distribution generalization. This work establishes a new paradigm for continuous-time representation learning by unifying principled differential equation modeling with expressive, structured latent priors.

This work addresses a critical yet previously unarticulated issue in time series forecasting—termed “latent chaos”—where conventional methods operating directly in the observation space learn representations that are temporally inconsistent and lack continuity, thereby failing to capture the true underlying dynamics of the system. To overcome this limitation, the paper introduces LatentTSF, a novel paradigm that leverages an autoencoder to construct a high-dimensional latent state space in which prediction is performed. By implicitly maximizing the mutual information among latent states, ground-truth system states, and observations, LatentTSF enforces temporal coherence and dynamical fidelity. Theoretical analysis and extensive experiments demonstrate that this approach substantially mitigates latent chaos and achieves state-of-the-art forecasting performance across multiple established benchmarks.

This study addresses the challenge of decoding latent dynamic structures underlying large-scale neuronal population activity by proposing a unified latent variable modeling framework that, for the first time, jointly integrates three core tasks: single-region dynamics modeling, inter-regional communication analysis, and behavioral alignment. The approach combines classical state-space models with cutting-edge deep generative architectures—including Transformers, diffusion models, and neural ordinary differential equations—to systematically construct a taxonomy and establish clear evaluation benchmarks. Emphasizing critical challenges such as causal inference and directional connectivity, this work provides both theoretical foundations and methodological tools for interpretable brain dynamics analysis and robust neural decoding.

This work addresses the quantitative relationship between hidden-state dynamics and generated text quality during large language model (LLM) inference. We formulate text generation as a controlled dynamical system on a semantic manifold, approximating hidden-state updates via continuous-time dynamics to uncover how attention and residual connections jointly drive semantic evolution. We introduce the first theoretical framework for hidden-space dynamic manifolds, defining three quantifiable metrics—state continuity, clustering quality, and topological persistence—based on Lyapunov stability theory. These metrics establish a causal explanatory chain linking trajectory properties in the hidden space to textual fluency, grammaticality, and semantic coherence. Empirical evaluation confirms the theoretical predictions’ accuracy across diverse LLMs and tasks. Moreover, our framework yields interpretable, reproducible principles for balancing creativity and consistency in decoding strategies, grounded in geometric and dynamical properties of the latent space.

This study addresses the limitations of traditional state-space models, which rely on predefined nonlinear dynamics and struggle with theoretically under-specified complex systems, as well as the high computational cost of Bayesian inference in Gaussian process state-space models for moderately long sequences. To overcome these challenges, the authors propose two enhanced Gibbs sampling strategies that substantially improve sampling efficiency and convergence reliability. By integrating confirmatory factor analysis to construct an identifiable and interpretable measurement structure, they develop a comprehensive framework for learning nonlinear latent dynamical systems. Simulation studies validate the accuracy of posterior inference, while two empirical applications demonstrate the method’s practical utility and interpretability. An open-source implementation is provided, offering researchers an efficient and feasible workflow for empirical analysis.

This work addresses the challenge of inferring unknown population dynamics solely from snapshots of time-series probability distributions, without access to individual trajectories or prescribed dynamical equations. To this end, it introduces a novel paradigm that decomposes the dynamics into a latent Ornstein–Uhlenbeck stochastic process and a geometric transport map. The former yields an analytically tractable Fokker–Planck equation, while the latter employs monotone neural networks to implement a Knothe–Rosenblatt rearrangement that captures distributional deformations. A deformation energy regularizer grounded in hyperelasticity theory is incorporated to enhance solution uniqueness and physical interpretability. Experiments demonstrate that the method accurately reconstructs complex probabilistic dynamics in nonlinear, multimodal distribution evolution tasks, while maintaining a compact and analytically manageable latent representation.

This work addresses the limited generalization of reinforcement learning policies under unmodeled or time-varying dynamics by proposing a trajectory-outcome-driven implicit dynamics representation that eschews reliance on predefined physical parameters. A task-specific smooth latent space is constructed via semi-supervised contrastive learning, and the authors theoretically establish a monotonic relationship between the regret bound in the target domain and the Lipschitz constant of the trajectory encoder. Leveraging this insight, they enforce Lipschitz constraints to optimize the geometry of the latent space, thereby enhancing robustness. Experiments on MuJoCo benchmarks demonstrate that the proposed method substantially outperforms parameter-centric baselines, effectively handling complex dynamics shifts while improving in-domain stability and interpretability of the latent representation.

This study addresses a key limitation of traditional latent-variable state-space models, which assume process noise is independent of the latent state and thus fail to capture state-dependent stochastic fluctuations commonly observed in biological and behavioral systems. To overcome this, the authors propose a state-coupled stochastic volatility framework that introduces a coupling parameter γ, allowing the variance of the latent process to dynamically scale with the deviation from an underlying latent equilibrium point. This work presents the first approach to modeling and identifying such coupling between latent states and process noise variance under partial observability. An efficient particle expectation-maximization algorithm, integrating guided particle filtering with backward trajectory smoothing, is developed for parameter estimation. Simulations demonstrate that the method substantially reduces parameter estimation bias under strong coupling and high observation noise, confirming its efficacy and robustness.

This study addresses the problem of recovering latent discrete states from the evolving weights of models trained on time-varying data streams to characterize non-stationary distributional shifts. The proposed approach trains classifiers over sliding time windows, aligns their weight trajectories, and fits a hidden Markov model (HMM) to these trajectories—enabling, for the first time, the identification of semantically coherent temporal phases solely from weight dynamics. Experiments on the Fakeddit and Yelp datasets demonstrate that transfer performance within the same inferred state significantly outperforms cross-state transfer, and this advantage persists independently of temporal proximity and shifts in class distribution. These findings confirm that model weights encode structural information about data distributions that extends beyond local temporal correlations.