learn latent dynamics

Modeling and interpreting low-dimensional manifold structures in high-dimensional neural time series remains challenging due to their intrinsic nonlinearity and temporal complexity. Method: We propose a hierarchical stochastic differential equation (SDE) framework that innovatively integrates Brownian bridge SDEs with multivariate marked point processes to enable continuous, differentiable latent-space dynamics modeling. Sparse sampling coupled with an SDE-driven observation mapping ensures efficient manifold trajectory reconstruction. Contribution/Results: The method achieves both interpretability and computational efficiency—its inference complexity scales linearly with sequence length, markedly outperforming conventional nonlinear dimensionality reduction and black-box deep SDE approaches. Extensive validation on synthetic benchmarks and real neural recordings—including electrophysiological data from macaque motor cortex—demonstrates accurate recovery of underlying manifold geometry and dynamics, alongside strong scalability.

Existing stochastic process models often struggle to perform efficient conditional sampling under nonlinear observations, non-Gaussian likelihoods, or global constraints, typically requiring bespoke and complex algorithms. This work proposes the first universal conditioning framework that requires no training and avoids neural network approximations. The approach represents stochastic processes via deterministic mappings of tractable latent innovation variables, recasting conditional sampling as an inference problem in latent space. Exact solutions are achieved through backward-time stochastic differential equations (SDEs). The method accommodates a broad class of heterogeneous processes—including spatial priors, nonlinear dynamics, stochastic partial differential equations, extreme-value processes, and discrete-state processes—and enables high-fidelity conditional sampling on a single CPU within seconds, achieving both theoretical exactness and computational efficiency.

This work addresses the challenge of causal identifiability in continuous-time stochastic point processes with latent variables by proposing MUTATE, a novel framework that achieves, for the first time, identifiable representation learning of high-dimensional continuous-time latent variables and their causal mechanisms. Built upon a variational autoencoder architecture, MUTATE integrates a time-adaptive transition module with geometric analysis in parameter space to effectively disentangle dynamically evolving latent factors from low-dimensional observations. Experiments on both synthetic and real-world data—including gene mutation accumulation trajectories and neuronal spike trains—demonstrate that MUTATE not only accurately recovers the underlying causal structure but also offers strong scientific interpretability, thereby establishing a new paradigm for continuous-time latent causal modeling.

This work addresses the challenges of complexity and poor interpretability in digital twin modeling, which often arise from high-dimensional inputs, heterogeneous data, and multi-timescale dynamics—particularly in control and data assimilation tasks under uncertainty. The authors propose an iterative sparsification method grounded in conditional generative modeling and Gaussian process variance decomposition (kernel ANOVA). This approach identifies input variables that critically shape the full conditional distribution of target outputs—including their variability, tail behavior, and multimodality—and automatically discovers a compact state-action-memory structure that enables approximate Markovian dynamics in control settings. The resulting parsimonious stochastic surrogate models exhibit both strong interpretability and high predictive performance, matching or closely approaching the downstream accuracy of full-variable models across diverse benchmarks, including stochastic dynamical systems, PDE-based control, reinforcement learning, and economic datasets.

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 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 a critical limitation in existing latent-variable world models, which rely on average prediction error over training data for training and selection—a metric that fails to reflect actual controller performance due to a mismatch between the evaluation distribution and the distribution queried by the planner. The authors propose instead to center model assessment on the discrepancy between predicted and true costs over states reachable by the planner. They establish, for the first time, a rigorous theoretical link between this discrepancy and control suboptimality, proving it provides a valid upper bound on performance loss, whereas conventional prediction errors neither bound nor track performance. Leveraging control theory, spectral analysis, and non-normal operator theory, they decompose the discrepancy into an intrinsic manifold residual and an off-manifold divergence term, and introduce a fidelity score to quantify alignment of the planner’s reachable distribution. Experiments on synthetic systems and model predictive control confirm that the proposed metric reliably tracks control performance, while single-step prediction error shows virtually no correlation.

This work addresses the challenge of non-identifiability in existing continuous-time latent-variable stochastic differential equation (SDE) models under nonlinear observations. The authors propose a novel approach based on additive-noise latent SDEs with shared drift but environment-dependent diffusion covariances, demonstrating that only two diagonal diffusion mechanisms suffice to disentangle latent variables via coordinate-wise variance ratio analysis—without requiring sparsity assumptions on the drift term. Theoretically, they establish, for the first time, identifiability of the latent variables up to permutation and scaling, and further recover the instantaneous causal graph encoded by the drift’s Jacobian. Leveraging a diffusivity-shift-based identifiability framework and a two-stage algorithm, the method successfully validates theoretical identifiability bounds on synthetic data and effectively disentangles real-world sensor trajectories from the Hardanger Bridge, demonstrating practical efficacy.

This work addresses the limitations of existing deep state-space models, which rely on Gaussian assumptions and struggle to capture complex, multimodal latent dynamics. While diffusion models offer strong expressive power, they lack structured mechanisms for temporal reasoning. To bridge this gap, we propose a novel latent variable state-space model that, for the first time, integrates a non-Gaussian diffusion process into the latent state transition mechanism and enables joint training of an autoencoder and a diffusion model on sequential data. This approach overcomes the restrictive Gaussian assumption and supports unified modeling and inference of multimodal temporal dynamics. Experiments demonstrate that our model significantly outperforms state-of-the-art deep state-space models in both fitting accuracy and predictive performance on synthetic time series with complex transition characteristics.