latent variable modeling

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 zero-shot imputation of missing values in time series generated by ordinary differential equation (ODE)-driven dynamical systems—without access to target-domain data for fine-tuning. We propose the first general-purpose framework that pretrains a neural identifier on large-scale synthetic ODE solutions and their sparse, noisy observations, enabling joint amortized inference of initial conditions and state derivatives, followed by numerical integration to reconstruct full trajectories. The method integrates amortized variational inference with neural operators to establish a probabilistic modeling and generalization architecture tailored to the ODE solution manifold. Evaluated across 63 diverse synthetic dynamical systems and 10 high-dimensional real-world benchmarks—including human motion capture, air quality monitoring, and Navier–Stokes simulations—our approach achieves state-of-the-art zero-shot performance, consistently outperforming task-specific fine-tuned methods. This establishes a new paradigm for zero-shot time-series imputation in ODE-driven systems.

This work addresses probabilistic inference—forecasting, abduction, and intermediate-state estimation—for high-dimensional time series. We propose a probabilistic representation framework grounded in temporal contrastive learning. We provide the first theoretical proof that the learned latent states follow a Gaussian Markov chain structure, thereby reducing complex probabilistic inference to closed-form algebraic operations in a low-dimensional space: matrix inversion for abduction and linear interpolation for intermediate-state estimation. Integrating temporal contrastive learning, Gaussian graphical models, and linear-algebraic inference, our approach enables analytically tractable, efficient, and interpretable probabilistic reasoning. Empirical validation on synthetic tasks with up to 46 dimensions confirms the validity and scalability of the closed-form solutions, achieving substantial reductions in computational complexity compared to conventional sampling- or optimization-based methods.

Unsupervised interpretable learning for high-dimensional natural data (e.g., images) remains challenging due to the lack of identifiable, semantically meaningful representations. Method: This paper models semantic concepts as discrete implicit causal variables and constructs an identifiable multilevel causal hierarchy. It formally defines discrete concepts as hierarchical causal latent variables and establishes novel identifiability conditions for continuous high-dimensional observations—enabling complex causal structures beyond trees and DAGs. The approach integrates causal representation learning, hierarchical latent modeling, identifiability analysis, and latent diffusion mechanisms. Contributions/Results: We theoretically prove identifiability of intricate hierarchical concepts under unsupervised learning. Synthetic experiments validate both effectiveness and robustness. Furthermore, we uncover and empirically substantiate a hierarchical generative mechanism for implicit concepts within latent diffusion models—revealing their intrinsic causal organization.

Multi-source short time-series data suffer from limited per-sequence length, hindering accurate modeling of complex dynamical mechanisms. Method: We propose the first hierarchical unsupervised generative framework that jointly learns population-level shared priors and domain-specific dynamics. Our approach integrates variational inference, multi-domain dynamical system reconstruction (DSR), and interpretable latent-space learning to construct a linearly controllable, low-dimensional feature space—enabling cross-parameter-domain transfer and fundamental dynamical modeling. Contributions/Results: (1) First automatic discovery of interpretable dynamical features under a hierarchical structure; (2) High-fidelity single-domain reconstruction on standard DSR benchmarks and real-world neuroscience/clinical datasets; (3) Significantly improved generalization to unseen parameter regimes and modeling robustness in few-shot settings.

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.

Existing latent variable models often suffer from under-constrained objectives, leading to non-identifiable, ambiguous, and poorly interpretable representations. This work proposes the Constrained Latent State Modeling (CLSM) framework, which systematically integrates six core constraints—namely predictive sufficiency, minimality, temporal consistency, and others—for the first time. Grounded in information theory and dynamical systems theory, CLSM formally characterizes the intrinsic couplings and trade-offs among these constraints. By reframing representation learning as a constrained optimization problem, the framework unifies diverse approaches such as variational autoencoders and state-space models, revealing that non-identifiability stems from insufficient constraints rather than technical shortcomings. CLSM thus provides a principled foundation for designing latent variable models that are interpretable, robust, and aligned with downstream tasks.

This work proposes a novel approach to time series anomaly detection that addresses the limitations of traditional observation-likelihood-based methods, which often fail to capture structured temporal dynamics and misclassify anomalies as normal patterns. By introducing inductive biases into the latent space of conditional normalizing flows, the method models time series as discrete-time state-space systems, enforcing latent trajectories to conform to prescribed dynamical laws. Anomalies are then defined as deviations from these expected dynamics. The approach frames anomaly detection as a goodness-of-fit test for dynamic consistency—a formulation introduced here for the first time—and evaluates compliance of latent trajectories accordingly. Experiments on both synthetic and real-world datasets demonstrate its effectiveness in detecting anomalies in frequency, amplitude, and noise characteristics, achieving high detection performance alongside strong interpretability.

This work proposes a Bayesian dynamic latent space model tailored for weighted temporal networks exhibiting complex characteristics such as integer-valued edge weights, zero-inflation, dynamically evolving node latent positions, and time-varying sparsity. The model captures the temporal dependencies of node latent features through vector autoregression and, for the first time in latent space network modeling, incorporates both contemporaneous and lagged dependencies across nodes and latent dimensions. To enhance inference efficiency, a non-recursive block-updating multi-step sampler is developed, integrating auxiliary mixture sampling, Laplace approximation, and partially collapsed Gibbs sampling to substantially improve Markov chain mixing and computational scalability. The framework flexibly accommodates both integer and continuous edge weights and can be readily extended to static or dynamic settings, enabling accurate and efficient inference for complex temporal networks.

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.