Continuous sign language recognition (CSLR) plays a crucial role in facilitating communication between deaf and hearing individuals. A key aspect of achieving precise CSLR is the alignment of the video segment of each sign with its gloss, namely its corresponding text representation in natural language. However, the coarticulation phenomenon, where contextual dependencies between adjacent signs blur the boundaries of individual signs, poses a significant challenge to this task. In this paper, we propose a novel boundary-aware sentence-gloss alignment network for CSLR to address this challenge. Our network first designs a task-relevant boundary-aware similarity measurement, evaluating sign frames by both appearance and their recognition contribution, mitigating coarticulation-induced transition noise to restore precise boundaries. For enhanced alignment, we propose a hierarchical sentence-gloss alignment: coarse sentence-level alignment reduces cross-modal disparity, while fine-grained gloss-level alignment refines video-to-token mapping. Finally, an adaptive class-divergence loss sharpens gloss decoding by maximizing inter-class discrimination. Our proposed framework provides a simple and effective solution to mitigate the boundary ambiguity caused by coarticulation, optimizing continuous sign language recognition algorithms from a new perspective. Extensive experiments conducted on four public sign language recognition (SLR) datasets demonstrate that our proposed boundary-aware sentence-gloss alignment network learns precise alignments and achieves state-of-the-art performance.

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time $t$. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, for example, identifiability and asymptotic properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory. When observations are disturbed by measurement noise, we prove that under mild conditions, the parameter estimator based on the Nonlinear Least Squares (NLS) method is consistent and asymptotic normal with $n^{-1/2}$ convergence rate. Based on the asymptotic normality property, we construct confidence sets for the unknown system parameters and propose a new method to infer the causal structure of the ODE system, that is, inferring whether there is a causal link between system variables. Furthermore, we extend the results to degraded observations, including aggregated and time-scaled ones. To the best of our knowledge, our work is the first systematic study of the identifiability and asymptotic properties in learning linear ODE systems. We also construct simulations with various system dimensions to illustrate the established theoretical results.

In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings.