Yue Cheng

Understanding the dynamics of causal structures is crucial for uncovering the underlying processes in time series data. Previous approaches rely on static assumptions, where contemporaneous and time-lagged dependencies are assumed to have invariant topological structures. However, these models fail to capture the evolving causal relationship between variables when the underlying process exhibits such dynamics. To address this limitation, we propose DyCAST, a novel framework designed to learn dynamic causal structures in time series using Neural Ordinary Differential Equations (Neural ODEs). The key innovation lies in modeling the temporal dynamics of the contemporaneous structure, drawing inspiration from recent advances in Neural ODEs on constrained manifolds. We reformulate the task of learning causal structures at each time step as solving the solution trajectory of a Neural ODE on the directed acyclic graph (DAG) manifold. To accommodate high-dimensional causal structures, we extend DyCAST by learning the temporal dynamics of the hidden state for contemporaneous causal structure. Experiments on both synthetic and real-world datasets demonstrate that DyCAST achieves superior or comparable performance compared to existing causal discovery models.

In recent years, the alignment between artificial neural network (ANN) embeddings and blood oxygenation level dependent (BOLD) responses in functional magnetic resonance imaging (fMRI) via neural encoding models has significantly advanced research on neural representation mechanisms and interpretability in the brain. However, these approaches remain limited in characterizing the brain’s inherently nonlinear response properties. To address this, we propose the Jacobian-based Nonlinearity Evaluation (JNE), an interpretability metric for nonlinear neural encoding models. JNE quantifies nonlinearity by statistically measuring the dispersion of local linear mappings (Jacobians) from model representations to predicted BOLD responses, thereby approximating the nonlinearity of BOLD signals. Centered on proposing JNE as a novel interpretability metric, we validated its effectiveness through controlled simulation experiments on various activation functions and network architectures, and further verified it on real fMRI data, demonstrating a hierarchical progression of nonlinear characteristics from primary to higher-order visual cortices, consistent with established cortical organization. We further extended JNE with Sample-Specificity (JNE-SS), revealing stimulus-selective nonlinear response patterns in functionally specialized brain regions. As the first interpretability metric for quantifying nonlinear responses, JNE provides new insights into brain information processing.

Long-tailed distributions are prevalent in real-world semi-supervised learning (SSL), where pseudo-labels tend to favor majority classes, leading to degraded generalization. Although numerous long-tailed SSL (LTSSL) methods have been proposed, the underlying mechanisms of class bias remain underexplored. In this work, we investigate LTSSL through the lens of learning dynamics and introduce the notion of baseline images to characterize accumulated bias during training. We provide a step-wise decomposition showing that baseline predictions are determined solely by shallow bias terms, making them reliable indicators of class priors. Building on this insight, we propose a novel framework, DyTrim, which leverages baseline images to guide data pruning. Specifically, we perform class-aware pruning on labeled data to balance class distribution and label-agnostic soft pruning with confidence filtering on unlabeled data to mitigate error accumulation. Theoretically, we show that our method implicitly realizes risk reweighting, effectively suppressing class bias. Extensive experiments on public benchmarks show that DyTrim consistently enhances the performance of existing LTSSL methods by improving representation quality and prediction accuracy.