Yici Yan

Yichi Zhang, Yici Yan, Alex Schwing et al.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Yichi Zhang, Yici Yan, Alex Schwing et al.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

Hongyu Shen, Yici Yan, Zhizhen Zhao

Model-X knockoff has garnered significant attention among various feature selection methods due to its guarantees for controlling the false discovery rate (FDR). Since its introduction in parametric design, knockoff techniques have evolved to handle arbitrary data distributions using deep learning-based generative models. However, we have observed limitations in the current implementations of the deep Model-X knockoff framework. Notably, the "swap property" that knockoffs require often faces challenges at the sample level, resulting in diminished selection power. To address these issues, we develop "Deep Dependency Regularized Knockoff (DeepDRK)," a distribution-free deep learning method that effectively balances FDR and power. In DeepDRK, we introduce a novel formulation of the knockoff model as a learning problem under multi-source adversarial attacks. By employing an innovative perturbation technique, we achieve lower FDR and higher power. Our model outperforms existing benchmarks across synthetic, semi-synthetic, and real-world datasets, particularly when sample sizes are small and data distributions are non-Gaussian.