A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift along the support of the data distribution but not away from it. In this work, we investigate this phenomenon of robustness of the support by taking a dynamical systems approach on the generating stochastic/deterministic process. Our perturbation analysis of the probability flow reveals that infinitesimal learning errors cause the predicted density to be different from the target density only on the data manifold for a wide class of generative models. Further, what is the dynamical mechanism that leads to the robustness of the support? We show that the alignment of the top Lyapunov vectors (most sensitive infinitesimal perturbation directions) with the tangent spaces along the boundary of the data manifold leads to robustness and prove a sufficient condition on the dynamics of the generating process to achieve this alignment. Moreover, the alignment condition is efficient to compute and, in practice, for robust generative models, automatically leads to accurate estimates of the tangent bundle of the data manifold. Using a finite-time linear perturbation analysis on samples paths as well as probability flows, our work complements and extends existing works on obtaining theoretical guarantees for generative models from a stochastic analysis, statistical learning and uncertainty quantification points of view. Our results apply across different dynamical generative models, such as conditional flow-matching and score-based generative models, and for different target distributions that may or may not satisfy the manifold hypothesis.

Nonlinear independent component analysis (ICA) is fundamental in unsupervised learning.

Inthisworkwepresenta scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models.

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a poor approximation of the much more complex true data generating process, leading to suboptimal estimation. The subtleties of the generative process are however captured in the data itself and we can ``learn to infer'', that is, learn a direct mapping from observations to explanatory latent variables. In this work we propose a hybrid model that combines graphical inference with a learned inverse model, which we structure as in a graph neural network, while the iterative algorithm as a whole is formulated as a recurrent neural network. By using cross-validation we can automatically balance the amount of work performed by graphical inference versus learned inference. We apply our ideas to the Kalman filter, a Gaussian hidden Markov model for time sequences, and show, among other things, that our model can estimate the trajectory of a noisy chaotic Lorenz Attractor much more accurately than either the learned or graphical inference run in isolation.

Generating sketches with specific patterns as expected, i.e., manipulating sketches in a controllable way, is a popular task. Recent studies control sketch features at stroke-level by editing values of stroke embeddings as conditions. However, in order to provide generator a global view about what a sketch is going to be drawn, all these edited conditions should be collected and fed into generator simultaneously before generation starts, i.e., no further manipulation is allowed during sketch generating process. In order to realize sketch drawing manipulation more flexibly, we propose a hierarchical auto-regressive sketch generating process. Instead of generating an entire sketch at once, each stroke in a sketch is generated in a three-staged hierarchy: 1) predicting a stroke embedding to represent which stroke is going to be drawn, and 2) anchoring the predicted stroke on the canvas, and 3) translating the embedding to a sequence of drawing actions to form the full sketch. Moreover, the stroke prediction, anchoring and translation are proceeded auto-regressively, i.e., both the recently generated strokes and their positions are considered to predict the current one, guiding model to produce an appropriate stroke at a suitable position to benefit the full sketch generation. It is flexible to manipulate stroke-level sketch drawing at any time during generation by adjusting the exposed editable stroke embeddings.

Nonlinear independent component analysis (ICA) is fundamental in unsupervised learning.