109 research outputs found
Wasserstein Hamiltonian flow with common noise on graph
We study the Wasserstein Hamiltonian flow with a common noise on the density
manifold of a finite graph. Under the framework of stochastic variational
principle, we first develop the formulation of stochastic Wasserstein
Hamiltonian flow and show the local existence of a unique solution. We also
establish a sufficient condition for the global existence of the solution.
Consequently, we obtain the global well-posedness for the nonlinear
Schr\"odinger equations with common noise on graph. In addition, using
Wong-Zakai approximation of common noise, we prove the existence of the
minimizer for an optimal control problem with common noise. We show that its
minimizer satisfies the stochastic Wasserstein Hamiltonian flow on graph as
well
A Pilot Study of Query-Free Adversarial Attack against Stable Diffusion
Despite the record-breaking performance in Text-to-Image (T2I) generation by
Stable Diffusion, less research attention is paid to its adversarial
robustness. In this work, we study the problem of adversarial attack generation
for Stable Diffusion and ask if an adversarial text prompt can be obtained even
in the absence of end-to-end model queries. We call the resulting problem
'query-free attack generation'. To resolve this problem, we show that the
vulnerability of T2I models is rooted in the lack of robustness of text
encoders, e.g., the CLIP text encoder used for attacking Stable Diffusion.
Based on such insight, we propose both untargeted and targeted query-free
attacks, where the former is built on the most influential dimensions in the
text embedding space, which we call steerable key dimensions. By leveraging the
proposed attacks, we empirically show that only a five-character perturbation
to the text prompt is able to cause the significant content shift of
synthesized images using Stable Diffusion. Moreover, we show that the proposed
target attack can precisely steer the diffusion model to scrub the targeted
image content without causing much change in untargeted image content.Comment: The 3rd Workshop of Adversarial Machine Learning on Computer Vision:
Art of Robustnes
Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis
Time-frequency analysis for non-linear and non-stationary signals is
extraordinarily challenging. To capture features in these signals, it is
necessary for the analysis methods to be local, adaptive and stable. In recent
years, decomposition based analysis methods, such as the empirical mode
decomposition (EMD) technique pioneered by Huang et al., were developed by
different research groups. These methods decompose a signal into a finite
number of components on which the time-frequency analysis can be applied more
effectively.
In this paper we consider the iterative filters (IFs) approach as an
alternative to EMD. We provide sufficient conditions on the filters that ensure
the convergence of IFs applied to any signal. Then we propose a new
technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the
IFs strategy together with an adaptive and data driven filter length selection
to achieve the decomposition. Furthermore we design smooth filters with compact
support from solutions of Fokker-Planck equations (FP filters) that can be used
within both IFs and ALIF methods. These filters fulfill the derived sufficient
conditions for the convergence of the IFs algorithm. Numerical examples are
given to demonstrate the performance and stability of IFs and ALIF techniques
with FP filters. In addition, in order to have a complete and truly local
analysis toolbox for non-linear and non-stationary signals, we propose a new
definition for the instantaneous frequency which depends exclusively on local
properties of a signal
Neural Parametric Fokker-Planck Equations
In this paper, we develop and analyze numerical methods for high dimensional
Fokker-Planck equations by leveraging generative models from deep learning. Our
starting point is a formulation of the Fokker-Planck equation as a system of
ordinary differential equations (ODEs) on finite-dimensional parameter space
with the parameters inherited from generative models such as normalizing flows.
We call such ODEs neural parametric Fokker-Planck equation. The fact that the
Fokker-Planck equation can be viewed as the -Wasserstein gradient flow of
Kullback-Leibler (KL) divergence allows us to derive the ODEs as the
constrained -Wasserstein gradient flow of KL divergence on the set of
probability densities generated by neural networks. For numerical computation,
we design a variational semi-implicit scheme for the time discretization of the
proposed ODE. Such an algorithm is sampling-based, which can readily handle
Fokker-Planck equations in higher dimensional spaces. Moreover, we also
establish bounds for the asymptotic convergence analysis of the neural
parametric Fokker-Planck equation as well as its error analysis for both the
continuous and discrete (forward-Euler time discretization) versions. Several
numerical examples are provided to illustrate the performance of the proposed
algorithms and analysis
Parameterized Wasserstein Hamiltonian Flow
In this work, we propose a numerical method to compute the Wasserstein
Hamiltonian flow (WHF), which is a Hamiltonian system on the probability
density manifold. Many well-known PDE systems can be reformulated as WHFs. We
use parameterized function as push-forward map to characterize the solution of
WHF, and convert the PDE to a finite-dimensional ODE system, which is a
Hamiltonian system in the phase space of the parameter manifold. We establish
error analysis results for the continuous time approximation scheme in
Wasserstein metric. For the numerical implementation, we use neural networks as
push-forward maps. We apply an effective symplectic scheme to solve the derived
Hamiltonian ODE system so that the method preserves some important quantities
such as total energy. The computation is done by fully deterministic symplectic
integrator without any neural network training. Thus, our method does not
involve direct optimization over network parameters and hence can avoid the
error introduced by stochastic gradient descent (SGD) methods, which is usually
hard to quantify and measure. The proposed algorithm is a sampling-based
approach that scales well to higher dimensional problems. In addition, the
method also provides an alternative connection between the Lagrangian and
Eulerian perspectives of the original WHF through the parameterized ODE
dynamics.Comment: We welcome any comments and suggestion
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