Improve Cross-domain Mixed Sampling with Guidance Training for Adaptive Segmentation

Unsupervised Domain Adaptation (UDA) endeavors to adjust models trained on a source domain to perform well on a target domain without requiring additional annotations. In the context of domain adaptive semantic segmentation, which tackles UDA for dense prediction, the goal is to circumvent the need for costly pixel-level annotations. Typically, various prevailing methods baseline rely on constructing intermediate domains via cross-domain mixed sampling techniques to mitigate the performance decline caused by domain gaps. However, such approaches generate synthetic data that diverge from real-world distributions, potentially leading the model astray from the true target distribution. To address this challenge, we propose a novel auxiliary task called Guidance Training. This task facilitates the effective utilization of cross-domain mixed sampling techniques while mitigating distribution shifts from the real world. Specifically, Guidance Training guides the model to extract and reconstruct the target-domain feature distribution from mixed data, followed by decoding the reconstructed target-domain features to make pseudo-label predictions. Importantly, integrating Guidance Training incurs minimal training overhead and imposes no additional inference burden. We demonstrate the efficacy of our approach by integrating it with existing methods, consistently improving performance. The implementation will be available at https://github.com/Wenlve-Zhou/Guidance-Training.

Sparse Variational Student-t Processes

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.

Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques. We demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to tens of thousands demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming SOTA Gaussian process methods. Furthermore, our method guarantees theoretically controlled prediction error for DGP models and demonstrates remarkable performance on various datasets. We are optimistic that NOVI has the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications

Double Normalizing Flows: Flexible Bayesian Gaussian Process ODEs Learning

Recently, Gaussian processes have been utilized to model the vector field of continuous dynamical systems. Bayesian inference for such models \cite{hegde2022variational} has been extensively studied and has been applied in tasks such as time series prediction, providing uncertain estimates. However, previous Gaussian Process Ordinary Differential Equation (ODE) models may underperform on datasets with non-Gaussian process priors, as their constrained priors and mean-field posteriors may lack flexibility. To address this limitation, we incorporate normalizing flows to reparameterize the vector field of ODEs, resulting in a more flexible and expressive prior distribution. Additionally, due to the analytically tractable probability density functions of normalizing flows, we apply them to the posterior inference of GP ODEs, generating a non-Gaussian posterior. Through these dual applications of normalizing flows, our model improves accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs. The effectiveness of our approach is demonstrated on simulated dynamical systems and real-world human motion data, including tasks such as time series prediction and missing data recovery. Experimental results indicate that our proposed method effectively captures model uncertainty while improving accuracy.

SciRE-Solver: Efficient Sampling of Diffusion Probabilistic Models by Score-integrand Solver with Recursive Derivative Estimation

Diffusion probabilistic models (DPMs) are a powerful class of generative models known for their ability to generate high-fidelity image samples. A major challenge in the implementation of DPMs is the slow sampling process. In this work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a score-based exact solution paradigm for the diffusion ODEs corresponding to the sampling process of DPMs, which introduces a new perspective on developing numerical algorithms for solving diffusion ODEs. To achieve an efficient sampler, we propose a recursive derivative estimation (RDE) method to reduce the estimation error. With our proposed solution paradigm and RDE method, we propose the score-integrand solver with the convergence order guarantee as efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver attains state-of-the-art (SOTA) sampling performance with a limited number of score function evaluations (NFE) on both discrete-time and continuous-time DPMs in comparison to existing training-free sampling algorithms. Such as, we achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for continuous-time DPMs on CIFAR10, respectively. Different from other samplers, SciRE-Solver has the promising potential to surpass the FIDs achieved in the original papers of some pre-trained models with a small NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of $3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of $2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA 64$\times$64.

TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speed

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on large datasets due to the incremental complexity of the neural ODE training. Optimal Transport theory has been applied to regularize the dynamics of the ODE to speed up training in recent works. In this paper, a temporal optimization is proposed by optimizing the evolutionary time for forward propagation of the neural ODE training. In this appoach, we optimize the network weights of the CNF alternately with evolutionary time by coordinate descent. Further with temporal regularization, stability of the evolution is ensured. This approach can be used in conjunction with the original regularization approach. We have experimentally demonstrated that the proposed approach can significantly accelerate training without sacrifying performance over baseline models.

Self-Verification in Image Denoising

We devise a new regularization, called self-verification, for image denoising. This regularization is formulated using a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output of the network as a ``prior'' that we denoise again after ``re-noising''. The comparison between the again denoised image and its prior can be interpreted as a self-verification of the network's denoising ability. We demonstrate that self-verification encourages the network to capture low-level image statistics needed to restore the image. Based on this self-verification regularization, we further show that the network can learn to denoise even if it has not seen any clean images. This learning strategy is self-supervised, and we refer to it as Self-Verification Image Denoising (SVID). SVID can be seen as a mixture of learning-based methods and traditional model-based denoising methods, in which regularization is adaptively formulated using the output of the network. We show the application of SVID to various denoising tasks using only observed corrupted data. It can achieve the denoising performance close to supervised CNNs.

Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning

Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seemed to have similar unit structure. However, to the best of our knowledge, there is no relative result to prove that these rogue waves have the similar patterns for different perturbations, partly due to that it is hard to measure the rogue wave pattern automatically. In this work, we address these problems from the perspective of computer vision via using deep neural networks. We propose a Rogue Wave Detection Network (RWD-Net) model to automatically and accurately detect RWs on the images, which directly indicates they have the similar computer vision patterns. For this purpose, we herein meanwhile have designed the related dataset, termed as Rogue Wave Dataset-$10$K (RWD-$10$K), which has $10,191$ RW images with bounding box annotations for each RW unit. In our detection experiments, we get $99.29\%$ average precision on the test splits of the RWD-$10$K dataset. Finally, we derive our novel metric, the density of RW units (DRW), to characterize the evolution of Gaussian perturbations and obtain the statistical results on them.