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Data valuation is critical in machine learning, as it helps enhance model transparency and protect data properties. Existing data valuation methods have primarily focused on discriminative models, neglecting deep generative models that have recently gained considerable attention. Similar to discriminative models, there is an urgent need to assess data contributions in deep generative models as well. However, previous data valuation approaches mainly relied on discriminative model performance metrics and required model retraining. Consequently, they cannot be applied directly and efficiently to recent deep generative models, such as generative adversarial networks and diffusion models, in practice. To bridge this gap, we formulate the data valuation problem in generative models from a similarity-matching perspective. Specifically, we introduce Generative Model Valuator (GMValuator), the first model-agnostic approach for any generative models, designed to provide data valuation for generation tasks. We have conducted extensive experiments to demonstrate the effectiveness of the proposed method. To the best of their knowledge, GMValuator is the first work that offers a training-free, post-hoc data valuation strategy for deep generative models.

The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the fact that many variants of GANs were developed following this paradigm, the current theoretical understanding of GANs and their practical algorithms are inconsistent. In this paper, we leverage Wasserstein gradient flows which characterize the evolution of particles in the sample space, to gain theoretical insights and algorithmic inspiration of GANs. We introduce a unified generative modeling framework - MonoFlow: the particle evolution is rescaled via a monotonically increasing mapping of the log density ratio. Under our framework, adversarial training can be viewed as a procedure first obtaining MonoFlow's vector field via training the discriminator and the generator learns to draw the particle flow defined by the corresponding vector field. We also reveal the fundamental difference between variational divergence minimization and adversarial training. This analysis helps us to identify what types of generator loss functions can lead to the successful training of GANs and suggest that GANs may have more loss designs beyond the literature (e.g., non-saturated loss), as long as they realize MonoFlow. Consistent empirical studies are included to validate the effectiveness of our framework.

In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of partial differential equations (PDEs) using neural network functions. Despite extremely extensive research activities in applying neural networks for numerical PDEs, there is still a serious lack of effective training algorithms that can achieve adequate accuracy, even for one-dimensional problems. Based on recent results on the spectral properties of linear layers and landscape analysis for single neuron problems, we develop a special type of subspace correction method that optimizes the linear layer and each neuron in the nonlinear layer separately. An optimal preconditioner that resolves the ill-conditioning of the linear layer is presented for one-dimensional problems, so that the linear layer is trained in a uniform number of iterations with respect to the number of neurons. In each single neuron problem, a good local minimum that avoids flat energy regions is found by a superlinearly convergent algorithm. Numerical experiments on function approximation problems and PDEs demonstrate better performance of the proposed method than other gradient-based methods.

In this experience report, we apply deep active learning to the field of design optimization to reduce the number of computationally expensive numerical simulations. We are interested in optimizing the design of structural components, where the shape is described by a set of parameters. If we can predict the performance based on these parameters and consider only the promising candidates for simulation, there is an enormous potential for saving computing power. We present two selection strategies for self-optimization to reduce the computational cost in multi-objective design optimization problems. Our proposed methodology provides an intuitive approach that is easy to apply, offers significant improvements over random sampling, and circumvents the need for uncertainty estimation. We evaluate our strategies on a large dataset from the domain of fluid dynamics and introduce two new evaluation metrics to determine the model's performance. Findings from our evaluation highlights the effectiveness of our selection strategies in accelerating design optimization. We believe that the introduced method is easily transferable to other self-optimization problems.

This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta (ARK) methods. We provide a rigorous proof of energy stability, unique solvability, and convergence. The proposed schemes generalizes some recently developed high-order, energy-stable schemes and address their shortcomings. On the one other hand, the proposed schemes can incorporate existing SAV-RK type methods after judiciously selecting the Butcher tables of ARK methods \cite{sav_li,sav_nlsw}. The order of a SAV-RKPC method can thus be confirmed theoretically by the order conditions of the corresponding ARK method. Several new schemes are constructed based on our framework, which perform to be more stable than existing SAV-RK type methods. On the other hand, the proposed schemes do not limit to a specific form of the nonlinear part of the free energy and can achieve high order with fewer intermediate stages compared to the convex splitting ARK methods \cite{csrk}. Numerical experiments demonstrate stability and efficiency of proposed schemes.

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired source and target samples drawn from arbitrary distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger bridge (SB) problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data.

Vertical federated learning (VFL) is a promising approach for collaboratively training machine learning models using private data partitioned vertically across different parties. Ideally in a VFL setting, the active party (party possessing features of samples with labels) benefits by improving its machine learning model through collaboration with some passive parties (parties possessing additional features of the same samples without labels) in a privacy preserving manner. However, motivating passive parties to participate in VFL can be challenging. In this paper, we focus on the problem of allocating incentives to the passive parties by the active party based on their contributions to the VFL process. We formulate this problem as a variant of the Nucleolus game theory concept, known as the Bankruptcy Problem, and solve it using the Talmud's division rule. We evaluate our proposed method on synthetic and real-world datasets and show that it ensures fairness and stability in incentive allocation among passive parties who contribute their data to the federated model. Additionally, we compare our method to the existing solution of calculating Shapley values and show that our approach provides a more efficient solution with fewer computations.

In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. However, these GANs often suffer from the problem of unstable training. In this paper, we analyze the stability of the training process of these GANs from the perspective of probability density dynamics. In our framework, we regard the discriminator $D$ in these GANs as a feature transformation mapping that maps high dimensional data into a feature space, while the generator $G$ maps random variables to samples that resemble real data in terms of feature space. This perspective enables us to perform stability analysis for the training of GANs using the Wasserstein gradient flow of the probability density function. We find that the training process of the discriminator is usually unstable due to the formulation of $\min_G \max_D E(G, D)$ in GANs. To address this issue, we add a stabilizing term in the discriminator loss function. We conduct experiments to validate our stability analysis and stabilizing method.

By combining the undecimated wavelet transform within a Word Embedded Semantic Marginal Autoencoder (WESMA), this research study provides a novel strategy for improving security measures and denoising multiple languages. The incorporation of these strategies is intended to address the issues of robustness, privacy, and multilingualism in data processing applications. The undecimated wavelet transform is used as a feature extraction tool to identify prominent language patterns and structural qualities in the input data. The proposed system may successfully capture significant information while preserving the temporal and geographical links within the data by employing this transform. This improves security measures by increasing the system's ability to detect abnormalities, discover hidden patterns, and distinguish between legitimate content and dangerous threats. The Word Embedded Semantic Marginal Autoencoder also functions as an intelligent framework for dimensionality and noise reduction. The autoencoder effectively learns the underlying semantics of the data and reduces noise components by exploiting word embeddings and semantic context. As a result, data quality and accuracy are increased in following processing stages. The suggested methodology is tested using a diversified dataset that includes several languages and security scenarios. The experimental results show that the proposed approach is effective in attaining security enhancement and denoising capabilities across multiple languages. The system is strong in dealing with linguistic variances, producing consistent outcomes regardless of the language used. Furthermore, incorporating the undecimated wavelet transform considerably improves the system's ability to efficiently address complex security concerns

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.