Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Ability

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep learning exhibit nice generalizability. On the other hand, algorithm-dependent generalization bounds, like stability bounds, often rely on strict assumptions. To establish generalizability under less stringent assumptions, this paper investigates the generalizability of neural networks that minimize or approximately minimize empirical risk. We establish a lower bound for population accuracy based on the expressiveness of these networks, which indicates that with an adequate large number of training samples and network sizes, these networks, including over-parameterized ones, can generalize effectively. Additionally, we provide a necessary condition for generalization, demonstrating that, for certain data distributions, the quantity of training data required to ensure generalization exceeds the network size needed to represent the corresponding data distribution. Finally, we provide theoretical insights into several phenomena in deep learning, including robust generalization, importance of over-parameterization, and effect of loss function on generalization.

Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization

Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard adversarial training which focuses on pointwise adversarial perturbations. However, WDRO still suffers fundamentally from the robust overfitting problem, as it does not consider statistical error. We address this gap by proposing a novel robust optimization framework under a new uncertainty set for adversarial noise via Wasserstein distance and statistical error via Kullback-Leibler divergence, called the Statistically Robust WDRO. We establish a robust generalization bound for the new optimization framework, implying that out-of-distribution adversarial performance is at least as good as the statistically robust training loss with high probability. Furthermore, we derive conditions under which Stackelberg and Nash equilibria exist between the learner and the adversary, giving an optimal robust model in certain sense. Finally, through extensive experiments, we demonstrate that our method significantly mitigates robust overfitting and enhances robustness within the framework of WDRO.

BridgePure: Revealing the Fragility of Black-box Data Protection

Availability attacks, or unlearnable examples, are defensive techniques that allow data owners to modify their datasets in ways that prevent unauthorized machine learning models from learning effectively while maintaining the data's intended functionality. It has led to the release of popular black-box tools for users to upload personal data and receive protected counterparts. In this work, we show such black-box protections can be substantially bypassed if a small set of unprotected in-distribution data is available. Specifically, an adversary can (1) easily acquire (unprotected, protected) pairs by querying the black-box protections with the unprotected dataset; and (2) train a diffusion bridge model to build a mapping. This mapping, termed BridgePure, can effectively remove the protection from any previously unseen data within the same distribution. Under this threat model, our method demonstrates superior purification performance on classification and style mimicry tasks, exposing critical vulnerabilities in black-box data protection.

PowerMLP: An Efficient Version of KAN

The Kolmogorov-Arnold Network (KAN) is a new network architecture known for its high accuracy in several tasks such as function fitting and PDE solving. The superior expressive capability of KAN arises from the Kolmogorov-Arnold representation theorem and learnable spline functions. However, the computation of spline functions involves multiple iterations, which renders KAN significantly slower than MLP, thereby increasing the cost associated with model training and deployment. The authors of KAN have also noted that ``the biggest bottleneck of KANs lies in its slow training. KANs are usually 10x slower than MLPs, given the same number of parameters.'' To address this issue, we propose a novel MLP-type neural network PowerMLP that employs simpler non-iterative spline function representation, offering approximately the same training time as MLP while theoretically demonstrating stronger expressive power than KAN. Furthermore, we compare the FLOPs of KAN and PowerMLP, quantifying the faster computation speed of PowerMLP. Our comprehensive experiments demonstrate that PowerMLP generally achieves higher accuracy and a training speed about 40 times faster than KAN in various tasks.

Generalizability of Memorization Neural Networks

The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using over-parameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic. Since using i.i.d. training data is a necessary condition for a learning algorithm to be generalizable, memorization and its generalization theory for i.i.d. datasets are developed under mild conditions on the data distribution. First, algorithms are given to construct memorization networks for an i.i.d. dataset, which have the smallest number of parameters and even a constant number of parameters. Second, we show that, in order for the memorization networks to be generalizable, the width of the network must be at least equal to the dimension of the data, which implies that the existing memorization networks with an optimal number of parameters are not generalizable. Third, a lower bound for the sample complexity of general memorization algorithms and the exact sample complexity for memorization algorithms with constant number of parameters are given. It is also shown that there exist data distributions such that, to be generalizable for them, the memorization network must have an exponential number of parameters in the data dimension. Finally, an efficient and generalizable memorization algorithm is given when the number of training samples is greater than the efficient memorization sample complexity of the data distribution.

T2VSafetyBench: Evaluating the Safety of Text-to-Video Generative Models

The recent development of Sora leads to a new era in text-to-video (T2V) generation. Along with this comes the rising concern about its security risks. The generated videos may contain illegal or unethical content, and there is a lack of comprehensive quantitative understanding of their safety, posing a challenge to their reliability and practical deployment. Previous evaluations primarily focus on the quality of video generation. While some evaluations of text-to-image models have considered safety, they cover fewer aspects and do not address the unique temporal risk inherent in video generation. To bridge this research gap, we introduce T2VSafetyBench, a new benchmark designed for conducting safety-critical assessments of text-to-video models. We define 12 critical aspects of video generation safety and construct a malicious prompt dataset using LLMs and jailbreaking prompt attacks. Based on our evaluation results, we draw several important findings, including: 1) no single model excels in all aspects, with different models showing various strengths; 2) the correlation between GPT-4 assessments and manual reviews is generally high; 3) there is a trade-off between the usability and safety of text-to-video generative models. This indicates that as the field of video generation rapidly advances, safety risks are set to surge, highlighting the urgency of prioritizing video safety. We hope that T2VSafetyBench can provide insights for better understanding the safety of video generation in the era of generative AI.

Alignment Calibration: Machine Unlearning for Contrastive Learning under Auditing

Machine unlearning provides viable solutions to revoke the effect of certain training data on pre-trained model parameters. Existing approaches provide unlearning recipes for classification and generative models. However, a category of important machine learning models, i.e., contrastive learning (CL) methods, is overlooked. In this paper, we fill this gap by first proposing the framework of Machine Unlearning for Contrastive learning (MUC) and adapting existing methods. Furthermore, we observe that several methods are mediocre unlearners and existing auditing tools may not be sufficient for data owners to validate the unlearning effects in contrastive learning. We thus propose a novel method called Alignment Calibration (AC) by explicitly considering the properties of contrastive learning and optimizing towards novel auditing metrics to easily verify unlearning. We empirically compare AC with baseline methods on SimCLR, MoCo and CLIP. We observe that AC addresses drawbacks of existing methods: (1) achieving state-of-the-art performance and approximating exact unlearning (retraining); (2) allowing data owners to clearly visualize the effect caused by unlearning through black-box auditing.

Generalization Bound and New Algorithm for Clean-Label Backdoor Attack

The generalization bound is a crucial theoretical tool for assessing the generalizability of learning methods and there exist vast literatures on generalizability of normal learning, adversarial learning, and data poisoning. Unlike other data poison attacks, the backdoor attack has the special property that the poisoned triggers are contained in both the training set and the test set and the purpose of the attack is two-fold. To our knowledge, the generalization bound for the backdoor attack has not been established. In this paper, we fill this gap by deriving algorithm-independent generalization bounds in the clean-label backdoor attack scenario. Precisely, based on the goals of backdoor attack, we give upper bounds for the clean sample population errors and the poison population errors in terms of the empirical error on the poisoned training dataset. Furthermore, based on the theoretical result, a new clean-label backdoor attack is proposed that computes the poisoning trigger by combining adversarial noise and indiscriminate poison. We show its effectiveness in a variety of settings.

Efficient Black-box Adversarial Attacks via Bayesian Optimization Guided by a Function Prior

This paper studies the challenging black-box adversarial attack that aims to generate adversarial examples against a black-box model by only using output feedback of the model to input queries. Some previous methods improve the query efficiency by incorporating the gradient of a surrogate white-box model into query-based attacks due to the adversarial transferability. However, the localized gradient is not informative enough, making these methods still query-intensive. In this paper, we propose a Prior-guided Bayesian Optimization (P-BO) algorithm that leverages the surrogate model as a global function prior in black-box adversarial attacks. As the surrogate model contains rich prior information of the black-box one, P-BO models the attack objective with a Gaussian process whose mean function is initialized as the surrogate model's loss. Our theoretical analysis on the regret bound indicates that the performance of P-BO may be affected by a bad prior. Therefore, we further propose an adaptive integration strategy to automatically adjust a coefficient on the function prior by minimizing the regret bound. Extensive experiments on image classifiers and large vision-language models demonstrate the superiority of the proposed algorithm in reducing queries and improving attack success rates compared with the state-of-the-art black-box attacks. Code is available at https://github.com/yibo-miao/PBO-Attack.

Efficient Availability Attacks against Supervised and Contrastive Learning Simultaneously

Availability attacks can prevent the unauthorized use of private data and commercial datasets by generating imperceptible noise and making unlearnable examples before release. Ideally, the obtained unlearnability prevents algorithms from training usable models. When supervised learning (SL) algorithms have failed, a malicious data collector possibly resorts to contrastive learning (CL) algorithms to bypass the protection. Through evaluation, we have found that most of the existing methods are unable to achieve both supervised and contrastive unlearnability, which poses risks to data protection. Different from recent methods based on contrastive error minimization, we employ contrastive-like data augmentations in supervised error minimization or maximization frameworks to obtain attacks effective for both SL and CL. Our proposed AUE and AAP attacks achieve state-of-the-art worst-case unlearnability across SL and CL algorithms with less computation consumption, showcasing prospects in real-world applications.