Likun Zhang

Likun Zhang, Hao Wu, Lingcui Zhang et al.

The emergence of text-to-image models has recently sparked significant interest, but the attendant is a looming shadow of potential infringement by violating the user terms. Specifically, an adversary may exploit data created by a commercial model to train their own without proper authorization. To address such risk, it is crucial to investigate the attribution of a suspicious model's training data by determining whether its training data originates, wholly or partially, from a specific source model. To trace the generated data, existing methods require applying extra watermarks during either the training or inference phases of the source model. However, these methods are impractical for pre-trained models that have been released, especially when model owners lack security expertise. To tackle this challenge, we propose an injection-free training data attribution method for text-to-image models. It can identify whether a suspicious model's training data stems from a source model, without additional modifications on the source model. The crux of our method lies in the inherent memorization characteristic of text-to-image models. Our core insight is that the memorization of the training dataset is passed down through the data generated by the source model to the model trained on that data, making the source model and the infringing model exhibit consistent behaviors on specific samples. Therefore, our approach involves developing algorithms to uncover these distinct samples and using them as inherent watermarks to verify if a suspicious model originates from the source model. Our experiments demonstrate that our method achieves an accuracy of over 80\% in identifying the source of a suspicious model's training data, without interfering the original training or generation process of the source model.

Likun Zhang, Wei Ma

Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown deep or the sample size is small. Conventional methods to reduce overfitting include pre-pruning and post-pruning, which constrain the growth of uninformative branches. In this paper, we propose a complementary approach by introducing a covariance-driven splitting criterion for regression trees (CovRT). This method is more robust to overfitting than the empirical risk minimization criterion used in CART, as it produces more balanced and stable splits and more effectively identifies covariates with true signals. We establish an oracle inequality of CovRT and prove that its predictive accuracy is comparable to that of CART in high-dimensional settings. We find that CovRT achieves superior prediction accuracy compared to CART in both simulations and real-world tasks.

R. C. Harwood, Likun Zhang, V. S. Manoranjan

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.