Deciding When to Switch: E-Processes for Adaptive Minimax Training for Generative Adversarial Nets

Modern data science increasingly gives rise to hypothesis-testing problems that are not naturally formulated in terms of parameters within prespecified statistical models. One important example is the dynamic evaluation of optimization algorithms, where decisions must be made during training about whether further updates remain beneficial or the algorithm should switch to a different phase. This issue is particularly relevant in stochastic min-max optimization. Generative adversarial networks (GANs) provide a canonical example, as their training requires repeated decisions about when to switch between discriminator and generator updates, yet existing methods typically rely on fixed update ratios or heuristic criteria. We formulate this switching problem as sequential hypothesis testing and develop an e-process-based adaptive training procedure. During discriminator updates, one e-process tests the null that the discriminator-induced separation between the empirical data distribution and the generator law remains below a target level. During generator updates, with the discriminator fixed, a second e-process tests the reverse null that this separation remains above a refresh level. Conditional on the observed training sample, we prove that fresh empirical indices and latent draws yield conditional e-values that can be accumulated into e-processes, providing anytime-valid Type I error control under adaptive model updates and data-dependent switching. Across multimodal synthetic distributions and image benchmark datasets, the proposed method matches or outperforms the best fixed-ratio baselines under several widely used GAN objectives.

Noise-Free One-Step LoRA for Task-Driven Image Restoration with Diffusion Priors

Degraded images not only reduce visual quality but also impair downstream high-level vision tasks. Task-driven image restoration (TDIR) addresses this issue by jointly optimizing restoration quality and task performance. Recent works show that pretrained diffusion priors benefit TDIR, yet diffusion-based restoration is inherently stochastic, as the sampling process depends on a random noise term, which can undermine task consistency. In this paper, we show that a deterministic, noise-free one-step forward pass with pretrained diffusion priors can substantially improve TDIR, but the benefit critically depends on the adaptation module: LoRA yields consistent gains, whereas ControlNet-style conditioning does not. This enables one-step forwarding that surpasses conventional multi-step diffusion TDIR baselines. Furthermore, we introduce a task-preserving GAN training strategy that improves perceptual quality without sacrificing task performance. Extensive experiments on classification, segmentation, and detection demonstrate consistent gains over prior TDIR methods, and we further validate generalization on real-world degraded images and OCR.