dual-discriminator training

This work addresses the lack of theoretical guarantees for generalization in existing discriminator-guided generative models. Building upon the strong duality of f-divergences, we propose a universal discriminator-guided refinement framework that enhances the generalization capability of any generative model, including diffusion models. We provide the first theoretical proof that this guidance mechanism provably reduces the generalization gap and establish a quantitative relationship between the gap reduction and the Rademacher complexity of the discriminator class. Furthermore, our framework offers a unified theoretical explanation for the empirical success of recent score-based diffusion methods. While maintaining broad applicability, the proposed approach delivers rigorous theoretical justification for widely used yet previously heuristic refinement strategies.

To address mode collapse in generative adversarial networks (GANs), this paper proposes the dual-discriminator α-GAN and establishes a generalized dual-discriminator GAN framework based on arbitrary convex functions defined on the positive reals. Theoretically, we prove that its optimization objective is equivalent to a weighted sum of an $f$-divergence and its inverse, thereby embedding the α-loss into the dual-discriminator architecture for the first time. This unifies and substantially extends the theoretical foundations of existing dual-discriminator approaches. Training proceeds via min-max collaborative optimization with tunable loss functions, ensuring stability. Experiments on 2D synthetic data demonstrate that the proposed method significantly improves training stability and generation diversity, consistently outperforming baseline models across multiple quantitative metrics.

To address the susceptibility of gradient-based optimization to local minima in two-layer neural networks under few-shot function approximation, this paper proposes a generative latent-feature initialization method. Specifically, it employs a deep generative model to learn a prior distribution over hidden-layer weights—replacing conventional random initialization—and integrates latent-space gradient fine-tuning with noise-robust ℓ₂ regularization; the output layer is solved in closed form via linear least squares. The approach preserves model lightness (i.e., few hidden units) while substantially improving generalization accuracy and training stability. Numerical experiments demonstrate consistent superiority over standard initialization schemes across multiple few-data benchmarks. This work establishes a new paradigm for reliable function approximation with shallow networks in data-scarce regimes.

This study systematically investigates the generalization mechanisms of Generative Flow Networks (GFlowNets) in discrete spaces. To rigorously test generalization hypotheses, we introduce a graph-structured benchmark environment with tunable reward difficulty, enabling exact computation of the true distribution $p(x)$ and precise quantification of generalization error. Methodologically, we establish a unified training–evaluation framework to conduct offline and off-policy generalization analysis, as well as experiments on implicit reward robustness. Our key contributions are threefold: (1) We empirically demonstrate that GFlowNet generalization arises from implicit structural priors encoded in the learned flow function—not from explicit regularization; (2) We reveal high sensitivity to training distribution shift, yet strong robustness to perturbations in implicit reward signals; (3) We challenge the prevailing assumption that GFlowNets inherently generalize better than alternatives, providing new empirical foundations and design insights for generalization theory in discrete generative modeling.

This work investigates the intrinsic relationship between generalization performance and optimization stability in Free Adversarial Training (FreeAT). Addressing the large generalization gap and poor training stability inherent in standard adversarial training, we first establish—within the algorithmic stability framework—that FreeAT achieves a tighter generalization error bound by jointly optimizing perturbations and model parameters. We further reveal that its synchronous min-max optimization mechanism is critical for narrowing the train-test accuracy gap. Theoretical analysis demonstrates that FreeAT’s generalization upper bound is significantly lower than that of standard adversarial training. Empirical evaluation confirms that, under identical iteration budgets, FreeAT consistently reduces the generalization gap by 15–22% across diverse benchmarks. Our implementation is publicly available.

Adversarial training (AT) suffers from degraded natural accuracy and poor cross-attack robustness generalization. To address these challenges, we propose a multi-task collaborative generalization framework that decomposes global robust learning into multiple specialized subtasks, each optimized by a dedicated base learner. Knowledge fusion and co-evolution between base learners and the global model are achieved via dynamic parameter interpolation, gradient synchronization, and periodic task reallocation—without incurring additional inference overhead. The framework supports three lightweight variants for diverse deployment scenarios. Theoretical analysis shows that our method reduces generalization error. Empirically, it achieves average improvements of 2.1% in natural accuracy and 3.7% in robust accuracy across multiple adversarial attacks, significantly outperforming baselines including PGD-AT and TRADES. This work advances the development of general-purpose robust classifiers.

This work addresses the instability in semi-supervised GAN training caused by the inherent conflict between maximizing classification accuracy and enhancing the discriminator’s ability to distinguish real from fake samples. To resolve this, the study introduces a multi-objective evolutionary algorithm into the training framework for the first time, formulating discriminator optimization as a multi-objective problem. By leveraging population-based evolutionary strategies and Pareto dominance, the method preserves a diverse set of non-dominated solutions without resorting to scalar loss aggregation. Evaluated on label-limited MNIST, the approach significantly improves training stability, and its elite variant achieves state-of-the-art classification accuracy, outperforming baseline models such as SSL-GAN and CE-SSL-GAN.

This work presents the first systematic survey and critical analysis of neural architecture search (NAS) methods tailored for generative adversarial networks (GANs), addressing the inefficiency and instability of manual GAN design, which often struggles to balance performance and generalization. The study organizes existing approaches through a structured comparison based on search strategies, evaluation metrics, and empirical performance. It advocates moving beyond conventional Inception Score (IS) and Fréchet Inception Distance (FID) toward more robust evaluation frameworks and diverse datasets. The analysis further highlights the complementary strengths of evolutionary algorithms and gradient-based methods across different scenarios. By clarifying the current limitations and untapped potential of NAS-GAN methodologies, this work establishes a foundation for future research and advances the standardization and performance of automated GAN architecture design.

This work addresses the inherent trade-offs among generation efficiency, training stability, and mapping interpretability in generative modeling by unifying adversarial generative networks (GANs) and normalizing flows. We propose the Adversarial Flow Model (AFM), which directly learns a deterministic optimal transport map from latent noise space to data space—eliminating stochasticity and iterative refinement, and enabling one-step (1-NFE) end-to-end generation. AFM incorporates a deep repeated architecture and an adversarial training objective to ensure convergence and gradient stability in deep networks. On ImageNet-256, the 1-NFE variant achieves a Fréchet Inception Distance (FID) of 2.38; deeper variants with 56 and 112 layers attain FIDs of 2.08 and 1.94, respectively—surpassing Consistency Models XL/2 and leading multi-step methods. To our knowledge, AFM is the first framework to achieve state-of-the-art performance in single-step generative modeling.

Existing methods struggle to generate conditional risk scenarios aligned with downstream risk objectives. This work proposes a Generative Adversarial Regression (GAR) framework that extends the elicitable regression properties of risk functionals—such as Value-at-Risk (VaR) and Expected Shortfall (ES)—from point prediction to generative modeling. GAR jointly optimizes a conditional generator and a strategy-aware discriminator through a minimax adversarial mechanism, ensuring risk consistency across a broad class of strategies without requiring a pre-specified set of candidate policies. The framework robustly produces scenarios that faithfully align with the true underlying risk distribution. Empirical experiments on S&P 500 data demonstrate that GAR-generated scenarios significantly outperform unconditional, econometric, and direct prediction baselines in terms of downstream risk accuracy, while maintaining stability under adversarial strategies.