arXiv:2603.02230v1 Announce Type: cross Abstract: Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such approaches often suffer from limited generalization and may impair reasoning performance. GIDD pioneers pretraining-based self-correction via a multi-step BERT-style uniform-absorbing objective. However, GIDD relies on a continuous interpolation-based pipeline with opaque interactions between uniform transitions and absorbing masks, which complicates hyperparameter tuning and hinders practical performance. In this work, we propose a Self-Correcting Discrete Diffusion (SCDD) model to reformulate pretrained self-correction with explicit state transitions and learn directly in discrete time. Our framework also simplifies the training noise schedule, eliminates a redundant remasking step, and relies exclusively on uniform transitions to learn self-correction. Experiments at the GPT-2 scale demonstrate that our method enables more efficient parallel decoding while preserving generation quality.

arXiv:2602.18515v1 Announce Type: cross Abstract: Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent PDEs via parameter evolution. The parameter updates are obtained by solving a linear system derived from the governing equation residuals at each time step. However, strong-form evolutionary approaches can yield ill-conditioned linear systems due to pointwise residual discretization, and their computational cost scales unfavorably with the number of training samples. To address these limitations, we propose a weak-form evolutionary Kolmogorov-Arnold Network (KAN) for the scalable and accurate prediction of PDE solutions. We decouple the linear system size from the number of training samples through the weak formulation, leading to improved scalability compared to strong-form approaches. We also rigorously enforce boundary conditions by constructing the trial space with boundary-constrained KANs to satisfy Dirichlet and periodic conditions, and by incorporating derivative boundary conditions directly into the weak formulation for Neumann conditions. In conclusion, the proposed weak-form evolutionary KAN framework provides a stable and scalable approach for PDEs and contributes to scientific machine learning with potential relevance to future engineering applications.