Speculative Refinement: A Hybrid Autoregressive Diffusion Decoding Strategy and Its Behavior Across Benchmarks

How should we evaluate generation systems that combine autoregressive (AR) and diffusion decoding? We study this question through Speculative Refinement (SpecRef), a training-free hybrid method that warm-starts a masked diffusion language model from an AR draft using entropy-guided selective masking. Evaluating SpecRef across six benchmarks (HumanEval, MBPP, GSM8K, BBH, ARC-Challenge, HellaSwag) with three distinct evaluation protocols (execution-based pass@1, exact-match, log-likelihood scoring), we surface several findings relevant beyond our specific system: (1) code benchmarks conflate structural discovery with logical correctness: providing a syntactic scaffold lifts accuracy from near zero to over 20% without changing the model, indicating that much of the baseline failure is structural; (2) a refinement tension phenomenon where multi-stage correction degrades already-correct tokens, exposing benchmark saturation ceilings invisible to single-model evaluation; (3) log-likelihood and generative evaluation produce different model rankings for the same model pair, suggesting they measure different capabilities; (4) standard Python post-processing silently breaks code evaluation for non-AR generators. These observations apply to any multi-stage or non-autoregressive generation pipeline and point toward more diagnostic evaluation practices.

A Gauss-Newton Approach for Min-Max Optimization in Generative Adversarial Networks

A novel first-order method is proposed for training generative adversarial networks (GANs). It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse. The method corresponds to a fixed-point method that ensures necessary contraction. To evaluate its effectiveness, numerical experiments are conducted on various datasets commonly used in image generation tasks, such as MNIST, Fashion MNIST, CIFAR10, FFHQ, and LSUN. Our method is capable of generating high-fidelity images with greater diversity across multiple datasets. It also achieves the highest inception score for CIFAR10 among all compared methods, including state-of-the-art second-order methods. Additionally, its execution time is comparable to that of first-order min-max methods.

Angle based dynamic learning rate for gradient descent

In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed expectation of gradient-based terms, we use the angle between the current gradient and the new gradient: this new gradient is computed from the direction orthogonal to the current gradient, which further helps us in determining a better adaptive learning rate based on angle history, thereby, leading to relatively better accuracy compared to the existing state-of-the-art optimizers. On a wide variety of benchmark datasets with prominent image classification architectures such as ResNet, DenseNet, EfficientNet, and VGG, we find that our method leads to the highest accuracy in most of the datasets. Moreover, we prove that our method is convergent.