Gregor Kornhardt

Gregor Kornhardt, Jannis Chemseddine, Christian Wald et al.

Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their computation to the complexity of a given problem. To address these limitations, we introduce a method based on learning a Markov transition kernel that is trained on its own outputs. This design enables tokens to be remasked, allowing the model to correct its previous mistakes. Furthermore, we do not need a fixed time schedule but use a trained stopping criterion. This allows for adaptation of the number of function evaluations to the difficulty of the reasoning problem. Our adaptation adds two lightweight prediction heads, enabling reuse and fine-tuning of existing pretrained models. On the Sudoku-Extreme dataset we clearly outperform other flow based methods with a validity of 95%. For the Countdown-4 we only need in average of 10 steps to solve almost 96% of them correctly, while many problems can be solved already in 2 steps.

Muhammad Fadli Damara, Gregor Kornhardt, Peter Jung

The projected gradient descent (PGD) method has shown to be effective in recovering compressed signals described in a data-driven way by a generative model, i.e., a generator which has learned the data distribution. Further reconstruction improvements for such inverse problems can be achieved by conditioning the generator on the measurement. The boundary equilibrium generative adversarial network (BEGAN) implements an equilibrium based loss function and an auto-encoding discriminator to better balance the performance of the generator and the discriminator. In this work we investigate a network-based projected gradient descent (NPGD) algorithm for measurement-conditional generative models to solve the inverse problem much faster than regular PGD. We combine the NPGD with conditional GAN/BEGAN to evaluate their effectiveness in solving compressed sensing type problems. Our experiments on the MNIST and CelebA datasets show that the combination of measurement conditional model with NPGD works well in recovering the compressed signal while achieving similar or in some cases even better performance along with a much faster reconstruction. The achieved reconstruction speed-up in our experiments is up to 140-175.