Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4 6%) and computation time (8 10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.

Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model's performance. While prior works have demonstrated the benefits of specific heuristic retraining schemes, the question of how to optimally combine the model's predictions and the provided labels remains largely open.

We introduce a simple yet powerful framework for training large language models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we propose a perturbation-based procedure that first transforms the prefix into a semantic neighbor and then conditions on this perturbed variant for next-token prediction. This yields a hierarchical model with a pre-post-additive noise structure. Within this framework, we develop a rigorous theory of extrapolability, namely, the capacity of a model class to make reliable predictions for token sequences that lie outside the empirical support of the training corpus. We evaluate the finite-sample performance of the proposed procedure using both synthetic and real-world language data. Results show that the proposed method consistently improves out-of-support prediction while maintaining competitive in-support performance, demonstrating that perturbation offers a practical route to language modeling.

Though achieving excellent performance in some cases, current unsupervised learning methods for single image denoising usually have constraints in applications. In this paper, we propose a new approach which is more general and applicable to complicated noise models. Utilizing the property of score function, the gradient of logarithmic probability, we define a solving system for denoising. Once the score function of noisy images has been estimated, the denoised result can be obtained through the solving system. Our approach can be applied to multiple noise models, such as the mixture of multiplicative and additive noise combined with structured correlation. Experimental results show that our method is comparable when the noise model is simple, and has good performance in complicated cases where other methods are not applicable or perform poorly.

Here we briefly consider why introducing a prior over the factor matrix enables automatic relevance determination. These ideas reflect results by Bishop [1] and our experiments in Section 3.1. For simplicity, we will first consider the case of factor analysis where p(X) = Q d,tN(xdt; 0,1).

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of loglikelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

We show that Deep Neural Networks introduce two heteroscedastic Gumbel noise sources into Q-Learning. To account for these noise sources, we propose Double Gumbel Q-Learning, a Deep Q-Learning algorithm applicable for both discrete and continuous control. In discrete control, we derive a closed-form expression for the loss function of our algorithm. In continuous control, this loss function is intractable and we therefore derive an approximation with a hyperparameter whose value regulates pessimism in Q-Learning. We present a default value for our pessimism hyperparameter that enables DoubleGum to outperform DDPG, TD3, SAC, XQL, quantile regression, and Mixture-of-Gaussian Critics in aggregate over 33 tasks from DeepMind Control, MuJoCo, MetaWorld, and Box2D and show that tuning this hyperparameter may further improve sample efficiency.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/