The performance of trained neural networks is robust to harsh levels of pruning.

Adversarial training is a popular method to give neural nets robustness against adversarial perturbations.

Second-order optimization has been shown to accelerate the training of deep neural networks in many applications, often yielding faster progress per iteration on the training loss compared to first-order optimizers. However, the generalization properties of second-order methods are still being debated. Theoretical investigations have proved difficult to carry out outside the tractable settings of heavily simplified model classes - thus, the relevance of existing theories to practical deep learning applications remains unclear. Similarly, empirical studies in large-scale models and real datasets are significantly confounded by the necessity to approximate second-order updates in practice. It is often unclear whether the observed generalization behaviour arises specifically from the second-order nature of the parameter updates, or instead reflects the specific structured (e.g.

However, most methods still require prior knowledge of demographics. In this study, we explore the potential for achieving fairness without compromising its utility when no prior demographics are provided to the training set, namely . We ascertain that such a fairness requirement with no prior demographic information essential promotes training losses to exhibit a Dirac delta distribution. To this end, we propose a simple but effective method named VFair to minimize the variance of training losses inside the optimal set of empirical losses. This problem is then optimized by a tailored dynamic update approach that operates in both loss and gradient dimensions, directing the model towards relatively fairer solutions while preserving its intact utility. Our experimental findings indicate that regression tasks, which are relatively unexplored from literature, can achieve significant fairness improvement through VFair regardless of any prior, whereas classification tasks usually do not because of their quantized utility measurements. The implementation of our method is publicly available at https://github.com/wxqpxw/VFair.

Vision Transformers (ViTs) have recently achieved comparable or superior performance to Convolutional neural networks (CNNs) in computer vision. This empirical breakthrough is even more remarkable since ViTs discards spatial information by mixing patch embeddings and positional encodings and do not embed any visual inductive bias (e.g.\ spatial locality). Yet, recent work showed that while minimizing their training loss, ViTs specifically learn spatially delocalized patterns. This raises a central question: how do ViTs learn this pattern by solely minimizing their training loss using gradient-based methods from \emph{random initialization}? We propose a structured classification dataset and a simplified ViT model to provide preliminary theoretical justification of this phenomenon. Our model relies on a simplified attention mechanism --the positional attention mechanism-- where the attention matrix solely depends on the positional encodings. While the problem admits multiple solutions that generalize, we show that our model implicitly learns the spatial structure of the dataset while generalizing. We finally prove that learning the structure helps to sample-efficiently transfer to downstream datasets that share the same structure as the pre-training one but with different features. We empirically verify that ViTs using only the positional attention mechanism perform similarly to the original one on CIFAR-10/100, SVHN and ImageNet.

Most reinforcement learning algorithms take advantage of an experience replay buffer to repeatedly train on samples the agent has observed in the past. Not all samples carry the same amount of significance and simply assigning equal importance to each of the samples is a naïve strategy. In this paper, we propose a method to prioritize samples based on how much we can learn from a sample. We define the learn-ability of a sample as the steady decrease of the training loss associated with this sample over time. We develop an algorithm to prioritize samples with high learn-ability, while assigning lower priority to those that are hard-to-learn, typically caused by noise or stochasticity. We empirically show that across multiple domains our method is more robust than random sampling and also better than just prioritizing with respect to the training loss, i.e. the temporal difference loss, which is used in prioritized experience replay.

Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have emerged as one of the most powerful classes of generative models for high-dimensional data, achieving state-of-the-art performance in image synthesis (Dhariwal and Nichol, 2021; Rombach et al., 2022) and other tasks such as action generation in robotic or protein design (Watson et al., 2023; Chi et al., 2025). However, sampling from these models is typically slow: many reverse-time steps are required to transform an initial Gaussian sample into a high-quality sample in data space (Ho et al., 2020; Song et al., 2020). This computational cost is especially problematic, and it restricts the practical deployment of diffusion models in real-time or resource-constrained settings (Salimans and Ho, 2022; Lu et al., 2022). Recent theoretical and empirical studies suggest that this inefficiency is closely related to a dynamical phase transition (bifurcation) that occurs during the reverse process (Raya and Ambrogioni, 2024; Biroli et al., 2024; Ambrogioni, 2025). In the early reverse steps, the trajectories stay near a stable fixed point whose distribution is close to the initial independent Gaussian, and little structure is present in the samples.