Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced datasets. While stochastic optimization of AUROC has been studied extensively, principled stochastic optimization of AUPRC has been rarely explored. In this work, we propose a principled technical method to optimize AUPRC for deep learning. Our approach is based on maximizing the averaged precision (AP), which is an unbiased point estimator of AUPRC.

Distributed learning paradigms such as federated learning often involve transmission of model updates, or gradients, over a network, thereby avoiding transmission of private data. However, it is possible for sensitive information about the training data to be revealed from such gradients. Prior works have demonstrated that labels can be revealed analytically from the last layer of certain models (e.g., ResNet), or they can be reconstructed jointly with model inputs by using Gradients Matching [1] with additional knowledge about the current state of the model. In this work, we propose a method to discover the set of labels of training samples from only the gradient of the last layer and the id to label mapping. Our method is applicable to a wide variety of model architectures across multiple domains. We demonstrate the effectiveness of our method for model training in two domains - image classification, and automatic speech recognition. Furthermore, we show that existing reconstruction techniques improve their efficacy when used in conjunction with our method. Conversely, we demonstrate that gradient quantization and sparsification can significantly reduce the success of the attack.

Graph neural networks (GNNs) have limited expressive power, failing to represent many graph classes correctly. While more expressive graph representation learning (GRL) alternatives can distinguish some of these classes, they are significantly harder to implement, may not scale well, and have not been shown to outperform well-tuned GNNs in real-world tasks. Thus, devising simple, scalable, and expressive GRL architectures that also achieve real-world improvements remains an open challenge.

Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural solvers for NPC problems by introducing a new graph-based diffusion framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0,1}-vector optimization problems and leverages graph-based denoising diffusion models to generate high-quality solutions. We investigate two types of diffusion models with Gaussian and Bernoulli noise, respectively, and devise an effective inference schedule to enhance the solution quality. We evaluate our methods on two well-studied NPC combinatorial optimization problems: Traveling Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results show that DIFUSCO strongly outperforms the previous state-of-the-art neural solvers, improving the performance gap between ground-truth and neural solvers from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19% to 2.58% on TSP-10000. For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark.

Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve their tractability. However, LA and LLA are still confronted with non-trivial inefficiency issues and should rely on Kronecker-factored, diagonal, or even lastlayer approximate GGN matrices in practical use. These approximations are likely to harm the fidelity of learning outcomes. To tackle this issue, inspired by the connections between LLA and neural tangent kernels (NTKs), we develop a Nyström approximation to NTKs to accelerate LLA.