Stein V ariational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm.

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

The entire process is end-to-end differentiable.

Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both function and gradient data -- on the generalization error of highly overparameterized predictive models in high dimensions. In this paper, we obtain a precise characterization of this training modality for random feature (RF) models in the limit where the number of trainable parameters, input dimensions, and training data tend proportionally to infinity. Our model for Sobolev training reflects practical implementations by sketching gradient data onto finite dimensional subspaces. By combining the replica method from statistical physics with linearizations in operator-valued free probability theory, we derive a closed-form description for the generalization errors of the trained RF models. For target functions described by single-index models, we demonstrate that supplementing function data with additional gradient data does not universally improve predictive performance. Rather, the degree of overparameterization should inform the choice of training method. More broadly, our results identify settings where models perform optimally by interpolating noisy function and gradient data.

Next-generation wireless communication systems must support ultra-reliable low-latency communication (URLLC) service for mission-critical applications. Meeting stringent URLLC requirements is challenging, especially for two-hop cooperative communication. In this paper, we develop an adaptive transmission design for a two-hop relaying communication system. Each hop transmission adaptively configures its transmission parameters separately, including numerology, mini-slot size, and modulation and coding scheme, for reliable packet transmission within a strict latency constraint. We formulate the hop-specific transceiver configuration as a Markov decision process (MDP) and propose a dual-agent reinforcement learning-based cooperative latency-aware transmission (DRL-CoLA) algorithm to learn latency-aware transmission policies in a distributed manner. Simulation results verify that the proposed algorithm achieves the near-optimal reliability while satisfying strict latency requirements.

Recent research has focused on mitigating algorithmic bias in clustering by incorporating fairness constraints into algorithmic design. Notions such as disparate impact, community cohesion, and cost per population have been implemented to enforce equitable outcomes. Among these, group fairness (balance) ensures that each protected group is proportionally represented within every cluster. However, incorporating balance as a metric of fairness into spectral clustering algorithms has led to computational times that can be improved. This study aims to enhance the efficiency of spectral clustering algorithms by reformulating the constrained optimization problem using a new formulation derived from the Lagrangian method and the Sherman-Morrison-Woodbury (SMW) identity, resulting in the Fair-SMW algorithm. Fair-SMW employs three alternatives to the Laplacian matrix with different spectral gaps to generate multiple variations of Fair-SMW, achieving clustering solutions with comparable balance to existing algorithms while offering improved runtime performance. We present the results of Fair-SMW, evaluated using the Stochastic Block Model (SBM) to measure both runtime efficiency and balance across real-world network datasets, including LastFM, FacebookNet, Deezer, and German. We achieve an improvement in computation time that is twice as fast as the state-of-the-art, and also flexible enough to achieve twice as much balance.

Graph Neural Networks (GNNs) often perform better for high-degree nodes than low-degree nodes on node classification tasks. This degree bias can reinforce social marginalization by, e.g., privileging celebrities and other high-degree actors in social networks during social and content recommendation. While researchers have proposed numerous hypotheses for why GNN degree bias occurs, we find via a survey of 38 degree bias papers that these hypotheses are often not rigorously validated, and can even be contradictory. Thus, we provide an analysis of the origins of degree bias in message-passing GNNs with different graph filters. We prove that high-degree test nodes tend to have a lower probability of misclassification regardless of how GNNs are trained. Moreover, we show that degree bias arises from a variety of factors that are associated with a node's degree (e.g., homophily of neighbors, diversity of neighbors). Furthermore, we show that during training, some GNNs may adjust their loss on low-degree nodes more slowly than on high-degree nodes; however, with sufficiently many epochs of training, message-passing GNNs can achieve their maximum possible training accuracy, which is not significantly limited by their expressive power. Throughout our analysis, we connect our findings to previously-proposed hypotheses for the origins of degree bias, supporting and unifying some while drawing doubt to others. We validate our theoretical findings on 8 common real-world networks, and based on our theoretical and empirical insights, describe a roadmap to alleviate degree bias.