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The expressivity of Graph Neural Networks (GNNs) can be entirely characterized by appropriate fragments of the first-order logic. Namely, any query of the two variable fragment of graded modal logic (GC2) interpreted over labeled graphs can be expressed using a GNN whose size depends only on the depth of the query. As pointed out by [Barcelo & Al., 2020, Grohe, 2021], this description holds for a family of activation functions, leaving the possibility for a hierarchy of logics expressible by GNNs depending on the chosen activation function. In this article, we show that such hierarchy indeed exists by proving that GC2 queries cannot be expressed by GNNs with polynomial activation functions. This implies a separation between polynomial and popular non-polynomial activations (such as ReLUs, sigmoid and hyperbolic tan and others) and answers an open question formulated by [Grohe, 2021].

We consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a d-uniform HSBM on N vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the N vertices into disjoint communities. In this work, we investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

Optical computing systems can provide high-speed and low-energy data processing but face deficiencies in computationally demanding training and simulation-to-reality gap. We propose a model-free solution for lightweight in situ optimization of optical computing systems based on the score gradient estimation algorithm. This approach treats the system as a black box and back-propagates loss directly to the optical weights' probabilistic distributions, hence circumventing the need for computation-heavy and biased system simulation. We demonstrate a superior classification accuracy on the MNIST and FMNIST datasets through experiments on a single-layer diffractive optical computing system. Furthermore, we show its potential for image-free and high-speed cell analysis. The inherent simplicity of our proposed method, combined with its low demand for computational resources, expedites the transition of optical computing from laboratory demonstrations to real-world applications.

In prediction settings where data are collected over time, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories. These measures can be estimated and the same approaches for inference can be applied regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics, and we illustrate their use by investigating the longitudinal importance of risk factors for suicide attempt.

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the decision we make about each edge only depends on its constant radius neighborhood. We show two applications of the algorithms: one is related to the Aldous-Lyons Conjecture, and the other is about approximating the neighborhood distribution of graphs by bounded-size graphs. The scope of our results can be extended to unimodular random graphs and networks. As a corollary, we generalize the Maximum Flow Minimum Cut Theorem to unimodular random flow networks.

Stochastic filtering is a vibrant area of research in both control theory and statistics, with broad applications in many scientific fields. Despite its extensive historical development, there still lacks an effective method for joint parameter-state estimation in SDEs. The state-of-the-art particle filtering methods suffer from either sample degeneracy or information loss, with both issues stemming from the dynamics of the particles generated to represent system parameters. This paper provides a novel and effective approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization. Our method operates in two layers: the first layer estimates the system states using a bootstrap particle filter, and the second layer marginalizes out system parameters explicitly. This strategy circumvents the need to generate particles representing system parameters, thereby mitigating their associated problems of sample degeneracy and information loss. Moreover, our method employs a modularization approach when integrating out the parameters, which significantly reduces the computational complexity. All these designs ensure the superior performance of our method. Finally, a numerical example is presented to illustrate that our method outperforms existing approaches by a large margin.

Exploring the semantic context in scene images is essential for indoor scene recognition. However, due to the diverse intra-class spatial layouts and the coexisting inter-class objects, modeling contextual relationships to adapt various image characteristics is a great challenge. Existing contextual modeling methods for indoor scene recognition exhibit two limitations: 1) During training, space-independent information, such as color, may hinder optimizing the network's capacity to represent the spatial context. 2) These methods often overlook the differences in coexisting objects across different scenes, suppressing scene recognition performance. To address these limitations, we propose SpaCoNet, which simultaneously models the Spatial relation and Co-occurrence of objects based on semantic segmentation. Firstly, the semantic spatial relation module (SSRM) is designed to explore the spatial relation among objects within a scene. With the help of semantic segmentation, this module decouples the spatial information from the image, effectively avoiding the influence of irrelevant features. Secondly, both spatial context features from the SSRM and deep features from the Image Feature Extraction Module are used to distinguish the coexisting object across different scenes. Finally, utilizing the discriminative features mentioned above, we employ the self-attention mechanism to explore the long-range co-occurrence among objects, and further generate a semantic-guided feature representation for indoor scene recognition. Experimental results on three widely used scene datasets demonstrate the effectiveness and generality of the proposed method. The code will be made publicly available after the blind review process is completed.

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is bounded from above and below. The adaptation methodology is based on extensions of Lepski's method and is over both the smoothness parameter ($s\in\mathbb{N}_{+}$) and the norm parameter ($M>0$) determining the constraints on the Sobolev space. Our results extend the non-adaptive result in \cite{green2021minimax}, established for a specific normalized graph Laplacian, to a wide class of weighted Laplacian matrices used in practice, including the unnormalized Laplacian and random walk Laplacian.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.