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Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of their ability to model interactions is lacking. The current paper aims to address this gap. Formalizing strength of interactions through an established measure known as separation rank, we quantify the ability of certain GNNs to model interaction between a given subset of vertices and its complement, i.e. between the sides of a given partition of input vertices. Our results reveal that the ability to model interaction is primarily determined by the partition's walk index -- a graph-theoretical characteristic defined by the number of walks originating from the boundary of the partition. Experiments with common GNN architectures corroborate this finding. As a practical application of our theory, we design an edge sparsification algorithm named Walk Index Sparsification (WIS), which preserves the ability of a GNN to model interactions when input edges are removed. WIS is simple, computationally efficient, and in our experiments has markedly outperformed alternative methods in terms of induced prediction accuracy. More broadly, it showcases the potential of improving GNNs by theoretically analyzing the interactions they can model.

Vision-language (VL) understanding tasks evaluate models' comprehension of complex visual scenes through multiple-choice questions. However, we have identified two dataset biases that models can exploit as shortcuts to resolve various VL tasks correctly without proper understanding. The first type of dataset bias is \emph{Unbalanced Matching} bias, where the correct answer overlaps the question and image more than the incorrect answers. The second type of dataset bias is \emph{Distractor Similarity} bias, where incorrect answers are overly dissimilar to the correct answer but significantly similar to other incorrect answers within the same sample. To address these dataset biases, we first propose Adversarial Data Synthesis (ADS) to generate synthetic training and debiased evaluation data. We then introduce Intra-sample Counterfactual Training (ICT) to assist models in utilizing the synthesized training data, particularly the counterfactual data, via focusing on intra-sample differentiation. Extensive experiments demonstrate the effectiveness of ADS and ICT in consistently improving model performance across different benchmarks, even in domain-shifted scenarios.

Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical computation of prime factors for an integer has exponential time complexity. Quantum computing offers the potential for significantly faster computational processes compared to classical processors. In this paper, we propose a new quantum algorithm, Shallow Depth Factoring (SDF), to factor a biprime integer. SDF consists of three steps. First, it converts a factoring problem to an optimization problem without an objective function. Then, it uses a Quantum Feasibility Labeling (QFL) method to label every possible solution according to whether it is feasible or infeasible for the optimization problem. Finally, it employs the Variational Quantum Search (VQS) to find all feasible solutions. The SDF utilizes shallow-depth quantum circuits for efficient factorization, with the circuit depth scaling linearly as the integer to be factorized increases. Through minimizing the number of gates in the circuit, the algorithm enhances feasibility and reduces vulnerability to errors.

We consider transformer encoders with hard attention (in which all attention is focused on exactly one position) and strict future masking (in which each position only attends to positions strictly to its left), and prove that the class of languages recognized by these networks is exactly the star-free languages. Adding position embeddings increases the class of recognized languages to other well-studied classes. A key technique in these proofs is Boolean RASP, a variant of RASP that is restricted to Boolean values. Via the star-free languages, we relate transformers to first-order logic, temporal logic, and algebraic automata theory.

This letter proposes a scheme assisted by a reconfigurable intelligent surface (RIS) for efficient uplink traffic multiplexing between enhanced mobile broadband (eMBB) and ultra-reliable-low-latency communication (URLLC). The scheme determines two RIS configurations based only on the eMBB channel state information (CSI) available at the base station (BS). The first optimizes eMBB quality of service, while the second reduces eMBB interference in URLLC traffic by temporarily silencing the eMBB traffic. Numerical results demonstrate that this approach, relying solely on eMBB CSI and without BS coordination, can outperform the state-of-the-art preemptive puncturing by 4.9 times in terms of URLLC outage probability.

For multi-transmission rate environments, access point (AP) connection methods have been proposed for maximizing system throughput, which is the throughput of an entire system, on the basis of the cooperative behavior of users. These methods derive optimal positions for the cooperative behavior of users, which means that new users move to improve the system throughput when connecting to an AP. However, the conventional method only considers the transmission rate of new users and does not consider existing users, even though it is necessary to consider the transmission rate of all users to improve system throughput. In addition, these method do not take into account the frequency of interference between users. In this paper, we propose an AP connection method which maximizes system throughput by considering the interference between users and the initial position of all users. In addition, our proposed method can improve system throughput by about 6% at most compared to conventional methods.

We develop a probabilistic graphical model (PGM) for artificially intelligent (AI) agents to infer human beliefs during a simulated urban search and rescue (USAR) scenario executed in a Minecraft environment with a team of three players. The PGM approach makes observable states and actions explicit, as well as beliefs and intentions grounded by evidence about what players see and do over time. This approach also supports inferring the effect of interventions, which are vital if AI agents are to assist human teams. The experiment incorporates manipulations of players' knowledge, and the virtual Minecraft-based testbed provides access to several streams of information, including the objects in the players' field of view. The participants are equipped with a set of marker blocks that can be placed near room entrances to signal the presence or absence of victims in the rooms to their teammates. In each team, one of the members is given a different legend for the markers than the other two, which may mislead them about the state of the rooms; that is, they will hold a false belief. We extend previous works in this field by introducing ToMCAT, an AI agent that can reason about individual and shared mental states. We find that the players' behaviors are affected by what they see in their in-game field of view, their beliefs about the meaning of the markers, and their beliefs about which meaning the team decided to adopt. In addition, we show that ToMCAT's beliefs are consistent with the players' actions and that it can infer false beliefs with accuracy significantly better than chance and comparable to inferences made by human observers.

All-digital massive multiuser (MU) multiple-input multiple-output (MIMO) at millimeter-wave (mmWave) frequencies is a promising technology for next-generation wireless systems. Low-resolution analog-to-digital converters (ADCs) can be utilized to reduce the power consumption of all-digital basestation (BS) designs. However, simultaneously transmitting user equipments (UEs) with vastly different BS-side receive powers either drown weak UEs in quantization noise or saturate the ADCs. To address this issue, we propose high dynamic range (HDR) MIMO, a new paradigm that enables simultaneous reception of strong and weak UEs with low-resolution ADCs. HDR MIMO combines an adaptive analog spatial transform with digital equalization: The spatial transform focuses strong UEs on a subset of ADCs in order to mitigate quantization and saturation artifacts; digital equalization is then used for data detection. We demonstrate the efficacy of HDR MIMO in a massive MU-MIMO mmWave scenario that uses Householder reflections as spatial transform.

Affine frequency division multiplexing (AFDM) is an emerging multicarrier waveform that offers a potential solution for achieving reliable communication for time-varying channels. This paper proposes two maximum likelihood (ML) estimators of symbol time offset and carrier frequency offset for AFDM systems. The joint ML estimator evaluates the arrival time and frequency offset by comparing the correlations of samples. Moreover, we propose the stepwise ML estimator to reduce the complexity. The proposed estimators exploit the redundant information contained within the chirp-periodic prefix inherent in AFDM symbols, thus dispensing with any additional pilots. To further mitigate the intercarrier interference resulting from the residual frequency offset, we design a mirror-mappingbased scheme for AFDM systems. Numerical results verify the effectiveness of the proposed time and frequency offset estimation criteria and the mirror-mapping-based modulation for AFDM systems.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.