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In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum circuits, which is constrained by the limited gate number and the presence of barren plateaus. In this work, we propose and numerically demonstrate a novel approach for VQAs, utilizing randomised quantum circuits to generate the variational wavefunction. We parameterize the distribution function of these random circuits using artificial neural networks and optimize it to find the solution. This random-circuit approach presents a trade-off between the expressive power of the variational wavefunction and time cost, in terms of the sampling cost of quantum circuits. Given a fixed gate number, we can systematically increase the expressive power by extending the quantum-computing time. With a sufficiently large permissible time cost, the variational wavefunction can approximate any quantum state with arbitrary accuracy. Furthermore, we establish explicit relationships between expressive power, time cost, and gate number for variational quantum eigensolvers. These results highlight the promising potential of the random-circuit approach in achieving a high expressive power in quantum computing.

We introduce a general technique for proving membership of search problems with exact rational solutions in PPAD, one of the most well-known classes containing total search problems with polynomial-time verifiable solutions. In particular, we construct a "pseudogate", coined the linear-OPT-gate, which can be used as a "plug-and-play" component in a piecewise-linear (PL) arithmetic circuit, as an integral component of the "Linear-FIXP" equivalent definition of the class. The linear-OPT-gate can solve several convex optimization programs, including quadratic programs, which often appear organically in the simplest existence proofs for these problems. This effectively transforms existence proofs to PPAD-membership proofs, and consequently establishes the existence of solutions described by rational numbers. Using the linear-OPT-gate, we are able to significantly simplify and generalize almost all known PPAD-membership proofs for finding exact solutions in the application domains of game theory, competitive markets, auto-bidding auctions, and fair division, as well as to obtain new PPAD-membership results for problems in these domains.

Motivated by the remarkable achievements of DETR-based approaches on COCO object detection and segmentation benchmarks, recent endeavors have been directed towards elevating their performance through self-supervised pre-training of Transformers while preserving a frozen backbone. Noteworthy advancements in accuracy have been documented in certain studies. Our investigation delved deeply into a representative approach, DETReg, and its performance assessment in the context of emerging models like $\mathcal{H}$-Deformable-DETR. Regrettably, DETReg proves inadequate in enhancing the performance of robust DETR-based models under full data conditions. To dissect the underlying causes, we conduct extensive experiments on COCO and PASCAL VOC probing elements such as the selection of pre-training datasets and strategies for pre-training target generation. By contrast, we employ an optimized approach named Simple Self-training which leads to marked enhancements through the combination of an improved box predictor and the Objects$365$ benchmark. The culmination of these endeavors results in a remarkable AP score of $59.3\%$ on the COCO val set, outperforming $\mathcal{H}$-Deformable-DETR + Swin-L without pre-training by $1.4\%$. Moreover, a series of synthetic pre-training datasets, generated by merging contemporary image-to-text(LLaVA) and text-to-image (SDXL) models, significantly amplifies object detection capabilities.

In recent years, circuit simulators and Boolean satisfiability (SAT) solvers have been tightly integrated to provide efficient logic synthesis and verification. Circuit simulation can generate highly expressive simulation patterns that can either enumerate or filter out most candidates for synthesis. Subsequently, SAT solvers are employed to check those that remain, thereby making the logic synthesis process more efficient. This paper introduces a novel circuit simulator of k-input lookup table (k-LUT) networks, based on semi-tensor product (STP). STP-based simulators use computation of logic matrices, the primitives of logic networks, as opposed to relying on bitwise logic operations for simulation of k-LUT networks. Experimental results show that our STP-based simulator reduces the runtime by an average of 7.2x. Furthermore, we integrate this proposed simulator into a SAT-sweeping engine known as SAT sweeper. Through a combination of structural hashing, simulation, and SAT queries, SAT sweeper simplifies logic networks by systematically merging graph vertices from input to output. To enhance the efficiency, we used STP-based exhaustive simulation, which significantly reduces the number of false equivalence class candidates, thereby improving the computational efficiency by reducing the number of SAT calls required. When compared to the SOTA SAT sweeper, our method demonstrates an average 35% runtime reduction.

We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior distributions in Bayesian inference of matrix-valued parameters, for example belonging to either the Stiefel or the Grassmann manifold. Our method, called geodesic slice sampling, is reversible with respect to the distribution of interest, and generalizes Hit-and-run slice sampling on $\mathbb{R}^{d}$ to Riemannian manifolds by using geodesics instead of straight lines. We demonstrate the robustness of our sampler's performance compared to other MCMC methods dealing with manifold valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate its remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning.

In the domain of Mobility Data Science, the intricate task of interpreting models trained on trajectory data, and elucidating the spatio-temporal movement of entities, has persistently posed significant challenges. Conventional XAI techniques, although brimming with potential, frequently overlook the distinct structure and nuances inherent within trajectory data. Observing this deficiency, we introduced a comprehensive framework that harmonizes pivotal XAI techniques: LIME (Local Interpretable Model-agnostic Explanations), SHAP (SHapley Additive exPlanations), Saliency maps, attention mechanisms, direct trajectory visualization, and Permutation Feature Importance (PFI). Unlike conventional strategies that deploy these methods singularly, our unified approach capitalizes on the collective efficacy of these techniques, yielding deeper and more granular insights for models reliant on trajectory data. In crafting this synthesis, we effectively address the multifaceted essence of trajectories, achieving not only amplified interpretability but also a nuanced, contextually rich comprehension of model decisions. To validate and enhance our framework, we undertook a survey to gauge preferences and reception among various user demographics. Our findings underscored a dichotomy: professionals with academic orientations, particularly those in roles like Data Scientist, IT Expert, and ML Engineer, showcased a profound, technical understanding and often exhibited a predilection for amalgamated methods for interpretability. Conversely, end-users or individuals less acquainted with AI and Data Science showcased simpler inclinations, such as bar plots indicating timestep significance or visual depictions pinpointing pivotal segments of a vessel's trajectory.

There is a fast-growing body of research on predicting future links in dynamic networks, with many new algorithms. Some benchmark data exists, and performance evaluations commonly rely on comparing the scores of observed network events (positives) with those of randomly generated ones (negatives). These evaluation measures depend on both the predictive ability of the model and, crucially, the type of negative samples used. Besides, as generally the case with temporal data, prediction quality may vary over time. This creates a complex evaluation space. In this work, we catalog the possibilities for negative sampling and introduce novel visualization methods that can yield insight into prediction performance and the dynamics of temporal networks. We leverage these visualization tools to investigate the effect of negative sampling on the predictive performance, at the node and edge level. We validate empirically, on datasets extracted from recent benchmarks that the error is typically not evenly distributed across different data segments. Finally, we argue that such visualization tools can serve as powerful guides to evaluate dynamic link prediction methods at different levels.

This paper studies the one-shot behavior of no-regret algorithms for stochastic bandits. Although many algorithms are known to be asymptotically optimal with respect to the expected regret, over a single run, their pseudo-regret seems to follow one of two tendencies: it is either smooth or bumpy. To measure this tendency, we introduce a new notion: the sliding regret, that measures the worst pseudo-regret over a time-window of fixed length sliding to infinity. We show that randomized methods (e.g. Thompson Sampling and MED) have optimal sliding regret, while index policies, although possibly asymptotically optimal for the expected regret, have the worst possible sliding regret under regularity conditions on their index (e.g. UCB, UCB-V, KL-UCB, MOSS, IMED etc.). We further analyze the average bumpiness of the pseudo-regret of index policies via the regret of exploration, that we show to be suboptimal as well.

Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.