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We consider the incomplete multi-graph matching problem, which is a generalization of the NP-hard quadratic assignment problem for matching multiple finite sets. Multi-graph matching plays a central role in computer vision, e.g., for matching images or shapes, so that a number of dedicated optimization techniques have been proposed. While the closely related NP-hard multi-dimensional assignment problem (MDAP) has been studied for decades in the operations research community, it only considers complete matchings and has a different cost structure. We bridge this gap and transfer well-known approximation algorithms for the MDAP to incomplete multi-graph matching. To this end, we revisit respective algorithms, adapt them to incomplete multi-graph matching, and propose their extended and parallelized versions. Our experimental validation shows that our new method substantially outperforms the previous state of the art in terms of objective and runtime. Our algorithm matches, for example, 29 images with more than 500 keypoints each in less than two minutes, whereas the fastest considered competitor requires at least half an hour while producing far worse results.

The waste of electrical and electronic equipment has been increased due to the fast evolution of technology products and competition of many IT sectors. Every year millions of tons of electronic waste are thrown into the environment which causes high consequences for human health. Therefore, it is crucial to control this waste flow using technology, especially using Artificial Intelligence but also reclamation of critical raw materials for new production processes. In this paper, we focused on the measurement of recyclability of waste electronic components (WECs) from waste printed circuit boards (WPCBs) using mathematical innovation model. This innovative approach evaluates both the recyclability and recycling difficulties of WECs, integrating an AI model for improved disassembly and sorting. Assessing the recyclability of individual electronic components present on WPCBs provides insight into the recovery potential of valuable materials and indicates the level of complexity involved in recycling in terms of economic worth and production utility. This novel measurement approach helps AI models in accurately determining the number of classes to be identified and sorted during the automated disassembly of discarded PCBs. It also facilitates the model in iterative training and validation of individual electronic components.

The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern sequences, which count the occurrences of a finite number of different patterns in the expansion of positive integers in any integer base, and analyze their partial sums.

Retrieval augmented generation (RAG) exhibits outstanding performance in promoting the knowledge capabilities of large language models (LLMs) with retrieved documents related to user queries. However, RAG only focuses on improving the response quality of LLMs via enhancing queries indiscriminately with retrieved information, paying little attention to what type of knowledge LLMs really need to answer original queries more accurately. In this paper, we suggest that long-tail knowledge is crucial for RAG as LLMs have already remembered common world knowledge during large-scale pre-training. Based on our observation, we propose a simple but effective long-tail knowledge detection method for LLMs. Specifically, the novel Generative Expected Calibration Error (GECE) metric is derived to measure the ``long-tailness'' of knowledge based on both statistics and semantics. Hence, we retrieve relevant documents and infuse them into the model for patching knowledge loopholes only when the input query relates to long-tail knowledge. Experiments show that, compared to existing RAG pipelines, our method achieves over 4x speedup in average inference time and consistent performance improvement in downstream tasks.

In the realm of deep learning, the Kolmogorov-Arnold Network (KAN) has emerged as a potential alternative to multilayer projections (MLPs). However, its applicability to vision tasks has not been extensively validated. In our study, we demonstrated the effectiveness of KAN for vision tasks through multiple trials on the MNIST, CIFAR10, and CIFAR100 datasets, using a training batch size of 32. Our results showed that while KAN outperformed the original MLP-Mixer on CIFAR10 and CIFAR100, it performed slightly worse than the state-of-the-art ResNet-18. These findings suggest that KAN holds significant promise for vision tasks, and further modifications could enhance its performance in future evaluations.Our contributions are threefold: first, we showcase the efficiency of KAN-based algorithms for visual tasks; second, we provide extensive empirical assessments across various vision benchmarks, comparing KAN's performance with MLP-Mixer, CNNs, and Vision Transformers (ViT); and third, we pioneer the use of natural KAN layers in visual tasks, addressing a gap in previous research. This paper lays the foundation for future studies on KANs, highlighting their potential as a reliable alternative for image classification tasks.

We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived from the paraxial Helmholtz equation and relate phase information to the intensity. The TIE is usually favored since the TPE is nonlinear. The main contribution of this paper is that we discuss situations in which it is possible to use the two equations in a hybrid manner: We show that 2-dimensional phase information retrieved by the TIE can be used as initial data for the TPE, enabling the acquisition of 3-dimensional phase information. The latter is solved using the method of characteristic and viscosity methods. Both the TIE and the viscosity method are numerically implemented with finite element methods.

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organisation of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. Fabric anisotropy originates from observed yarn-yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides a design space of knitted fabrics to embed functionalities by varying geometric configuration and material property in instructed procedures compatible to machine manufacturing. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.

This paper investigates the information theoretic limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter either jointly or independently send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is also available at the RIS and can be modulated through the adjustable phases at the RIS, significant improvement in the {degree-of-freedom} (DoF) of the overall channel is possible. For example, for an RIS system in which the signals are reflected from a transmitter with $M$ antennas to a receiver with $K$ antennas through an RIS with $N$ reflective elements, assuming no direct path between the transmitter and the receiver, joint transmission of the transmitter and the RIS can achieve a DoF of $\min\left(M+\frac{N}{2}-\frac{1}{2},N,K\right)$ as compared to the DoF of $\min(M,K)$ for the conventional multiple-input multiple-output (MIMO) channel. This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noise and by using results for characterizing the information dimension under projection. The result is further extended to the case with a direct path between the transmitter and the receiver, and also to the multiple access scenario, in which the transmitter and the RIS send independent information. Finally, this paper proposes a symbol-level precoding approach for modulating data through the phases of the RIS, and provides numerical simulation results to verify the theoretical DoF results.

Explainable Artificial Intelligence (XAI) is transforming the field of Artificial Intelligence (AI) by enhancing the trust of end-users in machines. As the number of connected devices keeps on growing, the Internet of Things (IoT) market needs to be trustworthy for the end-users. However, existing literature still lacks a systematic and comprehensive survey work on the use of XAI for IoT. To bridge this lacking, in this paper, we address the XAI frameworks with a focus on their characteristics and support for IoT. We illustrate the widely-used XAI services for IoT applications, such as security enhancement, Internet of Medical Things (IoMT), Industrial IoT (IIoT), and Internet of City Things (IoCT). We also suggest the implementation choice of XAI models over IoT systems in these applications with appropriate examples and summarize the key inferences for future works. Moreover, we present the cutting-edge development in edge XAI structures and the support of sixth-generation (6G) communication services for IoT applications, along with key inferences. In a nutshell, this paper constitutes the first holistic compilation on the development of XAI-based frameworks tailored for the demands of future IoT use cases.