Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite significant progress, there currently exists no universal neural-based method for approximating matrix inversion. This paper presents a theoretical analysis demonstrating the fundamental limitations of neural networks in developing a generalized matrix inversion model. We expand the class of Lipschitz functions to encompass a wider array of neural network models, thereby refining our theoretical approach. Moreover, we delineate specific conditions under which neural networks can effectively approximate matrix inverses. Our theoretical results are supported by experimental results from diverse matrix datasets, exploring the efficacy of neural networks in addressing the matrix inversion challenge.

While large language models (LLMs) have made strides in understanding tabular data, current tabular evaluation benchmarks, such as WikiTableQuestions and WikiSQL, are focus on single-table scenarios, which cannot necessarily reflect the complexity of real-world applications. To bridge this gap, we present a \textbf{M}ulti-table and Multi-hop Question Answering (MMQA) dataset to assess LLMs' understanding and reasoning capabilities in handling multi-table tasks. The MMQA dataset demands that models perform multiple inferences by drawing evidence from various tables, which are designed to be connected with each other and require models to identify and utilize relationships such as foreign and primary keys. Then, we introduce a comprehensive evaluation framework that tailors to assess LLMs' capabilities in several aspects including Multi-Table Retrieval, Text-to-SQL Generation, Multi-Table QA, Primary Key Selection, and Foreign Key Selection. Finally, we propose a novel multi-table retrieval method that achieves state-of-the-art (SOTA) performance on the MMQA dataset compared to several strong baselines. Our experiment results reveal that, compared with human performance, both open-source and commercial LLMs leave significant performance room for improvements in multi-table understanding and reasoning tasks. We believe that the MMQA benchmark will enhance and facilitate LLMs' multi-table capabilities in real-world scenarios.

Recently, Mamba has made significant strides in sequence modeling, with its global receptive field, dynamic weighting strategy and linear growth in computational complexity. In remote sensing (RS) change detection (CD), several studies have demonstrated that Mambas leverage a unique scanning mechanism to traverse images from various directions, showcasing excellent long-range modeling capabilities. However, as the network depth increases, Mamba often struggle to retain shallow textures and local features effectively. In particular, modern RS images frequently capture complex surface scenes, including seasonal climate variations and densely built environments, making local contextual details crucial for effective CD. Therefore, a difference enhancement and inter-scale interactive fusion Mamba (DEIF-Mamba) is proposed to alleviate the issue. This entire network framework integrates CNN and Mamba, utilizing CNN to capture local feature information, while Mamba employs a cross-scanning mechanism to integrate global information. To address the interference caused by mixed texture features and the missed detection of subtle changes in complex scenes, a differential feature enhancement module (DFEM) is proposed to enrich local contextual details and improve feature representation. In addition, we propose an inter-scale interactive fusion (ISIF) strategy to fully utilize the cross-scale interactive information and minimize information redundancy. Extensive experiments on four CD datasets demonstrate that the proposed DEIF-Mamba achieves an average F1 of 85.87%, and shows superior performance compared with other state-of-the-art (SOTA) methods. Code will be available online (https://github.com/Jyl199904/DEIF-Mamba).

The objective of change detection (CD) is to identify the altered region between dual-temporal images. In pursuit of more precise change maps, numerous state-of-the-art (SOTA) methods design neural networks with robust discriminative capabilities. The convolutional neural network (CNN)-transformer model is specifically designed to integrate the strengths of the CNN and transformer, facilitating effective coupling of feature information. However, previous CNN-transformer studies have not effectively mitigated the interference of feature distribution differences as well as pseudovariations between two images due to cloud occlusion, imaging conditions, and other factors. In this article, we propose a domain adaptive and interactive differential attention network (DA-IDANet). This model incorporates domain adaptive constraints (DACs) to mitigate the interference of pseudovariations by mapping the two images to the same deep feature space for feature alignment. Furthermore, we designed the interactive differential attention module (IDAM), which effectively improves the feature representation and promotes the coupling of interactive differential discriminant information, thereby minimizing the impact of irrelevant information. Experiments on four datasets demonstrate the superior validity and robustness of our proposed model compared to other SOTA methods, as evident from both quantitative analysis and qualitative comparisons. The code will be available online (https://github.com/Jyl199904/DA-IDANet).

Recent progress in music generation has been remarkably advanced by the state-of-the-art MusicLM, which comprises a hierarchy of three LMs, respectively, for semantic, coarse acoustic, and fine acoustic modelings. Yet, sampling with the MusicLM requires processing through these LMs one by one to obtain the fine-grained acoustic tokens, making it computationally expensive and prohibitive for a real-time generation. Efficient music generation with a quality on par with MusicLM remains a significant challenge. In this paper, we present **M**e**L**o**D**y (**M** for music; **L** for LM; **D** for diffusion), an LM-guided diffusion model that generates music audios of state-of-the-art quality meanwhile reducing 95.7\% to 99.6\% forward passes in MusicLM, respectively, for sampling 10s to 30s music. MeLoDy inherits the highest-level LM from MusicLM for semantic modeling, and applies a novel dual-path diffusion (DPD) model and an audio VAE-GAN to efficiently decode the conditioning semantic tokens into waveform. DPD is proposed to simultaneously model the coarse and fine acoustics by incorporating the semantic information into segments of latents effectively via cross-attention at each denoising step. Our experimental results suggest the superiority of MeLoDy, not only in its practical advantages on sampling speed and infinitely continuable generation, but also in its state-of-the-art musicality, audio quality, and text correlation. Our samples are available at https://Efficient-MeLoDy.github.io/.

Nonlinear monotone transformations are used extensively in normalizing flows to construct invertible triangular mappings from simple distributions to complex ones. In existing literature, monotonicity is usually enforced by restricting function classes or model parameters and the inverse transformation is often approximated by root-finding algorithms as a closed-form inverse is unavailable. In this paper, we introduce a new integral-based approach termed: Atomic Unrestricted Time Machine (AUTM), equipped with unrestricted integrands and easy-to-compute explicit inverse. AUTM offers a versatile and efficient way to the design of normalizing flows with explicit inverse and unrestricted function classes or parameters. Theoretically, we present a constructive proof that AUTM is universal: all monotonic normalizing flows can be viewed as limits of AUTM flows. We provide a concrete example to show how to approximate any given monotonic normalizing flow using AUTM flows with guaranteed convergence. The result implies that AUTM can be used to transform an existing flow into a new one equipped with explicit inverse and unrestricted parameters. The performance of the new approach is evaluated on high dimensional density estimation, variational inference and image generation. Experiments demonstrate superior speed and memory efficiency of AUTM.

A novel active-switched-capacitor-Γ-source inverter (ASCΓSI) is proposed in this paper. Compared to other topologies, the proposed inverter uses a Γ-shape coupled inductor and active-switched-capacitor cell to realize the higher voltage-boost ability, suppress the startup current and realize the continuous input current. The voltage gain can be adjusted by varying the turns ratio nrof Γ-shape coupled inductor within the narrow range of 1r≤ 2, and increase as the turn ratios decreases, which is beneficial to lower the turn ratios in the higher gain. The corresponding topologies and steady operation principles are analyzed. The simulation and experiment results have verified the validity of the theoretical analysis.