Syzygy of Thoughts: Improving LLM CoT with the Minimal Free Resolution

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Multi-Modal Hypergraph Enhanced LLM Learning for Recommendation

The burgeoning presence of Large Language Models (LLM) is propelling the development of personalized recommender systems. Most existing LLM-based methods fail to sufficiently explore the multi-view graph structure correlations inherent in recommendation scenarios. To this end, we propose a novel framework, Hypergraph Enhanced LLM Learning for multimodal Recommendation (HeLLM), designed to equip LLMs with the capability to capture intricate higher-order semantic correlations by fusing graph-level contextual signals with sequence-level behavioral patterns. In the recommender pre-training phase, we design a user hypergraph to uncover shared interest preferences among users and an item hypergraph to capture correlations within multimodal similarities among items. The hypergraph convolution and synergistic contrastive learning mechanism are introduced to enhance the distinguishability of learned representations. In the LLM fine-tuning phase, we inject the learned graph-structured embeddings directly into the LLM's architecture and integrate sequential features capturing each user's chronological behavior. This process enables hypergraphs to leverage graph-structured information as global context, enhancing the LLM's ability to perceive complex relational patterns and integrate multimodal information, while also modeling local temporal dynamics. Extensive experiments demonstrate the superiority of our proposed method over state-of-the-art baselines, confirming the advantages of fusing hypergraph-based context with sequential user behavior in LLMs for recommendation.

Wireless Hallucination in Generative AI-enabled Communications: Concepts, Issues, and Solutions

Generative AI (GenAI) is driving the intelligence of wireless communications. Due to data limitations, random generation, and dynamic environments, GenAI may generate channel information or optimization strategies that violate physical laws or deviate from actual real-world requirements. We refer to this phenomenon as wireless hallucination, which results in invalid channel information, spectrum wastage, and low communication reliability but remains underexplored. To address this gap, this article provides a comprehensive concept of wireless hallucinations in GenAI-driven communications, focusing on hallucination mitigation. Specifically, we first introduce the fundamental, analyze its causes based on the GenAI workflow, and propose mitigation solutions at the data, model, and post-generation levels. Then, we systematically examines representative hallucination scenarios in GenAI-enabled communications and their corresponding solutions. Finally, we propose a novel integrated mitigation solution for GenAI-based channel estimation. At the data level, we establish a channel estimation hallucination dataset and employ generative adversarial networks (GANs)-based data augmentation. Additionally, we incorporate attention mechanisms and large language models (LLMs) to enhance both training and inference performance. Experimental results demonstrate that the proposed hybrid solutions reduce the normalized mean square error (NMSE) by 0.19, effectively reducing wireless hallucinations.

Sensing-Assisted Channel Estimation for OFDM ISAC Systems: Framework, Algorithm, and Analysis

Integrated sensing and communication (ISAC) has garnered significant attention in recent years. In this paper, we delve into the topic of sensing-assisted communication within ISAC systems. More specifically, a novel sensing-assisted channel estimation scheme is proposed for bistatic orthogonal-frequency-division-multiplexing (OFDM) ISAC systems. A framework of sensing-assisted channel estimator is first developed, integrating a tailored low-complexity sensing algorithm to facilitate real-time channel estimation and decoding. To address the potential sensing errors caused by low-complexity sensing algorithms, a sensing-assisted linear minimum mean square error (LMMSE) estimation algorithm is then developed. This algorithm incorporates tolerance factors designed to account for deviations between estimated and true channel parameters, enabling the construction of robust correlation matrices for LMMSE estimation. Additionally, we establish a systematic mechanism for determining these tolerance factors. A comprehensive analysis of the normalized mean square error (NMSE) performance and computational complexity is finally conducted, providing valuable insights into the selection of the estimator's parameters. The effectiveness of our proposed scheme is validated by extensive simulations. Compared to existing methods, our proposed scheme demonstrates superior performance, particularly in high signal-to-noise ratio (SNR) regions or with large bandwidths, while maintaining low computational complexity.

Efficient Feature Fusion for UAV Object Detection

Object detection in unmanned aerial vehicle (UAV) remote sensing images poses significant challenges due to unstable image quality, small object sizes, complex backgrounds, and environmental occlusions. Small objects, in particular, occupy minimal portions of images, making their accurate detection highly difficult. Existing multi-scale feature fusion methods address these challenges to some extent by aggregating features across different resolutions. However, these methods often fail to effectively balance classification and localization performance for small objects, primarily due to insufficient feature representation and imbalanced network information flow. In this paper, we propose a novel feature fusion framework specifically designed for UAV object detection tasks to enhance both localization accuracy and classification performance. The proposed framework integrates hybrid upsampling and downsampling modules, enabling feature maps from different network depths to be flexibly adjusted to arbitrary resolutions. This design facilitates cross-layer connections and multi-scale feature fusion, ensuring improved representation of small objects. Our approach leverages hybrid downsampling to enhance fine-grained feature representation, improving spatial localization of small targets, even under complex conditions. Simultaneously, the upsampling module aggregates global contextual information, optimizing feature consistency across scales and enhancing classification robustness in cluttered scenes. Experimental results on two public UAV datasets demonstrate the effectiveness of the proposed framework. Integrated into the YOLO-V10 model, our method achieves a 2\% improvement in average precision (AP) compared to the baseline YOLO-V10 model, while maintaining the same number of parameters. These results highlight the potential of our framework for accurate and efficient UAV object detection.

UFGraphFR: An attempt at a federated recommendation system based on user text characteristics

Federated learning has become an important research area in 'private computing' due to the 'useable invisibility' of data during training. Inspired by Federated learning, the federated recommendation system has gradually become a new recommendation service architecture that can protect users' privacy. The use of user diagrams to enhance federated recommendations is a promising topic. How to use user diagrams to enhance federated recommendations is a promising research topic. However, it's a great challenge to construct a user diagram without compromising privacy in a federated learning scenario. Inspired by the simple idea that similar users often have the same attribute characteristics, we propose a personalized federated recommendation algorithm based on the user relationship graph constructed by the user text characteristics(Graph Federation Recommendation System based on User Text description Features, UFGraphFR). The method uses the embedding layer weight of the user's text feature description to construct the user relationship graph. It introduces the Transformer mechanism to capture the sequence modeling of the user's historical interaction sequence. Without access to user history interactions and specific user attributes, the federal learning privacy protection of data 'useable invisibility' is embodied. Preliminary experiments on some benchmark datasets demonstrate the superior performance of UFGraphFR. Our experiments show that this model can protect user privacy to some extent without affecting the performance of the recommendation system. The code will be easily available on https://github.com/trueWangSyutung/UFGraphFR.

Fundamental MMSE-Rate Performance Limits of Integrated Sensing and Communication Systems

Integrated sensing and communication (ISAC) demonstrates promise for 6G networks; yet its performance limits, which require addressing functional Pareto stochastic optimizations, remain underexplored. Existing works either overlook the randomness of ISAC signals or approximate ISAC limits from sensing and communication (SAC) optimum-achieving strategies, leading to loose bounds. In this paper, ISAC limits are investigated by considering a random ISAC signal designated to simultaneously estimate the sensing channel and convey information over the communication channel, adopting the modified minimum-mean-square-error (MMSE), a metric defined in accordance with the randomness of ISAC signals, and the Shannon rate as respective SAC metrics. First, conditions for optimal channel input and output distributions on the MMSE-Rate limit are derived employing variational approaches, leading to high-dimensional convolutional equations. Second, leveraging variational conditions, a Blahut-Arimoto-type algorithm is proposed to numerically determine optimal distributions and SAC performance, with its convergence to the limit proven. Third, closed-form SAC-optimal waveforms are derived, characterized by power allocation according to channel statistics/realization and waveform selection; existing methods to establish looser ISAC bounds are rectified. Finally, a compound signaling strategy is introduced for coincided SAC channels, which employs sequential SAC-optimal waveforms for channel estimation and data transmission, showcasing significant rate improvements over non-coherent "capacity". This study systematically investigates ISAC performance limits from joint estimation- and information-theoretic perspectives, highlighting key SAC tradeoffs and potential ISAC design benefits. The methodology readily extends to various metrics, such as estimation rate and the Cramer-Rao Bound.

Generative AI Enabled Matching for 6G Multiple Access

In wireless networks, applying deep learning models to solve matching problems between different entities has become a mainstream and effective approach. However, the complex network topology in 6G multiple access presents significant challenges for the real-time performance and stability of matching generation. Generative artificial intelligence (GenAI) has demonstrated strong capabilities in graph feature extraction, exploration, and generation, offering potential for graph-structured matching generation. In this paper, we propose a GenAI-enabled matching generation framework to support 6G multiple access. Specifically, we first summarize the classical matching theory, discuss common GenAI models and applications from the perspective of matching generation. Then, we propose a framework based on generative diffusion models (GDMs) that iteratively denoises toward reward maximization to generate a matching strategy that meets specific requirements. Experimental results show that, compared to decision-based AI approaches, our framework can generate more effective matching strategies based on given conditions and predefined rewards, helping to solve complex problems in 6G multiple access, such as task allocation.

HRGR: Enhancing Image Manipulation Detection via Hierarchical Region-aware Graph Reasoning

Image manipulation detection is to identify the authenticity of each pixel in images. One typical approach to uncover manipulation traces is to model image correlations. The previous methods commonly adopt the grids, which are fixed-size squares, as graph nodes to model correlations. However, these grids, being independent of image content, struggle to retain local content coherence, resulting in imprecise detection. To address this issue, we describe a new method named Hierarchical Region-aware Graph Reasoning (HRGR) to enhance image manipulation detection. Unlike existing grid-based methods, we model image correlations based on content-coherence feature regions with irregular shapes, generated by a novel Differentiable Feature Partition strategy. Then we construct a Hierarchical Region-aware Graph based on these regions within and across different feature layers. Subsequently, we describe a structural-agnostic graph reasoning strategy tailored for our graph to enhance the representation of nodes. Our method is fully differentiable and can seamlessly integrate into mainstream networks in an end-to-end manner, without requiring additional supervision. Extensive experiments demonstrate the effectiveness of our method in image manipulation detection, exhibiting its great potential as a plug-and-play component for existing architectures.

Generative Diffusion Model-based Downscaling of Observed Sea Surface Height over Kuroshio Extension since 2000

Satellite altimetry has been widely utilized to monitor global sea surface dynamics, enabling investigation of upper ocean variability from basin-scale to localized eddy ranges. However, the sparse spatial resolution of observational altimetry limits our understanding of oceanic submesoscale variability, prevalent at horizontal scales below 0.25o resolution. Here, we introduce a state-of-the-art generative diffusion model to train high-resolution sea surface height (SSH) reanalysis data and demonstrate its advantage in observational SSH downscaling over the eddy-rich Kuroshio Extension region. The diffusion-based model effectively downscales raw satellite-interpolated data from 0.25o resolution to 1/16o, corresponding to approximately 12-km wavelength. This model outperforms other high-resolution reanalysis datasets and neural network-based methods. Also, it successfully reproduces the spatial patterns and power spectra of satellite along-track observations. Our diffusion-based results indicate that eddy kinetic energy at horizontal scales less than 250 km has intensified significantly since 2004 in the Kuroshio Extension region. These findings underscore the great potential of deep learning in reconstructing satellite altimetry and enhancing our understanding of ocean dynamics at eddy scales.