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.

MSCRS: Multi-modal Semantic Graph Prompt Learning Framework for Conversational Recommender Systems

Conversational Recommender Systems (CRSs) aim to provide personalized recommendations by interacting with users through conversations. Most existing studies of CRS focus on extracting user preferences from conversational contexts. However, due to the short and sparse nature of conversational contexts, it is difficult to fully capture user preferences by conversational contexts only. We argue that multi-modal semantic information can enrich user preference expressions from diverse dimensions (e.g., a user preference for a certain movie may stem from its magnificent visual effects and compelling storyline). In this paper, we propose a multi-modal semantic graph prompt learning framework for CRS, named MSCRS. First, we extract textual and image features of items mentioned in the conversational contexts. Second, we capture higher-order semantic associations within different semantic modalities (collaborative, textual, and image) by constructing modality-specific graph structures. Finally, we propose an innovative integration of multi-modal semantic graphs with prompt learning, harnessing the power of large language models to comprehensively explore high-dimensional semantic relationships. Experimental results demonstrate that our proposed method significantly improves accuracy in item recommendation, as well as generates more natural and contextually relevant content in response generation. We have released the code and the expanded multi-modal CRS datasets to facilitate further exploration in related research\footnote{https://github.com/BIAOBIAO12138/MSCRS-main}.

DSPFusion: Image Fusion via Degradation and Semantic Dual-Prior Guidance

Existing fusion methods are tailored for high-quality images but struggle with degraded images captured under harsh circumstances, thus limiting the practical potential of image fusion. This work presents a \textbf{D}egradation and \textbf{S}emantic \textbf{P}rior dual-guided framework for degraded image \textbf{Fusion} (\textbf{DSPFusion}), utilizing degradation priors and high-quality scene semantic priors restored via diffusion models to guide both information recovery and fusion in a unified model. In specific, it first individually extracts modality-specific degradation priors, while jointly capturing comprehensive low-quality semantic priors. Subsequently, a diffusion model is developed to iteratively restore high-quality semantic priors in a compact latent space, enabling our method to be over $20 \times$ faster than mainstream diffusion model-based image fusion schemes. Finally, the degradation priors and high-quality semantic priors are employed to guide information enhancement and aggregation via the dual-prior guidance and prior-guided fusion modules. Extensive experiments demonstrate that DSPFusion mitigates most typical degradations while integrating complementary context with minimal computational cost, greatly broadening the application scope of image fusion.

Iterative Predictor-Critic Code Decoding for Real-World Image Dehazing

We propose a novel Iterative Predictor-Critic Code Decoding framework for real-world image dehazing, abbreviated as IPC-Dehaze, which leverages the high-quality codebook prior encapsulated in a pre-trained VQGAN. Apart from previous codebook-based methods that rely on one-shot decoding, our method utilizes high-quality codes obtained in the previous iteration to guide the prediction of the Code-Predictor in the subsequent iteration, improving code prediction accuracy and ensuring stable dehazing performance. Our idea stems from the observations that 1) the degradation of hazy images varies with haze density and scene depth, and 2) clear regions play crucial cues in restoring dense haze regions. However, it is non-trivial to progressively refine the obtained codes in subsequent iterations, owing to the difficulty in determining which codes should be retained or replaced at each iteration. Another key insight of our study is to propose Code-Critic to capture interrelations among codes. The Code-Critic is used to evaluate code correlations and then resample a set of codes with the highest mask scores, i.e., a higher score indicates that the code is more likely to be rejected, which helps retain more accurate codes and predict difficult ones. Extensive experiments demonstrate the superiority of our method over state-of-the-art methods in real-world dehazing.

New Dataset and Methods for Fine-Grained Compositional Referring Expression Comprehension via Specialist-MLLM Collaboration

Referring Expression Comprehension (REC) is a foundational cross-modal task that evaluates the interplay of language understanding, image comprehension, and language-to-image grounding. To advance this field, we introduce a new REC dataset with two key features. First, it is designed with controllable difficulty levels, requiring fine-grained reasoning across object categories, attributes, and relationships. Second, it incorporates negative text and images generated through fine-grained editing, explicitly testing a model's ability to reject non-existent targets, an often-overlooked yet critical challenge in existing datasets. To address fine-grained compositional REC, we propose novel methods based on a Specialist-MLLM collaboration framework, leveraging the complementary strengths of them: Specialist Models handle simpler tasks efficiently, while MLLMs are better suited for complex reasoning. Based on this synergy, we introduce two collaborative strategies. The first, Slow-Fast Adaptation (SFA), employs a routing mechanism to adaptively delegate simple tasks to Specialist Models and complex tasks to MLLMs. Additionally, common error patterns in both models are mitigated through a target-refocus strategy. The second, Candidate Region Selection (CRS), generates multiple bounding box candidates based on Specialist Model and uses the advanced reasoning capabilities of MLLMs to identify the correct target. Extensive experiments on our dataset and other challenging compositional benchmarks validate the effectiveness of our approaches. The SFA strategy achieves a trade-off between localization accuracy and efficiency, and the CRS strategy greatly boosts the performance of both Specialist Models and MLLMs. We aim for this work to offer valuable insights into solving complex real-world tasks by strategically combining existing tools for maximum effectiveness, rather than reinventing them.

Disentangled Modeling of Preferences and Social Influence for Group Recommendation

The group recommendation (GR) aims to suggest items for a group of users in social networks. Existing work typically considers individual preferences as the sole factor in aggregating group preferences. Actually, social influence is also an important factor in modeling users' contributions to the final group decision. However, existing methods either neglect the social influence of individual members or bundle preferences and social influence together as a unified representation. As a result, these models emphasize the preferences of the majority within the group rather than the actual interaction items, which we refer to as the preference bias issue in GR. Moreover, the self-supervised learning (SSL) strategies they designed to address the issue of group data sparsity fail to account for users' contextual social weights when regulating group representations, leading to suboptimal results. To tackle these issues, we propose a novel model based on Disentangled Modeling of Preferences and Social Influence for Group Recommendation (DisRec). Concretely, we first design a user-level disentangling network to disentangle the preferences and social influence of group members with separate embedding propagation schemes based on (hyper)graph convolution networks. We then introduce a socialbased contrastive learning strategy, selectively excluding user nodes based on their social importance to enhance group representations and alleviate the group-level data sparsity issue. The experimental results demonstrate that our model significantly outperforms state-of-the-art methods on two realworld datasets.

Ultra-Low Complexity On-Orbit Compression for Remote Sensing Imagery via Block Modulated Imaging

The growing field of remote sensing faces a challenge: the ever-increasing size and volume of imagery data are exceeding the storage and transmission capabilities of satellite platforms. Efficient compression of remote sensing imagery is a critical solution to alleviate these burdens on satellites. However, existing compression methods are often too computationally expensive for satellites. With the continued advancement of compressed sensing theory, single-pixel imaging emerges as a powerful tool that brings new possibilities for on-orbit image compression. However, it still suffers from prolonged imaging times and the inability to perform high-resolution imaging, hindering its practical application. This paper advances the study of compressed sensing in remote sensing image compression, proposing Block Modulated Imaging (BMI). By requiring only a single exposure, BMI significantly enhances imaging acquisition speeds. Additionally, BMI obviates the need for digital micromirror devices and surpasses limitations in image resolution. Furthermore, we propose a novel decoding network specifically designed to reconstruct images compressed under the BMI framework. Leveraging the gated 3D convolutions and promoting efficient information flow across stages through a Two-Way Cross-Attention module, our decoding network exhibits demonstrably superior reconstruction performance. Extensive experiments conducted on multiple renowned remote sensing datasets unequivocally demonstrate the efficacy of our proposed method. To further validate its practical applicability, we developed and tested a prototype of the BMI-based camera, which has shown promising potential for on-orbit image compression. The code is available at https://github.com/Johnathan218/BMNet.

Goal-Reaching Policy Learning from Non-Expert Observations via Effective Subgoal Guidance

In this work, we address the challenging problem of long-horizon goal-reaching policy learning from non-expert, action-free observation data. Unlike fully labeled expert data, our data is more accessible and avoids the costly process of action labeling. Additionally, compared to online learning, which often involves aimless exploration, our data provides useful guidance for more efficient exploration. To achieve our goal, we propose a novel subgoal guidance learning strategy. The motivation behind this strategy is that long-horizon goals offer limited guidance for efficient exploration and accurate state transition. We develop a diffusion strategy-based high-level policy to generate reasonable subgoals as waypoints, preferring states that more easily lead to the final goal. Additionally, we learn state-goal value functions to encourage efficient subgoal reaching. These two components naturally integrate into the off-policy actor-critic framework, enabling efficient goal attainment through informative exploration. We evaluate our method on complex robotic navigation and manipulation tasks, demonstrating a significant performance advantage over existing methods. Our ablation study further shows that our method is robust to observation data with various corruptions.

Towards Real-time Video Compressive Sensing on Mobile Devices

Video Snapshot Compressive Imaging (SCI) uses a low-speed 2D camera to capture high-speed scenes as snapshot compressed measurements, followed by a reconstruction algorithm to retrieve the high-speed video frames. The fast evolving mobile devices and existing high-performance video SCI reconstruction algorithms motivate us to develop mobile reconstruction methods for real-world applications. Yet, it is still challenging to deploy previous reconstruction algorithms on mobile devices due to the complex inference process, let alone real-time mobile reconstruction. To the best of our knowledge, there is no video SCI reconstruction model designed to run on the mobile devices. Towards this end, in this paper, we present an effective approach for video SCI reconstruction, dubbed MobileSCI, which can run at real-time speed on the mobile devices for the first time. Specifically, we first build a U-shaped 2D convolution-based architecture, which is much more efficient and mobile-friendly than previous state-of-the-art reconstruction methods. Besides, an efficient feature mixing block, based on the channel splitting and shuffling mechanisms, is introduced as a novel bottleneck block of our proposed MobileSCI to alleviate the computational burden. Finally, a customized knowledge distillation strategy is utilized to further improve the reconstruction quality. Extensive results on both simulated and real data show that our proposed MobileSCI can achieve superior reconstruction quality with high efficiency on the mobile devices. Particularly, we can reconstruct a 256 X 256 X 8 snapshot compressed measurement with real-time performance (about 35 FPS) on an iPhone 15. Code is available at https://github.com/mcao92/MobileSCI.

Diffusion Models as Optimizers for Efficient Planning in Offline RL

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves $\it 3$-$\it 10 \times$ faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model