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.

Safe Human Robot Navigation in Warehouse Scenario

The integration of autonomous mobile robots (AMRs) in industrial environments, particularly warehouses, has revolutionized logistics and operational efficiency. However, ensuring the safety of human workers in dynamic, shared spaces remains a critical challenge. This work proposes a novel methodology that leverages control barrier functions (CBFs) to enhance safety in warehouse navigation. By integrating learning-based CBFs with the Open Robotics Middleware Framework (OpenRMF), the system achieves adaptive and safety-enhanced controls in multi-robot, multi-agent scenarios. Experiments conducted using various robot platforms demonstrate the efficacy of the proposed approach in avoiding static and dynamic obstacles, including human pedestrians. Our experiments evaluate different scenarios in which the number of robots, robot platforms, speed, and number of obstacles are varied, from which we achieve promising performance.

Quality-focused Active Adversarial Policy for Safe Grasping in Human-Robot Interaction

Vision-guided robot grasping methods based on Deep Neural Networks (DNNs) have achieved remarkable success in handling unknown objects, attributable to their powerful generalizability. However, these methods with this generalizability tend to recognize the human hand and its adjacent objects as graspable targets, compromising safety during Human-Robot Interaction (HRI). In this work, we propose the Quality-focused Active Adversarial Policy (QFAAP) to solve this problem. Specifically, the first part is the Adversarial Quality Patch (AQP), wherein we design the adversarial quality patch loss and leverage the grasp dataset to optimize a patch with high quality scores. Next, we construct the Projected Quality Gradient Descent (PQGD) and integrate it with the AQP, which contains only the hand region within each real-time frame, endowing the AQP with fast adaptability to the human hand shape. Through AQP and PQGD, the hand can be actively adversarial with the surrounding objects, lowering their quality scores. Therefore, further setting the quality score of the hand to zero will reduce the grasping priority of both the hand and its adjacent objects, enabling the robot to grasp other objects away from the hand without emergency stops. We conduct extensive experiments on the benchmark datasets and a cobot, showing the effectiveness of QFAAP. Our code and demo videos are available here: https://github.com/clee-jaist/QFAAP.

Fewer May Be Better: Enhancing Offline Reinforcement Learning with Reduced Dataset

Offline reinforcement learning (RL) represents a significant shift in RL research, allowing agents to learn from pre-collected datasets without further interaction with the environment. A key, yet underexplored, challenge in offline RL is selecting an optimal subset of the offline dataset that enhances both algorithm performance and training efficiency. Reducing dataset size can also reveal the minimal data requirements necessary for solving similar problems. In response to this challenge, we introduce ReDOR (Reduced Datasets for Offline RL), a method that frames dataset selection as a gradient approximation optimization problem. We demonstrate that the widely used actor-critic framework in RL can be reformulated as a submodular optimization objective, enabling efficient subset selection. To achieve this, we adapt orthogonal matching pursuit (OMP), incorporating several novel modifications tailored for offline RL. Our experimental results show that the data subsets identified by ReDOR not only boost algorithm performance but also do so with significantly lower computational complexity.

LoyalDiffusion: A Diffusion Model Guarding Against Data Replication

Diffusion models have demonstrated significant potential in image generation. However, their ability to replicate training data presents a privacy risk, particularly when the training data includes confidential information. Existing mitigation strategies primarily focus on augmenting the training dataset, leaving the impact of diffusion model architecture under explored. In this paper, we address this gap by examining and mitigating the impact of the model structure, specifically the skip connections in the diffusion model's U-Net model. We first present our observation on a trade-off in the skip connections. While they enhance image generation quality, they also reinforce the memorization of training data, increasing the risk of replication. To address this, we propose a replication-aware U-Net (RAU-Net) architecture that incorporates information transfer blocks into skip connections that are less essential for image quality. Recognizing the potential impact of RAU-Net on generation quality, we further investigate and identify specific timesteps during which the impact on memorization is most pronounced. By applying RAU-Net selectively at these critical timesteps, we couple our novel diffusion model with a targeted training and inference strategy, forming a framework we refer to as LoyalDiffusion. Extensive experiments demonstrate that LoyalDiffusion outperforms the state-of-the-art replication mitigation method achieving a 48.63% reduction in replication while maintaining comparable image quality.

Pyramid-Monozone Synergistic Grasping Policy in Dense Clutter

Grasping a diverse range of novel objects from dense clutter poses a great challenge to robots because of the occlusion among these objects. In this work, we propose the Pyramid-Monozone Synergistic Grasping Policy (PMSGP) that enables robots to cleverly avoid most occlusions during grasping. Specifically, we initially construct the Pyramid Se quencing Policy (PSP) to sequence each object in the scene into a pyramid structure. By isolating objects layer-by-layer, the grasp candidates will focus on a single layer during each grasp. Then, we devise the Monozone Sampling Policy (MSP) to sample the grasp candidates in the top layer. Through this manner, each grasp will target the topmost object, thereby effectively avoiding most occlusions. We perform more than 7000 real world grasping among 300 novel objects in dense clutter scenes, demonstrating that PMSGP significantly outperforms seven competitive grasping methods. All grasping videos are available at: https://www.youtube.com/@chenghaoli4532/playlists.

A SAM-guided Two-stream Lightweight Model for Anomaly Detection

In industrial anomaly detection, model efficiency and mobile-friendliness become the primary concerns in real-world applications. Simultaneously, the impressive generalization capabilities of Segment Anything (SAM) have garnered broad academic attention, making it an ideal choice for localizing unseen anomalies and diverse real-world patterns. In this paper, considering these two critical factors, we propose a SAM-guided Two-stream Lightweight Model for unsupervised anomaly detection (STLM) that not only aligns with the two practical application requirements but also harnesses the robust generalization capabilities of SAM. We employ two lightweight image encoders, i.e., our two-stream lightweight module, guided by SAM's knowledge. To be specific, one stream is trained to generate discriminative and general feature representations in both normal and anomalous regions, while the other stream reconstructs the same images without anomalies, which effectively enhances the differentiation of two-stream representations when facing anomalous regions. Furthermore, we employ a shared mask decoder and a feature aggregation module to generate anomaly maps. Our experiments conducted on MVTec AD benchmark show that STLM, with about 16M parameters and achieving an inference time in 20ms, competes effectively with state-of-the-art methods in terms of performance, 98.26% on pixel-level AUC and 94.92% on PRO. We further experiment on more difficult datasets, e.g., VisA and DAGM, to demonstrate the effectiveness and generalizability of STLM.

LKCA: Large Kernel Convolutional Attention

We revisit the relationship between attention mechanisms and large kernel ConvNets in visual transformers and propose a new spatial attention named Large Kernel Convolutional Attention (LKCA). It simplifies the attention operation by replacing it with a single large kernel convolution. LKCA combines the advantages of convolutional neural networks and visual transformers, possessing a large receptive field, locality, and parameter sharing. We explained the superiority of LKCA from both convolution and attention perspectives, providing equivalent code implementations for each view. Experiments confirm that LKCA implemented from both the convolutional and attention perspectives exhibit equivalent performance. We extensively experimented with the LKCA variant of ViT in both classification and segmentation tasks. The experiments demonstrated that LKCA exhibits competitive performance in visual tasks. Our code will be made publicly available at https://github.com/CatworldLee/LKCA.

Large Scale Training of Graph Neural Networks for Optimal Markov-Chain Partitioning Using the Kemeny Constant

Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalise to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning representations of graph data provides new approaches to solving the problem. Previous work has shown GNNs to be capable of proposing partitionings using a variety of criteria, however, these approaches have not yet been extended to work on Markov chains or kinetic networks. These arise frequently in the study of molecular systems and are of particular interest to the biochemical modelling community. In this work, we propose several GNN-based architectures to tackle the graph partitioning problem for Markov Chains described as kinetic networks. This approach aims to minimize how much a proposed partitioning changes the Kemeny constant. We propose using an encoder-decoder architecture and show how simple GraphSAGE-based GNNs with linear layers can outperform much larger and more expressive attention-based models in this context. As a proof of concept, we first demonstrate the method's ability to cluster randomly connected graphs. We also use a linear chain architecture corresponding to a 1D free energy profile as our kinetic network. Subsequently, we demonstrate the effectiveness of our method through experiments on a data set derived from molecular dynamics. We compare the performance of our method to other partitioning techniques such as PCCA+. We explore the importance of feature and hyperparameter selection and propose a general strategy for large-scale parallel training of GNNs for discovering optimal graph partitionings.

Mitigate Replication and Copying in Diffusion Models with Generalized Caption and Dual Fusion Enhancement

While diffusion models demonstrate a remarkable capability for generating high-quality images, their tendency to `replicate' training data raises privacy concerns. Although recent research suggests that this replication may stem from the insufficient generalization of training data captions and duplication of training images, effective mitigation strategies remain elusive. To address this gap, our paper first introduces a generality score that measures the caption generality and employ large language model (LLM) to generalize training captions. Subsequently, we leverage generalized captions and propose a novel dual fusion enhancement approach to mitigate the replication of diffusion models. Our empirical results demonstrate that our proposed methods can significantly reduce replication by 43.5% compared to the original diffusion model while maintaining the diversity and quality of generations.