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.

Exploring Kernel Transformations for Implicit Neural Representations

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image representation, with pixel coordinates as input and pixel values as output. In contrast to prior works focusing on investigating the effect of the model's inside components (activation function, for instance), this work pioneers the exploration of the effect of kernel transformation of input/output while keeping the model itself unchanged. A byproduct of our findings is a simple yet effective method that combines scale and shift to significantly boost INR with negligible computation overhead. Moreover, we present two perspectives, depth and normalization, to interpret the performance benefits caused by scale and shift transformation. Overall, our work provides a new avenue for future works to understand and improve INR through the lens of kernel transformation.

A Complete Survey on LLM-based AI Chatbots

The past few decades have witnessed an upsurge in data, forming the foundation for data-hungry, learning-based AI technology. Conversational agents, often referred to as AI chatbots, rely heavily on such data to train large language models (LLMs) and generate new content (knowledge) in response to user prompts. With the advent of OpenAI's ChatGPT, LLM-based chatbots have set new standards in the AI community. This paper presents a complete survey of the evolution and deployment of LLM-based chatbots in various sectors. We first summarize the development of foundational chatbots, followed by the evolution of LLMs, and then provide an overview of LLM-based chatbots currently in use and those in the development phase. Recognizing AI chatbots as tools for generating new knowledge, we explore their diverse applications across various industries. We then discuss the open challenges, considering how the data used to train the LLMs and the misuse of the generated knowledge can cause several issues. Finally, we explore the future outlook to augment their efficiency and reliability in numerous applications. By addressing key milestones and the present-day context of LLM-based chatbots, our survey invites readers to delve deeper into this realm, reflecting on how their next generation will reshape conversational AI.

FedCCL: Federated Dual-Clustered Feature Contrast Under Domain Heterogeneity

Federated learning (FL) facilitates a privacy-preserving neural network training paradigm through collaboration between edge clients and a central server. One significant challenge is that the distributed data is not independently and identically distributed (non-IID), typically including both intra-domain and inter-domain heterogeneity. However, recent research is limited to simply using averaged signals as a form of regularization and only focusing on one aspect of these non-IID challenges. Given these limitations, this paper clarifies these two non-IID challenges and attempts to introduce cluster representation to address them from both local and global perspectives. Specifically, we propose a dual-clustered feature contrast-based FL framework with dual focuses. First, we employ clustering on the local representations of each client, aiming to capture intra-class information based on these local clusters at a high level of granularity. Then, we facilitate cross-client knowledge sharing by pulling the local representation closer to clusters shared by clients with similar semantics while pushing them away from clusters with dissimilar semantics. Second, since the sizes of local clusters belonging to the same class may differ for each client, we further utilize clustering on the global side and conduct averaging to create a consistent global signal for guiding each local training in a contrastive manner. Experimental results on multiple datasets demonstrate that our proposal achieves comparable or superior performance gain under intra-domain and inter-domain heterogeneity.

Logit Calibration and Feature Contrast for Robust Federated Learning on Non-IID Data

Federated learning (FL) is a privacy-preserving distributed framework for collaborative model training on devices in edge networks. However, challenges arise due to vulnerability to adversarial examples (AEs) and the non-independent and identically distributed (non-IID) nature of data distribution among devices, hindering the deployment of adversarially robust and accurate learning models at the edge. While adversarial training (AT) is commonly acknowledged as an effective defense strategy against adversarial attacks in centralized training, we shed light on the adverse effects of directly applying AT in FL that can severely compromise accuracy, especially in non-IID challenges. Given this limitation, this paper proposes FatCC, which incorporates local logit \underline{C}alibration and global feature \underline{C}ontrast into the vanilla federated adversarial training (\underline{FAT}) process from both logit and feature perspectives. This approach can effectively enhance the federated system's robust accuracy (RA) and clean accuracy (CA). First, we propose logit calibration, where the logits are calibrated during local adversarial updates, thereby improving adversarial robustness. Second, FatCC introduces feature contrast, which involves a global alignment term that aligns each local representation with unbiased global features, thus further enhancing robustness and accuracy in federated adversarial environments. Extensive experiments across multiple datasets demonstrate that FatCC achieves comparable or superior performance gains in both CA and RA compared to other baselines.

Towards Understanding Dual BN In Hybrid Adversarial Training

There is a growing concern about applying batch normalization (BN) in adversarial training (AT), especially when the model is trained on both adversarial samples and clean samples (termed Hybrid-AT). With the assumption that adversarial and clean samples are from two different domains, a common practice in prior works is to adopt Dual BN, where BN and BN are used for adversarial and clean branches, respectively. A popular belief for motivating Dual BN is that estimating normalization statistics of this mixture distribution is challenging and thus disentangling it for normalization achieves stronger robustness. In contrast to this belief, we reveal that disentangling statistics plays a less role than disentangling affine parameters in model training. This finding aligns with prior work (Rebuffi et al., 2023), and we build upon their research for further investigations. We demonstrate that the domain gap between adversarial and clean samples is not very large, which is counter-intuitive considering the significant influence of adversarial perturbation on the model accuracy. We further propose a two-task hypothesis which serves as the empirical foundation and a unified framework for Hybrid-AT improvement. We also investigate Dual BN in test-time and reveal that affine parameters characterize the robustness during inference. Overall, our work sheds new light on understanding the mechanism of Dual BN in Hybrid-AT and its underlying justification.

Sora as an AGI World Model? A Complete Survey on Text-to-Video Generation

Text-to-video generation marks a significant frontier in the rapidly evolving domain of generative AI, integrating advancements in text-to-image synthesis, video captioning, and text-guided editing. This survey critically examines the progression of text-to-video technologies, focusing on the shift from traditional generative models to the cutting-edge Sora model, highlighting developments in scalability and generalizability. Distinguishing our analysis from prior works, we offer an in-depth exploration of the technological frameworks and evolutionary pathways of these models. Additionally, we delve into practical applications and address ethical and technological challenges such as the inability to perform multiple entity handling, comprehend causal-effect learning, understand physical interaction, perceive object scaling and proportioning, and combat object hallucination which is also a long-standing problem in generative models. Our comprehensive discussion covers the topic of enablement of text-to-video generation models as human-assistive tools and world models, as well as eliciting model's shortcomings and summarizing future improvement direction that mainly centers around training datasets and evaluation metrics (both automatic and human-centered). Aimed at both newcomers and seasoned researchers, this survey seeks to catalyze further innovation and discussion in the growing field of text-to-video generation, paving the way for more reliable and practical generative artificial intelligence technologies.

Towards Robust Federated Learning via Logits Calibration on Non-IID Data

Federated learning (FL) is a privacy-preserving distributed management framework based on collaborative model training of distributed devices in edge networks. However, recent studies have shown that FL is vulnerable to adversarial examples (AEs), leading to a significant drop in its performance. Meanwhile, the non-independent and identically distributed (non-IID) challenge of data distribution between edge devices can further degrade the performance of models. Consequently, both AEs and non-IID pose challenges to deploying robust learning models at the edge. In this work, we adopt the adversarial training (AT) framework to improve the robustness of FL models against adversarial example (AE) attacks, which can be termed as federated adversarial training (FAT). Moreover, we address the non-IID challenge by implementing a simple yet effective logits calibration strategy under the FAT framework, which can enhance the robustness of models when subjected to adversarial attacks. Specifically, we employ a direct strategy to adjust the logits output by assigning higher weights to classes with small samples during training. This approach effectively tackles the class imbalance in the training data, with the goal of mitigating biases between local and global models. Experimental results on three dataset benchmarks, MNIST, Fashion-MNIST, and CIFAR-10 show that our strategy achieves competitive results in natural and robust accuracy compared to several baselines.

MobileSAMv2: Faster Segment Anything to Everything

Segment anything model (SAM) addresses two practical yet challenging segmentation tasks: \textbf{segment anything (SegAny)}, which utilizes a certain point to predict the mask for a single object of interest, and \textbf{segment everything (SegEvery)}, which predicts the masks for all objects on the image. What makes SegAny slow for SAM is its heavyweight image encoder, which has been addressed by MobileSAM via decoupled knowledge distillation. The efficiency bottleneck of SegEvery with SAM, however, lies in its mask decoder because it needs to first generate numerous masks with redundant grid-search prompts and then perform filtering to obtain the final valid masks. We propose to improve its efficiency by directly generating the final masks with only valid prompts, which can be obtained through object discovery. Our proposed approach not only helps reduce the total time on the mask decoder by at least 16 times but also achieves superior performance. Specifically, our approach yields an average performance boost of 3.6\% (42.5\% \textit{v.s.} 38.9\%) for zero-shot object proposal on the LVIS dataset with the mask AR@$K$ metric. Qualitative results show that our approach generates fine-grained masks while avoiding over-segmenting things. This project targeting faster SegEvery than the original SAM is termed MobileSAMv2 to differentiate from MobileSAM which targets faster SegAny. Moreover, we demonstrate that our new prompt sampling is also compatible with the distilled image encoders in MobileSAM, contributing to a unified framework for efficient SegAny and SegEvery. The code is available at the same link as MobileSAM Project \href{https://github.com/ChaoningZhang/MobileSAM}{\textcolor{red}{https://github.com/ChaoningZhang/MobileSAM}}. \end{abstract}

Single Image Reflection Removal with Reflection Intensity Prior Knowledge

Single Image Reflection Removal (SIRR) in real-world images is a challenging task due to diverse image degradations occurring on the glass surface during light transmission and reflection. Many existing methods rely on specific prior assumptions to resolve the problem. In this paper, we propose a general reflection intensity prior that captures the intensity of the reflection phenomenon and demonstrate its effectiveness. To learn the reflection intensity prior, we introduce the Reflection Prior Extraction Network (RPEN). By segmenting images into regional patches, RPEN learns non-uniform reflection prior in an image. We propose Prior-based Reflection Removal Network (PRRN) using a simple transformer U-Net architecture that adapts reflection prior fed from RPEN. Experimental results on real-world benchmarks demonstrate the effectiveness of our approach achieving state-of-the-art accuracy in SIRR.