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In this paper, we study transnormal and isoparametric functions on general Riemannian manifolds. We show that transnormal and isoparametric functions impose the same topological constraints on the manifold, which requires the underlying manifold to have a vector bundle structure or a linear double disk bundle decomposition. Conversely, any smooth manifold with either of these structures can be endowed with a Riemannian metric that admits a transnormal function, which, under suitable compactness conditions, can become isoparametric., Comment: 15 pages

While time series diffusion models have received considerable focus from many recent works, the performance of existing models remains highly unstable. Factors limiting time series diffusion models include insufficient time series datasets and the absence of guidance. To address these limitations, we propose a Retrieval- Augmented Time series Diffusion model (RATD). The framework of RATD consists of two parts: an embedding-based retrieval process and a reference-guided diffusion model. In the first part, RATD retrieves the time series that are most relevant to historical time series from the database as references. The references are utilized to guide the denoising process in the second part. Our approach allows leveraging meaningful samples within the database to aid in sampling, thus maximizing the utilization of datasets. Meanwhile, this reference-guided mechanism also compensates for the deficiencies of existing time series diffusion models in terms of guidance. Experiments and visualizations on multiple datasets demonstrate the effectiveness of our approach, particularly in complicated prediction tasks., Comment: NeurIPS 2024

Large language models (LLMs) like GPT-4, PaLM, and LLaMA have shown significant improvements in various reasoning tasks. However, smaller models such as Llama-3-8B and DeepSeekMath-Base still struggle with complex mathematical reasoning because they fail to effectively identify and correct reasoning errors. Recent reflection-based methods aim to address these issues by enabling self-reflection and self-correction, but they still face challenges in independently detecting errors in their reasoning steps. To overcome these limitations, we propose SuperCorrect, a novel two-stage framework that uses a large teacher model to supervise and correct both the reasoning and reflection processes of a smaller student model. In the first stage, we extract hierarchical high-level and detailed thought templates from the teacher model to guide the student model in eliciting more fine-grained reasoning thoughts. In the second stage, we introduce cross-model collaborative direct preference optimization (DPO) to enhance the self-correction abilities of the student model by following the teacher's correction traces during training. This cross-model DPO approach teaches the student model to effectively locate and resolve erroneous thoughts with error-driven insights from the teacher model, breaking the bottleneck of its thoughts and acquiring new skills and knowledge to tackle challenging problems. Extensive experiments consistently demonstrate our superiority over previous methods. Notably, our SuperCorrect-7B model significantly surpasses powerful DeepSeekMath-7B by 7.8%/5.3% and Qwen2.5-Math-7B by 15.1%/6.3% on MATH/GSM8K benchmarks, achieving new SOTA performance among all 7B models. Code: https://github.com/YangLing0818/SuperCorrect-llm, Comment: Project: https://github.com/YangLing0818/SuperCorrect-llm

Generating high-quality 3D assets from textual descriptions remains a pivotal challenge in computer graphics and vision research. Due to the scarcity of 3D data, state-of-the-art approaches utilize pre-trained 2D diffusion priors, optimized through Score Distillation Sampling (SDS). Despite progress, crafting complex 3D scenes featuring multiple objects or intricate interactions is still difficult. To tackle this, recent methods have incorporated box or layout guidance. However, these layout-guided compositional methods often struggle to provide fine-grained control, as they are generally coarse and lack expressiveness. To overcome these challenges, we introduce a novel SDS approach, Semantic Score Distillation Sampling (SemanticSDS), designed to effectively improve the expressiveness and accuracy of compositional text-to-3D generation. Our approach integrates new semantic embeddings that maintain consistency across different rendering views and clearly differentiate between various objects and parts. These embeddings are transformed into a semantic map, which directs a region-specific SDS process, enabling precise optimization and compositional generation. By leveraging explicit semantic guidance, our method unlocks the compositional capabilities of existing pre-trained diffusion models, thereby achieving superior quality in 3D content generation, particularly for complex objects and scenes. Experimental results demonstrate that our SemanticSDS framework is highly effective for generating state-of-the-art complex 3D content. Code: https://github.com/YangLing0818/SemanticSDS-3D, Comment: Project: https://github.com/YangLing0818/SemanticSDS-3D

Efficient data selection is crucial to accelerate the pretraining of large language models (LLMs). While various methods have been proposed to enhance data efficiency, limited research has addressed the inherent conflicts between these approaches to achieve optimal data selection for LLM pretraining. To tackle this problem, we propose a novel multi-agent collaborative data selection mechanism. In this framework, each data selection method serves as an independent agent, and an agent console is designed to dynamically integrate the information from all agents throughout the LLM training process. We conduct extensive empirical studies to evaluate our multi-agent framework. The experimental results demonstrate that our approach significantly improves data efficiency, accelerates convergence in LLM training, and achieves an average performance gain up to 10.5% across multiple language model benchmarks compared to the state-of-the-art methods.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing $\boldsymbol v$-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Advanced diffusion models like RPG, Stable Diffusion 3 and FLUX have made notable strides in compositional text-to-image generation. However, these methods typically exhibit distinct strengths for compositional generation, with some excelling in handling attribute binding and others in spatial relationships. This disparity highlights the need for an approach that can leverage the complementary strengths of various models to comprehensively improve the composition capability. To this end, we introduce IterComp, a novel framework that aggregates composition-aware model preferences from multiple models and employs an iterative feedback learning approach to enhance compositional generation. Specifically, we curate a gallery of six powerful open-source diffusion models and evaluate their three key compositional metrics: attribute binding, spatial relationships, and non-spatial relationships. Based on these metrics, we develop a composition-aware model preference dataset comprising numerous image-rank pairs to train composition-aware reward models. Then, we propose an iterative feedback learning method to enhance compositionality in a closed-loop manner, enabling the progressive self-refinement of both the base diffusion model and reward models over multiple iterations. Theoretical proof demonstrates the effectiveness and extensive experiments show our significant superiority over previous SOTA methods (e.g., Omost and FLUX), particularly in multi-category object composition and complex semantic alignment. IterComp opens new research avenues in reward feedback learning for diffusion models and compositional generation. Code: https://github.com/YangLing0818/IterComp, Comment: Project: https://github.com/YangLing0818/IterComp

Recent advances in diffusion models have demonstrated exceptional capabilities in image and video generation, further improving the effectiveness of 4D synthesis. Existing 4D generation methods can generate high-quality 4D objects or scenes based on user-friendly conditions, benefiting the gaming and video industries. However, these methods struggle to synthesize significant object deformation of complex 4D transitions and interactions within scenes. To address this challenge, we propose Trans4D, a novel text-to-4D synthesis framework that enables realistic complex scene transitions. Specifically, we first use multi-modal large language models (MLLMs) to produce a physic-aware scene description for 4D scene initialization and effective transition timing planning. Then we propose a geometry-aware 4D transition network to realize a complex scene-level 4D transition based on the plan, which involves expressive geometrical object deformation. Extensive experiments demonstrate that Trans4D consistently outperforms existing state-of-the-art methods in generating 4D scenes with accurate and high-quality transitions, validating its effectiveness. Code: https://github.com/YangLing0818/Trans4D, Comment: Project: https://github.com/YangLing0818/Trans4D

CNN-based object detection models that strike a balance between performance and speed have been gradually used in polyp detection tasks. Nevertheless, accurately locating polyps within complex colonoscopy video scenes remains challenging since existing methods ignore two key issues: intra-sequence distribution heterogeneity and precision-confidence discrepancy. To address these challenges, we propose a novel Temporal-Spatial self-correction detector (TSdetector), which first integrates temporal-level consistency learning and spatial-level reliability learning to detect objects continuously. Technically, we first propose a global temporal-aware convolution, assembling the preceding information to dynamically guide the current convolution kernel to focus on global features between sequences. In addition, we designed a hierarchical queue integration mechanism to combine multi-temporal features through a progressive accumulation manner, fully leveraging contextual consistency information together with retaining long-sequence-dependency features. Meanwhile, at the spatial level, we advance a position-aware clustering to explore the spatial relationships among candidate boxes for recalibrating prediction confidence adaptively, thus eliminating redundant bounding boxes efficiently. The experimental results on three publicly available polyp video dataset show that TSdetector achieves the highest polyp detection rate and outperforms other state-of-the-art methods. The code can be available at https://github.com/soleilssss/TSdetector.

Visual-language models have advanced the development of universal models, yet their application in medical imaging remains constrained by specific functional requirements and the limited data. Current general-purpose models are typically designed with task-specific branches and heads, which restricts the shared feature space and the flexibility of model. To address these challenges, we have developed a decomposed-composed universal medical imaging paradigm (UniMed) that supports tasks at all levels. To this end, we first propose a decomposed decoder that can predict two types of outputs -- pixel and semantic, based on a defined input queue. Additionally, we introduce a composed decoder that unifies the input and output spaces and standardizes task annotations across different levels into a discrete token format. The coupled design of these two components enables the model to flexibly combine tasks and mutual benefits. Moreover, our joint representation learning strategy skilfully leverages large amounts of unlabeled data and unsupervised loss, achieving efficient one-stage pretraining for more robust performance. Experimental results show that UniMed achieves state-of-the-art performance on eight datasets across all three tasks and exhibits strong zero-shot and 100-shot transferability. We will release the code and trained models upon the paper's acceptance.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into a student generator to achieve one-step generation, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack). DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of the teacher model, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the teacher model's intermediate distributions, and its reverse can be viewed as the convergence trajectory from the student generator to the teacher model. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions along the path to approximate the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance, with FID score of 1.38 on ImageNet 64x64 dataset. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack., Comment: https://github.com/SYZhang0805/DisBack

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various strategies including gradient normalization (GN) and gradient centralization (GC). Nevertheless, to the best of our knowledge, no one has considered to capture the optimal gradient descent trajectory, by adaptively controlling gradient descent direction. To address this concern, this paper is the first attempt to study a new optimization technique for deep neural networks, using the sum normalization of a gradient vector as coefficients, to dynamically regularize gradients and thus to effectively control optimization direction. The proposed technique is hence named as the adaptive gradient regularization (AGR). It can be viewed as an adaptive gradient clipping method. The theoretical analysis reveals that the AGR can effectively smooth the loss landscape, and hence can significantly improve the training efficiency and model generalization performance. We note that AGR can greatly improve the training efficiency of vanilla optimizers' including Adan and AdamW, by adding only three lines of code. The final experiments conducted on image generation, image classification, and language representation, demonstrate that the AGR method can not only improve the training efficiency but also enhance the model generalization performance., Comment: 12 pages, 13 figures

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching, Comment: Code: https://github.com/YangLing0818/consistency_flow_matching

Diffusion models have demonstrated great success in text-to-video (T2V) generation. However, existing methods may face challenges when handling complex (long) video generation scenarios that involve multiple objects or dynamic changes in object numbers. To address these limitations, we propose VideoTetris, a novel framework that enables compositional T2V generation. Specifically, we propose spatio-temporal compositional diffusion to precisely follow complex textual semantics by manipulating and composing the attention maps of denoising networks spatially and temporally. Moreover, we propose an enhanced video data preprocessing to enhance the training data regarding motion dynamics and prompt understanding, equipped with a new reference frame attention mechanism to improve the consistency of auto-regressive video generation. Extensive experiments demonstrate that our VideoTetris achieves impressive qualitative and quantitative results in compositional T2V generation. Code is available at: https://github.com/YangLing0818/VideoTetris, Comment: NeurIPS 2024. Code: https://github.com/YangLing0818/VideoTetris

We introduce Buffer of Thoughts (BoT), a novel and versatile thought-augmented reasoning approach for enhancing accuracy, efficiency and robustness of large language models (LLMs). Specifically, we propose meta-buffer to store a series of informative high-level thoughts, namely thought-template, distilled from the problem-solving processes across various tasks. Then for each problem, we retrieve a relevant thought-template and adaptively instantiate it with specific reasoning structures to conduct efficient reasoning. To guarantee the scalability and stability, we further propose buffer-manager to dynamically update the meta-buffer, thus enhancing the capacity of meta-buffer as more tasks are solved. We conduct extensive experiments on 10 challenging reasoning-intensive tasks, and achieve significant performance improvements over previous SOTA methods: 11% on Game of 24, 20% on Geometric Shapes and 51% on Checkmate-in-One. Further analysis demonstrate the superior generalization ability and model robustness of our BoT, while requiring only 12% of the cost of multi-query prompting methods (e.g., tree/graph of thoughts) on average. Notably, we find that our Llama3-8B+BoT has the potential to surpass Llama3-70B model. Our project is available at: https://github.com/YangLing0818/buffer-of-thought-llm, Comment: NeurIPS 2024 Spotlight. Project: https://github.com/YangLing0818/buffer-of-thought-llm

Multimodal large language models (MLLMs) enhance the capabilities of standard large language models by integrating and processing data from multiple modalities, including text, vision, audio, video, and 3D environments. Data plays a pivotal role in the development and refinement of these models. In this survey, we comprehensively review the literature on MLLMs from a data-centric perspective. Specifically, we explore methods for preparing multimodal data during the pretraining and adaptation phases of MLLMs. Additionally, we analyze the evaluation methods for the datasets and review the benchmarks for evaluating MLLMs. Our survey also outlines potential future research directions. This work aims to provide researchers with a detailed understanding of the data-driven aspects of MLLMs, fostering further exploration and innovation in this field.

Glycans are basic biomolecules and perform essential functions within living organisms. The rapid increase of functional glycan data provides a good opportunity for machine learning solutions to glycan understanding. However, there still lacks a standard machine learning benchmark for glycan property and function prediction. In this work, we fill this blank by building a comprehensive benchmark for Glycan Machine Learning (GlycanML). The GlycanML benchmark consists of diverse types of tasks including glycan taxonomy prediction, glycan immunogenicity prediction, glycosylation type prediction, and protein-glycan interaction prediction. Glycans can be represented by both sequences and graphs in GlycanML, which enables us to extensively evaluate sequence-based models and graph neural networks (GNNs) on benchmark tasks. Furthermore, by concurrently performing eight glycan taxonomy prediction tasks, we introduce the GlycanML-MTL testbed for multi-task learning (MTL) algorithms. Also, we evaluate how taxonomy prediction can boost other three function prediction tasks by MTL. Experimental results show the superiority of modeling glycans with multi-relational GNNs, and suitable MTL methods can further boost model performance. We provide all datasets and source codes at https://github.com/GlycanML/GlycanML and maintain a leaderboard at https://GlycanML.github.io/project, Comment: Research project paper. All code and data are released

Diffusion models have significantly improved the performance of image editing. Existing methods realize various approaches to achieve high-quality image editing, including but not limited to text control, dragging operation, and mask-and-inpainting. Among these, instruction-based editing stands out for its convenience and effectiveness in following human instructions across diverse scenarios. However, it still focuses on simple editing operations like adding, replacing, or deleting, and falls short of understanding aspects of world dynamics that convey the realistic dynamic nature in the physical world. Therefore, this work, EditWorld, introduces a new editing task, namely world-instructed image editing, which defines and categorizes the instructions grounded by various world scenarios. We curate a new image editing dataset with world instructions using a set of large pretrained models (e.g., GPT-3.5, Video-LLava and SDXL). To enable sufficient simulation of world dynamics for image editing, our EditWorld trains model in the curated dataset, and improves instruction-following ability with designed post-edit strategy. Extensive experiments demonstrate our method significantly outperforms existing editing methods in this new task. Our dataset and code will be available at https://github.com/YangLing0818/EditWorld, Comment: Project: https://github.com/YangLing0818/EditWorld

Graph Neural Networks (GNNs) have demonstrated effectiveness in various graph-based tasks. However, their inefficiency in training and inference presents challenges for scaling up to real-world and large-scale graph applications. To address the critical challenges, a range of algorithms have been proposed to accelerate training and inference of GNNs, attracting increasing attention from the research community. In this paper, we present a systematic review of acceleration algorithms in GNNs, which can be categorized into three main topics based on their purpose: training acceleration, inference acceleration, and execution acceleration. Specifically, we summarize and categorize the existing approaches for each main topic, and provide detailed characterizations of the approaches within each category. Additionally, we review several libraries related to acceleration algorithms in GNNs and discuss our Scalable Graph Learning (SGL) library. Finally, we propose promising directions for future research. A complete summary is presented in our GitHub repository: https://github.com/PKU-DAIR/SGL/blob/main/Awsome-GNN-Acceleration.md., Comment: 9 pages,3 figures

With the advancement of AIGC, video frame interpolation (VFI) has become a crucial component in existing video generation frameworks, attracting widespread research interest. For the VFI task, the motion estimation between neighboring frames plays a crucial role in avoiding motion ambiguity. However, existing VFI methods always struggle to accurately predict the motion information between consecutive frames, and this imprecise estimation leads to blurred and visually incoherent interpolated frames. In this paper, we propose a novel diffusion framework, motion-aware latent diffusion models (MADiff), which is specifically designed for the VFI task. By incorporating motion priors between the conditional neighboring frames with the target interpolated frame predicted throughout the diffusion sampling procedure, MADiff progressively refines the intermediate outcomes, culminating in generating both visually smooth and realistic results. Extensive experiments conducted on benchmark datasets demonstrate that our method achieves state-of-the-art performance significantly outperforming existing approaches, especially under challenging scenarios involving dynamic textures with complex motion., Comment: 17 pages, 4 figures

The scale and quality of a dataset significantly impact the performance of deep models. However, acquiring large-scale annotated datasets is both a costly and time-consuming endeavor. To address this challenge, dataset expansion technologies aim to automatically augment datasets, unlocking the full potential of deep models. Current data expansion techniques include image transformation and image synthesis methods. Transformation-based methods introduce only local variations, leading to limited diversity. In contrast, synthesis-based methods generate entirely new content, greatly enhancing informativeness. However, existing synthesis methods carry the risk of distribution deviations, potentially degrading model performance with out-of-distribution samples. In this paper, we propose DistDiff, a training-free data expansion framework based on the distribution-aware diffusion model. DistDiff constructs hierarchical prototypes to approximate the real data distribution, optimizing latent data points within diffusion models with hierarchical energy guidance. We demonstrate its capability to generate distribution-consistent samples, significantly improving data expansion tasks. DistDiff consistently enhances accuracy across a diverse range of datasets compared to models trained solely on original data. Furthermore, our approach consistently outperforms existing synthesis-based techniques and demonstrates compatibility with widely adopted transformation-based augmentation methods. Additionally, the expanded dataset exhibits robustness across various architectural frameworks. Our code is available at https://github.com/haoweiz23/DistDiff, Comment: Project: https://github.com/haoweiz23/DistDiff

In this paper, we study the rigidity problem for compact minimal Legendrian submanifolds in the unit Euclidean spheres via eigenvalues of fundamental matrices, which measure the squared norms of the second fundamental form on all normal directions. By using Lu's inequality on the upper bound of the squared norm of Lie brackets of symmetric matrices, we establish an optimal pinching theorem for such submanifolds of all dimensions, giving a new characterization for the Calabi tori. This pinching condition can also be described by the eigenvalues of the Ricci curvature tensor. Moreover, when the third large eigenvalue of the fundamental matrix vanishes everywhere, we get an optimal rigidity theorem under a weaker pinching condition., Comment: 19 pages