We study the mixing time of the single-site update Markov chain, known as the Glauber dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal convergence results for arbitrary trees. We consider the more general problem of sampling from the Gibbs distribution in the hard-core model where independent sets are weighted by a parameter $\lambda>0$. Previous work of Martinelli, Sinclair and Weitz (2004) obtained optimal mixing time bounds for the complete $\Delta$-regular tree for all $\lambda$. However, Restrepo et al. (2014) showed that for sufficiently large $\lambda$ there are bounded-degree trees where optimal mixing does not hold. Recent work of Eppstein and Frishberg (2022) proved a polynomial mixing time bound for the Glauber dynamics for arbitrary trees, and more generally for graphs of bounded tree-width. We establish an optimal bound on the relaxation time (i.e., inverse spectral gap) of $O(n)$ for the Glauber dynamics for unweighted independent sets on arbitrary trees. Moreover, for $\lambda\leq .44$ we prove an optimal mixing time bound of $O(n\log{n})$. We stress that our results hold for arbitrary trees and there is no dependence on the maximum degree $\Delta$. Interestingly, our results extend (far) beyond the uniqueness threshold which is on the order $\lambda=O(1/\Delta)$. Our proof approach is inspired by recent work on spectral independence. In fact, we prove that spectral independence holds with a constant independent of the maximum degree for any tree, but this does not imply mixing for general trees as the optimal mixing results of Chen, Liu, and Vigoda (2021) only apply for bounded degree graphs. We instead utilize the combinatorial nature of independent sets to directly prove approximate tensorization of variance/entropy via a non-trivial inductive proof.
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The investigation of the similarity between artists and music is crucial in music retrieval and recommendation, and addressing the challenge of the long-tail phenomenon is increasingly important. This paper proposes a Long-Tail Friendly Representation Framework (LTFRF) that utilizes neural networks to model the similarity relationship. Our approach integrates music, user, metadata, and relationship data into a unified metric learning framework, and employs a meta-consistency relationship as a regular term to introduce the Multi-Relationship Loss. Compared to the Graph Neural Network (GNN), our proposed framework improves the representation performance in long-tail scenarios, which are characterized by sparse relationships between artists and music. We conduct experiments and analysis on the AllMusic dataset, and the results demonstrate that our framework provides a favorable generalization of artist and music representation. Specifically, on similar artist/music recommendation tasks, the LTFRF outperforms the baseline by 9.69%/19.42% in Hit Ratio@10, and in long-tail cases, the framework achieves 11.05%/14.14% higher than the baseline in Consistent@10.
We present a novel method, Aerial Diffusion, for generating aerial views from a single ground-view image using text guidance. Aerial Diffusion leverages a pretrained text-image diffusion model for prior knowledge. We address two main challenges corresponding to domain gap between the ground-view and the aerial view and the two views being far apart in the text-image embedding manifold. Our approach uses a homography inspired by inverse perspective mapping prior to finetuning the pretrained diffusion model. Additionally, using the text corresponding to the ground-view to finetune the model helps us capture the details in the ground-view image at a relatively low bias towards the ground-view image. Aerial Diffusion uses an alternating sampling strategy to compute the optimal solution on complex high-dimensional manifold and generate a high-fidelity (w.r.t. ground view) aerial image. We demonstrate the quality and versatility of Aerial Diffusion on a plethora of images from various domains including nature, human actions, indoor scenes, etc. We qualitatively prove the effectiveness of our method with extensive ablations and comparisons. To the best of our knowledge, Aerial Diffusion is the first approach that performs ground-to-aerial translation in an unsupervised manner.
We propose SMPLitex, a method for estimating and manipulating the complete 3D appearance of humans captured from a single image. SMPLitex builds upon the recently proposed generative models for 2D images, and extends their use to the 3D domain through pixel-to-surface correspondences computed on the input image. To this end, we first train a generative model for complete 3D human appearance, and then fit it into the input image by conditioning the generative model to the visible parts of the subject. Furthermore, we propose a new dataset of high-quality human textures built by sampling SMPLitex conditioned on subject descriptions and images. We quantitatively and qualitatively evaluate our method in 3 publicly available datasets, demonstrating that SMPLitex significantly outperforms existing methods for human texture estimation while allowing for a wider variety of tasks such as editing, synthesis, and manipulation
Training a generative model with limited number of samples is a challenging task. Current methods primarily rely on few-shot model adaption to train the network. However, in scenarios where data is extremely limited (less than 10), the generative network tends to overfit and suffers from content degradation. To address these problems, we propose a novel phasic content fusing few-shot diffusion model with directional distribution consistency loss, which targets different learning objectives at distinct training stages of the diffusion model. Specifically, we design a phasic training strategy with phasic content fusion to help our model learn content and style information when t is large, and learn local details of target domain when t is small, leading to an improvement in the capture of content, style and local details. Furthermore, we introduce a novel directional distribution consistency loss that ensures the consistency between the generated and source distributions more efficiently and stably than the prior methods, preventing our model from overfitting. Finally, we propose a cross-domain structure guidance strategy that enhances structure consistency during domain adaptation. Theoretical analysis, qualitative and quantitative experiments demonstrate the superiority of our approach in few-shot generative model adaption tasks compared to state-of-the-art methods. The source code is available at: //github.com/sjtuplayer/few-shot-diffusion.
In this study, we present a method for synthesizing novel views from a single 360-degree RGB-D image based on the neural radiance field (NeRF) . Prior studies relied on the neighborhood interpolation capability of multi-layer perceptrons to complete missing regions caused by occlusion and zooming, which leads to artifacts. In the method proposed in this study, the input image is reprojected to 360-degree RGB images at other camera positions, the missing regions of the reprojected images are completed by a 2D image generative model, and the completed images are utilized to train the NeRF. Because multiple completed images contain inconsistencies in 3D, we introduce a method to learn the NeRF model using a subset of completed images that cover the target scene with less overlap of completed regions. The selection of such a subset of images can be attributed to the maximum weight independent set problem, which is solved through simulated annealing. Experiments demonstrated that the proposed method can synthesize plausible novel views while preserving the features of the scene for both artificial and real-world data.
Music editing primarily entails the modification of instrument tracks or remixing in the whole, which offers a novel reinterpretation of the original piece through a series of operations. These music processing methods hold immense potential across various applications but demand substantial expertise. Prior methodologies, although effective for image and audio modifications, falter when directly applied to music. This is attributed to music's distinctive data nature, where such methods can inadvertently compromise the intrinsic harmony and coherence of music. In this paper, we develop InstructME, an Instruction guided Music Editing and remixing framework based on latent diffusion models. Our framework fortifies the U-Net with multi-scale aggregation in order to maintain consistency before and after editing. In addition, we introduce chord progression matrix as condition information and incorporate it in the semantic space to improve melodic harmony while editing. For accommodating extended musical pieces, InstructME employs a chunk transformer, enabling it to discern long-term temporal dependencies within music sequences. We tested InstructME in instrument-editing, remixing, and multi-round editing. Both subjective and objective evaluations indicate that our proposed method significantly surpasses preceding systems in music quality, text relevance and harmony. Demo samples are available at //musicedit.github.io/
This paper explores the instruction fine-tuning technique for speech semantic understanding by introducing a unified end-to-end (E2E) framework that generates semantic labels conditioned on a task-related prompt for audio data. We pre-train the model using large and diverse data, where instruction-speech pairs are constructed via a text-to-speech (TTS) system. Extensive experiments demonstrate that our proposed model significantly outperforms state-of-the-art (SOTA) models after fine-tuning downstream tasks. Furthermore, the proposed model achieves competitive performance in zero-shot and few-shot scenarios. To facilitate future work on instruction fine-tuning for speech-to-semantic tasks, we release our instruction dataset and code.
Music source separation (MSS) aims to separate a music recording into multiple musically distinct stems, such as vocals, bass, drums, and more. Recently, deep learning approaches such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have been used, but the improvement is still limited. In this paper, we propose a novel frequency-domain approach based on a Band-Split RoPE Transformer (called BS-RoFormer). BS-RoFormer replies on a band-split module to project the input complex spectrogram into subband-level representations, and then arranges a stack of hierarchical Transformers to model the inner-band as well as inter-band sequences for multi-band mask estimation. To facilitate training the model for MSS, we propose to use the Rotary Position Embedding (RoPE). The BS-RoFormer system trained on MUSDB18HQ and 500 extra songs ranked the first place in the MSS track of Sound Demixing Challenge (SDX23). Benchmarking a smaller version of BS-RoFormer on MUSDB18HQ, we achieve state-of-the-art result without extra training data, with 9.80 dB of average SDR.
This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.
We propose a novel single shot object detection network named Detection with Enriched Semantics (DES). Our motivation is to enrich the semantics of object detection features within a typical deep detector, by a semantic segmentation branch and a global activation module. The segmentation branch is supervised by weak segmentation ground-truth, i.e., no extra annotation is required. In conjunction with that, we employ a global activation module which learns relationship between channels and object classes in a self-supervised manner. Comprehensive experimental results on both PASCAL VOC and MS COCO detection datasets demonstrate the effectiveness of the proposed method. In particular, with a VGG16 based DES, we achieve an mAP of 81.7 on VOC2007 test and an mAP of 32.8 on COCO test-dev with an inference speed of 31.5 milliseconds per image on a Titan Xp GPU. With a lower resolution version, we achieve an mAP of 79.7 on VOC2007 with an inference speed of 13.0 milliseconds per image.
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