This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time. We derive results for both the theoretical setting, where we assume access to the entire process sample path, and a more practical one, which develops methods for estimating the quantities of interest from sampled time series. The latter estimates are accurately computable in reasonable time by solving the relevant linear integral equation using the iterative thresholding method due to Daubechies, Defrise and De~Mol. We exemplify our new methods by computing spectral and autocovariance estimates on irregularly-spaced heart-rate data obtained from a recent sleep-state study.
Structure-from-motion (SfM) is a long-standing problem in the computer vision community, which aims to reconstruct the camera poses and 3D structure of a scene from a set of unconstrained 2D images. Classical frameworks solve this problem in an incremental manner by detecting and matching keypoints, registering images, triangulating 3D points, and conducting bundle adjustment. Recent research efforts have predominantly revolved around harnessing the power of deep learning techniques to enhance specific elements (e.g., keypoint matching), but are still based on the original, non-differentiable pipeline. Instead, we propose a new deep pipeline VGGSfM, where each component is fully differentiable and thus can be trained in an end-to-end manner. To this end, we introduce new mechanisms and simplifications. First, we build on recent advances in deep 2D point tracking to extract reliable pixel-accurate tracks, which eliminates the need for chaining pairwise matches. Furthermore, we recover all cameras simultaneously based on the image and track features instead of gradually registering cameras. Finally, we optimise the cameras and triangulate 3D points via a differentiable bundle adjustment layer. We attain state-of-the-art performance on three popular datasets, CO3D, IMC Phototourism, and ETH3D.
We present a first step towards 4D (3D and time) human video stylization, which addresses style transfer, novel view synthesis and human animation within a unified framework. While numerous video stylization methods have been developed, they are often restricted to rendering images in specific viewpoints of the input video, lacking the capability to generalize to novel views and novel poses in dynamic scenes. To overcome these limitations, we leverage Neural Radiance Fields (NeRFs) to represent videos, conducting stylization in the rendered feature space. Our innovative approach involves the simultaneous representation of both the human subject and the surrounding scene using two NeRFs. This dual representation facilitates the animation of human subjects across various poses and novel viewpoints. Specifically, we introduce a novel geometry-guided tri-plane representation, significantly enhancing feature representation robustness compared to direct tri-plane optimization. Following the video reconstruction, stylization is performed within the NeRFs' rendered feature space. Extensive experiments demonstrate that the proposed method strikes a superior balance between stylized textures and temporal coherence, surpassing existing approaches. Furthermore, our framework uniquely extends its capabilities to accommodate novel poses and viewpoints, making it a versatile tool for creative human video stylization.
This work aims to leverage pre-trained foundation models, such as contrastive language-image pre-training (CLIP) and segment anything model (SAM), to address weakly supervised semantic segmentation (WSSS) using image-level labels. To this end, we propose a coarse-to-fine framework based on CLIP and SAM for generating high-quality segmentation seeds. Specifically, we construct an image classification task and a seed segmentation task, which are jointly performed by CLIP with frozen weights and two sets of learnable task-specific prompts. A SAM-based seeding (SAMS) module is designed and applied to each task to produce either coarse or fine seed maps. Moreover, we design a multi-label contrastive loss supervised by image-level labels and a CAM activation loss supervised by the generated coarse seed map. These losses are used to learn the prompts, which are the only parts need to be learned in our framework. Once the prompts are learned, we input each image along with the learned segmentation-specific prompts into CLIP and the SAMS module to produce high-quality segmentation seeds. These seeds serve as pseudo labels to train an off-the-shelf segmentation network like other two-stage WSSS methods. Experiments show that our method achieves the state-of-the-art performance on PASCAL VOC 2012 and competitive results on MS COCO 2014.
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In a typical existing approach, one first tries to make a good initial guess for the parameter values. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. A downside of this approach is non-robustness, as there are no guarantees for the result of the loop iterations to be predictably close to the true parameter values. In this paper, we propose a new approach, which does not suffer from the above non-robustness. In particular, it does not require making good initial guesses for the parameter values. Instead, it uses differential algebra, interpolation of the data using rational functions, and multivariate polynomial system solving, and has a potential for a complete user control over the error of the estimation (the actual error analysis is left for the future research). We also compare the performance of the resulting software with several other estimation software packages.
Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.
In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.