The unstructured nature of point clouds demands that local aggregation be adaptive to different local structures. Previous methods meet this by explicitly embedding spatial relations into each aggregation process. Although this coupled approach has been shown effective in generating clear semantics, aggregation can be greatly slowed down due to repeated relation learning and redundant computation to mix directional and point features. In this work, we propose to decouple the explicit modelling of spatial relations from local aggregation. We theoretically prove that basic neighbor pooling operations can too function without loss of clarity in feature fusion, so long as essential spatial information has been encoded in point features. As an instantiation of decoupled local aggregation, we present DeLA, a lightweight point network, where in each learning stage relative spatial encodings are first formed, and only pointwise convolutions plus edge max-pooling are used for local aggregation then. Further, a regularization term is employed to reduce potential ambiguity through the prediction of relative coordinates. Conceptually simple though, experimental results on five classic benchmarks demonstrate that DeLA achieves state-of-the-art performance with reduced or comparable latency. Specifically, DeLA achieves over 90\% overall accuracy on ScanObjectNN and 74\% mIoU on S3DIS Area 5. Our code is available at //github.com/Matrix-ASC/DeLA .
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Current point cloud registration methods are mainly based on local geometric information and usually ignore the semantic information contained in the scenes. In this paper, we treat the point cloud registration problem as a semantic instance matching and registration task, and propose a deep semantic graph matching method (DeepSGM) for large-scale outdoor point cloud registration. Firstly, the semantic categorical labels of 3D points are obtained using a semantic segmentation network. The adjacent points with the same category labels are then clustered together using the Euclidean clustering algorithm to obtain the semantic instances, which are represented by three kinds of attributes including spatial location information, semantic categorical information, and global geometric shape information. Secondly, the semantic adjacency graph is constructed based on the spatial adjacency relations of semantic instances. To fully explore the topological structures between semantic instances in the same scene and across different scenes, the spatial distribution features and the semantic categorical features are learned with graph convolutional networks, and the global geometric shape features are learned with a PointNet-like network. These three kinds of features are further enhanced with the self-attention and cross-attention mechanisms. Thirdly, the semantic instance matching is formulated as an optimal transport problem, and solved through an optimal matching layer. Finally, the geometric transformation matrix between two point clouds is first estimated by the SVD algorithm and then refined by the ICP algorithm. Experimental results conducted on the KITTI Odometry dataset demonstrate that the proposed method improves the registration performance and outperforms various state-of-the-art methods.
Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject to ongoing research. So far, works with sharp bounds are restricted to fairly simple settings (e.g., a single binary treatment). In this paper, we propose a unified framework for causal sensitivity analysis under unobserved confounding in various settings. For this, we propose a flexible generalization of the marginal sensitivity model (MSM) and then derive sharp bounds for a large class of causal effects. This includes (conditional) average treatment effects, effects for mediation analysis and path analysis, and distributional effects. Furthermore, our sensitivity model is applicable to discrete, continuous, and time-varying treatments. It allows us to interpret the partial identification problem under unobserved confounding as a distribution shift in the latent confounders while evaluating the causal effect of interest. In the special case of a single binary treatment, our bounds for (conditional) average treatment effects coincide with recent optimality results for causal sensitivity analysis. Finally, we propose a scalable algorithm to estimate our sharp bounds from observational data.
Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.
Interacting with the actual environment to acquire data is often costly and time-consuming in robotic tasks. Model-based offline reinforcement learning (RL) provides a feasible solution. On the one hand, it eliminates the requirements of interaction with the actual environment. On the other hand, it learns the transition dynamics and reward function from the offline datasets and generates simulated rollouts to accelerate training. Previous model-based offline RL methods adopt probabilistic ensemble neural networks (NN) to model aleatoric uncertainty and epistemic uncertainty. However, this results in an exponential increase in training time and computing resource requirements. Furthermore, these methods are easily disturbed by the accumulative errors of the environment dynamics models when simulating long-term rollouts. To solve the above problems, we propose an uncertainty-aware sequence modeling architecture called Environment Transformer. It models the probability distribution of the environment dynamics and reward function to capture aleatoric uncertainty and treats epistemic uncertainty as a learnable noise parameter. Benefiting from the accurate modeling of the transition dynamics and reward function, Environment Transformer can be combined with arbitrary planning, dynamics programming, or policy optimization algorithms for offline RL. In this case, we perform Conservative Q-Learning (CQL) to learn a conservative Q-function. Through simulation experiments, we demonstrate that our method achieves or exceeds state-of-the-art performance in widely studied offline RL benchmarks. Moreover, we show that Environment Transformer's simulated rollout quality, sample efficiency, and long-term rollout simulation capability are superior to those of previous model-based offline RL methods.
In color spaces where the chromatic term is given in polar coordinates, the shortest distance between colors of the same value is circular. By converting such a space into a complex polar form with a real-valued value axis, a color algebra for combining colors is immediately available. In this work, we introduce two complex space operations utilizing this observation: circular average filtering and circular linear interpolation. These operations produce Archimedean Spirals, thus guaranteeing that they operate along the shortest paths. We demonstrate that these operations provide an intuitive way to work in certain color spaces and that they are particularly useful for obtaining better filtering and interpolation results. We present a set of examples based on the perceptually uniform color space CIELAB or L*a*b* with its polar form CIEHLC. We conclude that representing colors in a complex space with circular operations can provide better visual results by exploitation of the strong algebraic properties of complex space C.
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec.
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