Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The convexity of ICNNs is achieved by using non-decreasing convex activation functions and non-negative weights. Because of these peculiarities, previous initialisation strategies, which implicitly assume centred weights, are not effective for ICNNs. By studying signal propagation through layers with non-negative weights, we are able to derive a principled weight initialisation for ICNNs. Concretely, we generalise signal propagation theory by removing the assumption that weights are sampled from a centred distribution. In a set of experiments, we demonstrate that our principled initialisation effectively accelerates learning in ICNNs and leads to better generalisation. Moreover, we find that, in contrast to common belief, ICNNs can be trained without skip-connections when initialised correctly. Finally, we apply ICNNs to a real-world drug discovery task and show that they allow for more effective molecular latent space exploration.
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In spiking neural networks (SNN), at each node, an incoming sequence of weighted Dirac pulses is converted into an output sequence of weighted Dirac pulses by a leaky-integrate-and-fire (LIF) neuron model based on spike aggregation and thresholding. We show that this mapping can be understood as a quantization operator and state a corresponding formula for the quantization error by means of the Alexiewicz norm. This analysis has implications for rethinking re-initialization in the LIF model, leading to the proposal of 'reset-to-mod' as a modulo-based reset variant.
Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. To open the black-box of these deep learning models, post-hoc instance-level explanation methods have been proposed to understand GNN predictions. These methods seek to discover substructures that explain the prediction behavior of a trained GNN. In this paper, we show analytically that for a large class of explanation tasks, conventional approaches, which are based on the principle of graph information bottleneck (GIB), admit trivial solutions that do not align with the notion of explainability. Instead, we argue that a modified GIB principle may be used to avoid the aforementioned trivial solutions. We further introduce a novel factorized explanation model with theoretical performance guarantees. The modified GIB is used to analyze the structural properties of the proposed factorized explainer. We conduct extensive experiments on both synthetic and real-world datasets to validate the effectiveness of our proposed factorized explainer.
Hand motion capture data is now relatively easy to obtain, even for complicated grasps; however this data is of limited use without the ability to retarget it onto the hands of a specific character or robot. The target hand may differ dramatically in geometry, number of degrees of freedom (DOFs), or number of fingers. We present a simple, but effective framework capable of kinematically retargeting multiple human hand-object manipulations from a publicly available dataset to a wide assortment of kinematically and morphologically diverse target hands through the exploitation of contact areas. We do so by formulating the retarget operation as a non-isometric shape matching problem and use a combination of both surface contact and marker data to progressively estimate, refine, and fit the final target hand trajectory using inverse kinematics (IK). Foundational to our framework is the introduction of a novel shape matching process, which we show enables predictable and robust transfer of contact data over full manipulations while providing an intuitive means for artists to specify correspondences with relatively few inputs. We validate our framework through thirty demonstrations across five different hand shapes and six motions of different objects. We additionally compare our method against existing hand retargeting approaches. Finally, we demonstrate our method enabling novel capabilities such as object substitution and the ability to visualize the impact of design choices over full trajectories.
Learning robust 3D shape segmentation functions with deep neural networks has emerged as a powerful paradigm, offering promising performance in producing a consistent part segmentation of each 3D shape. Generalizing across 3D shape segmentation functions requires robust learning of priors over the respective function space and enables consistent part segmentation of shapes in presence of significant 3D structure variations. Existing generalization methods rely on extensive training of 3D shape segmentation functions on large-scale labeled datasets. In this paper, we proposed to formalize the learning of a 3D shape segmentation function space as a meta-learning problem, aiming to predict a 3D segmentation model that can be quickly adapted to new shapes with no or limited training data. More specifically, we define each task as unsupervised learning of shape-conditioned 3D segmentation function which takes as input points in 3D space and predicts the part-segment labels. The 3D segmentation function is trained by a self-supervised 3D shape reconstruction loss without the need for part labels. Also, we introduce an auxiliary deep neural network as a meta-learner which takes as input a 3D shape and predicts the prior over the respective 3D segmentation function space. We show in experiments that our meta-learning approach, denoted as Meta-3DSeg, leads to improvements on unsupervised 3D shape segmentation over the conventional designs of deep neural networks for 3D shape segmentation functions.
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seemlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications.
In Vehicle-to-Everything networks that involve multi-hop communication, the Road Side Units (RSUs) typically aim to collect location information from the participating vehicles to provide security and network diagnostics features. While the vehicles commonly use the Global Positioning System (GPS) for navigation, they may refrain from sharing their precise GPS coordinates with the RSUs due to privacy concerns. Therefore, to jointly address the high localization requirements by the RSUs as well as the vehicles' privacy, we present a novel spatial-provenance framework wherein each vehicle uses Bloom filters to embed their partial location information when forwarding the packets. In this framework, the RSUs and the vehicles agree upon fragmenting the coverage area into several smaller regions so that the vehicles can embed the identity of their regions through Bloom filters. Given the probabilistic nature of Bloom filters, we derive an analytical expression on the error-rates in provenance recovery and then pose an optimization problem to choose the underlying parameters. With the help of extensive simulation results, we show that our method offers near-optimal Bloom filter parameters in learning spatial provenance. Some interesting trade-offs between the communication-overhead, spatial privacy of the vehicles and the error rates in provenance recovery are also discussed.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
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