Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.
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Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the complexity of solving $\omega$-regular games played on temporal graphs where the edge availability is ultimately periodic and fixed a priori. We show that solving parity games on temporal graphs is decidable in PSPACE, only assuming the edge predicate itself is in PSPACE. A matching lower bound already holds for what we call punctual reachability games on static graphs, where one player wants to reach the target at a given, binary encoded, point in time. We further study syntactic restrictions that imply more efficient procedures. In particular, if the edge predicate is in $P$ and is monotonically increasing for one player and decreasing for the other, then the complexity of solving games is only polynomially increased compared to static graphs.
Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large, multivariate datasets today. Two well-known limitations of the method include sensitivity to outliers and noise and no clear methodology for the uncertainty quantification of the principle components or their associated explained variances. Whereas previous work has focused on each of these problems individually, we propose a scalable method called Ensemble PCA (EPCA) that addresses them simultaneously for data which has an inherently low-rank structure. EPCA combines boostrapped PCA with k-means cluster analysis to handle challenges associated with sign-ambiguity and the re-ordering of components in the PCA subsamples. EPCA provides a noise-resistant extension of PCA that lends itself naturally to uncertainty quantification. We test EPCA on data corrupted with white noise, sparse noise, and outliers against both classical PCA and Robust PCA (RPCA) and show that EPCA performs competitively across different noise scenarios, with a clear advantage on datasets containing outliers and orders of magnitude reduction in computational cost compared to RPCA.
Dataset distillation is a newly emerging task that synthesizes a small-size dataset used in training deep neural networks (DNNs) for reducing data storage and model training costs. The synthetic datasets are expected to capture the essence of the knowledge contained in real-world datasets such that the former yields a similar performance as the latter. Recent advancements in distillation methods have produced notable improvements in generating synthetic datasets. However, current state-of-the-art methods treat the entire synthetic dataset as a unified entity and optimize each synthetic instance equally. This static optimization approach may lead to performance degradation in dataset distillation. Specifically, we argue that static optimization can give rise to a coupling issue within the synthetic data, particularly when a larger amount of synthetic data is being optimized. This coupling issue, in turn, leads to the failure of the distilled dataset to extract the high-level features learned by the deep neural network (DNN) in the latter epochs. In this study, we propose a new dataset distillation strategy called Sequential Subset Matching (SeqMatch), which tackles this problem by adaptively optimizing the synthetic data to encourage sequential acquisition of knowledge during dataset distillation. Our analysis indicates that SeqMatch effectively addresses the coupling issue by sequentially generating the synthetic instances, thereby enhancing its performance significantly. Our proposed SeqMatch outperforms state-of-the-art methods in various datasets, including SVNH, CIFAR-10, CIFAR-100, and Tiny ImageNet. Our code is available at //github.com/shqii1j/seqmatch.
We present a learning-based dynamics model for granular material manipulation. Inspired by the Eulerian approach commonly used in fluid dynamics, our method adopts a fully convolutional neural network that operates on a density field-based representation of object piles and pushers, allowing it to exploit the spatial locality of inter-object interactions as well as the translation equivariance through convolution operations. Furthermore, our differentiable action rendering module makes the model fully differentiable and can be directly integrated with a gradient-based trajectory optimization algorithm. We evaluate our model with a wide array of piles manipulation tasks both in simulation and real-world experiments and demonstrate that it significantly exceeds existing latent or particle-based methods in both accuracy and computation efficiency, and exhibits zero-shot generalization capabilities across various environments and tasks.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.
Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.
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