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Register a new userNeural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks
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Added by
Francis Williams
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural network-based techniques and widely used Poisson Surface Reconstruction (which, as we demonstrate, can also be viewed as a type of kernel method). Because our approach is based on a simple kernel formulation, it is easy to analyze and can be accelerated by general techniques designed for kernel-based learning. We provide explicit analytical expressions for our kernel and argue that our formulation can be seen as a generalization of cubic spline interpolation to higher dimensions. In particular, the RKHS norm associated with Neural Splines biases toward smooth interpolants.
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We propose a novel approach for 3D video synthesis that is able to represent multi-view video recordings of a dynamic real-world scene in a compact, yet expressive representation that enables high-quality view synthesis and motion interpolation. Our approach takes the high quality and compactness of static neural radiance fields in a new direction: to a model-free, dynamic setting. At the core of our approach is a novel time-conditioned neural radiance fields that represents scene dynamics using a set of compact latent codes. To exploit the fact that changes between adjacent frames of a video are typically small and locally consistent, we propose two novel strategies for efficient training of our neural network: 1) An efficient hierarchical training scheme, and 2) an importance sampling strategy that selects the next rays for training based on the temporal variation of the input videos. In combination, these two strategies significantly boost the training speed, lead to fast convergence of the training process, and enable high quality results. Our learned representation is highly compact and able to represent a 10 second 30 FPS multi-view video recording by 18 cameras with a model size of just 28MB. We demonstrate that our method can render high-fidelity wide-angle novel views at over 1K resolution, even for highly complex and dynamic scenes. We perform an extensive qualitative and quantitative evaluation that shows that our approach outperforms the current state of the art. We include additional video and information at: https://neural-3d-video.github.io/
In this preliminary work, we study the generalization properties of infinite ensembles of infinitely-wide neural networks. Amazingly, this model family admits tractable calculations for many information-theoretic quantities. We report analytical and empirical investigations in the search for signals that correlate with generalization.
This paper presents new designs of graph convolutional neural networks (GCNs) on 3D meshes for 3D object segmentation and classification. We use the faces of the mesh as basic processing units and represent a 3D mesh as a graph where each node corresponds to a face. To enhance the descriptive power of the graph, we introduce a 1-ring face neighbourhood structure to derive novel multi-dimensional spatial and structure features to represent the graph nodes. Based on this new graph representation, we then design a densely connected graph convolutional block which aggregates local and regional features as the key construction component to build effective and efficient practical GCN models for 3D object classification and segmentation. We will present experimental results to show that our new technique outperforms state of the art where our models are shown to have the smallest number of parameters and consietently achieve the highest accuracies across a number of benchmark datasets. We will also present ablation studies to demonstrate the soundness of our design principles and the effectiveness of our practical models.
We analyze the learning dynamics of infinitely wide neural networks with a finite sized bottle-neck. Unlike the neural tangent kernel limit, a bottleneck in an otherwise infinite width network al-lows data dependent feature learning in its bottle-neck representation. We empirically show that a single bottleneck in infinite networks dramatically accelerates training when compared to purely in-finite networks, with an improved overall performance. We discuss the acceleration phenomena by drawing similarities to infinitely wide deep linear models, where the acceleration effect of a bottleneck can be understood theoretically.
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et al., 2012], we derive simple characterizations of the convex hulls of the corresponding atomic sets for this problem under several different constraints on the weights and biases of the network, thus obtaining equivalent convex formulations for these problems. A modest extension of our proposed framework to a binary classification problem is also presented. We explore the efficacy of the resulting formulations experimentally, and compare with networks trained via gradient descent.
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