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Register a new userPhase Transitions, Distance Functions, and Implicit Neural Representations
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Added by
Yaron Lipman
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Yaron Lipman
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Representing surfaces as zero level sets of neural networks recently emerged as a powerful modeling paradigm, named Implicit Neural Representations (INRs), serving numerous downstream applications in geometric deep learning and 3D vision. Training INRs previously required choosing between occupancy and distance function representation and different losses with unknown limit behavior and/or bias. In this paper we draw inspiration from the theory of phase transitions of fluids and suggest a loss for training INRs that learns a density function that converges to a proper occupancy function, while its log transform converges to a distance function. Furthermore, we analyze the limit minimizer of this loss showing it satisfies the reconstruction constraints and has minimal surface perimeter, a desirable inductive bias for surface reconstruction. Training INRs with this new loss leads to state-of-the-art reconstructions on a standard benchmark.
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Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signals spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or Sirens, are ideally suited for representing complex natural signals and their derivatives. We analyze Siren activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how Sirens can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine Sirens with hypernetworks to learn priors over the space of Siren functions.
We propose a new simple approach for image compression: instead of storing the RGB values for each pixel of an image, we store the weights of a neural network overfitted to the image. Specifically, to encode an image, we fit it with an MLP which maps pixel locations to RGB values. We then quantize and store the weights of this MLP as a code for the image. To decode the image, we simply evaluate the MLP at every pixel location. We found that this simple approach outperforms JPEG at low bit-rates, even without entropy coding or learning a distribution over weights. While our framework is not yet competitive with state of the art compression methods, we show that it has various attractive properties which could make it a viable alternative to other neural data compression approaches.
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined state vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform the state-of-the-art GNN models.
The recent success of implicit neural scene representations has presented a viable new method for how we capture and store 3D scenes. Unlike conventional 3D representations, such as point clouds, which explicitly store scene properties in discrete, localized units, these implicit representations encode a scene in the weights of a neural network which can be queried at any coordinate to produce these same scene properties. Thus far, implicit representations have primarily been optimized to estimate only the appearance and/or 3D geometry information in a scene. We take the next step and demonstrate that an existing implicit representation (SRNs) is actually multi-modal; it can be further leveraged to perform per-point semantic segmentation while retaining its ability to represent appearance and geometry. To achieve this multi-modal behavior, we utilize a semi-supervised learning strategy atop the existing pre-trained scene representation. Our method is simple, general, and only requires a few tens of labeled 2D segmentation masks in order to achieve dense 3D semantic segmentation. We explore two novel applications for this semantically aware implicit neural scene representation: 3D novel view and semantic label synthesis given only a single input RGB image or 2D label mask, as well as 3D interpolation of appearance and semantics.
Implicit neural representation is a recent approach to learn shape collections as zero level-sets of neural networks, where each shape is represented by a latent code. So far, the focus has been shape reconstruction, while shape generalization was mostly left to generic encoder-decoder or auto-decoder regularization. In this paper we advocate deformation-aware regularization for implicit neural representations, aiming at producing plausible deformations as latent code changes. The challenge is that implicit representations do not capture correspondences between different shapes, which makes it difficult to represent and regularize their deformations. Thus, we propose to pair the implicit representation of the shapes with an explicit, piecewise linear deformation field, learned as an auxiliary function. We demonstrate that, by regularizing these deformation fields, we can encourage the implicit neural representation to induce natural deformations in the learned shape space, such as as-rigid-as-possible deformations.
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