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3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

In this paper, we present an in-depth investigation of the convolutional autoencoder (CAE) bottleneck. Autoencoders (AE), and especially their convolutional variants, play a vital role in the current deep learning toolbox. Researchers and…

Deep convolutional neural networks (CNNs) have proven highly effective for visual recognition, where learning a universal representation from activations of convolutional layer plays a fundamental problem. In this paper, we present Fisher…

We present Kernel Point Convolution (KPConv), a new design of point convolution, i.e. that operates on point clouds without any intermediate representation. The convolution weights of KPConv are located in Euclidean space by kernel points,…

Recent advances in representation learning have successfully leveraged the underlying domain-specific structure of data across various fields. However, representing diverse and complex entities stored in tabular format within a latent space…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…

Accurate numerical integration over non-uniform point clouds is a challenge for modern mesh-free machine learning solvers for partial differential equations (PDEs) using variational principles. While standard Monte Carlo (MC) methods are…

In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel…

Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however,…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

We present an unsupervised 3D shape co-segmentation method which learns a set of deformable part templates from a shape collection. To accommodate structural variations in the collection, our network composes each shape by a selected subset…

We propose a Point-Voxel DeConvolution (PVDeConv) module for 3D data autoencoder. To demonstrate its efficiency we learn to synthesize high-resolution point clouds of 10k points that densely describe the underlying geometry of Computer…

We present a novel algorithm for point cloud segmentation. Our approach transforms unstructured point clouds into regular voxel grids, and further uses a kernel-based interpolated variational autoencoder (VAE) architecture to encode the…

In this paper we demonstrate methods for reliable and efficient training of discrete representation using Vector-Quantized Variational Auto-Encoder models (VQ-VAEs). Discrete latent variable models have been shown to learn nontrivial…

We present a novel method for constructing Variational Autoencoder (VAE). Instead of using pixel-by-pixel loss, we enforce deep feature consistency between the input and the output of a VAE, which ensures the VAE's output to preserve the…

Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

We introduce a novel weighted convolution operator that enhances traditional convolutional neural networks (CNNs) by integrating a spatial density function into the convolution operator. This extension enables the network to differentially…