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We present Factor Fields, a novel framework for modeling and representing signals. Factor Fields decomposes a signal into a product of factors, each of which is represented by a neural or regular field representation operating on a coordinate transformed input signal. We show that this decomposition yields a unified framework that generalizes several recent signal representations including NeRF, PlenOxels, EG3D, Instant-NGP, and TensoRF. Moreover, the framework allows for the creation of powerful new signal representations, such as the Coefficient-Basis Factorization (CoBaFa) which we propose in this paper. As evidenced by our experiments, CoBaFa leads to improvements over previous fast reconstruction methods in terms of the three critical goals in neural signal representation: approximation quality, compactness and efficiency. Experimentally, we demonstrate that our representation achieves better image approximation quality on 2D image regression tasks, higher geometric quality when reconstructing 3D signed distance fields and higher compactness for radiance field reconstruction tasks compared to previous fast reconstruction methods. Besides, our CoBaFa representation enables generalization by sharing the basis across signals during training, enabling generalization tasks such as image regression with sparse observations and few-shot radiance field reconstruction.

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.

This paper presents an inverse kinematic optimization layer (IKOL) for 3D human pose and shape estimation that leverages the strength of both optimization- and regression-based methods within an end-to-end framework. IKOL involves a nonconvex optimization that establishes an implicit mapping from an image's 3D keypoints and body shapes to the relative body-part rotations. The 3D keypoints and the body shapes are the inputs and the relative body-part rotations are the solutions. However, this procedure is implicit and hard to make differentiable. So, to overcome this issue, we designed a Gauss-Newton differentiation (GN-Diff) procedure to differentiate IKOL. GN-Diff iteratively linearizes the nonconvex objective function to obtain Gauss-Newton directions with closed form solutions. Then, an automatic differentiation procedure is directly applied to generate a Jacobian matrix for end-to-end training. Notably, the GN-Diff procedure works fast because it does not rely on a time-consuming implicit differentiation procedure. The twist rotation and shape parameters are learned from the neural networks and, as a result, IKOL has a much lower computational overhead than most existing optimization-based methods. Additionally, compared to existing regression-based methods, IKOL provides a more accurate mesh-image correspondence. This is because it iteratively reduces the distance between the keypoints and also enhances the reliability of the pose structures. Extensive experiments demonstrate the superiority of our proposed framework over a wide range of 3D human pose and shape estimation methods.

Multi-sequence MRIs can be necessary for reliable diagnosis in clinical practice due to the complimentary information within sequences. However, redundant information exists across sequences, which interferes with mining efficient representations by modern machine learning or deep learning models. To handle various clinical scenarios, we propose a sequence-to-sequence generation framework (Seq2Seq) for imaging-differentiation representation learning. In this study, not only do we propose arbitrary 3D/4D sequence generation within one model to generate any specified target sequence, but also we are able to rank the importance of each sequence based on a new metric estimating the difficulty of a sequence being generated. Furthermore, we also exploit the generation inability of the model to extract regions that contain unique information for each sequence. We conduct extensive experiments using three datasets including a toy dataset of 20,000 simulated subjects, a brain MRI dataset of 1,251 subjects, and a breast MRI dataset of 2,101 subjects, to demonstrate that (1) our proposed Seq2Seq is efficient and lightweight for complex clinical datasets and can achieve excellent image quality; (2) top-ranking sequences can be used to replace complete sequences with non-inferior performance; (3) combining MRI with our imaging-differentiation map leads to better performance in clinical tasks such as glioblastoma MGMT promoter methylation status prediction and breast cancer pathological complete response status prediction. Our code is available at //github.com/fiy2W/mri_seq2seq.

In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.

We present Neural Shape Deformation Priors, a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements. State-of-the-art methods cast this problem as an optimization task, where the input source mesh is iteratively deformed to minimize an objective function according to hand-crafted regularizers such as ARAP. In this work, we learn the deformation behavior based on the underlying geometric properties of a shape, while leveraging a large-scale dataset containing a diverse set of non-rigid deformations. Specifically, given a source mesh and desired target locations of handles that describe the partial surface deformation, we predict a continuous deformation field that is defined in 3D space to describe the space deformation. To this end, we introduce transformer-based deformation networks that represent a shape deformation as a composition of local surface deformations. It learns a set of local latent codes anchored in 3D space, from which we can learn a set of continuous deformation functions for local surfaces. Our method can be applied to challenging deformations and generalizes well to unseen deformations. We validate our approach in experiments using the DeformingThing4D dataset, and compare to both classic optimization-based and recent neural network-based methods.

We present a novel neural surface reconstruction method, called NeuS, for reconstructing objects and scenes with high fidelity from 2D image inputs. Existing neural surface reconstruction approaches, such as DVR and IDR, require foreground mask as supervision, easily get trapped in local minima, and therefore struggle with the reconstruction of objects with severe self-occlusion or thin structures. Meanwhile, recent neural methods for novel view synthesis, such as NeRF and its variants, use volume rendering to produce a neural scene representation with robustness of optimization, even for highly complex objects. However, extracting high-quality surfaces from this learned implicit representation is difficult because there are not sufficient surface constraints in the representation. In NeuS, we propose to represent a surface as the zero-level set of a signed distance function (SDF) and develop a new volume rendering method to train a neural SDF representation. We observe that the conventional volume rendering method causes inherent geometric errors (i.e. bias) for surface reconstruction, and therefore propose a new formulation that is free of bias in the first order of approximation, thus leading to more accurate surface reconstruction even without the mask supervision. Experiments on the DTU dataset and the BlendedMVS dataset show that NeuS outperforms the state-of-the-arts in high-quality surface reconstruction, especially for objects and scenes with complex structures and self-occlusion.

This paper presents a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet representation with a pair of coarse and detail coefficient volumes to implicitly represent 3D shapes via truncated signed distance functions and multi-scale biorthogonal wavelets. Then, we design a pair of neural networks: a diffusion-based generator to produce diverse shapes in the form of the coarse coefficient volumes and a detail predictor to produce compatible detail coefficient volumes for introducing fine structures and details. Further, we may jointly train an encoder network to learn a latent space for inverting shapes, allowing us to enable a rich variety of whole-shape and region-aware shape manipulations. Both quantitative and qualitative experimental results manifest the compelling shape generation, inversion, and manipulation capabilities of our approach over the state-of-the-art methods.

Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, to allow efficient decoding over repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming, for a broad range of topological codes, the existing neural and classical decoders, which are often computationally prohibitive.

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.