Grounding and Enhancing Grid-based Models for Neural Fields

Many contemporary studies utilize grid-based models for neural field representation, but a systematic analysis of grid-based models is still missing, hindering the improvement of those models. Therefore, this paper introduces a theoretical framework for grid-based models. This framework points out that these models' approximation and generalization behaviors are determined by grid tangent kernels (GTK), which are intrinsic properties of grid-based models. The proposed framework facilitates a consistent and systematic analysis of diverse grid-based models. Furthermore, the introduced framework motivates the development of a novel grid-based model named the Multiplicative Fourier Adaptive Grid (MulFAGrid). The numerical analysis demonstrates that MulFAGrid exhibits a lower generalization bound than its predecessors, indicating its robust generalization performance. Empirical studies reveal that MulFAGrid achieves state-of-the-art performance in various tasks, including 2D image fitting, 3D signed distance field (SDF) reconstruction, and novel view synthesis, demonstrating superior representation ability. The project website is available at https://sites.google.com/view/cvpr24-2034-submission/home.

Enhancing the Performance of Neural Networks Through Causal Discovery and Integration of Domain Knowledge

In this paper, we develop a generic methodology to encode hierarchical causality structure among observed variables into a neural network in order to improve its predictive performance. The proposed methodology, called causality-informed neural network (CINN), leverages three coherent steps to systematically map the structural causal knowledge into the layer-to-layer design of neural network while strictly preserving the orientation of every causal relationship. In the first step, CINN discovers causal relationships from observational data via directed acyclic graph (DAG) learning, where causal discovery is recast as a continuous optimization problem to avoid the combinatorial nature. In the second step, the discovered hierarchical causality structure among observed variables is systematically encoded into neural network through a dedicated architecture and customized loss function. By categorizing variables in the causal DAG as root, intermediate, and leaf nodes, the hierarchical causal DAG is translated into CINN with a one-to-one correspondence between nodes in the causal DAG and units in the CINN while maintaining the relative order among these nodes. Regarding the loss function, both intermediate and leaf nodes in the DAG graph are treated as target outputs during CINN training so as to drive co-learning of causal relationships among different types of nodes. As multiple loss components emerge in CINN, we leverage the projection of conflicting gradients to mitigate gradient interference among the multiple learning tasks. Computational experiments across a broad spectrum of UCI data sets demonstrate substantial advantages of CINN in predictive performance over other state-of-the-art methods. In addition, an ablation study underscores the value of integrating structural and quantitative causal knowledge in enhancing the neural network's predictive performance incrementally.

CTformer: Convolution-free Token2Token Dilated Vision Transformer for Low-dose CT Denoising

Low-dose computed tomography (LDCT) denoising is an important problem in CT research. Compared to the normal dose CT (NDCT), LDCT images are subjected to severe noise and artifacts. Recently in many studies, vision transformers have shown superior feature representation ability over convolutional neural networks (CNNs). However, unlike CNNs, the potential of vision transformers in LDCT denoising was little explored so far. To fill this gap, we propose a Convolution-free Token2Token Dilated Vision Transformer for low-dose CT denoising. The CTformer uses a more powerful token rearrangement to encompass local contextual information and thus avoids convolution. It also dilates and shifts feature maps to capture longer-range interaction. We interpret the CTformer by statically inspecting patterns of its internal attention maps and dynamically tracing the hierarchical attention flow with an explanatory graph. Furthermore, an overlapped inference mechanism is introduced to effectively eliminate the boundary artifacts that are common for encoder-decoder-based denoising models. Experimental results on Mayo LDCT dataset suggest that the CTformer outperforms the state-of-the-art denoising methods with a low computation overhead.

Low-dimensional Manifold Constrained Disentanglement Network for Metal Artifact Reduction

Deep neural network based methods have achieved promising results for CT metal artifact reduction (MAR), most of which use many synthesized paired images for training. As synthesized metal artifacts in CT images may not accurately reflect the clinical counterparts, an artifact disentanglement network (ADN) was proposed with unpaired clinical images directly, producing promising results on clinical datasets. However, without sufficient supervision, it is difficult for ADN to recover structural details of artifact-affected CT images based on adversarial losses only. To overcome these problems, here we propose a low-dimensional manifold (LDM) constrained disentanglement network (DN), leveraging the image characteristics that the patch manifold is generally low-dimensional. Specifically, we design an LDM-DN learning algorithm to empower the disentanglement network through optimizing the synergistic network loss functions while constraining the recovered images to be on a low-dimensional patch manifold. Moreover, learning from both paired and unpaired data, an efficient hybrid optimization scheme is proposed to further improve the MAR performance on clinical datasets. Extensive experiments demonstrate that the proposed LDM-DN approach can consistently improve the MAR performance in paired and/or unpaired learning settings, outperforming competing methods on synthesized and clinical datasets.

On Interpretability of Artificial Neural Networks

Deep learning has achieved great successes in many important areas to dealing with text, images, video, graphs, and so on. However, the black-box nature of deep artificial neural networks has become the primary obstacle to their public acceptance and wide popularity in critical applications such as diagnosis and therapy. Due to the huge potential of deep learning, interpreting neural networks has become one of the most critical research directions. In this paper, we systematically review recent studies in understanding the mechanism of neural networks and shed light on some future directions of interpretability research (This work is still in progress).

Quadratic Autoencoder for Low-Dose CT Denoising

Recently, deep learning has transformed many fields including medical imaging. Inspired by diversity of biological neurons, our group proposed quadratic neurons in which the inner product in current artificial neurons is replaced with a quadratic operation on inputs, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power of quadratic neurons in representative network architectures, towards quadratic neuron based deep learning. In this regard, our prior theoretical studies have shown important merits of quadratic neurons and networks. In this paper, we use quadratic neurons to construct an encoder-decoder structure, referred to as the quadratic auto-encoder, and apply it for low-dose CT de-noising. Then, we perform experiments on the Mayo low-dose CT dataset to demonstrate that the quadratic auto-encoder yields a better de-noising performance.

Soft-Autoencoder and Its Wavelet Shrinkage Interpretation

Deep learning is a main focus of artificial intelligence and has greatly impacted other fields. However, deep learning is often criticized for its lack of interpretation. As a successful unsupervised model in deep learning, various autoencoders, especially convolutional autoencoders, are very popular and important. Since these autoencoders need improvements and insights, in this paper we shed light on the nonlinearity of a deep convolutional autoencoder in perspective of perfect signal recovery. In particular, we propose a new type of convolutional autoencoders, termed as Soft-Autoencoder (Soft-AE), in which the activations of encoding layers are implemented with adaptable soft-thresholding units while decoding layers are realized with linear units. Consequently, Soft-AE can be naturally interpreted as a learned cascaded wavelet shrinkage system. Our denoising numerical experiments on CIFAR-10, BSD-300 and Mayo Clinical Challenge Dataset demonstrate that Soft-AE gives a competitive performance relative to its counterparts.

Universal Approximation by a Slim Network with Sparse Shortcut Connections

Over recent years, deep learning has become a mainstream method in machine learning. More advanced networks are being actively developed to solve real-world problems in many important areas. Among successful features of network architectures, shortcut connections are well established to take the outputs of earlier layers as the inputs to later layers, and produce excellent results such as in ResNet and DenseNet. Despite the power of shortcuts, there remain important questions on the underlying mechanism and associated functionalities. For example, will adding shortcuts lead to a more compact structure? How to use shortcuts for an optimal efficiency and capacity of the network model? Along this direction, here we demonstrate that given only one neuron in each layer, the shortcuts can be sparsely placed to let the slim network become an universal approximator. Potentially, our theoretically-guaranteed sparse network model can achieve a learning performance comparable to densely-connected networks on well-known benchmarks.