The Implicit Regularization of Momentum Gradient Descent with Early Stopping

The study on the implicit regularization induced by gradient-based optimization is a longstanding pursuit. In the present paper, we characterize the implicit regularization of momentum gradient descent (MGD) with early stopping by comparing with the explicit $\ell_2$-regularization (ridge). In details, we study MGD in the continuous-time view, so-called momentum gradient flow (MGF), and show that its tendency is closer to ridge than the gradient descent (GD) [Ali et al., 2019] for least squares regression. Moreover, we prove that, under the calibration $t=\sqrt{2/\lambda}$, where $t$ is the time parameter in MGF and $\lambda$ is the tuning parameter in ridge regression, the risk of MGF is no more than 1.54 times that of ridge. In particular, the relative Bayes risk of MGF to ridge is between 1 and 1.035 under the optimal tuning. The numerical experiments support our theoretical results strongly.

Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse problems of the (2+1)-dimensional KP-I equation and spin-NLS equation are studied via deep learning. The main idea of the data-driven forward and inverse problems is to use the deep neural networks with the activation function to approximate the solutions of the considered (2+1)-dimensional nonlinear wave equations by optimizing the chosen loss functions related to the considered nonlinear wave equations.

Data-driven discovery of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes

We introduce a deep neural network learning scheme to learn the B\"acklund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively. The first scheme takes advantage of some solution (or soliton equation) information to study the data-driven BT of sine-Gordon equation, and complex and real Miura transforms between the defocusing (focusing) mKdV equation and KdV equation, as well as the data-driven mKdV equation discovery via the Miura transforms. The second deep learning scheme uses the explicit/implicit BTs generating the higher-order solitons to train the data-driven discovery of mKdV and sine-Gordon equations, in which the high-order solution informations are more powerful for the enhanced leaning soliton equations with higher accurates.

Mathematical Models for Local Sensing Hashes

As data volumes continue to grow, searches in data are becoming increasingly time-consuming. Classical index structures for neighbor search are no longer sustainable due to the "curse of dimensionality". Instead, approximated index structures offer a good opportunity to significantly accelerate the neighbor search for clustering and outlier detection and to have the lowest possible error rate in the results of the algorithms. Local sensing hashes is one of those. We indicate directions to mathematically model the properties of it.

Practical and Light-weight Secure Aggregation for Federated Submodel Learning

Recently, Niu, et. al. introduced a new variant of Federated Learning (FL), called Federated Submodel Learning (FSL). Different from traditional FL, each client locally trains the submodel (e.g., retrieved from the servers) based on its private data and uploads a submodel at its choice to the servers. Then all clients aggregate all their submodels and finish the iteration. Inevitably, FSL introduces two privacy-preserving computation tasks, i.e., Private Submodel Retrieval (PSR) and Secure Submodel Aggregation (SSA). Existing work fails to provide a loss-less scheme, or has impractical efficiency. In this work, we leverage Distributed Point Function (DPF) and cuckoo hashing to construct a practical and light-weight secure FSL scheme in the two-server setting. More specifically, we propose two basic protocols with few optimisation techniques, which ensures our protocol practicality on specific real-world FSL tasks. Our experiments show that our proposed protocols can finish in less than 1 minute when weight sizes $\leq 2^{15}$, we also demonstrate protocol efficiency by comparing with existing work and by handling a real-world FSL task.

Dispensed Transformer Network for Unsupervised Domain Adaptation

Accurate segmentation is a crucial step in medical image analysis and applying supervised machine learning to segment the organs or lesions has been substantiated effective. However, it is costly to perform data annotation that provides ground truth labels for training the supervised algorithms, and the high variance of data that comes from different domains tends to severely degrade system performance over cross-site or cross-modality datasets. To mitigate this problem, a novel unsupervised domain adaptation (UDA) method named dispensed Transformer network (DTNet) is introduced in this paper. Our novel DTNet contains three modules. First, a dispensed residual transformer block is designed, which realizes global attention by dispensed interleaving operation and deals with the excessive computational cost and GPU memory usage of the Transformer. Second, a multi-scale consistency regularization is proposed to alleviate the loss of details in the low-resolution output for better feature alignment. Finally, a feature ranking discriminator is introduced to automatically assign different weights to domain-gap features to lessen the feature distribution distance, reducing the performance shift of two domains. The proposed method is evaluated on large fluorescein angiography (FA) retinal nonperfusion (RNP) cross-site dataset with 676 images and a wide used cross-modality dataset from the MM-WHS challenge. Extensive results demonstrate that our proposed network achieves the best performance in comparison with several state-of-the-art techniques.

Joint Model and Data Driven Receiver Design for Data-Dependent Superimposed Training Scheme with Imperfect Hardware

Data-dependent superimposed training (DDST) scheme has shown the potential to achieve high bandwidth efficiency, while encounters symbol misidentification caused by hardware imperfection. To tackle these challenges, a joint model and data driven receiver scheme is proposed in this paper. Specifically, based on the conventional linear receiver model, the least squares (LS) estimation and zero forcing (ZF) equalization are first employed to extract the initial features for channel estimation and data detection. Then, shallow neural networks, named CE-Net and SD-Net, are developed to refine the channel estimation and data detection, where the imperfect hardware is modeled as a nonlinear function and data is utilized to train these neural networks to approximate it. Simulation results show that compared with the conventional minimum mean square error (MMSE) equalization scheme, the proposed one effectively suppresses the symbol misidentification and achieves similar or better bit error rate (BER) performance without the second-order statistics about the channel and noise.

Enhanced ELM Based Channel Estimation for RIS-Assisted OFDM systems with Insufficient CP and Imperfect Hardware

Reconfigurable intelligent surface (RIS)-assisted orthogonal frequency division multiplexing (OFDM) systems have aroused extensive research interests due to the controllable communication environment and the performance of combating multi-path interference. However, as the premise of RIS-assisted OFDM systems, the accuracy of channel estimation is severely degraded by the increased possibility of insufficient cyclic prefix (CP) produced by extra cascaded channels of RIS and the nonlinear distortion lead by imperfect hardware. To address these issues, an enhanced extreme learning machine (ELM)- based channel estimation (eELM-CE) is proposed in this letter to facilitate accurate channel estimation. Based on the model-driven mode, least square (LS) estimation is employed to highlight the initial linear features for channel estimation. Then, according to the obtained initial features, an enhanced ELM network is constructed to refine the channel estimation. In particular, we start from the perspective of guiding it to recognize the feature, and normalize the data after the network activation function to enhance the ability of identifying non-linear factors. Experiment results show that, compared with existing methods, the proposed method achieves a much lower normalized mean square error (NMSE) given insufficient CP and imperfect hardware. In addition, the simulation results indicate that the proposed method possesses robustness against the parameter variations.

Wav2vec-S: Semi-Supervised Pre-Training for Speech Recognition

Self-supervised pre-training has dramatically improved the performance of automatic speech recognition (ASR). However, most existing self-supervised pre-training approaches are task-agnostic, i.e., could be applied to various downstream tasks. And there is a gap between the task-agnostic pre-training and the task-specific downstream fine-tuning, which may degrade the downstream performance. In this work, we propose a novel pre-training paradigm called wav2vec-S, where we use task-specific semi-supervised pre-training to bridge this gap. Specifically, the semi-supervised pre-training is conducted on the basis of self-supervised pre-training such as wav2vec 2.0. Experiments on ASR show that compared to wav2vec 2.0, wav2vec-S only requires marginal increment of pre-training time but could significantly improve ASR performance on in-domain, cross-domain and cross-lingual datasets. The average relative WER reductions are 26.3% and 6.3% for 1h and 10h fine-tuning, respectively.

Two-Stage Mesh Deep Learning for Automated Tooth Segmentation and Landmark Localization on 3D Intraoral Scans

Accurately segmenting teeth and identifying the corresponding anatomical landmarks on dental mesh models are essential in computer-aided orthodontic treatment. Manually performing these two tasks is time-consuming, tedious, and, more importantly, highly dependent on orthodontists' experiences due to the abnormality and large-scale variance of patients' teeth. Some machine learning-based methods have been designed and applied in the orthodontic field to automatically segment dental meshes (e.g., intraoral scans). In contrast, the number of studies on tooth landmark localization is still limited. This paper proposes a two-stage framework based on mesh deep learning (called TS-MDL) for joint tooth labeling and landmark identification on raw intraoral scans. Our TS-MDL first adopts an end-to-end \emph{i}MeshSegNet method (i.e., a variant of the existing MeshSegNet with both improved accuracy and efficiency) to label each tooth on the downsampled scan. Guided by the segmentation outputs, our TS-MDL further selects each tooth's region of interest (ROI) on the original mesh to construct a light-weight variant of the pioneering PointNet (i.e., PointNet-Reg) for regressing the corresponding landmark heatmaps. Our TS-MDL was evaluated on a real-clinical dataset, showing promising segmentation and localization performance. Specifically, \emph{i}MeshSegNet in the first stage of TS-MDL reached an averaged Dice similarity coefficient (DSC) at $0.953\pm0.076$, significantly outperforming the original MeshSegNet. In the second stage, PointNet-Reg achieved a mean absolute error (MAE) of $0.623\pm0.718 \, mm$ in distances between the prediction and ground truth for $44$ landmarks, which is superior compared with other networks for landmark detection. All these results suggest the potential usage of our TS-MDL in clinical practices.