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In molecular systems, the ultrafast motion of electrons initiates the process of chemical change. Tracking this electronic motion across molecules requires coupling attosecond time resolution to atomic-scale spatial sensitivity. In this work, we employ a pair of attosecond x-ray pulses from an x-ray free-electron laser to follow electron motion resulting from the sudden removal of an electron from a prototypical aromatic system, para-aminophenol. X-ray absorption enables tracking this motion with atomic-site specificity. Our measurements are compared with state-of-the-art computational modeling, reproducing the observed response across multiple timescales. Sub-femtosecond dynamics are assigned to states undergoing non-radiative decay, while few-femtosecond oscillatory motion is associated with electronic wavepacket motion in stable cation states, that will eventually couple to nuclear motion. Our work provides insight on the ultrafast charge motion preceding and initiating chemical transformations in moderately complex systems, and provides a powerful benchmark for computational models of ultrafast charge motion in matter.

Objective: Mitigating algorithmic disparities is a critical challenge in healthcare research, where ensuring equity and fairness is paramount. While large-scale healthcare data exist across multiple institutions, cross-institutional collaborations often face privacy constraints, highlighting the need for privacy-preserving solutions that also promote fairness. Materials and Methods: In this study, we present Fair Federated Machine Learning (FairFML), a model-agnostic solution designed to reduce algorithmic bias in cross-institutional healthcare collaborations while preserving patient privacy. As a proof of concept, we validated FairFML using a real-world clinical case study focused on reducing gender disparities in cardiac arrest outcome prediction. Results: We demonstrate that the proposed FairFML framework enhances fairness in federated learning (FL) models without compromising predictive performance. Our findings show that FairFML improves model fairness by up to 65% compared to the centralized model, while maintaining performance comparable to both local and centralized models, as measured by receiver operating characteristic analysis. Discussion and Conclusion: FairFML offers a promising and flexible solution for FL collaborations, with its adaptability allowing seamless integration with various FL frameworks and models, from traditional statistical methods to deep learning techniques. This makes FairFML a robust approach for developing fairer FL models across diverse clinical and biomedical applications.

Direct speech translation (ST) models often struggle with rare words. Incorrect translation of these words can have severe consequences, impacting translation quality and user trust. While rare word translation is inherently challenging for neural models due to sparse learning signals, real-world scenarios often allow access to translations of past recordings on similar topics. To leverage these valuable resources, we propose a retrieval-and-demonstration approach to enhance rare word translation accuracy in direct ST models. First, we adapt existing ST models to incorporate retrieved examples for rare word translation, which allows the model to benefit from prepended examples, similar to in-context learning. We then develop a cross-modal (speech-to-speech, speech-to-text, text-to-text) retriever to locate suitable examples. We demonstrate that standard ST models can be effectively adapted to leverage examples for rare word translation, improving rare word translation accuracy over the baseline by 17.6% with gold examples and 8.5% with retrieved examples. Moreover, our speech-to-speech retrieval approach outperforms other modalities and exhibits higher robustness to unseen speakers. Our code is publicly available (https://github.com/SiqiLii/Retrieve-and-Demonstration-ST)., Comment: EMNLP 2024

Retrieval-augmented generation (RAG) is a framework enabling large language models (LLMs) to enhance their accuracy and reduce hallucinations by integrating external knowledge bases. In this paper, we introduce a hybrid RAG system enhanced through a comprehensive suite of optimizations that significantly improve retrieval quality, augment reasoning capabilities, and refine numerical computation ability. We refined the text chunks and tables in web pages, added attribute predictors to reduce hallucinations, conducted LLM Knowledge Extractor and Knowledge Graph Extractor, and finally built a reasoning strategy with all the references. We evaluated our system on the CRAG dataset through the Meta CRAG KDD Cup 2024 Competition. Both the local and online evaluations demonstrate that our system significantly enhances complex reasoning capabilities. In local evaluations, we have significantly improved accuracy and reduced error rates compared to the baseline model, achieving a notable increase in scores. In the meanwhile, we have attained outstanding results in online assessments, demonstrating the performance and generalization capabilities of the proposed system. The source code for our system is released in \url{https://gitlab.aicrowd.com/shizueyy/crag-new}., Comment: Technical report for 3rd prize in Task 1 of Meta CRAG KDD Cup 2024

Binary Neural Networks~(BNNs) have been proven to be highly effective for deploying deep neural networks on mobile and embedded platforms. Most existing works focus on minimizing quantization errors, improving representation ability, or designing gradient approximations to alleviate gradient mismatch in BNNs, while leaving the weight sign flipping, a critical factor for achieving powerful BNNs, untouched. In this paper, we investigate the efficiency of weight sign updates in BNNs. We observe that, for vanilla BNNs, over 50\% of the weights remain their signs unchanged during training, and these weights are not only distributed at the tails of the weight distribution but also universally present in the vicinity of zero. We refer to these weights as ``silent weights'', which slow down convergence and lead to a significant accuracy degradation. Theoretically, we reveal this is due to the independence of the BNNs gradient from the latent weight distribution. To address the issue, we propose Overcome Silent Weights~(OvSW). OvSW first employs Adaptive Gradient Scaling~(AGS) to establish a relationship between the gradient and the latent weight distribution, thereby improving the overall efficiency of weight sign updates. Additionally, we design Silence Awareness Decaying~(SAD) to automatically identify ``silent weights'' by tracking weight flipping state, and apply an additional penalty to ``silent weights'' to facilitate their flipping. By efficiently updating weight signs, our method achieves faster convergence and state-of-the-art performance on CIFAR10 and ImageNet1K dataset with various architectures. For example, OvSW obtains 61.6\% and 65.5\% top-1 accuracy on the ImageNet1K using binarized ResNet18 and ResNet34 architecture respectively. Codes are available at \url{https://github.com/JingyangXiang/OvSW}., Comment: Accepted by the 18th European Conference on Computer Vision (ECCV 2024)

Clinical and biomedical research in low-resource settings often faces significant challenges due to the need for high-quality data with sufficient sample sizes to construct effective models. These constraints hinder robust model training and prompt researchers to seek methods for leveraging existing knowledge from related studies to support new research efforts. Transfer learning (TL), a machine learning technique, emerges as a powerful solution by utilizing knowledge from pre-trained models to enhance the performance of new models, offering promise across various healthcare domains. Despite its conceptual origins in the 1990s, the application of TL in medical research has remained limited, especially beyond image analysis. In our review of TL applications in structured clinical and biomedical data, we screened 3,515 papers, with 55 meeting the inclusion criteria. Among these, only 2% (one out of 55) utilized external studies, and 7% (four out of 55) addressed scenarios involving multi-site collaborations with privacy constraints. To achieve actionable TL with structured medical data while addressing regional disparities, inequality, and privacy constraints in healthcare research, we advocate for the careful identification of appropriate source data and models, the selection of suitable TL frameworks, and the validation of TL models with proper baselines.

Standard Patlak plot is widely used to describe FDG kinetics for dynamic PET imaging. Whole-body Patlak parametric imaging remains constrained due to the need for a full-time input function. Here, we demonstrate the Relative Patlak (RP) plot, which eliminates the need for the early-time input function, for total-body parametric imaging and its application to clinical 20-min scan acquired in list-mode. We demonstrated that the RP intercept b' is equivalent to a ratio of standardized uptake value relative to the blood, while the RP slope Ki' is equal to the standard Patlak Ki multiplied by a global scaling factor for each subject. One challenge in applying RP to a short scan duration (20 min) is the high noise in parametric images. We applied a deep kernel method for noise reduction. Using the standard Patlak plot as the reference, the RP method was evaluated for lesion quantification, lesion-to-background contrast, and myocardial visualization in total-body parametric imaging with uEXPLORER in 22 human subjects who underwent a 1-h dynamic 18F-FDG scan. The RP method was also applied to the dynamic data regenerated from a clinical standard 20-min scan either at 1-h or 2-h post-injection for two cancer patients. We demonstrated that it is feasible to obtain high-quality parametric images from 20-min dynamic scans using the RP plot with a self-supervised deep-kernel noise reduction strategy. The RP Ki' highly correlated with Ki in lesions and major organs, demonstrating its quantitative potential across subjects. Compared to conventional SUVs, the Ki' images significantly improved lesion contrast and enabled visualization of the myocardium for potential cardiac assessment. The application of RP parametric imaging to two clinical scans also showed similar benefits. Total-body PET with the RP plot is feasible to generate parametric images from the dynamic data of a 20-min clinical scan.

Robotic manipulation with two-finger grippers is challenged by objects lacking distinct graspable features. Traditional pre-grasping methods, which typically involve repositioning objects or utilizing external aids like table edges, are limited in their adaptability across different object categories and environments. To overcome these limitations, we introduce PreAfford, a novel pre-grasping planning framework incorporating a point-level affordance representation and a relay training approach. Our method significantly improves adaptability, allowing effective manipulation across a wide range of environments and object types. When evaluated on the ShapeNet-v2 dataset, PreAfford not only enhances grasping success rates by 69% but also demonstrates its practicality through successful real-world experiments. These improvements highlight PreAfford's potential to redefine standards for robotic handling of complex manipulation tasks in diverse settings., Comment: Project Page: https://air-discover.github.io/PreAfford/

Electron beam shaping allows the control of the temporal properties of x-ray free-electron laser pulses from femtosecond to attosecond timescales. Here we demonstrate the use of a laser heater to shape electron bunches and enable the generation of attosecond x-ray pulses. We demonstrate that this method can be applied in a selective way, shaping a targeted subset of bunches while leaving the remaining bunches unchanged. This experiment enables the delivery of shaped x-ray pulses to multiple undulator beamlines, with pulse properties tailored to specialized scientific applications.

Action recognition from video data forms a cornerstone with wide-ranging applications. Single-view action recognition faces limitations due to its reliance on a single viewpoint. In contrast, multi-view approaches capture complementary information from various viewpoints for improved accuracy. Recently, event cameras have emerged as innovative bio-inspired sensors, leading to advancements in event-based action recognition. However, existing works predominantly focus on single-view scenarios, leaving a gap in multi-view event data exploitation, particularly in challenges like information deficit and semantic misalignment. To bridge this gap, we introduce HyperMV, a multi-view event-based action recognition framework. HyperMV converts discrete event data into frame-like representations and extracts view-related features using a shared convolutional network. By treating segments as vertices and constructing hyperedges using rule-based and KNN-based strategies, a multi-view hypergraph neural network that captures relationships across viewpoint and temporal features is established. The vertex attention hypergraph propagation is also introduced for enhanced feature fusion. To prompt research in this area, we present the largest multi-view event-based action dataset $\text{THU}^{\text{MV-EACT}}\text{-50}$, comprising 50 actions from 6 viewpoints, which surpasses existing datasets by over tenfold. Experimental results show that HyperMV significantly outperforms baselines in both cross-subject and cross-view scenarios, and also exceeds the state-of-the-arts in frame-based multi-view action recognition., Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI 2024)

Structured pruning methods are developed to bridge the gap between the massive scale of neural networks and the limited hardware resources. Most current structured pruning methods rely on training datasets to fine-tune the compressed model, resulting in high computational burdens and being inapplicable for scenarios with stringent requirements on privacy and security. As an alternative, some data-free methods have been proposed, however, these methods often require handcraft parameter tuning and can only achieve inflexible reconstruction. In this paper, we propose the Automatic Data-Free Pruning (AutoDFP) method that achieves automatic pruning and reconstruction without fine-tuning. Our approach is based on the assumption that the loss of information can be partially compensated by retaining focused information from similar channels. Specifically, We formulate data-free pruning as an optimization problem, which can be effectively addressed through reinforcement learning. AutoDFP assesses the similarity of channels for each layer and provides this information to the reinforcement learning agent, guiding the pruning and reconstruction process of the network. We evaluate AutoDFP with multiple networks on multiple datasets, achieving impressive compression results. For instance, on the CIFAR-10 dataset, AutoDFP demonstrates a 2.87\% reduction in accuracy loss compared to the recently proposed data-free pruning method DFPC with fewer FLOPs on VGG-16. Furthermore, on the ImageNet dataset, AutoDFP achieves 43.17\% higher accuracy than the SOTA method with the same 80\% preserved ratio on MobileNet-V1., Comment: 11 pages, 16 figures

Survival analysis serves as a fundamental component in numerous healthcare applications, where the determination of the time to specific events (such as the onset of a certain disease or death) for patients is crucial for clinical decision-making. Scoring systems are widely used for swift and efficient risk prediction. However, existing methods for constructing survival scores presume that data originates from a single source, posing privacy challenges in collaborations with multiple data owners. We propose a novel framework for building federated scoring systems for multi-site survival outcomes, ensuring both privacy and communication efficiency. We applied our approach to sites with heterogeneous survival data originating from emergency departments in Singapore and the United States. Additionally, we independently developed local scores at each site. In testing datasets from each participant site, our proposed federated scoring system consistently outperformed all local models, evidenced by higher integrated area under the receiver operating characteristic curve (iAUC) values, with a maximum improvement of 11.6%. Additionally, the federated score's time-dependent AUC(t) values showed advantages over local scores, exhibiting narrower confidence intervals (CIs) across most time points. The model developed through our proposed method exhibits effective performance on each local site, signifying noteworthy implications for healthcare research. Sites participating in our proposed federated scoring model training gained benefits by acquiring survival models with enhanced prediction accuracy and efficiency. This study demonstrates the effectiveness of our privacy-preserving federated survival score generation framework and its applicability to real-world heterogeneous survival data.

The photoelectric effect is not truly instantaneous, but exhibits attosecond delays that can reveal complex molecular dynamics. Sub-femtosecond duration light pulses provide the requisite tools to resolve the dynamics of photoionization. Accordingly, the past decade has produced a large volume of work on photoionization delays following single photon absorption of an extreme ultraviolet (XUV) photon. However, the measurement of time-resolved core-level photoionization remained out of reach. The required x-ray photon energies needed for core-level photoionization were not available with attosecond tabletop sources. We have now measured the x-ray photoemission delay of core-level electrons, and here report unexpectedly large delays, ranging up to 700 attoseconds in NO near the oxygen K-shell threshold. These measurements exploit attosecond soft x-ray pulses from a free-electron laser (XFEL) to scan across the entire region near the K-shell threshold. Furthermore, we find the delay spectrum is richly modulated, suggesting several contributions including transient trapping of the photoelectron due to shape resonances, collisions with the Auger-Meitner electron that is emitted in the rapid non-radiative relaxation of the molecule, and multi-electron scattering effects. The results demonstrate how x-ray attosecond experiments, supported by comprehensive theoretical modelling, can unravel the complex correlated dynamics of core-level photoionization.

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments., Comment: 13 pages

X-ray computed tomography (CT) in PET/CT is commonly operated with a single energy, resulting in a limitation of lacking tissue composition information. Dual-energy (DE) spectral CT enables material decomposition by using two different x-ray energies and may be combined with PET for improved multimodality imaging, but would either require hardware upgrade or increase radiation dose due to the added second x-ray CT scan. Recently proposed PET-enabled DECT method allows dual-energy spectral imaging using a conventional PET/CT scanner without the need for a second x-ray CT scan. A gamma-ray CT (gCT) image at 511 keV can be generated from the existing time-of-flight PET data with the maximum-likelihood attenuation and activity (MLAA) approach and is then combined with the low-energy x-ray CT image to form dual-energy spectral imaging. To improve the image quality of gCT, a kernel MLAA method was further proposed by incorporating x-ray CT as a priori information. The concept of this PET-enabled DECT has been validated using simulation studies, but not yet with 3D real data. In this work, we developed a general open-source implementation for gCT reconstruction from PET data and use this implementation for the first real data validation with both a physical phantom study and a human subject study on a uEXPLORER total-body PET/CT system. These results have demonstrated the feasibility of this method for spectral imaging and material decomposition., Comment: 20 pages, 7 figures

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including formulas for the cumulative distribution function and the characteristic function, as well as asymptotic approximations for the density, tail probabilities and the quantile function. As special cases, we deduce some key distributional properties for the product of two independent asymmetric Laplace random variables as well as the product of four jointly correlated zero mean normal random variables with a particular block diagonal covariance matrix. As a by-product of our analysis, we deduce some new reduction formulas for the Meijer $G$-function., Comment: 24 pages, 2 figures

Soft filter pruning~(SFP) has emerged as an effective pruning technique for allowing pruned filters to update and the opportunity for them to regrow to the network. However, this pruning strategy applies training and pruning in an alternative manner, which inevitably causes inconsistent representations between the reconstructed network~(R-NN) at the training and the pruned network~(P-NN) at the inference, resulting in performance degradation. In this paper, we propose to mitigate this gap by learning consistent representation for soft filter pruning, dubbed as CR-SFP. Specifically, for each training step, CR-SFP optimizes the R-NN and P-NN simultaneously with different distorted versions of the same training data, while forcing them to be consistent by minimizing their posterior distribution via the bidirectional KL-divergence loss. Meanwhile, the R-NN and P-NN share backbone parameters thus only additional classifier parameters are introduced. After training, we can export the P-NN for inference. CR-SFP is a simple yet effective training framework to improve the accuracy of P-NN without introducing any additional inference cost. It can also be combined with a variety of pruning criteria and loss functions. Extensive experiments demonstrate our CR-SFP achieves consistent improvements across various CNN architectures. Notably, on ImageNet, our CR-SFP reduces more than 41.8\% FLOPs on ResNet18 with 69.2\% top-1 accuracy, improving SFP by 2.1\% under the same training settings. The code will be publicly available on GitHub., Comment: 11 pages, 4 figures

N:M sparsity has received increasing attention due to its remarkable performance and latency trade-off compared with structured and unstructured sparsity. However, existing N:M sparsity methods do not differentiate the relative importance of weights among blocks and leave important weights underappreciated. Besides, they directly apply N:M sparsity to the whole network, which will cause severe information loss. Thus, they are still sub-optimal. In this paper, we propose an efficient and effective Multi-Axis Query methodology, dubbed as MaxQ, to rectify these problems. During the training, MaxQ employs a dynamic approach to generate soft N:M masks, considering the weight importance across multiple axes. This method enhances the weights with more importance and ensures more effective updates. Meanwhile, a sparsity strategy that gradually increases the percentage of N:M weight blocks is applied, which allows the network to heal from the pruning-induced damage progressively. During the runtime, the N:M soft masks can be precomputed as constants and folded into weights without causing any distortion to the sparse pattern and incurring additional computational overhead. Comprehensive experiments demonstrate that MaxQ achieves consistent improvements across diverse CNN architectures in various computer vision tasks, including image classification, object detection and instance segmentation. For ResNet50 with 1:16 sparse pattern, MaxQ can achieve 74.6\% top-1 accuracy on ImageNet and improve by over 2.8\% over the state-of-the-art. Codes and checkpoints are available at \url{https://github.com/JingyangXiang/MaxQ}., Comment: Accepted by the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2024 (CVPR2024)

Federated learning (FL) has shown promising potential in safeguarding data privacy in healthcare collaborations. While the term "FL" was originally coined by the engineering community, the statistical field has also explored similar privacy-preserving algorithms. Statistical FL algorithms, however, remain considerably less recognized than their engineering counterparts. Our goal was to bridge the gap by presenting the first comprehensive comparison of FL frameworks from both engineering and statistical domains. We evaluated five FL frameworks using both simulated and real-world data. The results indicate that statistical FL algorithms yield less biased point estimates for model coefficients and offer convenient confidence interval estimations. In contrast, engineering-based methods tend to generate more accurate predictions, sometimes surpassing central pooled and statistical FL models. This study underscores the relative strengths and weaknesses of both types of methods, emphasizing the need for increased awareness and their integration in future FL applications.

The study of sparsity in Convolutional Neural Networks (CNNs) has become widespread to compress and accelerate models in environments with limited resources. By constraining N consecutive weights along the output channel to be group-wise non-zero, the recent network with 1$\times$N sparsity has received tremendous popularity for its three outstanding advantages: 1) A large amount of storage space saving by a \emph{Block Sparse Row} matrix. 2) Excellent performance at a high sparsity. 3) Significant speedups on CPUs with Advanced Vector Extensions. Recent work requires selecting and fine-tuning 1$\times$N sparse weights based on dense pre-trained weights, leading to the problems such as expensive training cost and memory access, sub-optimal model quality, as well as unbalanced workload across threads (different sparsity across output channels). To overcome them, this paper proposes a novel \emph{\textbf{S}oft \textbf{U}niform \textbf{B}lock \textbf{P}runing} (SUBP) approach to train a uniform 1$\times$N sparse structured network from scratch. Specifically, our approach tends to repeatedly allow pruned blocks to regrow to the network based on block angular redundancy and importance sampling in a uniform manner throughout the training process. It not only makes the model less dependent on pre-training, reduces the model redundancy and the risk of pruning the important blocks permanently but also achieves balanced workload. Empirically, on ImageNet, comprehensive experiments across various CNN architectures show that our SUBP consistently outperforms existing 1$\times$N and structured sparsity methods based on pre-trained models or training from scratch. Source codes and models are available at \url{https://github.com/JingyangXiang/SUBP}., Comment: 14 pages, 4 figures, Accepted by 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

Combining dual-energy computed tomography (DECT) with positron emission tomography (PET) offers many potential clinical applications but typically requires expensive hardware upgrades or increases radiation doses on PET/CT scanners due to an extra X-ray CT scan. The recent PET-enabled DECT method allows DECT imaging on PET/CT without requiring a second X-ray CT scan. It combines the already existing X-ray CT image with a 511 keV \gamma-ray CT (gCT) image reconstructed from time-of-flight PET emission data. A kernelized framework has been developed for reconstructing gCT image but this method has not fully exploited the potential of prior knowledge. Use of deep neural networks may explore the power of deep learning in this application. However, common approaches require a large database for training, which is impractical for a new imaging method like PET-enabled DECT. Here, we propose a single-subject method by using neural-network representation as a deep coefficient prior to improving gCT image reconstruction without population-based pre-training. The resulting optimization problem becomes the tomographic estimation of nonlinear neural-network parameters from gCT projection data. This complicated problem can be efficiently solved by utilizing the optimization transfer strategy with quadratic surrogates. Each iteration of the proposed neural optimization transfer algorithm includes: PET activity image update; gCT image update; and least-square neural-network learning in the gCT image domain. This algorithm is guaranteed to monotonically increase the data likelihood. Results from computer simulation, real phantom data and real patient data have demonstrated that the proposed method can significantly improve gCT image quality and consequent multi-material decomposition as compared to other methods.

Metasurface enables the generation and manipulation of multiphoton entanglement with flat optics, providing a more efficient platform for large-scale photonic quantum information processing. Here, we show that a single metasurface optical device would allow more efficient characterizations of multiphoton entangled states, such as shadow tomography, which generally requires fast and complicated control of optical setups to perform information-complete measurements, a demanding task using conventional optics. The compact and stable device here allows implementations of general positive observable value measures with a reduced sample complexity and significantly alleviates the experimental complexity to implement shadow tomography. Integrating self-learning and calibration algorithms, we observe notable advantages in the reconstruction of multiphoton entanglement, including using fewer measurements, having higher accuracy, and being robust against experimental imperfections. Our work unveils the feasibility of metasurface as a favorable integrated optical device for efficient characterization of multiphoton entanglement, and sheds light on scalable photonic quantum technologies with ultra-thin optical devices., Comment: 24 pages, 12 figures

This paper presents a comprehensive technical overview of the Linac Coherent Light Source II (LCLS-II) photoinjector laser system, its first and foremost component. The LCLS-II photoinjector laser system serves as an upgrade to the original LCLS at SLAC National Accelerator Laboratory. This advanced laser system generates high-quality laser beams for LCLS-II, contributing to the instrument's unprecedented brightness, precision, and flexibility. Our discussion extends to the various subsystems that comprise the photoinjector, including the photocathode laser, laser heater, and beam transport systems. Lastly, we draw attention to the ongoing research and development infrastructure underway to enhance the functionality and efficiency of the LCLS-II, and similar X-ray free-electron laser facilities around the world, thereby contributing to the future of laser technology and its applications., Comment: Published by High Power Laser Science and Engineering

Self-Supervised Learning (SSL) Automatic Speech Recognition (ASR) models have shown great promise over Supervised Learning (SL) ones in low-resource settings. However, the advantages of SSL are gradually weakened when the amount of labeled data increases in many industrial applications. To further improve the ASR performance when abundant labels are available, we first explore the potential of combining SL and SSL ASR models via analyzing their complementarity in recognition accuracy and optimization property. Then, we propose a novel Optimal Transport based Fusion (OTF) method for SL and SSL models without incurring extra computation cost in inference. Specifically, optimal transport is adopted to softly align the layer-wise weights to unify the two different networks into a single one. Experimental results on the public 1k-hour English LibriSpeech dataset and our in-house 2.6k-hour Chinese dataset show that OTF largely outperforms the individual models with lower error rates., Comment: Accepted by Interspeech 2023