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In this paper, we prove the strong Morse inequalities for the area functional in the space of embedded tori and spheres in the three sphere. As a consequence, we prove that in the three dimensional sphere with positive Ricci curvature, there exist at least 4 distinct embedded minimal tori. Suppose in addition that the metric is bumpy, then the three-sphere contains at least 9 distinct embedded minimal tori. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory proved by the second author and X. Zhou., Comment: 28 pages; comments are welcome

An LLM is pretrained on trillions of tokens, but the pretrained LLM may still generate undesired responses. To solve this problem, alignment techniques such as RLHF, DPO and KTO are proposed. However, these alignment techniques have limitations. For example, RLHF requires training the reward model and policy separately, which is complex, time-consuming, memory intensive and unstable during training processes. DPO proposes a mapping between an optimal policy and a reward, greatly simplifying the training process of RLHF. However, it can not take full advantages of a reward model and it is limited to pairwise preference data. In this paper, we propose \textbf{UN}ified \textbf{A}lignment (UNA) which unifies RLHF/PPO, DPO and KTO. Firstly, we mathematically prove that given the classical RLHF objective, the optimal policy is induced by a generalize implicit reward function. With this novel mapping between a reward model and an optimal policy, UNA can 1. unify RLHF/PPO, DPO and KTO into a supervised learning of minimizing the difference between an implicit reward and an explicit reward; 2. outperform RLHF/PPO while simplify, stabilize, speed up and reduce memory burden of RL fine-tuning process; 3. accommodate different feedback types including pairwise, binary and scalar feedback. Downstream experiments show UNA outperforms DPO, KTO and RLHF.

StreamVoice has recently pushed the boundaries of zero-shot voice conversion (VC) in the streaming domain. It uses a streamable language model (LM) with a context-aware approach to convert semantic features from automatic speech recognition (ASR) into acoustic features with the desired speaker timbre. Despite its innovations, StreamVoice faces challenges due to its dependency on a streaming ASR within a cascaded framework, which complicates system deployment and optimization, affects VC system's design and performance based on the choice of ASR, and struggles with conversion stability when faced with low-quality semantic inputs. To overcome these limitations, we introduce StreamVoice+, an enhanced LM-based end-to-end streaming framework that operates independently of streaming ASR. StreamVoice+ integrates a semantic encoder and a connector with the original StreamVoice framework, now trained using a non-streaming ASR. This model undergoes a two-stage training process: initially, the StreamVoice backbone is pre-trained for voice conversion and the semantic encoder for robust semantic extraction. Subsequently, the system is fine-tuned end-to-end, incorporating a LoRA matrix to activate comprehensive streaming functionality. Furthermore, StreamVoice+ mainly introduces two strategic enhancements to boost conversion quality: a residual compensation mechanism in the connector to ensure effective semantic transmission and a self-refinement strategy that leverages pseudo-parallel speech pairs generated by the conversion backbone to improve speech decoupling. Experiments demonstrate that StreamVoice+ not only achieves higher naturalness and speaker similarity in voice conversion than its predecessor but also provides versatile support for both streaming and non-streaming conversion scenarios.

Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus has been on studying the proportional asymptotic regime, $n \asymp d$, where $n$ is the number of training samples and $d$ is the dimension of the dataset. In this regime, under certain conditions on the data distribution, the kernel random matrix involved in KRR exhibits behavior akin to that of a linear kernel. In this work, we extend the study of kernel regression to the quadratic asymptotic regime, where $n \asymp d^2$. In this regime, we demonstrate that a broad class of inner-product kernels exhibit behavior similar to a quadratic kernel. Specifically, we establish an operator norm approximation bound for the difference between the original kernel random matrix and a quadratic kernel random matrix with additional correction terms compared to the Taylor expansion of the kernel functions. The approximation works for general data distributions under a Gaussian-moment-matching assumption with a covariance structure. This new approximation is utilized to obtain a limiting spectral distribution of the original kernel matrix and characterize the precise asymptotic training and generalization errors for KRR in the quadratic regime when $n/d^2$ converges to a non-zero constant. The generalization errors are obtained for both deterministic and random teacher models. Our proof techniques combine moment methods, Wick's formula, orthogonal polynomials, and resolvent analysis of random matrices with correlated entries., Comment: 75 pages

With advancements in self-supervised learning, the availability of trillions tokens in a pre-training corpus, instruction fine-tuning, and the development of large Transformers with billions of parameters, large language models (LLMs) are now capable of generating factual and coherent responses to human queries. However, the mixed quality of training data can lead to the generation of undesired responses, presenting a significant challenge. Over the past two years, various methods have been proposed from different perspectives to enhance LLMs, particularly in aligning them with human expectation. Despite these efforts, there has not been a comprehensive survey paper that categorizes and details these approaches. In this work, we aim to address this gap by categorizing these papers into distinct topics and providing detailed explanations of each alignment method, thereby helping readers gain a thorough understanding of the current state of the field.

Generative design (GD) methods aim to automatically generate a wide variety of designs that satisfy functional or aesthetic design requirements. However, research to date generally lacks considerations of manufacturability of the generated designs. To this end, we propose a novel GD approach by using deep neural networks to encode design for manufacturing (DFM) rules, thereby modifying part designs to make them manufacturable by a given manufacturing process. Specifically, a three-step approach is proposed: first, an instance segmentation method, Mask R-CNN, is used to decompose a part design into subregions. Second, a conditional generative adversarial neural network (cGAN), Pix2Pix, transforms unmanufacturable decomposed subregions into manufacturable subregions. The transformed subregions of designs are subsequently reintegrated into a unified manufacturable design. These three steps, Mask-RCNN, Pix2Pix, and reintegration, form the basis of the proposed Manufacturable conditional GAN (McGAN) framework. Experimental results show that McGAN can transform existing unmanufacturable designs to generate their corresponding manufacturable counterparts automatically that realize the specified manufacturing rules in an efficient and robust manner. The effectiveness of McGAN is demonstrated through two-dimensional design case studies of an injection molding process.

Large language models (LLMs) have shown remarkable abilities in diverse natural language processing (NLP) tasks. The LLMs generally undergo supervised fine-tuning (SFT) followed by preference alignment to be usable in downstream applications. However, this sequential training pipeline leads to alignment tax that degrades the LLM performance. This paper introduces PAFT, a new PArallel training paradigm for effective LLM Fine-Tuning, which independently performs SFT and preference alignment (e.g., DPO and ORPO, etc.) with the same pre-trained model on respective datasets. The model produced by SFT and the model from preference alignment are then merged into a final model by parameter fusing for use in downstream applications. This work reveals important findings that preference alignment like DPO naturally results in a sparse model while SFT leads to a natural dense model which needs to be sparsified for effective model merging. This paper introduces an effective interference resolution which reduces the redundancy by sparsifying the delta parameters. The LLM resulted from the new training paradigm achieved Rank #1 on the HuggingFace Open LLM Leaderboard. Comprehensive evaluation shows the effectiveness of the parallel training paradigm.

The advent of large language models (LLMs) has revolutionized the deep learning paradigm, yielding impressive results across a wide array of tasks. However, the pre-training or fine-tuning of LLMs within a federated learning (FL) framework poses substantial challenges, including considerable computational and memory resource demands, as well as communication bottlenecks between servers and clients. Existing solutions either make the unrealistic assumption that the entire model is exchanged for training, or apply parameter-effective fine-tuning methods from centralized learning to train LLMs in FL which tend to underperform during training or fine-tuning stages due to the limited search subspace of parameter updating. In this paper, we introduce a novel method for the efficient training and fine-tuning of LLMs in FL, with minimal resource consumption. Our approach, termed FedCyBGD, utilizes Cycle Block Gradient Descent to periodically update the model. In particular, we design a compression scheme for FedCyBGD, aiming to further decrease the model download cost. It enables full parameter training in FL with only selected block updates and uploads, thereby reducing communication, computation, and memory costs. Our method achieves state-of-the-art performance for FL LLM training, while significantly reducing associated costs. Codes are provided here.

Zero-shot voice conversion (VC) aims to transform source speech into arbitrary unseen target voice while keeping the linguistic content unchanged. Recent VC methods have made significant progress, but semantic losses in the decoupling process as well as training-inference mismatch still hinder conversion performance. In this paper, we propose Vec-Tok-VC+, a novel prompt-based zero-shot VC model improved from Vec-Tok Codec, achieving voice conversion given only a 3s target speaker prompt. We design a residual-enhanced K-Means decoupler to enhance the semantic content extraction with a two-layer clustering process. Besides, we employ teacher-guided refinement to simulate the conversion process to eliminate the training-inference mismatch, forming a dual-mode training strategy. Furthermore, we design a multi-codebook progressive loss function to constrain the layer-wise output of the model from coarse to fine to improve speaker similarity and content accuracy. Objective and subjective evaluations demonstrate that Vec-Tok-VC+ outperforms the strong baselines in naturalness, intelligibility, and speaker similarity., Comment: Accepted by INTERSPEECH2024

Streaming voice conversion has become increasingly popular for its potential in real-time applications. The recently proposed DualVC 2 has achieved robust and high-quality streaming voice conversion with a latency of about 180ms. Nonetheless, the recognition-synthesis framework hinders end-to-end optimization, and the instability of automatic speech recognition (ASR) model with short chunks makes it challenging to further reduce latency. To address these issues, we propose an end-to-end model, DualVC 3. With speaker-independent semantic tokens to guide the training of the content encoder, the dependency on ASR is removed and the model can operate under extremely small chunks, with cascading errors eliminated. A language model is trained on the content encoder output to produce pseudo context by iteratively predicting future frames, providing more contextual information for the decoder to improve conversion quality. Experimental results demonstrate that DualVC 3 achieves comparable performance to DualVC 2 in subjective and objective metrics, with a latency of only 50 ms., Comment: Accepted by Interspeech 2024

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue distribution, and fall short of providing precise quantitative characterizations of the ''spike'' eigenvalues and eigenvectors that often capture the low-dimensional signal structure of the learning problem. In this work, we characterize these signal eigenvalues and eigenvectors for a nonlinear version of the spiked covariance model, including the CK as a special case. Using this general result, we give a quantitative description of how spiked eigenstructure in the input data propagates through the hidden layers of a neural network with random weights. As a second application, we study a simple regime of representation learning where the weight matrix develops a rank-one signal component over training and characterize the alignment of the target function with the spike eigenvector of the CK on test data., Comment: 55 pages

Since their discovery, the infinite-layer nickelates have been regarded as an appealing system for gaining deeper insights into high temperature superconductivity (HTSC). However, the synthesis of superconducting samples has been proved to be challenging. Here, we develop an ultrahigh vacuum (UHV) ${\mathrm{\textit{in situ}}}$ reduction method using atomic hydrogen as reducing agent and apply it in lanthanum nickelate system. The reduction parameters, including the reduction temperature (${\mathrm{\textit{T}_{R}}}$) and hydrogen pressure (${\mathrm{\textit{P}_{H}}}$), are systematically explored. We found that the reduction window for achieving superconducting transition is quite wide, reaching nearly 80$^\circ$C in ${\mathrm{\textit{T}_{R}}}$ and 3 orders of magnitude in ${\mathrm{\textit{P}_{H}}}$ when the reduction time is set to 30 mins. And there exists an optimal ${\mathrm{\textit{P}_{H}}}$ for achieving the highest ${\mathrm{\textit{T}_{c}}}$ if both ${\mathrm{\textit{T}_{R}}}$ and reduction time are fixed. More prominently, as confirmed by atomic force microscopy and scanning transmission electron microscopy, the atomically flat surface can be preserved during the ${\mathrm{\textit{in situ}}}$ reduction process, providing advantages over the ${\mathrm{\textit{ex situ}}}$ CaH$_2$ method for surface-sensitive experiments., Comment: 5 pages, 4 figures

Recent language model (LM) advancements have showcased impressive zero-shot voice conversion (VC) performance. However, existing LM-based VC models usually apply offline conversion from source semantics to acoustic features, demanding the complete source speech and limiting their deployment to real-time applications. In this paper, we introduce StreamVoice, a novel streaming LM-based model for zero-shot VC, facilitating real-time conversion given arbitrary speaker prompts and source speech. Specifically, to enable streaming capability, StreamVoice employs a fully causal context-aware LM with a temporal-independent acoustic predictor, while alternately processing semantic and acoustic features at each time step of autoregression which eliminates the dependence on complete source speech. To address the potential performance degradation from the incomplete context in streaming processing, we enhance the context-awareness of the LM through two strategies: 1) teacher-guided context foresight, using a teacher model to summarize the present and future semantic context during training to guide the model's forecasting for missing context; 2) semantic masking strategy, promoting acoustic prediction from preceding corrupted semantic and acoustic input, enhancing context-learning ability. Notably, StreamVoice is the first LM-based streaming zero-shot VC model without any future look-ahead. Experiments demonstrate StreamVoice's streaming conversion capability while achieving zero-shot performance comparable to non-streaming VC systems., Comment: Accepted by ACL2024 (Main)

Preserving privacy and reducing communication costs for edge users pose significant challenges in recommendation systems. Although federated learning has proven effective in protecting privacy by avoiding data exchange between clients and servers, it has been shown that the server can infer user ratings based on updated non-zero gradients obtained from two consecutive rounds of user-uploaded gradients. Moreover, federated recommendation systems (FRS) face the challenge of heterogeneity, leading to decreased recommendation performance. In this paper, we propose FedRec+, an ensemble framework for FRS that enhances privacy while addressing the heterogeneity challenge. FedRec+ employs optimal subset selection based on feature similarity to generate near-optimal virtual ratings for pseudo items, utilizing only the user's local information. This approach reduces noise without incurring additional communication costs. Furthermore, we utilize the Wasserstein distance to estimate the heterogeneity and contribution of each client, and derive optimal aggregation weights by solving a defined optimization problem. Experimental results demonstrate the state-of-the-art performance of FedRec+ across various reference datasets., Comment: Accepted by 59th Annual Allerton Conference on Communication, Control, and Computing

Zero-shot speaker cloning aims to synthesize speech for any target speaker unseen during TTS system building, given only a single speech reference of the speaker at hand. Although more practical in real applications, the current zero-shot methods still produce speech with undesirable naturalness and speaker similarity. Moreover, endowing the target speaker with arbitrary speaking styles in the zero-shot setup has not been considered. This is because the unique challenge of zero-shot speaker and style cloning is to learn the disentangled speaker and style representations from only short references representing an arbitrary speaker and an arbitrary style. To address this challenge, we propose U-Style, which employs Grad-TTS as the backbone, particularly cascading a speaker-specific encoder and a style-specific encoder between the text encoder and the diffusion decoder. Thus, leveraging signal perturbation, U-Style is explicitly decomposed into speaker- and style-specific modeling parts, achieving better speaker and style disentanglement. To improve unseen speaker and style modeling ability, these two encoders conduct multi-level speaker and style modeling by skip-connected U-nets, incorporating the representation extraction and information reconstruction process. Besides, to improve the naturalness of synthetic speech, we adopt mean-based instance normalization and style adaptive layer normalization in these encoders to perform representation extraction and condition adaptation, respectively. Experiments show that U-Style significantly surpasses the state-of-the-art methods in unseen speaker cloning regarding naturalness and speaker similarity. Notably, U-Style can transfer the style from an unseen source speaker to another unseen target speaker, achieving flexible combinations of desired speaker timbre and style in zero-shot voice cloning.

This paper introduces the T23 team's system submitted to the Singing Voice Conversion Challenge 2023. Following the recognition-synthesis framework, our singing conversion model is based on VITS, incorporating four key modules: a prior encoder, a posterior encoder, a decoder, and a parallel bank of transposed convolutions (PBTC) module. We particularly leverage Whisper, a powerful pre-trained ASR model, to extract bottleneck features (BNF) as the input of the prior encoder. Before BNF extraction, we perform pitch perturbation to the source signal to remove speaker timbre, which effectively avoids the leakage of the source speaker timbre to the target. Moreover, the PBTC module extracts multi-scale F0 as the auxiliary input to the prior encoder, thereby capturing better pitch variations of singing. We design a three-stage training strategy to better adapt the base model to the target speaker with limited target speaker data. Official challenge results show that our system has superior performance in naturalness, ranking 1st and 2nd respectively in Task 1 and 2. Further ablation justifies the effectiveness of our system design.

In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant computational overhead. Pioneer works improve its smoothing efficiency by adopting supervised learning to learn smoothing methods from high-quality meshes. However, they pose difficulty in smoothing the mesh nodes with varying degrees and also need data augmentation to address the node input sequence problem. Additionally, the required labeled high-quality meshes further limit the applicability of the proposed method. In this paper, we present GMSNet, a lightweight neural network model for intelligent mesh smoothing. GMSNet adopts graph neural networks to extract features of the node's neighbors and output the optimal node position. During smoothing, we also introduce a fault-tolerance mechanism to prevent GMSNet from generating negative volume elements. With a lightweight model, GMSNet can effectively smoothing mesh nodes with varying degrees and remain unaffected by the order of input data. A novel loss function, MetricLoss, is also developed to eliminate the need for high-quality meshes, which provides a stable and rapid convergence during training. We compare GMSNet with commonly used mesh smoothing methods on two-dimensional triangle meshes. The experimental results show that GMSNet achieves outstanding mesh smoothing performances with 5% model parameters of the previous model, and attains 13.56 times faster than optimization-based smoothing.

In addition to conveying the linguistic content from source speech to converted speech, maintaining the speaking style of source speech also plays an important role in the voice conversion (VC) task, which is essential in many scenarios with highly expressive source speech, such as dubbing and data augmentation. Previous work generally took explicit prosodic features or fixed-length style embedding extracted from source speech to model the speaking style of source speech, which is insufficient to achieve comprehensive style modeling and target speaker timbre preservation. Inspired by the style's multi-scale nature of human speech, a multi-scale style modeling method for the VC task, referred to as MSM-VC, is proposed in this paper. MSM-VC models the speaking style of source speech from different levels. To effectively convey the speaking style and meanwhile prevent timbre leakage from source speech to converted speech, each level's style is modeled by specific representation. Specifically, prosodic features, pre-trained ASR model's bottleneck features, and features extracted by a model trained with a self-supervised strategy are adopted to model the frame, local, and global-level styles, respectively. Besides, to balance the performance of source style modeling and target speaker timbre preservation, an explicit constraint module consisting of a pre-trained speech emotion recognition model and a speaker classifier is introduced to MSM-VC. This explicit constraint module also makes it possible to simulate the style transfer inference process during the training to improve the disentanglement ability and alleviate the mismatch between training and inference. Experiments performed on the highly expressive speech corpus demonstrate that MSM-VC is superior to the state-of-the-art VC methods for modeling source speech style while maintaining good speech quality and speaker similarity., Comment: This work was submitted on April 10, 2022 and accepted on August 29, 2023

The advent of ChatGPT has introduced innovative methods for information gathering and analysis. However, the information provided by ChatGPT is limited to text, and the visualization of this information remains constrained. Previous research has explored zero-shot text-to-video (TTV) approaches to transform text into videos. However, these methods lacked control over the identity of the generated audio, i.e., not identity-agnostic, hindering their effectiveness. To address this limitation, we propose a novel two-stage framework for person-agnostic video cloning, specifically focusing on TTV generation. In the first stage, we leverage pretrained zero-shot models to achieve text-to-speech (TTS) conversion. In the second stage, an audio-driven talking head generation method is employed to produce compelling videos privided the audio generated in the first stage. This paper presents a comparative analysis of different TTS and audio-driven talking head generation methods, identifying the most promising approach for future research and development. Some audio and videos samples can be found in the following link: https://github.com/ZhichaoWang970201/Text-to-Video/tree/main., Comment: 6 pages

We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive constant admits a singular foliation by surfaces of controlled area and diameter., Comment: 19 pages; 3 figures; comments are welcome!

We prove the $C^{1,1}$-regularity for stationary $C^{1,\alpha}$ ($\alpha\in(0,1)$) solutions to the multiple membrane problem. This regularity estimate was essentially used in our recent work on Yau's four minimal spheres conjecture., Comment: 44 pages; minor revisions; comments welcome

Freestanding perovskite oxide membranes have drawn great attention recently since they offer exceptional structural tunability and stacking ability, providing new opportunities in fundamental research and potential device applications in silicon-based semiconductor technology. Among different types of sacrificial layers, the $ \mathrm{(Ca, Sr, Ba)}_{3}\mathrm{Al}_{2}\mathrm{O}_{6}$ compounds are most widely used since they can be dissolved in water and prepare high-quality perovskite oxide membranes with clean and sharp surfaces and interfaces. However, the typical transfer process takes a long time (up to hours) in obtaining millimeter-size freestanding membranes, let alone realize wafer-scale samples with high yield. Here, we introduce a new member of the $ \mathrm{SrO-}\mathrm{Al}_{2}\mathrm{O}_{3}$ family,$ \mathrm{Sr}_{4}\mathrm{Al}_{2}\mathrm{O}_{7},$, and demonstrate its high dissolution rate, about 10 times higher than that of $ \mathrm{Sr}_{3}\mathrm{Al}_{2}\mathrm{O}_{6}$. The high-dissolution-rate of $ \mathrm{Sr}_{4}\mathrm{Al}_{2}\mathrm{O}_{7}$ is most likely related to the more discrete Al-O networks and higher concentration of water-soluble Sr-O species in this compound. Our work significantly facilitates the preparation of freestanding membranes and sheds light on the integration of multifunctional perovskite oxides in practical electronic devices., Comment: 11 pages,4 figures

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks. However, original PINNs often suffer from bottlenecks, such as low accuracy and non-convergence, limiting their applicability in complex physical contexts. To alleviate these issues, we proposed auxiliary-task learning-based physics-informed neural networks (ATL-PINNs), which provide four different auxiliary-task learning modes and investigate their performance compared with original PINNs. We also employ the gradient cosine similarity algorithm to integrate auxiliary problem loss with the primary problem loss in ATL-PINNs, which aims to enhance the effectiveness of the auxiliary-task learning modes. To the best of our knowledge, this is the first study to introduce auxiliary-task learning modes in the context of physics-informed learning. We conduct experiments on three PDE problems across different fields and scenarios. Our findings demonstrate that the proposed auxiliary-task learning modes can significantly improve solution accuracy, achieving a maximum performance boost of 96.62% (averaging 28.23%) compared to the original single-task PINNs. The code and dataset are open source at https://github.com/junjun-yan/ATL-PINN.

Language model (LM) based audio generation frameworks, e.g., AudioLM, have recently achieved new state-of-the-art performance in zero-shot audio generation. In this paper, we explore the feasibility of LMs for zero-shot voice conversion. An intuitive approach is to follow AudioLM - Tokenizing speech into semantic and acoustic tokens respectively by HuBERT and SoundStream, and converting source semantic tokens to target acoustic tokens conditioned on acoustic tokens of the target speaker. However, such an approach encounters several issues: 1) the linguistic content contained in semantic tokens may get dispersed during multi-layer modeling while the lengthy speech input in the voice conversion task makes contextual learning even harder; 2) the semantic tokens still contain speaker-related information, which may be leaked to the target speech, lowering the target speaker similarity; 3) the generation diversity in the sampling of the LM can lead to unexpected outcomes during inference, leading to unnatural pronunciation and speech quality degradation. To mitigate these problems, we propose LM-VC, a two-stage language modeling approach that generates coarse acoustic tokens for recovering the source linguistic content and target speaker's timbre, and then reconstructs the fine for acoustic details as converted speech. Specifically, to enhance content preservation and facilitates better disentanglement, a masked prefix LM with a mask prediction strategy is used for coarse acoustic modeling. This model is encouraged to recover the masked content from the surrounding context and generate target speech based on the target speaker's utterance and corrupted semantic tokens. Besides, to further alleviate the sampling error in the generation, an external LM, which employs window attention to capture the local acoustic relations, is introduced to participate in the coarse acoustic modeling.

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast PDE solving in various applications. To address the issue of low accuracy and convergence problems of existing PINNs, we propose a self-training physics-informed neural network, ST-PINN. Specifically, ST-PINN introduces a pseudo label based self-learning algorithm during training. It employs governing equation as the pseudo-labeled evaluation index and selects the highest confidence examples from the sample points to attach the pseudo labels. To our best knowledge, we are the first to incorporate a self-training mechanism into physics-informed learning. We conduct experiments on five PDE problems in different fields and scenarios. The results demonstrate that the proposed method allows the network to learn more physical information and benefit convergence. The ST-PINN outperforms existing physics-informed neural network methods and improves the accuracy by a factor of 1.33x-2.54x. The code of ST-PINN is available at GitHub: https://github.com/junjun-yan/ST-PINN.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk)., Comment: 9 pages, 2 figures, 3 tables Updated 3/11/2024 various additions/clarifications after ICLR review. Accepted as a Spotlight paper at ICLR 2024

We prove that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This confirms a conjecture of S. T. Yau in 1982 for bumpy metrics and metrics with positive Ricci curvature. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory., Comment: 60 pages; minor revision: typo corrected, an appendix on the Lusternik-Schnirelmann inequality added, references updated; comments welcome

Zero-shot voice conversion (VC) converts source speech into the voice of any desired speaker using only one utterance of the speaker without requiring additional model updates. Typical methods use a speaker representation from a pre-trained speaker verification (SV) model or learn speaker representation during VC training to achieve zero-shot VC. However, existing speaker modeling methods overlook the variation of speaker information richness in temporal and frequency channel dimensions of speech. This insufficient speaker modeling hampers the ability of the VC model to accurately represent unseen speakers who are not in the training dataset. In this study, we present a robust zero-shot VC model with multi-level temporal-channel retrieval, referred to as MTCR-VC. Specifically, to flexibly adapt to the dynamic-variant speaker characteristic in the temporal and channel axis of the speech, we propose a novel fine-grained speaker modeling method, called temporal-channel retrieval (TCR), to find out when and where speaker information appears in speech. It retrieves variable-length speaker representation from both temporal and channel dimensions under the guidance of a pre-trained SV model. Besides, inspired by the hierarchical process of human speech production, the MTCR speaker module stacks several TCR blocks to extract speaker representations from multi-granularity levels. Furthermore, to achieve better speech disentanglement and reconstruction, we introduce a cycle-based training strategy to simulate zero-shot inference recurrently. We adopt perpetual constraints on three aspects, including content, style, and speaker, to drive this process. Experiments demonstrate that MTCR-VC is superior to the previous zero-shot VC methods in modeling speaker timbre while maintaining good speech naturalness., Comment: Submitted to TASLP

Ensuring fairness is a crucial aspect of Federated Learning (FL), which enables the model to perform consistently across all clients. However, designing an FL algorithm that simultaneously improves global model performance and promotes fairness remains a formidable challenge, as achieving the latter often necessitates a trade-off with the former. To address this challenge, we propose a new FL algorithm, FedEBA+, which enhances fairness while simultaneously improving global model performance. FedEBA+ incorporates a fair aggregation scheme that assigns higher weights to underperforming clients and an alignment update method. In addition, we provide theoretical convergence analysis and show the fairness of FedEBA+. Extensive experiments demonstrate that FedEBA+ outperforms other SOTA fairness FL methods in terms of both fairness and global model performance.