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Federated Learning (FL) offers a decentralized approach to model training, where data remains local and only model parameters are shared between the clients and the central server. Traditional methods, such as Federated Averaging (FedAvg), linearly aggregate these parameters which are usually trained on heterogeneous data distributions, potentially overlooking the complex, high-dimensional nature of the parameter space. This can result in degraded performance of the aggregated model. While personalized FL approaches can mitigate the heterogeneous data issue to some extent, the limitation of linear aggregation remains unresolved. To alleviate this issue, we investigate the generative approach of diffusion model and propose a novel generative parameter aggregation framework for personalized FL, \texttt{pFedGPA}. In this framework, we deploy a diffusion model on the server to integrate the diverse parameter distributions and propose a parameter inversion method to efficiently generate a set of personalized parameters for each client. This inversion method transforms the uploaded parameters into a latent code, which is then aggregated through denoising sampling to produce the final personalized parameters. By encoding the dependence of a client's model parameters on the specific data distribution using the high-capacity diffusion model, \texttt{pFedGPA} can effectively decouple the complexity of the overall distribution of all clients' model parameters from the complexity of each individual client's parameter distribution. Our experimental results consistently demonstrate the superior performance of the proposed method across multiple datasets, surpassing baseline approaches.

Weakly Supervised Object Detection (WSOD) with only image-level annotation has recently attracted wide attention. Many existing methods ignore the inter-image relationship of instances which share similar characteristics while can certainly be determined not to belong to the same category. Therefore, in order to make full use of the weak label, we propose the Negative Prototypes Guided Contrastive learning (NPGC) architecture. Firstly, we define Negative Prototype as the proposal with the highest confidence score misclassified for the category that does not appear in the label. Unlike other methods that only utilize category positive feature, we construct an online updated global feature bank to store both positive prototypes and negative prototypes. Meanwhile, we propose a pseudo label sampling module to mine reliable instances and discard the easily misclassified instances based on the feature similarity with corresponding prototypes in global feature bank. Finally, we follow the contrastive learning paradigm to optimize the proposal's feature representation by attracting same class samples closer and pushing different class samples away in the embedding space. Extensive experiments have been conducted on VOC07, VOC12 datasets, which shows that our proposed method achieves the state-of-the-art performance.

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical systems whose solutions exhibit multi-scale or turbulent behavior over time. The reason is that PINNs may violate the temporal causality property since all the temporal features in the PINNs loss are trained simultaneously. This paper proposes to use implicit time differencing schemes to enforce temporal causality, and use transfer learning to sequentially update the PINNs in space as surrogates for PDE solutions in different time frames. The evolving PINNs are better able to capture the varying complexities of the evolutionary equations, while only requiring minor updates between adjacent time frames. Our method is theoretically proven to be convergent if the time step is small and each PINN in different time frames is well-trained. In addition, we provide state-of-the-art (SOTA) numerical results for a variety of benchmarks for which existing PINNs formulations may fail or be inefficient. We demonstrate that the proposed method improves the accuracy of PINNs approximation for evolutionary PDEs and improves efficiency by a factor of 4-40x., Comment: 23 pages, 20 figures

Non-fungible tokens (NFTs) are decentralized digital tokens to represent the unique ownership of items. Recently, NFTs have been gaining popularity and at the same time bringing up issues, such as scams, racism, and sexism. Decentralization, a key attribute of NFT, contributes to some of the issues that are easier to regulate under centralized schemes, which are intentionally left out of the NFT marketplace. In this work, we delved into this centralization-decentralization dilemma in the NFT space through mixed quantitative and qualitative methods. Centralization-decentralization dilemma is the dilemma caused by the conflict between the slogan of decentralization and the interests of stakeholders. We first analyzed over 30,000 NFT-related tweets to obtain a high-level understanding of stakeholders' concerns in the NFT space. We then interviewed 15 NFT stakeholders (both creators and collectors) to obtain their in-depth insights into these concerns and potential solutions. Our findings identify concerning issues among users: financial scams, counterfeit NFTs, hacking, and unethical NFTs. We further reflected on the centralization-decentralization dilemma drawing upon the perspectives of the stakeholders in the interviews. Finally, we gave some inferences to solve the centralization-decentralization dilemma in the NFT market and thought about the future of NFT and decentralization., Comment: Accepted by CSCW 2024

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for $A_8$, $D_8$ and $E_8$ for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output -- the invariants -- is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results., Comment: v1: 34 pages, 16 Figures, 12 Tables. v2: Typos corrected and some comments added. Matches the author-accepted version for publication in Advances in Applied Clifford Algebras

Video colorization task has recently attracted wide attention. Recent methods mainly work on the temporal consistency in adjacent frames or frames with small interval. However, it still faces severe challenge of the inconsistency between frames with large interval.To address this issue, we propose a novel video colorization framework, which combines semantic correspondence into automatic video colorization to keep long-range consistency. Firstly, a reference colorization network is designed to automatically colorize the first frame of each video, obtaining a reference image to supervise the following whole colorization process. Such automatically colorized reference image can not only avoid labor-intensive and time-consuming manual selection, but also enhance the similarity between reference and grayscale images. Afterwards, a semantic correspondence network and an image colorization network are introduced to colorize a series of the remaining frames with the help of the reference. Each frame is supervised by both the reference image and the immediately colorized preceding frame to improve both short-range and long-range temporal consistency. Extensive experiments demonstrate that our method outperforms other methods in maintaining temporal consistency both qualitatively and quantitatively. In the NTIRE 2023 Video Colorization Challenge, our method ranks at the 3rd place in Color Distribution Consistency (CDC) Optimization track.

Exemplar-based image colorization aims to colorize a target grayscale image based on a color reference image, and the key is to establish accurate pixel-level semantic correspondence between these two images. Previous methods search for correspondence across the entire reference image, and this type of global matching is easy to get mismatch. We summarize the difficulties in two aspects: (1) When the reference image only contains a part of objects related to target image, improper correspondence will be established in unrelated regions. (2) It is prone to get mismatch in regions where the shape or texture of the object is easily confused. To overcome these issues, we propose SPColor, a semantic prior guided exemplar-based image colorization framework. Different from previous methods, SPColor first coarsely classifies pixels of the reference and target images to several pseudo-classes under the guidance of semantic prior, then the correspondences are only established locally between the pixels in the same class via the newly designed semantic prior guided correspondence network. In this way, improper correspondence between different semantic classes is explicitly excluded, and the mismatch is obviously alleviated. Besides, to better reserve the color from reference, a similarity masked perceptual loss is designed. Noting that the carefully designed SPColor utilizes the semantic prior provided by an unsupervised segmentation model, which is free for additional manual semantic annotations. Experiments demonstrate that our model outperforms recent state-of-the-art methods both quantitatively and qualitatively on public dataset.

Exemplar-based video colorization is an essential technique for applications like old movie restoration. Although recent methods perform well in still scenes or scenes with regular movement, they always lack robustness in moving scenes due to their weak ability in modeling long-term dependency both spatially and temporally, leading to color fading, color discontinuity or other artifacts. To solve this problem, we propose an exemplar-based video colorization framework with long-term spatiotemporal dependency. To enhance the long-term spatial dependency, a parallelized CNN-Transformer block and a double head non-local operation are designed. The proposed CNN-Transformer block can better incorporate long-term spatial dependency with local texture and structural features, and the double head non-local operation further leverages the performance of augmented feature. While for long-term temporal dependency enhancement, we further introduce the novel linkage subnet. The linkage subnet propagate motion information across adjacent frame blocks and help to maintain temporal continuity. Experiments demonstrate that our model outperforms recent state-of-the-art methods both quantitatively and qualitatively. Also, our model can generate more colorful, realistic and stabilized results, especially for scenes where objects change greatly and irregularly.

Amoebae from tropical geometry and the Mahler measure from number theory play important roles in quiver gauge theories and dimer models. Their dependencies on the coefficients of the Newton polynomial closely resemble each other, and they are connected via the Ronkin function. Genetic symbolic regression methods are employed to extract the numerical relationships between the 2d and 3d amoebae components and the Mahler measure. We find that the volume of the bounded complement of a d-dimensional amoeba is related to the gas phase contribution to the Mahler measure by a degree-d polynomial, with d = 2 and 3. These methods are then further extended to numerical analyses of the non-reflexive Mahler measure. Furthermore, machine learning methods are used to directly learn the topology of 3d amoebae, with strong performance. Additionally, analytic expressions for boundaries of certain amoebae are given., Comment: 45 pages; 33 Figures

Objective: To predict structure and function of Glutamine synthetase (GS) from Pseudoalteromonas sp. by bioinformatics technology, and to provide a theoretical basis for further study. Methods: Open reading frame (ORF) of GS sequence from Pseudoalteromonas sp. was obtained by ORF finder and was translated into amino acid residue. The structure domain was analyzed by Blast. By the method of analysis tools: Protparam, ProtScale, SignalP-4.0, TMHMM, SOPMA, SWISS-MODEL, NCBI SMART-BLAST and MAGA 7.0, the structure and function of the protein were predicted and analyzed. Results: The results showed that the sequence was GS with 468 amino acid residues, theoretical molecular weight was 51986.64 Da. The protein has the closest evolutionary status with Shewanella oneidensis. Then it had no signal peptide site and transmembrane domain. Secondary structure of GS contained 35.04% alpha-helix, 16.67% Extended chain, 5.34% beta-turn, 42.95% RandomCoil. Conclusions: This GU was a variety of biological functions of protein that may be used as a molecular samples of microbial nitrogen metabolism in extreme environments., Comment: 8 pages, 8 figures