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In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements. By accounting for dependencies across time and space, our models better reflect the complexities of real-world data, enhancing both predictive performance and theoretical robustness. We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data. We broaden existing theoretical findings of temporal-spatial analysis by applying them to neural networks in more general contexts and demonstrate that our proof techniques are effective for models with short-range dependence. Our empirical simulations across various synthetic response functions underscore the superior performance of our method, outperforming established approaches in the existing literature. These findings provide valuable insights into the strong capabilities of dense neural networks for temporal-spatial modeling across a broad range of function classes.

Visual prompting (VP) is a new technique that adapts well-trained frozen models for source domain tasks to target domain tasks. This study examines VP's benefits for black-box model-level backdoor detection. The visual prompt in VP maps class subspaces between source and target domains. We identify a misalignment, termed class subspace inconsistency, between clean and poisoned datasets. Based on this, we introduce \textsc{BProm}, a black-box model-level detection method to identify backdoors in suspicious models, if any. \textsc{BProm} leverages the low classification accuracy of prompted models when backdoors are present. Extensive experiments confirm \textsc{BProm}'s effectiveness.

The gas dynamics of galaxies provide critical insights into the evolution of both baryons and dark matter (DM) across cosmic time. In this context, galaxies at cosmic noon -- the period characterized by the most intense star formation and black hole activities -- are particularly significant. In this work, we present an analysis of the gas dynamics of PKS 0529-549: a galaxy at $z\simeq2.6$, hosting a radio-loud active galactic nucleus (AGN). We use new ALMA observations of the [CI] (2-1) line at a spatial resolution of 0.18$''$ ($\sim$1.5 kpc). We find that (1) the molecular gas forms a rotation-supported disk with $V_{\rm rot}/\sigma_{\rm v}=6\pm3$ and displays a flat rotation curve out to 3.3 kpc; (2) there are several non-circular components including a kinematically anomalous structure near the galaxy center, a gas tail to the South-West, and possibly a second weaker tail to the East; (3) dynamical estimates of gas and stellar masses from fitting the rotation curve are inconsistent with photometric estimates using standard gas conversion factors and stellar population models, respectively; these discrepancies may be due to systematic uncertainties in the photometric masses, in the dynamical masses, or in the case a more massive radio-loud AGN-host galaxy is hidden behind the gas-rich [CI] emitting starburst galaxy along the line of sight. Our work shows that in-depth investigations of 3D line cubes are crucial for revealing the complexity of gas dynamics in high-$z$ galaxies, in which regular rotation may coexist with non-circular motions and possibly tidal structures., Comment: 17 pages, 15 figures, 4 tables. Accepted for publication in Astronomy & Astrophysics. A companion paper (arXiv:2411.04290) is accepted in ApJ. Comments are welcome

Literature reviews play a crucial role in scientific research for understanding the current state of research, identifying gaps, and guiding future studies on specific topics. However, the process of conducting a comprehensive literature review is yet time-consuming. This paper proposes a novel framework, collaborative knowledge minigraph agents (CKMAs), to automate scholarly literature reviews. A novel prompt-based algorithm, the knowledge minigraph construction agent (KMCA), is designed to identify relationships between information pieces from academic literature and automatically constructs knowledge minigraphs. By leveraging the capabilities of large language models on constructed knowledge minigraphs, the multiple path summarization agent (MPSA) efficiently organizes information pieces and relationships from different viewpoints to generate literature review paragraphs. We evaluate CKMAs on three benchmark datasets. Experimental results demonstrate that the proposed techniques generate informative, complete, consistent, and insightful summaries for different research problems, promoting the use of LLMs in more professional fields.

We present new ALMA observations of a starburst galaxy at cosmic noon hosting a radio-loud active galactic nucleus: PKS 0529-549 at $z=2.57$. To investigate the conditions of its cold interstellar medium, we use ALMA observations which spatially resolve the [CI] fine-structure lines, [CI] (2-1) and [CI] (1-0), CO rotational lines, CO (7-6) and CO (4-3), and the rest-frame continuum emission at 461 and 809 GHz. The four emission lines display different morphologies, suggesting spatial variation in the gas excitation conditions. The radio jets have just broken out of the molecular gas but not through the more extended ionized gas halo. The [CI] (2-1) emission is more extended ($\approx8\,{\rm kpc}\times5\,{\rm kpc}$) than detected in previous shallower ALMA observations. The [CI] luminosity ratio implies an excitation temperature of $44\pm16$ K, similar to the dust temperature. Using the [CI] lines, CO (4-3), and 227 GHz dust continuum, we infer the mass of molecular gas $M_{\mathrm{mol}}$ using three independent approaches and typical assumptions in the literature. All approaches point to a massive molecular gas reservoir of about $10^{11}$ $M_{\odot}$, but the exact values differ by up to a factor of 4. Deep observations are critical in correctly characterizing the distribution of cold gas in high-redshift galaxies, and highlight the need to improve systematic uncertainties in inferring accurate molecular gas masses., Comment: 15 pages, 4 figures, 5 tables, accepted in ApJ

Different from the previous treatment in a two-body framework, we introduce the dimeson distribution amplitudes (DAs) to describe the strong dynamics between the S-wave resonances $a_0(980, 1450)$ and the $K\bar K (\pi\eta)$ pair, where the Gegenbauer coefficient required is determined from the experimental data on the time-like form factors involved. The branching ratios and direct CP asymmetries of the decays $B \to a^{(\prime)}_0 h \to K\bar K(\pi\eta) h$, with $a_0=a_0(980)$, $a^{\prime}_0=a_0(1450)$ and $h$ referring to a pion or a kaon, are then calculated in the perturbative QCD (PQCD) approach. We find that the branching ratios of the corresponding quasi-two-body decays $B\to a^{(\prime)}_0 K$ obtained with the narrow width approximation are closer to those predicted in the QCD factorization (QCDF) approach compared to the previous PQCD calculations, no matter a three-body or a two-body framework is assumed. Furthermore, all our predictions for these $B\to a^{(\prime)}_0 K$ decays are below the current experimental upper limits except for those of decays $B^0\to a^{(\prime)-}_0K^+$, which are (slightly) larger than the upper limits. Under the narrow width approximation, the branching ratios of the decays $B^+\to a^{(\prime)+}_0\pi^0$, $B^0\to a^{(\prime)+}_0\pi^-$ and $B^0\to a^{(\prime)0}_0\pi^0$ are comparable to or agree well with the previous PQCD and the QCDF calculations. While for the decays $B^+\to a^{(\prime)0}_0\pi^+$ and $B^0\to a^{(\prime)-}_0\pi^+$, their branching ratios are predicted to be unexpectedly large, for example, the obtained branching ratio of decay $B^+\to a^0_0\pi^+$ is even higher than the current experimental upper limit., Comment: 22 pages, 2 figures

As Open Radio Access Networks (O-RAN) continue to expand, AI-driven applications (xApps) are increasingly being deployed enhance network management. However, developing xApps without formal verification risks introducing logical inconsistencies, particularly in balancing energy efficiency and service availability. In this paper, we argue that prior to their development, the formal analysis of xApp models should be a critical early step in the O-RAN design process. Using the PRISM model checker, we demonstrate how our results provide realistic insights into the thresholds between energy efficiency and service availability. While our models are simplified, the findings highlight how AI-informed decisions can enable more effective cell-switching policies. We position formal verification as an essential practice for future xApp development, avoiding fallacies in real-world applications and ensuring networks operate efficiently., Comment: 22 pages, 9 figures, 2 tables

Lifelong reinforcement learning (RL) has been developed as a paradigm for extending single-task RL to more realistic, dynamic settings. In lifelong RL, the "life" of an RL agent is modeled as a stream of tasks drawn from a task distribution. We propose EPIC (\underline{E}mpirical \underline{P}AC-Bayes that \underline{I}mproves \underline{C}ontinuously), a novel algorithm designed for lifelong RL using PAC-Bayes theory. EPIC learns a shared policy distribution, referred to as the \textit{world policy}, which enables rapid adaptation to new tasks while retaining valuable knowledge from previous experiences. Our theoretical analysis establishes a relationship between the algorithm's generalization performance and the number of prior tasks preserved in memory. We also derive the sample complexity of EPIC in terms of RL regret. Extensive experiments on a variety of environments demonstrate that EPIC significantly outperforms existing methods in lifelong RL, offering both theoretical guarantees and practical efficacy through the use of the world policy.

In this paper we present a statistical study of the [C II] 158 $\mu$m line and the CO(1-0) emission for a sample of $\sim$200 local and high-$z$ (32 sources with $z>1$) galaxies with much different physical conditions. We explore the correlation between the luminosities of [C II] and CO(1-0) lines, and obtain a strong linear relationship, confirming that [C II] is able to trace total molecular gas mass, with a small difference between (U)LIRGs and less-luminous galaxies. The tight and linear relation between [C II] and CO(1-0) is likely determined by the average value of the observed visual extinction $A_V$ and the range of $G_0/n$ in galaxies. Further investigations into the dependence of $L_{\mathrm{[CII]}}/L_{\mathrm{CO(1-0)}}$ on different physical properties show that $L_{\mathrm{[CII]}}/L_{\mathrm{CO(1-0)}}$ (1) anti-correlates with $\Sigma_{\mathrm{IR}}$, and the correlation becomes steeper when $\Sigma_{\mathrm{IR}} \gtrsim 10^{11}$ $L_\odot\,\mathrm{kpc}^{-2}$; (2) correlates positively with the distance from the main sequence $\Delta(\mathrm{MS})$ when $\Delta(\mathrm{MS})\lesssim 0$; and (3) tends to show a systematically smaller value in systems where the [C II] emission is dominated by ionized gas. Our results imply that caution needs to be taken when applying a constant [[C II]-to-$M_{\mathrm{H_2}}$ conversion factor to estimate the molecular gas content in extreme cases, such as galaxies having low-level star formation activity or high SFR surface density., Comment: Accepted for publication in ApJ; 18 pages, 2 tables and 8 figures

Recent years have witnessed a clear trend towards language models with an ever-increasing number of parameters, as well as the growing training overhead and memory usage. Distributed training, particularly through Sharded Data Parallelism (ShardedDP) which partitions optimizer states among workers, has emerged as a crucial technique to mitigate training time and memory usage. Yet, a major challenge in the scalability of ShardedDP is the intensive communication of weights and gradients. While compression techniques can alleviate this issue, they often result in worse accuracy. Driven by this limitation, we propose SDP4Bit (Toward 4Bit Communication Quantization in Sharded Data Parallelism for LLM Training), which effectively reduces the communication of weights and gradients to nearly 4 bits via two novel techniques: quantization on weight differences, and two-level gradient smooth quantization. Furthermore, SDP4Bit presents an algorithm-system co-design with runtime optimization to minimize the computation overhead of compression. In addition to the theoretical guarantees of convergence, we empirically evaluate the accuracy of SDP4Bit on the pre-training of GPT models with up to 6.7 billion parameters, and the results demonstrate a negligible impact on training loss. Furthermore, speed experiments show that SDP4Bit achieves up to 4.08$\times$ speedup in end-to-end throughput on a scale of 128 GPUs., Comment: Accepted by NeurIPS 2024

Advancements in reinforcement learning have led to the development of sophisticated models capable of learning complex decision-making tasks. However, efficiently integrating world models with decision transformers remains a challenge. In this paper, we introduce a novel approach that combines the Dreamer algorithm's ability to generate anticipatory trajectories with the adaptive learning strengths of the Online Decision Transformer. Our methodology enables parallel training where Dreamer-produced trajectories enhance the contextual decision-making of the transformer, creating a bidirectional enhancement loop. We empirically demonstrate the efficacy of our approach on a suite of challenging benchmarks, achieving notable improvements in sample efficiency and reward maximization over existing methods. Our results indicate that the proposed integrated framework not only accelerates learning but also showcases robustness in diverse and dynamic scenarios, marking a significant step forward in model-based reinforcement learning.

Mixture-of-Experts (MoE) architectures face challenges such as high memory consumption and redundancy in experts. Pruning MoE can reduce network weights while maintaining model performance. Motivated by the recent observation of emergent large magnitude features in Large Language Models (LLM) and MoE routing policy, we propose MoE-Pruner, a method that prunes weights with the smallest magnitudes multiplied by the corresponding input activations and router weights, on each output neuron. Our pruning method is one-shot, requiring no retraining or weight updates. We evaluate our method on Mixtral-8x7B and Mixtral-8x22B across multiple language benchmarks. Experimental results show that our pruning method significantly outperforms state-of-the-art LLM pruning methods. Furthermore, our pruned MoE models can benefit from a pretrained teacher model through expert-wise knowledge distillation, improving performance post-pruning. Experimental results demonstrate that the Mixtral-8x7B model with 50% sparsity maintains 99% of the performance of the original model after the expert-wise knowledge distillation.

The semileptonic and nonleptonic decays of the b-flavor vector mesons $B^{*}_{u,d,s}$ and $B_{c}^{*}$ are investigated within the covariant light-front quark model (CLFQM). By calculating the form factors of the transitions $B_{u, d, s, c}^{*}\to P$ under the CLFQM, with $P$ denoting a pseudoscalar meson, i.e., $\pi, K, \eta_c(1S,2S), D_{(s)}, B_{(s)}$, we predict and discuss several physical observables, including the branching ratios, polarization fractions $f_{L}, f_{\|}$, and forward-backward asymmetries $A_{FB}$. The total widths of the single-photon radiative decay channels for these b-flavor vector mesons are estimated using their partial widths. In these considered decays, one can find that the semileptonic decays $B_{s}^{*0}\to D_{s}^{-}\ell^{\prime+}{\nu}_{\ell^\prime}$ and $B_{c}^{*+}\to B_{s}^{0}\ell^{\prime+}{\nu}_{\ell^\prime}, \eta_{c}\ell^{\prime+}{\nu}_{\ell^\prime}$, with $\ell^\prime$ being $e$ or $\tau$, and the nonleptonic channels $B_{c}^{*+}\to B^0_{s} \pi^{+}, B^0_{s} \rho^{+}$ have the largest branching ratios, which can reach up to the $10^{-7}$ order, and are most likely to be accessible at the future high-luminosity LHCb and Belle-II experiments., Comment: 30 pages, 4 figures,accepted for publication in Chin. Phys. C

Gradient descent computed by backpropagation (BP) is a widely used learning method for training artificial neural networks but has several limitations: it is computationally demanding, requires frequent manual tuning of the network architecture, and is prone to catastrophic forgetting when learning incrementally. To address these issues, we introduce a brain-mimetic developmental spiking neural network (BDNN) that mimics the postnatal development of neural circuits. We validate its performance through a neuromorphic tactile system capable of learning to recognize objects through grasping. Unlike traditional BP-based methods, BDNN exhibits strong knowledge transfer, supporting efficient incremental learning of new tactile information. It requires no hyperparameter tuning and dynamically adapts to incoming data. Moreover, compared to the BP-based counterpart, it achieves classification accuracy on par with BP while learning over ten times faster in ideal conditions and up to two or three orders of magnitude faster in practical settings. These features make BDNN well-suited for fast data processing on edge devices., Comment: 24 pages, 8 figures, 2 tables

We address the challenge of online Reinforcement Learning from Human Feedback (RLHF) with a focus on self-rewarding alignment methods. In online RLHF, obtaining feedback requires interaction with the environment, which can be costly when using additional reward models or the GPT-4 API. Current self-rewarding approaches rely heavily on the discriminator's judgment capabilities, which are effective for large-scale models but challenging to transfer to smaller ones. To address these limitations, we propose a novel, only-prompting self-rewarding online algorithm that generates preference datasets without relying on judgment capabilities. Additionally, we employ fine-grained arithmetic control over the optimality gap between positive and negative examples, generating more hard negatives in the later stages of training to help the model better capture subtle human preferences. Finally, we conduct extensive experiments on two base models, Mistral-7B and Mistral-Instruct-7B, which significantly bootstrap the performance of the reference model, achieving 34.5% in the Length-controlled Win Rates of AlpacaEval 2.0.

Electric control of spin in insulators is desired for low-consumption and ultrafast spintronics, but the underlying mechanism remains largely unexplored. Here, we propose an intrinsic effect of dynamic spin generation driven by time-varying electric field. In the intraband response regime, it can be nicely formulated as a Berry curvature effect and leads to two phenomena that are forbidden in the $dc$ limit: linear spin generation in nonmagnetic insulators and intrinsic N{\'e}el spin-orbit torque in $\mathcal{PT}$-symmetric antiferromagnetic insulators. These phenomena are driven by the time derivative of field rather than the field itself, and have a quantum origin in the first-order dynamic anomalous spin polarizability. Combined with first-principles calculations, we predict sizable effects driven by terahertz field in nonmagnetic monolayer Bi and in antiferromagnetic even-layer MnBi$_2$Te$_4$, which can be detected in experiment.

Federated Learning is a well-researched approach for collaboratively training machine learning models across decentralized data while preserving privacy. However, integrating Homomorphic Encryption to ensure data confidentiality introduces significant computational and communication overheads, particularly in heterogeneous environments where clients have varying computational capacities and security needs. In this paper, we propose HERL, a Reinforcement Learning-based approach that uses Q-Learning to dynamically optimize encryption parameters, specifically the polynomial modulus degree, $N$, and the coefficient modulus, $q$, across different client tiers. Our proposed method involves first profiling and tiering clients according to the chosen clustering approach, followed by dynamically selecting the most suitable encryption parameters using an RL-agent. Experimental results demonstrate that our approach significantly reduces the computational overhead while maintaining utility and a high level of security. Empirical results show that HERL improves utility by 17%, reduces the convergence time by up to 24%, and increases convergence efficiency by up to 30%, with minimal security loss.

Just like other heavy flavor mesons, the weak decays of $D^*_{(s)}$ mesons can also provide a platform to check the Standard Model (SM), explore new physics (NP) and understand the mechanisms of weak interactions. At present, the theoretical and experimental researches on $D^*_{(s)}$ mesons are relatively limited. In addition to the dominant electromagnetic decays, the $D^*_{(s)}$ weak decays should also be feasible to explore the $D^*_{(s)}$ mesons. In this paper, we use the covariant light-front quark model (CLFQM) to study the branching ratios of the semi-leptonic decays $D^*_{(s)}\to P\ell^{+}\nu_{\ell}$ and the non-leptonic decays $D^*_{(s)}\to PP, PV$ with $P=\pi, K, \eta^{(\prime)}, V=\rho, K^*, \phi$ and $\ell=e, \mu$, which are within the range $10^{-13}\sim 10^{-6}$. Among these decays, the channels $D_{s}^{*+}\to\eta \ell^{+}\nu_{\ell}$ and $D^{*+}_{s}\to \eta\rho^{+}$ possess the largest branching ratios, which can reach up to $10^{-6}$ order. These decays are most likely to be accessible at the future high-luminosity experiments. One can find that the branching ratios $\mathcal{B}r(D_{s}^{*+}\to\eta \ell^{+}\nu_{\ell})=1.46\times10^{-6}$ and $\mathcal{B}r(D_{s}^{*+}\to\eta \rho^{+})=1.04\times10^{-6}$ correspond to tens of thousands of events in the $e^+e^-$ collider experiments, such as the STCF, CEPC and FCC-ee, and tens of millions of events at the HL-LHC. In a word, it is feasible to study the $D^*_{(s)}$ meson weak decays in the future experiments. Furthermore, we also predict and discuss another two physical observations, that is, the longitudinal polarization fraction $f_{L}$ and the forward-backward asymmetry $A_{FB}$, for our considered decays., Comment: 23 pages, 4 figures. arXiv admin note: text overlap with arXiv:2311.04431

Pre-trained Artificial Neural Networks (ANNs) exhibit robust pattern recognition capabilities and share extensive similarities with the human brain, specifically Biological Neural Networks (BNNs). We are particularly intrigued by these models' ability to acquire new knowledge through fine-tuning. In this regard, Parameter-efficient Fine-tuning (PEFT) has gained widespread adoption as a substitute for full fine-tuning due to its cost reduction in training and mitigation of over-fitting risks by limiting the number of trainable parameters during adaptation. Since both ANNs and BNNs propagate information layer-by-layer, a common analogy can be drawn: weights in ANNs represent synapses in BNNs, while features (also known as latent variables or logits) in ANNs represent neurotransmitters released by neurons in BNNs. Mainstream PEFT methods aim to adjust feature or parameter values using only a limited number of trainable parameters (usually less than 1% of the total parameters), yet achieve surprisingly good results. Building upon this clue, we delve deeper into exploring the connections between feature adjustment and parameter adjustment, resulting in our proposed method Synapses & Neurons (SAN) that learns scaling matrices for features and propagates their effects towards posterior weight matrices. Our approach draws strong inspiration from well-known neuroscience phenomena - Long-term Potentiation (LTP) and Long-term Depression (LTD), which also reveal the relationship between synapse development and neurotransmitter release levels. We conducted extensive comparisons of PEFT on 26 datasets using attention-based networks as well as convolution-based networks, leading to significant improvements compared to other tuning methods (+8.5% over fully-finetune, +7% over Visual Prompt Tuning, and +3.2% over LoRA). The codes would be released.

Changing-look Active Galactic Nuclei (CL AGN) exhibit drastic variations in broad emission lines (BELs), the mechanism of which remains unclear. Expanding the sample of CL AGN is helpful to reveal the mechanism. This study aims to identify more CL AGNs by cross-matching spectroscopic data from the Sloan Digital Sky Survey (SDSS) and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). Our approach to identify CL AGN candidates is based on the automatic spectral fitting, followed by detailed visual inspections. Through this method, we present a sample of 88 CL AGNs, in which 77 sources being newly discovered. Within this sample, 59 CL AGNs primarily show the variability of the H$\beta$ line, 22 exhibit changes in both the H$\beta$ and H$\alpha$ lines, and 7 mainly display variations in the H$\alpha$ line. Our findings reveal that the sequence of appearance and disappearance of the BELs aligns with the known CL sequence. We estimate the black hole mass and Eddington ratio for these CL AGNs, which range from $2.5\times 10^6$ to $8.0\times 10^8 M_\odot$ and from 0.001 to 0.13, respectively. The Eddington ratio is lower than that of most typical AGNs, and is consistent with the results of previous studies on CL AGN. Our results support the hypothesis that the CL behavior is driven by the state transitions of the accretion disk., Comment: 14 pages, 4 figures, to be submitted

Conventional geometry-based SLAM systems lack dense 3D reconstruction capabilities since their data association usually relies on feature correspondences. Additionally, learning-based SLAM systems often fall short in terms of real-time performance and accuracy. Balancing real-time performance with dense 3D reconstruction capabilities is a challenging problem. In this paper, we propose a real-time RGB-D SLAM system that incorporates a novel view synthesis technique, 3D Gaussian Splatting, for 3D scene representation and pose estimation. This technique leverages the real-time rendering performance of 3D Gaussian Splatting with rasterization and allows for differentiable optimization in real time through CUDA implementation. We also enable mesh reconstruction from 3D Gaussians for explicit dense 3D reconstruction. To estimate accurate camera poses, we utilize a rotation-translation decoupled strategy with inverse optimization. This involves iteratively updating both in several iterations through gradient-based optimization. This process includes differentiably rendering RGB, depth, and silhouette maps and updating the camera parameters to minimize a combined loss of photometric loss, depth geometry loss, and visibility loss, given the existing 3D Gaussian map. However, 3D Gaussian Splatting (3DGS) struggles to accurately represent surfaces due to the multi-view inconsistency of 3D Gaussians, which can lead to reduced accuracy in both camera pose estimation and scene reconstruction. To address this, we utilize depth priors as additional regularization to enforce geometric constraints, thereby improving the accuracy of both pose estimation and 3D reconstruction. We also provide extensive experimental results on public benchmark datasets to demonstrate the effectiveness of our proposed methods in terms of pose accuracy, geometric accuracy, and rendering performance.

Overfitting commonly occurs when applying deep neural networks (DNNs) on small-scale datasets, where DNNs do not generalize well from existing data to unseen data. The main reason resulting in overfitting is that small-scale datasets cannot reflect the situations of the real world. Label smoothing (LS) is an effective regularization method to prevent overfitting, avoiding it by mixing one-hot labels with uniform label vectors. However, LS only focuses on labels while ignoring the distribution of existing data. In this paper, we introduce the distributionally robust optimization (DRO) to LS, achieving shift the existing data distribution flexibly to unseen domains when training DNNs. Specifically, we prove that the regularization of LS can be extended to a regularization term for the DNNs parameters when integrating DRO. The regularization term can be utilized to shift existing data to unseen domains and generate new data. Furthermore, we propose an approximate gradient-iteration label smoothing algorithm (GI-LS) to achieve the findings and train DNNs. We prove that the shift for the existing data does not influence the convergence of GI-LS. Since GI-LS incorporates a series of hyperparameters, we further consider using Bayesian optimization (BO) to find the relatively optimal combinations of these hyperparameters. Taking small-scale anomaly classification tasks as a case, we evaluate GI-LS, and the results clearly demonstrate its superior performance.

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More specifically, we focus on solving the Wasserstein-distance-based distributionally robust optimization (DRO) model for the problem, which maximizes the worst-case expected objective over an uncertainty set including all distributions closed enough to a nominal distribution with respect to the Wasserstein distance. We develop a stochastic gradient descent algorithm based on the idea of data augmentation to solve the model efficiently. The algorithm iteratively a) does a bootstrapping sample from the nominal distribution; b) perturbs the adversarially and c) updates decisions. Accordingly, the computational time of the algorithm is only determined by the number of iterations and the complexity of computing the gradient of a single sample. Except for efficiently solving the model, the algorithm provide additional advantages that the proposed algorithm can cope with any nominal distributions and therefore is extendable to solve the problem in an online setting. We also prove that the algorithm converges to the optimal solution of the DRO model at a rate of a $O(1/\sqrt{T})$, where $T$ is the number of iterations of bootstrapping. Consequently, the performance guarantee of the algorithm is that of the DRO model plus $O(1/\sqrt{T})$. Through extensive numerical experiments, we demonstrate the superior performance of the proposed algorithm to several benchmarks.

In recent years, nonlinear Hall effect has attracted great attention with three different terms contributed by Drude effect, Berry curvature dipole and Berry connection polarizability. In this work, we theoretically predict an intrinsic second order spin current induced by spin-dependent Berry curvature polarizability based on time-independent perturbation theory. We show other two second order spin conductivities contributed by the group velocity and spin-dependent Berry curvature dipole.A two-dimensional Rashba-Dresselhaus spin-orbit coupled system is studied as an example, and it is found that the intrinsic second order contribution plays a major role in the region of $\mu>0$, while current mainly comes from the extrinsic terms when $\mu<0$. Thus, the dependence of spin conductivity on chemical potential is expected to distinguish the extrinsic and intrinsic contributions experimentally., Comment: 13 pages,4 figures

Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain and poor prediction ability beyond the sampling domain which are usually mitigated by adding the physical properties of PDEs into the loss function or by employing smart techniques to change the form of loss function for special PDEs. In this paper, we design a symmetry-enhanced deep neural network (sDNN) which makes the architecture of neural networks invariant under the finite group through expanding the dimensions of weight matrixes and bias vectors in each hidden layers by the order of finite group if the group has matrix representations, otherwise extending the set of input data and the hidden layers except for the first hidden layer by the order of finite group. However, the total number of training parameters is only about one over the order of finite group of the original PINN size due to the symmetric architecture of sDNN. Furthermore, we give special forms of weight matrixes and bias vectors of sDNN, and rigorously prove that the architecture itself is invariant under the finite group and the sDNN has the universal approximation ability to learn the function keeping the finite group. Numerical results show that the sDNN has strong predicted abilities in and beyond the sampling domain and performs far better than the vanilla PINN with fewer training points and simpler architecture.

In recent years, Large Language Models (LLM) have demonstrated impressive capabilities in the field of natural language processing (NLP). This paper explores the application of LLMs in negotiation transcript analysis by the Vanderbilt AI Negotiation Lab. Starting in September 2022, we applied multiple strategies using LLMs from zero shot learning to fine tuning models to in-context learning). The final strategy we developed is explained, along with how to access and use the model. This study provides a sense of both the opportunities and roadblocks for the implementation of LLMs in real life applications and offers a model for how LLMs can be applied to coding in other fields.

In this work, we investigate a typical scenario in code generation where a developer edits existing code in real time and requests a code assistant, e.g., a large language model, to re-predict the next token or next line on the fly. Naively, the LLM needs to re-encode the entire KV cache to provide an accurate prediction. However, this process is computationally expensive, especially when the sequence length is long. Simply encoding the edited subsequence and integrating it to the original KV cache meets the temporal confusion problem, leading to significantly worse performance. We address this efficiency and accuracy trade-off by introducing \underline{\textbf{Positional \textbf{I}ntegrity \textbf{E}ncoding} (PIE). Building upon the rotary positional encoding, PIE first removes the rotary matrices in the Key cache that introduce temporal confusion and then reapplies the correct rotary matrices. This process ensures that positional relationships between tokens are correct and requires only a single round of matrix multiplication. We validate the effectiveness of PIE through extensive experiments on the RepoBench-C-8k dataset, utilizing DeepSeek-Coder models with 1.3B, 6.7B, and 33B parameters. Our evaluation includes three real-world coding tasks: code insertion, code deletion, and multi-place code editing. Results demonstrate that PIE reduces computational overhead by over 85% compared to the standard full recomputation approach across all model sizes and tasks while well approximating the model performance., Comment: Preprint. Work in Progress

In this paper, an interference cancellation based neural receiver for superimposed pilot (SIP) in multi-layer transmission is proposed, where the data and pilot are non-orthogonally superimposed in the same time-frequency resource. Specifically, to deal with the intra-layer and inter-layer interference of SIP under multi-layer transmission, the interference cancellation with superimposed symbol aided channel estimation is leveraged in the neural receiver, accompanied by the pre-design of pilot code-division orthogonal mechanism at transmitter. In addition, to address the complexity issue for inter-vendor collaboration and the generalization problem in practical deployments, respectively, this paper also provides a fixed SIP (F-SIP) design based on constant pilot power ratio and scalable mechanisms for different modulation and coding schemes (MCSs) and transmission layers. Simulation results demonstrate the superiority of the proposed schemes on the performance of block error rate and throughput compared with existing counterparts.

We report two binary systems, LAMOST J035540+381550 (hereafter J035540) and LAMOST J035916+400732 (hereafter J035916), identified through the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low-resolution survey (LRS). Each of these two systems contains an M-type star orbiting with a invisible compact object candidate. Follow-up spectroscopic observations of Palomar 200-inch telescope (P200) enhance radial velocity measurements. We use radial velocities from LAMOST and P200, as well as light curves from Zwicky Transient Facility (ZTF) to constrain orbital parameters. The masses of the visible M-type stars are estimated by fitting the MIST isochrones and SEDs. The mass functions for the unseen companions are: $0.22\pm 0.01 M_{\odot}$ for J035540 and $0.16\pm 0.01 M_{\odot}$ for J035916. With the orbital and stellar parameters derived above and assuming the orbital inclination is 90 degree (edge-on), we find that the minimum masses of the invisible companions exceeds that of the visible stars. The single-lined feature and the dynamical evidence suggest the presence of compact objects. J035540's ZTF light curve, modeled with PHOEBE, yields a compact object mass of $0.70^{+0.12}_{-0.05} M_{\odot}$. For J035916, ellipsoidal modulation analysis constrains the light curve amplitude, yielding a compact object mass range of $0.57-0.90 M_{\odot}$. The mass estimates indicate that both are likely white dwarfs. These findings underscore the efficiency of optical time-domain surveys and dynamical methods in identifying faint, massive white dwarfs, along with other compact objects in binaries., Comment: 12 pages, 9 figures, accepted for publication in MNRAS

Accurate flux density calibration is essential for precise analysis and interpretation of observations across different observation modes and instruments. In this research, we firstly introduce the flux calibration model incorporated in HIFAST pipeline, designed for processing HI 21-cm spectra. Furthermore, we investigate different calibration techniques and assess the dependence of the gain parameter on the time and environmental factors. A comparison is carried out in various observation modes (e.g. tracking and scanning modes) to determine the flux density gain ($G$), revealing insignificant discrepancies in $G$ among different methods. Long-term monitoring data shows a linear correlation between $G$ and atmospheric temperature. After subtracting the $G$--Temperature dependence, the dispersion of $G$ is reduced to $<$3% over a one-year time scale. The stability of the receiver response of FAST is considered sufficient to facilitate HI observations that can accommodate a moderate error in flux calibration (e.g., $>\sim5\%$) when utilizing a constant $G$ for calibration purposes. Our study will serve as a useful addition to the results provided by Jiang et al. (2020). Detailed measurement of $G$ for the 19 beams of FAST, covering the frequency range 1000 MHz -- 1500 MHz can be found on the HIFAST homepage: https://hifast.readthedocs.io/fluxgain., Comment: 14 pages, 15 figures, accepted by RAA

In spacetime dimensions of 4D (i.e., 3+1D) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes, despite the absence of anyons. Our understanding of these topological data remains less mature compared to 3D, where anyons have been extensively studied and can be fully described through diagrammatic representations. Inspired by recent advancements in field theory descriptions of higher-dimensional topological orders, this paper systematically constructs diagrammatic representations for 4D and 5D topological orders, generalizable to higher dimensions. We introduce elementary diagrams for fusion and shrinking processes, treating them as vectors in fusion and shrinking spaces, respectively, and build complex diagrams by combining these elementary diagrams. Within these vector spaces, we design unitary operations represented by \(F\)-, \(\Delta\)-, and \(\Delta^2\)-symbols to transform between different bases. We uncover \textit{pentagon equations} and \textit{(hierarchical) shrinking-fusion hexagon equations} that impose constraints on the legitimate forms of these unitary operations. We conjecture that all anomaly-free higher-dimensional topological orders must satisfy these conditions, with any violations indicating a quantum anomaly. This work opens promising avenues for future research, including the exploration of diagrammatic representations involving braiding and implications for noninvertible symmetries and Symmetry Topological Field Theory., Comment: title adjusted. This paper is part of a series of work with 1703.01926, 2012.13761, 2104.07067, 2208.09228, 2306.14611, and 2307.09983

As the current initialization method in the state-of-the-art Stereo Visual-Inertial SLAM framework, ORB-SLAM3 has limitations. Its success depends on the performance of the pure stereo SLAM system and is based on the underlying assumption that pure visual SLAM can accurately estimate the camera trajectory, which is essential for inertial parameter estimation. Meanwhile, the further improved initialization method for ORB-SLAM3, known as Stereo-NEC, is time-consuming due to applying keypoint tracking to estimate gyroscope bias with normal epipolar constraints. To address the limitations of previous methods, this paper proposes a method aimed at enhancing translation accuracy during the initialization stage. The fundamental concept of our method is to improve the translation estimate with a 3 Degree-of-Freedom (DoF) Bundle Adjustment (BA), independently, while the rotation estimate is fixed, instead of using ORB-SLAM3's 6-DoF BA. Additionally, the rotation estimate will be updated by considering IMU measurements and gyroscope bias, unlike ORB-SLAM3's rotation, which is directly obtained from stereo visual odometry and may yield inferior results when operating in challenging scenarios. We also conduct extensive evaluations on the public benchmark, the EuRoC dataset, demonstrating that our method excels in accuracy.

The stellar spectra from LAMOST Medium Resolution Survey can be used to search for compact objects in binaries. The LAMOST DR10 catalog includes > 980, 000 targets with multiple medium resolution spectra. We select the targets with large or rapid radial velocity variation, and obtained an input-sample of 1822 sources. We use light curves and spectra to identify and exclude eclipsing binaries and double-lined spectroscopic binaries in the input-sample. We finally derive a catalog of 89 candidates with well-folded radial velocity, which are all single-lined spectroscopic binaries, indicating an unseen companion residing in each system. The mass function of each system can be well constrained based on the radial velocity curve. In our sample, 26 sources have mass function higher than 0.1 $M_{\odot}$, among which 18 sources have ellipsoidal type light curves. In our opinion, compact objects are likely existent in all these 26 binaries, which are worth follow-up identification., Comment: 20 pages, 10 figures, accepted for publication in ApJ

We revisit the Feynman approach to the Josephson effect, which employs a pair of linear coupling equations for its modeling. It is found that while the exact solutions can account for the AC Josephson effect when the coupling strength is significantly less than the voltage, they fail to produce the DC Josephson effect in any practical scenario. To address this fundamental discrepancy, we derive the coupled Ginzburg-Landau (GL) equations for two interconnected superconductors based on BCS theory. These equations reveal that the nonlinear coupling, which is overlooked in the Feynman method, is crucial in describing the spontaneous symmetry breaking in superconductors, a critical factor for achieving the DC Josephson effect. When the coupled GL equations are applied to a double junction, a sawtooth current pattern emerges, a result unattainable via the Feynman approach., Comment: 9 pages, 3 figures

Recent observations and theories have presented a strong challenge to the universality of the stellar initial mass function (IMF) in extreme environments. A notable example has been found for starburst conditions, where evidence favours a top-heavy IMF, i.e. there is a bias toward massive stars compared to the IMF that is responsible for the stellar mass function and elemental abundances observed in the Milky Way. Local starburst galaxies have star-formation rates similar to those in high-redshift main-sequence galaxies, which appear to dominate the stellar mass budget at early epochs. However, the IMF of high-redshift main-sequence galaxies is yet to be probed. Since $^{13}$CO and C$^{18}$O isotopologues are sensitive to the IMF, we have observed these lines towards four strongly-lensed high-redshift main-sequence galaxies using the Atacama Large Millimeter/sub-millimeter Array. Of our four targets, SDSS J0901+1814, at $z \approx 2.26$, is seen clearly in $^{13}$CO and C$^{18}$O, the first detection of CO isotopologues in the high-redshift main-sequence galaxy population. The observed $^{13}$C/$^{18}$O ratio, $2.4 \pm 0.8$, is significantly lower than that of local main-sequence galaxies. We estimate the isotope ratio, oxygen abundance and stellar mass using a series of chemical evolution models with varying star-formation histories and IMFs. All models favour an IMF that is more top-heavy than that of the Milky Way. Thus, as with starburst galaxies, main-sequence galaxies in the high-redshift Universe have a greater fraction of massive stars than a Milky-Way IMF would imply., Comment: 15 pages, 8 figures, accepted by ApJ

The Stellar Initial Mass Function (IMF) characterizes the mass distribution of newly formed stars in various cosmic environments, serving as a fundamental assumption in astrophysical research. Recent findings challenge the prevalent notion of a universal and static IMF, proposing instead that the IMF's shape is contingent upon the star formation environment. In this study, we analyze the galaxy-wide variation of the IMF for low-mass stars in both dwarf and massive galaxies with diverse observational methods. Despite systematic discrepancies between different approaches, an IMF model with a metallicity-dependent slope for the low-mass stars aligns with the majority of observations, indicating a high degree of uniformity in the star formation processes across the universe. We also emphasize the need for a more comprehensive understanding of the variation of the low-mass IMF, considering measurement biases and factors beyond metallicity., Comment: 15 pages, 5 figures, accepted for publication in The Astrophysical Journal

Ninety gravitational wave events have been detected by the LIGO-Virgo-KAGRA network and are released in the Gravitational-Wave Transient Catalog. Among these events, 83 cases are definitely binary black hole mergers since the masses of all the objects involved significantly exceed the upper limit of neutron stars. The black holes in these merger events naturally form two interesting samples, a pre-merger sample that includes all the black holes before the mergers and a post-merger sample that consists of the black holes generated during the merging processes. The former represents black holes that once existed in the Universe, while the latter represents newly born black holes. Here we present a statistical analysis on these two samples. The non-parametric $\tau$ statistic method is adopted to correct for the observational selection effect. The Lynden-Bell's $C^{-}$ method is further applied to derive the mass distribution and density function of black holes. It is found that the mass distribution can be expressed as a broken power-law function. More interestingly, the power-law index in the high mass region is comparable for the two samples. The number density of black holes is found to depend on redshift as $\rho(z) \propto z^{-2.06}$ -- $z^{-2.12}$ based on the two samples. Implications of these findings on the origin of black holes are discussed., Comment: 18 pages, 7 figures, 1 table, ApJ accepted

The CO-dark molecular gas (DMG), which refers to the molecular gas not traced by CO emission, is crucial for the evolution of the interstellar medium (ISM). While the gas properties of DMG have been widely explored in the Solar neighborhood, whether or not they are similar in the outer disk regions of the Milky Way is still not well understood. In this Letter, we confirm the existence of DMG toward a cold HI arc structure at 13 kpc away from the Galactic center with both OH emission and HI narrow self-absorption (HINSA). This is the first detection of HINSA in the outer disk region, in which the HINSA fraction ($N_{\rm HINSA}$/$N_{\rm H_2}$ = 0.022$\pm$0.011) is an order of magnitude higher than the average value observed in nearby evolved dark clouds, but is consistent with that of the early evolutionary stage of dark clouds. The inferred H$_2$ column density from both extinction and OH emission ($N_{\rm H_2} \approx 10^{20}$ cm$^{-2}$) is an order of magnitude higher than previously estimated. Although the ISM environmental parameters are expected to be different between the outer Galactic disk regions and the Solar neighborhood, we find that the visual extinction ($A_{\rm V}$ = 0.19$\pm$0.03 mag), H$_2$-gas density ($n_{\rm H_2} = 91\pm46$ cm$^{-3}$), and molecular fraction (58\%$\pm$28\%) of the DMG are rather similar to those of nearby diffuse molecular clouds. The existence of DMG associated with the expanding HI supershell supports a scenario where the expansion of supershells may trigger the formation of molecular clouds within a crossing timescale of the shock wave ($\sim$10$^6$ yr)., Comment: 9 pages, 5 figures, accepted by A&A Letter

In this work, we investigate the form factors of the transitions $B_{(s)} \to D_{0}^{\ast}(2300),D_{s0}^{\ast}(2317),$ $ D_{s1}(2460) $ and $ D_{s1}(2536)$ in the covariant light-front quark model (CLFQM), where these final states are considered as P-wave excited charmed mesons. In order to obtain the form factors for the physical transition processes, we need to extend these form factors from the space-like region to the time-like region. The $q^{2}$-dependence for each transition form factor is also plotted. Then, combined with those form factors, the branching ratios of the two-body nonleptonic decays $B_{(s)}\to D^*_{(s)0}(2300,2317)M, D_{s1}(2460,2536)M$ with $M$ being a light pseudoscalar (vector) meson or a charmed meson are calculated by considering the QCD radiative corrections to the hadronic matrix elements with the QCD factorization approach. Most of our predictions are comparable to the results given by other theoretical approaches and the present available data., Comment: 30 pages, 4 figures

Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of efficient tools for dealing with the interfaces between two adjacent sub-domains heavily hinders the training effects, even leads to the discontinuity of the learned solutions. In this paper, we propose a symmetry group based domain decomposition strategy to enhance the PINN for solving the forward and inverse problems of the PDEs possessing a Lie symmetry group. Specifically, for the forward problem, we first deploy the symmetry group to generate the dividing-lines having known solution information which can be adjusted flexibly and are used to divide the whole training domain into a finite number of non-overlapping sub-domains, then utilize the PINN and the symmetry-enhanced PINN methods to learn the solutions in each sub-domain and finally stitch them to the overall solution of PDEs. For the inverse problem, we first utilize the symmetry group acting on the data of the initial and boundary conditions to generate labeled data in the interior domain of PDEs and then find the undetermined parameters as well as the solution by only training the neural networks in a sub-domain. Consequently, the proposed method can predict high-accuracy solutions of PDEs which are failed by the vanilla PINN in the whole domain and the extended physics-informed neural network in the same sub-domains. Numerical results of the Korteweg-de Vries equation with a translation symmetry and the nonlinear viscous fluid equation with a scaling symmetry show that the accuracies of the learned solutions are improved largely.

The geometric properties of parameter space are mostly described by Berry curvature and quantum metric, which are the imaginary and real part of quantum geometric tensor, respectively. In this work, we calculate the dressed Berry curvature and quantum metric containing eight Feynman diagrams, which are proportional to the leading-order of the concentration of impurities. For a two-band gapped graphene model, we find the disorder does not break the original symmetry but decrease (increase) the absolute value of Berry curvature and quantum metric in conduction (valence) band. We show how impurities affect the Berry curvature and quantum metric, deepening our understanding of the impurity effect on the electron transport properties in two-band gapped graphene., Comment: 14 pages,5 figures

In this paper, we investigate the quasi-two-body decays $B_c \to K_0^{*}(1430,1950) D_{(s)} \to K \pi D_{(s)}$ within the perterbative QCD (PQCD) framework. The S-wave two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $K\pi$ pair, which involve the time-like form factors and the Gegenbauer polynomials. In the calculations, we adopt two kinds of parameterization schemes to describe the time-like form factors: One is the relativistic Breit-Wigner (RBW) formula, which is usually more siutable for the narrow resonances, and the other is the LASS line shape proposed by the LASS Collaboration, which includes both the resonant and nonresonant components. We find that the branching ratios and the direct CP violations for the decays $B_c \to K_0^{*}(1430) D_{(s)}$ obtained from those of the quasi-two-body decays $B_c \to K_0^{*}(1430) D_{(s)} \to K \pi D_{(s)}$ under the narrow width approximation (NWA) can be consistent well with the previous PQCD results calculated in the two-body framework by assuming that $K^*_0(1430)$ being the lowest lying $\bar q s$ state, which is so-called scenario II (SII). We conclude that the LASS parameterization is more siutable to describe the $K_0^{*}(1430)$ than the RBW formula, and the nonresonant components play an important role in the branching ratios of the decays $B_c \to K_0^{*}(1430) D_{(s)} \to K \pi D_{(s)}$. In view of the large difference between the decay width measurements for the $K_0^{*}(1950)$ given by BaBar and LASS collaborations, we calculate the branching ratios and the CP violations for the quasi-two-body decays $B_c \to K_0^{*}(1950) D_{(s)} \to K \pi D_{(s)}$ by using two values, $\Gamma_{K^*_0(1950)}=0.100\pm0.04$ GeV and $\Gamma_{K^*_0(1950)}=0.201\pm0.034$ GeV, besides the two kinds of parameterizations for the resonance $K^*_0(1950)$., Comment: 16 pages, 3 figures

In this work, we generalize the notion of character for 2-representations of finite 2-groups. The properties of 2-characters bear strong similarities to those classical characters of finite groups, including conjugation invariance, additivity, multiplicativity and orthogonality. With a careful analysis using homotopy fixed points and quotients for categories with 2-group actions, we prove that the category of class functors on a 2-group $\mathcal G$ is equivalent to the Drinfeld center of the 2-group algebra $\mathrm{Vec}_{\mathcal G}$, which categorifies the Fourier transform on finite abelian groups. After transferring the canonical nondegenerate braided monoidal structure from $\mathfrak Z_1(\mathrm{Vec}_{\mathcal G})$, we discover that irreducible 2-characters of $\mathcal G$ coincide with full centers of the corresponding 2-representations, which are in a one-to-one correspondence with Lagrangian algebras in the category of class functors on $\mathcal G$. In particular, the fusion rule of $2\mathrm{Rep}(\mathcal G)$ can be calculated from the pointwise product of Lagrangian algebras as class functors. From a topological quantum field theory (TQFT) point of view, the commutative Frobenius algebra structure on a 2-character is induced from a 2D topological sigma-model with target space $\lvert \mathrm{B} \mathcal G \rvert$., Comment: 30 pages. Comments are welcome

We identify a fading AGN SDSS J220141.64+115124.3 from the internal Product Launch-11 (MPL-11) in Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. The central region with a projected radius of $\sim$2.4 kpc is characterized as LINER-like line ratios while the outskirts extended to $\sim$15 kpc show Seyfert-like line ratios. The [OIII]$\lambda$5007 luminosity of the Seyfert regions is a factor of 37 (2) higher than the LINER regions without (with) dust attenuation correction, suggesting that the AGN activity decreases at least $\sim$8 $\times$ 10$^3$ yrs ($\sim$2.4 kpc/light-speed) ago. We model the emission line spectra in the central region with double Gaussian components (a narrow core and a broad wing) and analyze the properties of each component. The narrow core component mostly co-rotates with the stellar disc, whereas the broad wing component with a median of the velocity dispersion $\sim$300 km s$^{-1}$ is related to a wind outflow. The kinematic position angle (PA) of the ionized gas shows a $\sim$20{\deg} twist from the galaxy center to 1.5 effective radius. The median of the PA difference between the gas and stellar components is as large as $\sim$50{\deg} within 0.4 effective radius. The tidal feature in DESI image and star-gas misalignment suggest this galaxy is a merger remnant. Combining all these observational results as well as public available X-ray and MIR luminosities, we confirm this is a fading AGN, the merger process kick-started the central engine to quasar phase which ionized gas composed of tidal debris, and now the activity of the central black hole decreases. The discontinuity in [OIII]$\lambda$5007 flux and EQW maps is due to multiple AGN outbursts triggered by merger remnant gas inflows., Comment: Accepted for publication in MNRAS. 12 pages, 10 figures, 1 table

Personal digital data is a critical asset, and governments worldwide have enforced laws and regulations to protect data privacy. Data users have been endowed with the right to be forgotten of their data. In the course of machine learning (ML), the forgotten right requires a model provider to delete user data and its subsequent impact on ML models upon user requests. Machine unlearning emerges to address this, which has garnered ever-increasing attention from both industry and academia. While the area has developed rapidly, there is a lack of comprehensive surveys to capture the latest advancements. Recognizing this shortage, we conduct an extensive exploration to map the landscape of machine unlearning including the (fine-grained) taxonomy of unlearning algorithms under centralized and distributed settings, debate on approximate unlearning, verification and evaluation metrics, challenges and solutions for unlearning under different applications, as well as attacks targeting machine unlearning. The survey concludes by outlining potential directions for future research, hoping to serve as a guide for interested scholars.

We develop a unified theory of defect condensations for topological orders in all dimensions based on higher categories, higher algebras and higher representations. We show that condensing a $k$-codimensional topological defect $A$ in an $n$+1D (potentially anomalous) topological order $\mathsf C^{n+1}$ amounts to a $k$-step process. In the first step, we condense $A$ along one of the transversal directions, thus obtaining a $(k-1)$-codimensional defect $\Sigma A$, which can be further condensed as the second step, so on and so forth. In the $k$-th step, condensing $\Sigma^{k-1}A$ along the only transversal direction defines a phase transition to a new phase $\mathsf D^{n+1}$. Mathematically, a $k$-codimensional defect $A$ is condensable if it is equipped with the structure of a condensable $E_k$-algebra. In this case, $\Sigma A$ is naturally a condensable $E_{k-1}$-algebra, thus it can be further condensed. The condensed phase $\mathsf D^{n+1}$ consists of all deconfined topological defects in $\mathsf C^{n+1}$. A $k$-codimensional topological defect is deconfined if and only if it is equipped with a $k$-dimensional $A$-action, which defines an $E_k$-module over $A$. When $\mathsf C^{n+1}$ is anomaly-free, the same condensation can be alternatively defined by replacing the last two steps by a single step of condensing the $E_2$-algebra $\Sigma^{k-2}A$ directly. The condensed phase $\mathsf D^{n+1}$ is determined by the category of $E_2$-modules over $\Sigma^{k-2}A$. When $n=2$, this modified last step is precisely a usual anyon condensation in a 2+1D topological order. The proofs of the most mathematical results will appear in a mathematical companion of this paper. We also briefly discuss some generalizations and applications that naturally arise from our condensation theory such as higher Morita theory, factorization homology and the condensation theory of non-topological defects., Comment: 120 pages. We are preparing the second version, in which more remarks, examples and references will be added. Comments are welcome

A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic specifications only using observation samples and without the knowledge of the model, and provide a probabilistic guarantee on the satisfaction of the specification. We first propose the theoretical results for using non-parametric estimation to estimate an asymptotic upper bound for the \emph{Lipschitz constant} of the stochastic system, which can determine a finite abstraction of the system. Our results prove that the asymptotic convergence rate of the estimation is $O(n^{-\frac{1}{3+d}})$, where $d$ is the dimension of the system and $n$ is the data scale. We then construct interval Markov decision processes using two different data-driven methods, namely non-parametric estimation and empirical estimation of transition probabilities, to perform formal verification against a given temporal logic specification. Multiple case studies are presented to validate the effectiveness of the proposed methods.