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Optimization · Convex

Y. Jennifer Sun, Zhou Lu

Unlike classical control theory, such as Linear Quadratic Control (LQC), real-world control problems are highly complex. These problems often involve adversarial perturbations, bandit feedback models, and non-quadratic, adversarially chosen cost functions. A fundamental yet unresolved question is whether optimal regret can be achieved for these general control problems. The standard approach to addressing this problem involves a reduction to bandit convex optimization with memory. In the bandit setting, constructing a gradient estimator with low variance is challenging due to the memory structure and non-quadratic loss functions.In this paper, we provide an affirmative answer to this question. Our main contribution is an algorithm that achieves an $\tilde{O}(\sqrt{T})$ optimal regret for bandit non-stochastic control with strongly-convex and smooth cost functions in the presence of adversarial perturbations, improving the previously known $\tilde{O}(T^{2/3})$ regret bound from \citep{cassel2020bandit}. Our algorithm overcomes the memory issue by reducing the problem to Bandit Convex Optimization (BCO) without memory and addresses general strongly-convex costs using recent advancements in BCO from \citep{suggala2024second}. Along the way, we develop an improved algorithm for BCO with memory, which may be of independent interest.

Optimization · Discrete and Combinatorial Optimization

Yaming Guo, chen zhu, Hengshu Zhu, Tieru Wu

Optimization over permutations is typically an NP-hard problem that arises extensively in ranking, matching, tracking, etc. Birkhoff polytope-based relaxation methods have made significant advancements, particularly in penalty-free optimization and probabilistic inference. Relaxation onto the orthogonal group offers unique potential advantages such as a lower representation dimension and preservation of inner products; however, equally effective approaches remain unexplored. To bridge the gap, we present a temperature-controlled differentiable transformation that maps unconstrained vector space to the orthogonal group, where the temperature, in the limit, concentrates orthogonal matrices near permutation matrices. This transformation naturally implements a parameterization for the relaxation of permutation matrices, allowing for gradient-based optimization of problems involving permutations. Additionally, by deriving a re-parameterized gradient estimator, this transformation also provides efficient stochastic optimization over the latent permutations. Extensive experiments involving the optimization over permutation matrices validate the effectiveness of the proposed method.

Xin Yang, YAN WENDING, Michael Bi Mi, Yuan Yuan, Robby Tan

Adverse weather conditions can significantly degrade the video frames, causing existing video semantic segmentation methods to produce erroneous predictions. In this work, we target adverse weather conditions and introduce an end-to-end domain adaptation strategy that leverages a fusion block, temporal-spatial teacher-student learning, and a temporal weather degradation augmentation approach. The fusion block integrates temporal information from adjacent frames at the feature level, trained end-to-end, eliminating the need for pretrained optical flow, distinguishing our method from existing approaches. Our teacher-student approach involves two teachers: one focuses on exploring temporal information from adjacent frames, and the other harnesses spatial information from the current frame. Finally, we apply temporal weather degradation augmentation to consecutive frames to more accurately represent adverse weather degradations. Our method achieves a performance of 25.4 and 33.0 mIoU on the adaptation from VIPER and Synthia to MVSS, respectively, representing an improvement of 4.3 and 5.8 mIoU over the existing state-of-the-art method.

Statistical Methods

Jiacheng Miao, Qiongshi Lu

Machine learning (ML) is playing an increasingly important role in scientific research. In conjunction with classical statistical approaches, ML-assisted analytical strategies have shown great promise in accelerating research findings. This has also opened a whole field of methodological research focusing on integrative approaches that leverage both ML and statistics to tackle data science challenges. One type of study that has quickly gained popularity employs ML to predict unobserved outcomes in massive samples, and then uses predicted outcomes in downstream statistical inference. However, existing methods designed to ensure the validity of this type of post-prediction inference are limited to very basic tasks such as linear regression analysis. This is because any extension of these approaches to new, more sophisticated statistical tasks requires task-specific algebraic derivations and software implementations, which ignores the massive library of existing software tools already developed for the same scientific problem given observed data. This severely constrains the scope of application for post-prediction inference. To address this challenge, we introduce a novel statistical framework named PSPS for task-agnostic ML-assisted inference. It provides a post-prediction inference solution that can be easily plugged into almost any established data analysis routines. It delivers valid and efficient inference that is robust to arbitrary choice of ML model, allowing nearly all existing statistical frameworks to be incorporated into the analysis of ML-predicted data. Through extensive experiments, we showcase our method’s validity, versatility, and superiority compared to existing approaches. Our software is available at https://github.com/qlu-lab/psps.

Applications

Ruizhe Zhong, Xingbo Du, Shixiong Kai, Zhentao Tang, Siyuan Xu, Jianye Hao, Mingxuan Yuan, Junchi Yan

In the Integrated Circuit (IC) design flow, floorplanning (FP) determines the position and shape of each block. Serving as a prototype for downstream tasks, it is critical and establishes the upper bound of the final PPA (Power, Performance, Area). However, with the emergence of 3D IC with stacked layers, existing methods are not flexible enough to handle the versatile constraints. Besides, they typically face difficulties in aligning the cross-die modules in 3D ICs due to their heuristic representations, which could potentially result in severe data transfer failures. To address these issues, we propose FlexPlanner, a flexible learning-based method in hybrid action space with multi-modality representation to simultaneously handle position, aspect ratio, and alignment of blocks. To our best knowledge, FlexPlanner is the first learning-based approach to discard heuristic-based search in the 3D FP task. Thus, the solution space is not limited by the heuristic floorplanning representation, allowing for significant improvements in both wirelength and alignment scores. Specifically, FlexPlanner models 3D FP based on multi-modalities, including vision, graph, and sequence. To address the non-trivial heuristic-dependent issue, we design a sophisticated policy network with hybrid action space and asynchronous layer decision mechanism that allow for determining the versatile properties of each block. Experiments on public benchmarks MCNC and GSRC show the effectiveness. We significantly improve the alignment score from 0.474 to 0.940 and achieve an average reduction of 16% in wirelength. Moreover, our method also demonstrates zero-shot transferability on unseen circuits.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Yixiong Zou, Shuai Yi, Yuhua Li, Ruixuan Li

Vision Transformer (ViT) has shown great power in learning from large-scale datasets. However, collecting sufficient data for expert knowledge is always difficult. To handle this problem, Cross-Domain Few-Shot Learning (CDFSL) has been proposed to transfer the source-domain knowledge learned from sufficient data to target domains where only scarce data is available. In this paper, we find an intriguing phenomenon neglected by previous works for the CDFSL task based on ViT: leaving the CLS token to random initialization, instead of loading source-domain trained parameters, could consistently improve target-domain performance. We then delve into this phenomenon for an interpretation. We find **the CLS token naturally absorbs domain information** due to the inherent structure of the ViT, which is represented as the low-frequency component in the Fourier frequency space of images. Based on this phenomenon and interpretation, we further propose a method for the CDFSL task to decouple the domain information in the CLS token during the source-domain training, and adapt the CLS token on the target domain for efficient few-shot learning. Extensive experiments on four benchmarks validate our rationale and state-of-the-art performance. Our codes are available at https://github.com/Zoilsen/CLS_Token_CDFSL.

Multimodal Models

Xin Wen, Bingchen Zhao, Yilun Chen, Jiangmiao Pang, Xiaojuan Qi

Severe data imbalance naturally exists among web-scale vision-language datasets. Despite this, we find CLIP pre-trained thereupon exhibits notable robustness to the data imbalance compared to supervised learning, and demonstrates significant effectiveness in learning generalizable representations. With an aim to investigate the reasons behind this finding, we conduct controlled experiments to study various underlying factors, and reveal that CLIP's pretext task forms a dynamic classification problem wherein only a subset of classes is present in training. This isolates the bias from dominant classes and implicitly balances the learning signal. Furthermore, the robustness and discriminability of CLIP improve with more descriptive language supervision, larger data scale, and broader open-world concepts, which are inaccessible to supervised learning. Our study not only uncovers the mechanisms behind CLIP's generalizability beyond data imbalance but also provides transferable insights for the research community. The findings are validated in both supervised and self-supervised learning, enabling models trained on imbalanced data to achieve CLIP-level performance on diverse recognition tasks. Code and data are available at: https://github.com/CVMI-Lab/clip-beyond-tail.

Optimization

Xufeng Cai, Cheuk Yin Lin, Jelena Diakonikolas

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets \emph{without replacement} and with (possible) reshuffling at each epoch, the theoretical counterpart of SGD usually relies on the assumption of \emph{sampling with replacement}. It is only very recently that SGD using sampling without replacement -- shuffled SGD -- has been analyzed with matching upper and lower bounds. However, we observe that those bounds are too pessimistic to explain often superior empirical performance of data permutations (sampling without replacement) over vanilla counterparts (sampling with replacement) on machine learning problems. Through fine-grained analysis in the lens of primal-dual cyclic coordinate methods and the introduction of novel smoothness parameters, we present several results for shuffled SGD on smooth and non-smooth convex losses, where our novel analysis framework provides tighter convergence bounds over all popular shuffling schemes (IG, SO, and RR). Notably, our new bounds predict faster convergence than existing bounds in the literature -- by up to a factor of $O(\sqrt{n})$, mirroring benefits from tighter convergence bounds using component smoothness parameters in randomized coordinate methods. Lastly, we numerically demonstrate on common machine learning datasets that our bounds are indeed much tighter, thus offering a bridge between theory and practice.

Generative Models

Avinash Kori, Francesco Locatello, Ainkaran Santhirasekaram, Francesca Toni, Ben Glocker, Fabio De Sousa Ribeiro

Learning modular object-centric representations is said to be crucial for systematic generalization. Existing methods show promising object-binding capabilities empirically, but theoretical identifiability guarantees remain relatively underdeveloped. Understanding when object-centric representations can theoretically be identified is important for scaling slot-based methods to high-dimensional images with correctness guarantees. To that end, we propose a probabilistic slot-attention algorithm that imposes an *aggregate* mixture prior over object-centric slot representations, thereby providing slot identifiability guarantees without supervision, up to an equivalence relation. We provide empirical verification of our theoretical identifiability result using both simple 2-dimensional data and high-resolution imaging datasets.

Applications

Yuxin Chen, Junfei Tan, An Zhang, Zhengyi Yang, Leheng Sheng, Enzhi Zhang, Xiang Wang, Tat-Seng Chua

Recommender systems aim to predict personalized rankings based on user preference data. With the rise of Language Models (LMs), LM-based recommenders have been widely explored due to their extensive world knowledge and powerful reasoning abilities. Most of the LM-based recommenders convert historical interactions into language prompts, pairing with a positive item as the target response and fine-tuning LM with a language modeling loss. However, the current objective fails to fully leverage preference data and is not optimized for personalized ranking tasks, which hinders the performance of LM-based recommenders. Inspired by the current advancement of Direct Preference Optimization (DPO) in human preference alignment and the success of softmax loss in recommendations, we propose Softmax-DPO (\textbf{S-DPO}) to instill ranking information into the LM to help LM-based recommenders distinguish preferred items from negatives, rather than solely focusing on positives. Specifically, we incorporate multiple negatives in user preference data and devise an alternative version of DPO loss tailored for LM-based recommenders, which is extended from the traditional full-ranking Plackett-Luce (PL) model to partial rankings and connected to softmax sampling strategies. Theoretically, we bridge S-DPO with the softmax loss over negative sampling and find that it has an inherent benefit of mining hard negatives, which assures its exceptional capabilities in recommendation tasks. Empirically, extensive experiments conducted on three real-world datasets demonstrate the superiority of S-DPO to effectively model user preference and further boost recommendation performance while providing better rewards for preferred items. Our codes are available at https://github.com/chenyuxin1999/S-DPO.

Yiping Wang, Yifang Chen, Wendan Yan, Alex Fang, Wenjing Zhou, Kevin Jamieson, Simon Du

Data selection has emerged as a core issue for large-scale visual-language model pretaining (e.g., CLIP), particularly with noisy web-curated datasets. Three main data selection approaches are: (1) leveraging external non-CLIP models to aid data selection, (2) training new CLIP-style embedding models that are more effective at selecting high-quality data than the original OpenAI CLIP model, and (3) designing better metrics or strategies universally applicable to any CLIP embedding without requiring specific model properties (e.g., CLIPScore is one popular metric). While the first two approaches have been extensively studied, the third remains under-explored. In this paper, we advance the third approach by proposing two new methods. Firstly, instead of classical CLIP scores that only consider the alignment between two modalities from a single sample, we introduce $\textbf{negCLIPLoss}$, a method inspired by CLIP training loss that adds the alignment between one sample and its contrastive pairs as an extra normalization term to CLIPScore for better quality measurement. Secondly, when downstream tasks are known, we propose a new norm-based metric, $\textbf{NormSim}$, to measure the similarity between pretraining data and target data. We test our methods on the data selection benchmark, DataComp [Gadre et al., 2023]. Compared to the best baseline using only OpenAI's CLIP-L/14, our methods achieve a 5.3\% improvement on ImageNet-1k and a 2.8\% improvement on 38 downstream evaluation tasks. Moreover, both $\textbf{negCLIPLoss}$ and $\textbf{NormSim}$ are compatible with existing techniques. By combining our methods with the current best methods DFN [Fang et al., 2023] and HYPE [Kim et al., 2024], we can boost average performance on downstream tasks by 0.9\%, achieving a new state-of-the-art on the DataComp-medium benchmark.

Generative Models · Diffusion models

Kushagra Pandey, Ruihan Yang, Stephan Mandt

Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving *inverse problems*, such as super-resolution, inpainting, or deblurring, still require hundreds to thousands of iterative steps to obtain high-quality results. We propose a plug-and-play framework for constructing efficient samplers for inverse problems, requiring only *pre-trained* diffusion or flow-matching models. We present *Conditional Conjugate Integrators*, which leverage the specific form of the inverse problem to project the respective conditional diffusion/flow dynamics into a more amenable space for sampling. Our method complements popular posterior approximation methods for solving inverse problems using diffusion/flow models. We evaluate the proposed method's performance on various linear image restoration tasks across multiple datasets, employing diffusion and flow-matching models. Notably, on challenging inverse problems like 4x super-resolution on the ImageNet dataset, our method can generate high-quality samples in as few as *5* conditional sampling steps and outperforms competing baselines requiring 20-1000 steps. Our code will be publicly available at https://github.com/mandt-lab/c-pigdm.

Computer Vision

Wenyuan Zhang, Yu-Shen Liu, Zhizhong Han

It is vital to infer a signed distance function (SDF) for multi-view based surface reconstruction. 3D Gaussian splatting (3DGS) provides a novel perspective for volume rendering, and shows advantages in rendering efficiency and quality. Although 3DGS provides a promising neural rendering option, it is still hard to infer SDFs for surface reconstruction with 3DGS due to the discreteness, the sparseness, and the off-surface drift of 3D Gaussians. To resolve these issues, we propose a method that seamlessly merge 3DGS with the learning of neural SDFs. Our key idea is to more effectively constrain the SDF inference with the multi-view consistency. To this end, we dynamically align 3D Gaussians on the zero-level set of the neural SDF, and then render the aligned 3D Gaussians through the differentiable rasterization. Meanwhile, we update the neural SDF by pulling neighboring space to the pulled 3D Gaussians, which progressively refine the signed distance field near the surface. With both differentiable pulling and splatting, we jointly optimize 3D Gaussians and the neural SDF with both RGB and geometry constraints, which recovers more accurate, smooth, and complete surfaces with more geometry details. Our numerical and visual comparisons show our superiority over the state-of-the-art results on the widely used benchmarks.

Generative Models · Diffusion models

Dominik Hintersdorf, Lukas Struppek, Kristian Kersting, Adam Dziedzic, Franziska Boenisch

Diffusion models (DMs) produce very detailed and high-quality images. Their power results from extensive training on large amounts of data - usually scraped from the internet without proper attribution or consent from content creators. Unfortunately, this practice raises privacy and intellectual property concerns, as DMs can memorize and later reproduce their potentially sensitive or copyrighted training images at inference time. Prior efforts prevent this issue by either changing the input to the diffusion process, thereby preventing the DM from generating memorized samples during inference, or removing the memorized data from training altogether. While those are viable solutions when the DM is developed and deployed in a secure and constantly monitored environment, they hold the risk of adversaries circumventing the safeguards and are not effective when the DM itself is publicly released. To solve the problem, we introduce NeMo, the first method to localize memorization of individual data samples down to the level of neurons in DMs' cross-attention layers. Through our experiments, we make the intriguing finding that in many cases, single neurons are responsible for memorizing particular training samples. By deactivating these memorization neurons, we can avoid the replication of training data at inference time, increase the diversity in the generated outputs, and mitigate the leakage of private and copyrighted data. In this way, our NeMo contributes to a more responsible deployment of DMs.

Optimization · Convex

Anton Rodomanov, Xiaowen Jiang, Sebastian Stich

We present adaptive gradient methods (both basic and accelerated) for solvingconvex composite optimization problems in which the main part is approximatelysmooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a(potentially biased) stochastic gradient oracle.This setting covers many interesting examples including Hölder smooth problemsand various inexact computations of the stochastic gradient.Our methods use AdaGrad stepsizes and are adaptive in the sense that they donot require knowing any problem-dependent constants except an estimate of thediameter of the feasible set but nevertheless achieve the best possibleconvergence rates as if they knew the corresponding constants.We demonstrate that AdaGrad stepsizes work in a variety of situationsby proving, in a unified manner, three types of new results.First, we establish efficiency guarantees for our methods in the classicalsetting where the oracle's variance is uniformly bounded.We then show that, under more refined assumptions on the variance,the same methods without any modifications enjoy implicit variancereduction properties allowing us to express their complexity estimates interms of the variance only at the minimizer.Finally, we show how to incorporate explicit SVRG-type variance reduction intoour methods and obtain even faster algorithms.In all three cases, we present both basic and accelerated algorithmsachieving state-of-the-art complexity bounds.As a direct corollary of our results, we obtain universal stochastic gradientmethods for Hölder smooth problems which can be used in all situations.

Deep Learning · Theory

Lijia Yu, Xiao-Shan Gao, Lijun Zhang, Yibo Miao

The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using overparameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic. Since using i.i.d. training data is a necessary condition for a learning algorithm to be generalizable, memorization and its generalization theory for i.i.d. datasets are developed under mild conditions on the data distribution. First, algorithms are given to construct memorization networks for an i.i.d. dataset, which have the smallest number of parameters and even a constant number of parameters. Second, we show that, in order for the memorization networks to be generalizable, the width of the network must be at least equal to the dimension of the data, which implies that the existing memorization networks with an optimal number of parameters are not generalizable. Third, a lower bound for the sample complexity of general memorization algorithms and the exact sample complexity for memorization algorithms with constant number of parameters are given. As a consequence, it is shown that there exist data distributions such that, to be generalizable for them, the memorization network must have an exponential number of parameters in the data dimension. Finally, an efficient and generalizable memorization algorithm is given when the number of training samples is greater than the efficient memorization sample complexity of the data distribution.

Generative Models · Diffusion models

Junlei Zhou, Jiashi Gao, Xiangyu Zhao, Xin Yao, Xuetao Wei

Text-to-Image (T2I) has witnessed significant advancements, demonstrating superior performance for various generative tasks. However, the presence of stereotypes in T2I introduces harmful biases that require urgent attention as the T2I technology becomes more prominent.Previous work for stereotype mitigation mainly concentrated on mitigating stereotypes engendered with individual objects within images, which failed to address stereotypes engendered by the association of multiple objects, referred to as *Association-Engendered Stereotypes*. For example, mentioning ''black people'' and ''houses'' separately in prompts may not exhibit stereotypes. Nevertheless, when these two objects are associated in prompts, the association of ''black people'' with ''poorer houses'' becomes more pronounced. To tackle this issue, we propose a novel framework, MAS, to Mitigate Association-engendered Stereotypes. This framework models the stereotype problem as a probability distribution alignment problem, aiming to align the stereotype probability distribution of the generated image with the stereotype-free distribution. The MAS framework primarily consists of the *Prompt-Image-Stereotype CLIP* (*PIS CLIP*) and *Sensitive Transformer*. The *PIS CLIP* learns the association between prompts, images, and stereotypes, which can establish the mapping of prompts to stereotypes. The *Sensitive Transformer* produces the sensitive constraints, which guide the stereotyped image distribution to align with the stereotype-free probability distribution. Moreover, recognizing that existing metrics are insufficient for accurately evaluating association-engendered stereotypes, we propose a novel metric, *Stereotype-Distribution-Total-Variation*(*SDTV*), to evaluate stereotypes in T2I. Comprehensive experiments demonstrate that our framework effectively mitigates association-engendered stereotypes.

Computer Vision

Zhixiong Nan, Li Xianghong, Tao Xiang, Jifeng Dai

This paper is motivated by an interesting phenomenon: the performance of object detection lags behind that of instance segmentation (i.e., performance imbalance) when investigating the intermediate results from the beginning transformer decoder layer of MaskDINO (i.e., the SOTA model for joint detection and segmentation). This phenomenon inspires us to think about a question: will the performance imbalance at the beginning layer of transformer decoder constrain the upper bound of the final performance? With this question in mind, we further conduct qualitative and quantitative pre-experiments, which validate the negative impact of detection-segmentation imbalance issue on the model performance. To address this issue, this paper proposes DI-MaskDINO model, the core idea of which is to improve the final performance by alleviating the detection-segmentation imbalance. DI-MaskDINO is implemented by configuring our proposed De-Imbalance (DI) module and Balance-Aware Tokens Optimization (BATO) module to MaskDINO. DI is responsible for generating balance-aware query, and BATO uses the balance-aware query to guide the optimization of the initial feature tokens. The balance-aware query and optimized feature tokens are respectively taken as the Query and Key&Value of transformer decoder to perform joint object detection and instance segmentation. DI-MaskDINO outperforms existing joint object detection and instance segmentation models on COCO and BDD100K benchmarks, achieving +1.2 $AP^{box}$ and +0.9 $AP^{mask}$ improvements compared to SOTA joint detection and segmentation model MaskDINO. In addition, DI-MaskDINO also obtains +1.0 $AP^{box}$ improvement compared to SOTA object detection model DINO and +3.0 $AP^{mask}$ improvement compared to SOTA segmentation model Mask2Former.

Optimization · Discrete and Combinatorial Optimization

Arpit Agarwal, Eric Balkanski

In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often exhibits patterns, we ask the following question: can predictions be used to accelerate the update time of dynamic submodular maximization algorithms? We consider the model for dynamic algorithms with predictions where predictions regarding the insertion and deletion times of elements can be used for preprocessing. Our main result is an algorithm with an $O(\text{poly}(\log \eta, \log w, \log k))$ amortized update time over the sequence of updates that achieves a $1/2 - \epsilon$ approximation for dynamic monotone submodular maximization under a cardinality constraint $k$, where the prediction error $\eta$ is the number of elements that are not inserted and deleted within $w$ time steps of their predicted insertion and deletion times. This amortized update time is independent of the length of the stream and instead depends on the prediction error.

Robotics

Yueming Xu, Haochen Jiang, Zhongyang Xiao, Jianfeng Feng, Li Zhang

Achieving robust and precise pose estimation in dynamic scenes is a significant research challenge in Visual Simultaneous Localization and Mapping (SLAM). Recent advancements integrating Gaussian Splatting into SLAM systems have proven effective in creating high-quality renderings using explicit 3D Gaussian models, significantly improving environmental reconstruction fidelity. However, these approaches depend on a static environment assumption and face challenges in dynamic environments due to inconsistent observations of geometry and photometry. To address this problem, we propose DG-SLAM, the first robust dynamic visual SLAM system grounded in 3D Gaussians, which provides precise camera pose estimation alongside high-fidelity reconstructions. Specifically, we propose effective strategies, including motion mask generation, adaptive Gaussian point management, and a hybrid camera tracking algorithm to improve the accuracy and robustness of pose estimation. Extensive experiments demonstrate that DG-SLAM delivers state-of-the-art performance in camera pose estimation, map reconstruction, and novel-view synthesis in dynamic scenes, outperforming existing methods meanwhile preserving real-time rendering ability.