Shaowen Wang

Shaowen Wang, Linxi Yu, Jian Li

Fine-tuning large-scale pretrained models is prohibitively expensive in terms of computational and memory costs. LoRA, as one of the most popular Parameter-Efficient Fine-Tuning (PEFT) methods, offers a cost-effective alternative by fine-tuning an auxiliary low-rank model that has significantly fewer parameters. Although LoRA reduces the computational and memory requirements significantly at each iteration, extensive empirical evidence indicates that it converges at a considerably slower rate compared to full fine-tuning, ultimately leading to increased overall compute and often worse test performance. In our paper, we perform an in-depth investigation of the initialization method of LoRA and show that careful initialization (without any change of the architecture and the training algorithm) can significantly enhance both efficiency and performance. In particular, we introduce a novel initialization method, LoRA-GA (Low Rank Adaptation with Gradient Approximation), which aligns the gradients of low-rank matrix product with those of full fine-tuning at the first step. Our extensive experiments demonstrate that LoRA-GA achieves a convergence rate comparable to that of full fine-tuning (hence being significantly faster than vanilla LoRA as well as various recent improvements) while simultaneously attaining comparable or even better performance. For example, on the subset of the GLUE dataset with T5-Base, LoRA-GA outperforms LoRA by 5.69% on average. On larger models such as Llama 2-7B, LoRA-GA shows performance improvements of 0.34, 11.52%, and 5.05% on MT-bench, GSM8K, and Human-eval, respectively. Additionally, we observe up to 2-4 times convergence speed improvement compared to vanilla LoRA, validating its effectiveness in accelerating convergence and enhancing model performance. Code is available at https://github.com/Outsider565/LoRA-GA.

Jimeng Shi, Vitalii Stebliankin, Zhaonan Wang et al.

Floods can be very destructive causing heavy damage to life, property, and livelihoods. Global climate change and the consequent sea-level rise have increased the occurrence of extreme weather events, resulting in elevated and frequent flood risk. Therefore, accurate and timely flood forecasting in coastal river systems is critical to facilitate good flood management. However, the computational tools currently used are either slow or inaccurate. In this paper, we propose a Flood prediction tool using Graph Transformer Network (FloodGTN) for river systems. More specifically, FloodGTN learns the spatio-temporal dependencies of water levels at different monitoring stations using Graph Neural Networks (GNNs) and an LSTM. It is currently implemented to consider external covariates such as rainfall, tide, and the settings of hydraulic structures (e.g., outflows of dams, gates, pumps, etc.) along the river. We use a Transformer to learn the attention given to external covariates in computing water levels. We apply the FloodGTN tool to data from the South Florida Water Management District, which manages a coastal area prone to frequent storms and hurricanes. Experimental results show that FloodGTN outperforms the physics-based model (HEC-RAS) by achieving higher accuracy with 70% improvement while speeding up run times by at least 500x.

Jiashuo Sun, Jimeng Shi, Yixuan Xie et al.

Retrieval-Augmented Generation (RAG) has become a standard approach for knowledge-intensive question answering, but existing systems remain brittle on multi-hop questions, where solving the task requires chaining multiple retrieval and reasoning steps. Key challenges are that current methods represent reasoning through free-form natural language, where intermediate states are implicit, retrieval queries can drift from intended entities, and errors are detected by the same model that produces them making self-reflection an unreliable, ungrounded signal. We observe that multi-hop question answering is a typical form of step-by-step computation, and that this structured process aligns closely with how code-specialized language models are trained to operate. Motivated by this, we introduce \pyrag, a framework that reformulates multi-hop RAG as program synthesis and execution. Instead of free-form reasoning trajectories, \pyrag represents the reasoning process as an executable Python program over retrieval and QA tools, exposing intermediate states as variables, producing deterministic feedback through execution, and yielding an inspectable trace of the entire reasoning process. This formulation further enables compiler-grounded self-repair and execution-driven adaptive retrieval without any additional training. Experiments on five QA benchmarks (PopQA, HotpotQA, 2WikiMultihopQA, MuSiQue, and Bamboogle) show that \pyrag consistently outperforms strong baselines under both training-free and RL-trained settings, with especially large gains on compositional multi-hop datasets. Our code, data and models are publicly available at https://github.com/GasolSun36/PyRAG.

Kexian Tang, Jiani Wang, Shaowen Wang et al.

While large language models (LLMs) are pretrained on massive amounts of data, their knowledge coverage remains incomplete in specialized, data-scarce domains, motivating extensive efforts to study synthetic data generation for knowledge injection. We propose SPA (Scaling Prompt-engineered Augmentation), a simple but tough-to-beat baseline that uses a small set of carefully designed prompts to generate large-scale synthetic data for knowledge injection. Through systematic comparisons, we find that SPA outperforms several strong baselines. Furthermore, we identify two key limitations of prior approaches: (1) while RL-based methods may improve the token efficiency of LLM-based data augmentation at small scale, they suffer from diversity collapse as data scales, leading to diminishing returns; and (2) while multi-stage prompting may outperform simple augmentation methods, their advantages can disappear after careful prompt tuning. Our results suggest that, for knowledge injection, careful prompt design combined with straightforward large-scale augmentation can be surprisingly effective, and we hope SPA can serve as a strong baseline for future studies in this area. Our code is available at https://github.com/Tangkexian/SPA.

Shaowen Wang, Yiqi Dong, Ruinian Chang et al.

Despite substantial advances, large language models (LLMs) continue to exhibit hallucinations, generating plausible yet incorrect responses. In this paper, we highlight a critical yet previously underexplored class of hallucinations driven by spurious correlations -- superficial but statistically prominent associations between features (e.g., surnames) and attributes (e.g., nationality) present in the training data. We demonstrate that these spurious correlations induce hallucinations that are confidently generated, immune to model scaling, evade current detection methods, and persist even after refusal fine-tuning. Through systematically controlled synthetic experiments and empirical evaluations on state-of-the-art open-source and proprietary LLMs (including GPT-5), we show that existing hallucination detection methods, such as confidence-based filtering and inner-state probing, fundamentally fail in the presence of spurious correlations. Our theoretical analysis further elucidates why these statistical biases intrinsically undermine confidence-based detection techniques. Our findings thus emphasize the urgent need for new approaches explicitly designed to address hallucinations caused by spurious correlations.

Xingwei Qu, Shaowen Wang, Zihao Huang et al.

Large Language Models (LLMs) apply uniform computation to all tokens, despite language exhibiting highly non-uniform information density. This token-uniform regime wastes capacity on locally predictable spans while under-allocating computation to semantically critical transitions. We propose $\textbf{Dynamic Large Concept Models (DLCM)}$, a hierarchical language modeling framework that learns semantic boundaries from latent representations and shifts computation from tokens to a compressed concept space where reasoning is more efficient. DLCM discovers variable-length concepts end-to-end without relying on predefined linguistic units. Hierarchical compression fundamentally changes scaling behavior. We introduce the first $\textbf{compression-aware scaling law}$, which disentangles token-level capacity, concept-level reasoning capacity, and compression ratio, enabling principled compute allocation under fixed FLOPs. To stably train this heterogeneous architecture, we further develop a $\textbf{decoupled $μ$P parametrization}$ that supports zero-shot hyperparameter transfer across widths and compression regimes. At a practical setting ($R=4$, corresponding to an average of four tokens per concept), DLCM reallocates roughly one-third of inference compute into a higher-capacity reasoning backbone, achieving a $\textbf{+2.69$\%$ average improvement}$ across 12 zero-shot benchmarks under matched inference FLOPs.

Jimeng Shi, Azam Shirali, Bowen Jin et al.

Physics-based numerical models have been the bedrock of atmospheric sciences for decades, offering robust solutions but often at the cost of significant computational resources. Deep learning (DL) models have emerged as powerful tools in meteorology, capable of analyzing complex weather and climate data by learning intricate dependencies and providing rapid predictions once trained. While these models demonstrate promising performance in weather prediction, often surpassing traditional physics-based methods, they still face critical challenges. This paper presents a comprehensive survey of recent deep learning and foundation models for weather prediction. We propose a taxonomy to classify existing models based on their training paradigms: deterministic predictive learning, probabilistic generative learning, and pre-training and fine-tuning. For each paradigm, we delve into the underlying model architectures, address major challenges, offer key insights, and propose targeted directions for future research. Furthermore, we explore real-world applications of these methods and provide a curated summary of open-source code repositories and widely used datasets, aiming to bridge research advancements with practical implementations while fostering open and trustworthy scientific practices in adopting cutting-edge artificial intelligence for weather prediction. The related sources are available at https://github.com/JimengShi/ DL-Foundation-Models-Weather.

Xinyuan Chen, Yao Xu, Shaowen Wang et al.

We propose Uni-Animator, a novel Diffusion Transformer (DiT)-based framework for unified image and video sketch colorization. Existing sketch colorization methods struggle to unify image and video tasks, suffering from imprecise color transfer with single or multiple references, inadequate preservation of high-frequency physical details, and compromised temporal coherence with motion artifacts in large-motion scenes. To tackle imprecise color transfer, we introduce visual reference enhancement via instance patch embedding, enabling precise alignment and fusion of reference color information. To resolve insufficient physical detail preservation, we design physical detail reinforcement using physical features that effectively capture and retain high-frequency textures. To mitigate motion-induced temporal inconsistency, we propose sketch-based dynamic RoPE encoding that adaptively models motion-aware spatial-temporal dependencies. Extensive experimental results demonstrate that Uni-Animator achieves competitive performance on both image and video sketch colorization, matching that of task-specific methods while unlocking unified cross-domain capabilities with high detail fidelity and robust temporal consistency.

Jiashuo Sun, Yixuan Xie, Jimeng Shi et al.

Retrieval-Augmented Generation (RAG) helps large language models (LLMs) answer knowledge-intensive and time-sensitive questions by conditioning generation on external evidence. However, most RAG systems still retrieve unstructured chunks and rely on one-shot generation, which often yields redundant context, low information density, and brittle multi-hop reasoning. While structured RAG pipelines can improve grounding, they typically require costly and error-prone graph construction or impose rigid entity-centric structures that do not align with the query's reasoning chain. We propose \textsc{TaSR-RAG}, a taxonomy-guided structured reasoning framework for evidence selection. We represent both queries and documents as relational triples, and constrain entity semantics with a lightweight two-level taxonomy to balance generalization and precision. Given a complex question, \textsc{TaSR-RAG} decomposes it into an ordered sequence of triple sub-queries with explicit latent variables, then performs step-wise evidence selection via hybrid triple matching that combines semantic similarity over raw triples with structural consistency over typed triples. By maintaining an explicit entity binding table across steps, \textsc{TaSR-RAG} resolves intermediate variables and reduces entity conflation without explicit graph construction or exhaustive search. Experiments on multiple multi-hop question answering benchmarks show that \textsc{TaSR-RAG} consistently outperforms strong RAG and structured-RAG baselines by up to 14\%, while producing clearer evidence attribution and more faithful reasoning traces.

Shaowen Wang, Tariq Alkhalifah

Weight initialization plays a crucial role in the optimization behavior and convergence efficiency of neural networks. Most existing initialization methods, such as Xavier and Kaiming initializations, rely on random sampling and do not exploit information from the optimization process itself. We propose a simple, yet effective, initialization strategy based on self-supervised pre-training using random noise as the target. Instead of directly training the network from random weights, we first pre-train it to fit random noise, which leads to a structured and non-random parameter configuration. We show that this noise-driven pre-training significantly improves convergence speed in subsequent tasks, without requiring additional data or changes to the network architecture. The proposed method is particularly effective for implicit neural representations (INRs) and Deep Image Prior (DIP)-style networks, which are known to exhibit a strong low-frequency bias during optimization. After noise-based pre-training, the network is able to capture high-frequency components much earlier in training, leading to faster and more stable convergence. Although random noise contains no semantic information, it serves as an effective self-supervised signal (considering its white spectrum nature) for shaping the initialization of neural networks. Overall, this work demonstrates that noise-based pre-training offers a lightweight and general alternative to traditional random initialization, enabling more efficient optimization of deep neural networks.

Lance Legel, Qin Huang, Brandon Voelker et al.

We present DeepEarth, a self-supervised multi-modal world model with Earth4D, a novel planetary-scale 4D space-time positional encoder. Earth4D extends 3D multi-resolution hash encoding to include time, efficiently scaling across the planet over centuries with sub-meter, sub-second precision. Multi-modal encoders (e.g. vision-language models) are fused with Earth4D embeddings and trained via masked reconstruction. We demonstrate Earth4D's expressive power by achieving state-of-the-art performance on an ecological forecasting benchmark. Earth4D with learnable hash probing surpasses a multi-modal foundation model pre-trained on substantially more data. Access open source code and download models at: https://github.com/legel/deepearth

Ji Qi, Xinchang Zhang, Dingqi Ye et al.

The rapid advancement of generative artificial intelligence is producing fake remote sensing imagery (RSI) that is increasingly difficult to detect, potentially leading to erroneous intelligence, fake news, and even conspiracy theories. Existing forgery detection methods typically rely on single visual features to capture predefined artifacts, such as spatial-domain cues to detect forged objects like roads or buildings in RSI, or frequency-domain features to identify artifacts from up-sampling operations in adversarial generative networks (GANs). However, the nature of artifacts can significantly differ depending on geographic terrain, land cover types, or specific features within the RSI. Moreover, these complex artifacts evolve as generative models become more sophisticated. In short, over-reliance on a single visual cue makes existing forgery detectors struggle to generalize across diverse remote sensing data. This paper proposed a novel forgery detection framework called SFNet, designed to identify fake images in diverse remote sensing data by leveraging spatial and frequency domain features. Specifically, to obtain rich and comprehensive visual information, SFNet employs two independent feature extractors to capture spatial and frequency domain features from input RSIs. To fully utilize the complementary domain features, the domain feature mapping module and the hybrid domain feature refinement module(CBAM attention) of SFNet are designed to successively align and fuse the multi-domain features while suppressing redundant information. Experiments on three datasets show that SFNet achieves an accuracy improvement of 4%-15.18% over the state-of-the-art RS forgery detection methods and exhibits robust generalization capabilities. The code is available at https://github.com/GeoX-Lab/RSTI/tree/main/SFNet.

Jimeng Shi, Sizhe Zhou, Bowen Jin et al.

Large language models (LLMs) often need to incorporate external knowledge to solve theme-specific problems. Retrieval-augmented generation (RAG) has shown its high promise, empowering LLMs to generate more qualified responses with retrieved external data and knowledge. However, most RAG methods retrieve relevant documents based on either sparse or dense retrieval methods or their combinations, which overlooks the essential, multi-dimensional, and structured semantic information present in documents. This structured information plays a critical role in finding concise yet highly relevant information for domain knowledge-intensive tasks, such as scientific question-answering (QA). In this work, we introduce a multi-dimensional (cube) structure, Hypercube, which can index and allocate documents in a pre-defined multi-dimensional space. Built on the hypercube, we further propose Hypercube-RAG, a novel RAG framework for precise and efficient retrieval. Given a query, Hypercube-RAG first decomposes it based on its entities, phrases, and topics along with pre-defined hypercube dimensions, and then retrieves relevant documents from cubes by aligning these decomposed components with corresponding dimensions. Experiments on three datasets across different domains demonstrate that our method improves response accuracy by 3.7% and retrieval accuracy by 5.3% over the strongest RAG baseline. It also boosts retrieval efficiency (speed) by one or two magnitudes faster than graph-based RAG. Notably, our Hypercube-RAG inherently offers explainability by revealing those underlying dimensions used for retrieval. The code and data are available at https://github.com/JimengShi/Hypercube-RAG.

Tianping Zhang, Shaowen Wang, Shuicheng Yan et al.

Recently, the topic of table pre-training has attracted considerable research interest. However, how to employ table pre-training to boost the performance of tabular prediction remains an open challenge. In this paper, we propose TapTap, the first attempt that leverages table pre-training to empower models for tabular prediction. After pre-training on a large corpus of real-world tabular data, TapTap can generate high-quality synthetic tables to support various applications on tabular data, including privacy protection, low resource regime, missing value imputation, and imbalanced classification. Extensive experiments on 12 datasets demonstrate that TapTap outperforms a total of 16 baselines in different scenarios. Meanwhile, it can be easily combined with various backbone models, including LightGBM, Multilayer Perceptron (MLP) and Transformer. Moreover, with the aid of table pre-training, models trained using synthetic data generated by TapTap can even compete with models using the original dataset on half of the experimental datasets, marking a milestone in the development of synthetic tabular data generation. The codes are available at https://github.com/ZhangTP1996/TapTap.

Li Chen, Zewei Xu, Yongjian Fu et al.

Airborne Laser Scanning (ALS) point clouds have complex structures, and their 3D semantic labeling has been a challenging task. It has three problems: (1) the difficulty of classifying point clouds around boundaries of objects from different classes, (2) the diversity of shapes within the same class, and (3) the scale differences between classes. In this study, we propose a novel double self-attention convolutional network called the DAPnet. The double self-attention includes the point attention module (PAM) and the group attention module (GAM). For problem (1), the PAM can effectively assign different weights based on the relevance of point clouds in adjacent areas. Meanwhile, for the problem (2), the GAM enhances the correlation between groups, i.e., grouped features within the same classes. To solve the problem (3), we adopt a multiscale radius to construct the groups and concatenate extracted hierarchical features with the output of the corresponding upsampling process. Under the ISPRS 3D Semantic Labeling Contest dataset, the DAPnet outperforms the benchmark by 85.2\% with an overall accuracy of 90.7\%. By conducting ablation comparisons, we find that the PAM effectively improves the model than the GAM. The incorporation of the double self-attention module has an average of 7\% improvement on the pre-class accuracy. Plus, the DAPnet consumes a similar training time to those without the attention modules for model convergence. The DAPnet can assign different weights to features based on the relevance between point clouds and their neighbors, which effectively improves classification performance. The source codes are available at: https://github.com/RayleighChen/point-attention.

Liyuan Liu, Zihan Wang, Jingbo Shang et al.

Taking word sequences as the input, typical named entity recognition (NER) models neglect errors from pre-processing (e.g., tokenization). However, these errors can influence the model performance greatly, especially for noisy texts like tweets. Here, we introduce Neural-Char-CRF, a raw-to-end framework that is more robust to pre-processing errors. It takes raw character sequences as inputs and makes end-to-end predictions. Word embedding and contextualized representation models are further tailored to capture textual signals for each character instead of each word. Our model neither requires the conversion from character sequences to word sequences, nor assumes tokenizer can correctly detect all word boundaries. Moreover, we observe our model performance remains unchanged after replacing tokenization with string matching, which demonstrates its potential to be tokenization-free. Extensive experimental results on two public datasets demonstrate the superiority of our proposed method over the state of the art. The implementations and datasets are made available at: https://github.com/LiyuanLucasLiu/Raw-to-End.

Zhenlong Li, Huan Ning, Song Gao et al.

The advent of generative AI exemplified by large language models (LLMs) opens new ways to represent and compute geographic information and transcends the process of geographic knowledge production, driving geographic information systems (GIS) towards autonomous GIS. Leveraging LLMs as the decision core, autonomous GIS can independently generate and execute geoprocessing workflows to perform spatial analysis. In this vision paper, we further elaborate on the concept of autonomous GIS and present a conceptual framework that defines its five autonomous goals, five autonomous levels, five core functions, and three operational scales. We demonstrate how autonomous GIS could perform geospatial data retrieval, spatial analysis, and map making with four proof-of-concept GIS agents. We conclude by identifying critical challenges and future research directions, including fine-tuning and self-growing decision-cores, autonomous modeling, and examining the societal and practical implications of autonomous GIS. By establishing the groundwork for a paradigm shift in GIScience, this paper envisions a future where GIS moves beyond traditional workflows to autonomously reason, derive, innovate, and advance geospatial solutions to pressing global challenges. Meanwhile, as we design and deploy increasingly intelligent geospatial systems, we carry a responsibility to ensure they are developed in socially responsible ways, serve the public good, and support the continued value of human geographic insight in an AI-augmented future.

Zhixuan Pan, Shaowen Wang, Jian Li

Large Language Models (LLMs) have demonstrated remarkable capabilities across numerous tasks, yet principled explanations for their underlying mechanisms and several phenomena, such as scaling laws, hallucinations, and related behaviors, remain elusive. In this work, we revisit the classical relationship between compression and prediction, grounded in Kolmogorov complexity and Shannon information theory, to provide deeper insights into LLM behaviors. By leveraging the Kolmogorov Structure Function and interpreting LLM compression as a two-part coding process, we offer a detailed view of how LLMs acquire and store information across increasing model and data scales -- from pervasive syntactic patterns to progressively rarer knowledge elements. Motivated by this theoretical perspective and natural assumptions inspired by Heap's and Zipf's laws, we introduce a simplified yet representative hierarchical data-generation framework called the Syntax-Knowledge model. Under the Bayesian setting, we show that prediction and compression within this model naturally lead to diverse learning and scaling behaviors observed in LLMs. In particular, our theoretical analysis offers intuitive and principled explanations for both data and model scaling laws, the dynamics of knowledge acquisition during training and fine-tuning, factual knowledge hallucinations in LLMs. The experimental results validate our theoretical predictions.

Elizabeth G. Campolongo, Yuan-Tang Chou, Ekaterina Govorkova et al.

Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not conform to the norms are an indication that the rules of science governing the data are incomplete, and something new needs to be present to explain these unexpected outliers. The challenge of finding anomalies can be confounding since it requires codifying a complete knowledge of the known scientific behaviors and then projecting these known behaviors on the data to look for deviations. When utilizing machine learning, this presents a particular challenge since we require that the model not only understands scientific data perfectly but also recognizes when the data is inconsistent and out of the scope of its trained behavior. In this paper, we present three datasets aimed at developing machine learning-based anomaly detection for disparate scientific domains covering astrophysics, genomics, and polar science. We present the different datasets along with a scheme to make machine learning challenges around the three datasets findable, accessible, interoperable, and reusable (FAIR). Furthermore, we present an approach that generalizes to future machine learning challenges, enabling the possibility of large, more compute-intensive challenges that can ultimately lead to scientific discovery.

Shaowen Wang, Anan Liu, Jian Xiao et al.

Modern recommendation systems frequently employ online learning to dynamically update their models with freshly collected data. The most commonly used optimizer for updating neural networks in these contexts is the Adam optimizer, which integrates momentum ($m_t$) and adaptive learning rate ($v_t$). However, the volatile nature of online learning data, characterized by its frequent distribution shifts and presence of noise, poses significant challenges to Adam's standard optimization process: (1) Adam may use outdated momentum and the average of squared gradients, resulting in slower adaptation to distribution changes, and (2) Adam's performance is adversely affected by data noise. To mitigate these issues, we introduce CAdam, a confidence-based optimization strategy that assesses the consistency between the momentum and the gradient for each parameter dimension before deciding on updates. If momentum and gradient are in sync, CAdam proceeds with parameter updates according to Adam's original formulation; if not, it temporarily withholds updates and monitors potential shifts in data distribution in subsequent iterations. This method allows CAdam to distinguish between the true distributional shifts and mere noise, and to adapt more quickly to new data distributions. In various settings with distribution shift or noise, our experiments demonstrate that CAdam surpasses other well-known optimizers, including the original Adam. Furthermore, in large-scale A/B testing within a live recommendation system, CAdam significantly enhances model performance compared to Adam, leading to substantial increases in the system's gross merchandise volume (GMV).

Peidong Liu, Junjiang Lin, Shaowen Wang et al.

Contextual Markov Decision Processes (CMDPs) offer a framework for sequential decision-making under external signals, but existing methods often fail to generalize in high-dimensional or unstructured contexts, resulting in excessive computation and unstable performance. We propose an information-theoretic summarization approach that uses large language models (LLMs) to compress contextual inputs into low-dimensional, semantically rich summaries. These summaries augment states by preserving decision-critical cues while reducing redundancy. Building on the notion of approximate context sufficiency, we provide, to our knowledge, the first regret bounds and a latency-entropy trade-off characterization for CMDPs. Our analysis clarifies how informativeness impacts computational cost. Experiments across discrete, continuous, visual, and recommendation benchmarks show that our method outperforms raw-context and non-context baselines, improving reward, success rate, and sample efficiency, while reducing latency and memory usage. These findings demonstrate that LLM-based summarization offers a scalable and interpretable solution for efficient decision-making in context-rich, resource-constrained environments.

Xinru Mu, Omar M. Saad, Shaowen Wang et al.

Full waveform inversion (FWI) iteratively updates the velocity model by minimizing the difference between observed and simulated data. Due to the high computational cost and memory requirements associated with global optimization algorithms, FWI is typically implemented using local optimization methods. However, when the initial velocity model is inaccurate and low-frequency seismic data (e.g., below 3 Hz) are absent, the mismatch between simulated and observed data may exceed half a cycle, a phenomenon known as cycle skipping. In such cases, local optimization algorithms (e.g., gradient-based local optimizers) tend to converge to local minima, leading to inaccurate inversion results. In machine learning, neural network training is also an optimization problem prone to local minima. It often employs gradient-based optimizers with a relatively large learning rate (beyond the theoretical limits of local optimization that are usually determined numerically by a line search), which allows the optimization to behave like a quasi-global optimizer. Consequently, after training for several thousand iterations, we can obtain a neural network model with strong generative capability. In this study, we also employ gradient-based optimizers with a relatively large learning rate for FWI. Results from both synthetic and field data experiments show that FWI may initially converge to a local minimum; however, with sufficient additional iterations, the inversion can gradually approach the global minimum, slowly from shallow subsurface to deep, ultimately yielding an accurate velocity model. Furthermore, numerical examples indicate that, given sufficient iterations, reasonable velocity inversion results can still be achieved even when low-frequency data below 5 Hz are missing.