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Computer Vision · Everything Else

Hainuo Wang, Qiming Hu, Xiaojie Guo

Restoring images degraded by adverse weather remains a significant challenge due to the highly non-uniform and spatially heterogeneous nature of weather-induced artifacts, \emph{e.g.}, fine-grained rain streaks versus widespread haze. Accurately estimating the underlying degradation can intuitively provide restoration models with more targeted and effective guidance, enabling adaptive processing strategies. To this end, we propose a Morton-Order Degradation Estimation Mechanism (MODEM) for adverse weather image restoration. Central to MODEM is the Morton-Order 2D-Selective-Scan Module (MOS2D), which integrates Morton-coded spatial ordering with selective state-space models to capture long-range dependencies while preserving local structural coherence. Complementing MOS2D, we introduce a Dual Degradation Estimation Module (DDEM) that disentangles and estimates both global and local degradation priors. These priors dynamically condition the MOS2D modules, facilitating adaptive and context-aware restoration. Extensive experiments and ablation studies demonstrate that MODEM achieves state-of-the-art results across multiple benchmarks and weather types, highlighting its effectiveness in modeling complex degradation dynamics. Our code will be released soon.

Applications · Everything Else

Tianyi Ma, Yiyue Qian, Zheyuan Zhang, Zehong Wang, Xiaoye Qian, Feifan Bai, Yifan Ding, Xuwei Luo, Shinan Zhang, Keerthiram Murugesan 等

The exponential growth of data-driven systems and AI technologies has intensified the demand for high-quality web-sourced datasets. While existing datasets have proven valuable, conventional web data collection approaches face significant limitations in terms of human effort and scalability. Current data collecting solutions fall into two categories: wrapper-based methods that struggle with adaptability and reproducibility, and large language model (LLM)-based approaches that incur substantial computational and financial costs. To address these challenges, we propose AutoData, a novel multi-agent system for Automated web Data collection, that requires minimal human intervention, i.e., only necessitating a natural language instruction specifying the desired dataset. In addition, AutoData is designed for a robust multi-agent architecture, featuring a novel oriented message hypergraph coordinated by a central task manager, to efficiently organize agents across research and development squads. Besides, we introduce a novel hypergraph cache system to advance the multi-agent collaboration process that enables efficient automated data collection and mitigates the token cost issues prevalent in existing LLM-based systems. Moreover, we introduce Instruct2DS, a new benchmark dataset supporting live data collection from web sources across three domains: academic, finance, and sports. Comprehensive evaluations over Instruct2DS and three existing benchmark datasets demonstrate AutoData's superior performance compared to baseline methods. Case studies on challenging tasks such as picture book collection and paper extraction from surveys further validate its applicability.

Probabilistic Methods · Everything Else

Taeseong Yoon, Heeyoung Kim

Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency with the ability to generalize across diverse scenarios. Evidential deep learning (EDL) achieves efficiency by modeling uncertainty through the prediction of a Dirichlet distribution over class probabilities. However, the restrictive assumption of Dirichlet-distributed class probabilities limits EDL's robustness, particularly in complex or unforeseen situations. To address this, we propose *flexible evidential deep learning* ($\mathcal{F}$-EDL), which extends EDL by predicting a flexible Dirichlet distribution—a generalization of the Dirichlet distribution—over class probabilities. This approach provides a more expressive and adaptive representation of uncertainty, significantly enhancing UQ generalization and reliability under challenging scenarios. We theoretically establish several advantages of $\mathcal{F}$-EDL and empirically demonstrate its state-of-the-art UQ performance across diverse evaluation settings, including classical, long-tailed, and noisy in-distribution scenarios.

Reinforcement Learning · Everything Else

Xiaoxue Cheng, Junyi Li, Zhenduo Zhang, Xinyu Tang, Xin Zhao, Xinyu Kong, Zhiqiang Zhang

Large reasoning models (LRMs) have demonstrated strong performance on complex reasoning tasks, but often suffer from overthinking, generating redundant content regardless of task difficulty. Inspired by the dual process theory in cognitive science, we propose Adaptive Cognition Policy Optimization (ACPO), a reinforcement learning framework that enables LRMs to achieve efficient reasoning through adaptive cognitive allocation and dynamic system switch. ACPO incorporates two key components: (1) introducing system-aware reasoning tokens to explicitly represent the thinking modes thereby making the model's cognitive process transparent, and (2) integrating online difficulty estimation and token length budget to guide adaptive system switch and reasoning during reinforcement learning. To this end, we propose a two-stage training strategy. The first stage begins with supervised fine-tuning to cold start the model, enabling it to generate reasoning paths with explicit thinking modes. In the second stage, we apply ACPO to further enhance adaptive system switch for difficulty-aware reasoning. Experimental results demonstrate that ACPO effectively reduces redundant reasoning while adaptively adjusting cognitive allocation based on task complexity, achieving efficient hybrid reasoning.

Deep Learning · Everything Else

Zhengliang Shi, Lingyong Yan, Dawei Yin, Suzan Verberne, Maarten Rijke, Zhaochun Ren

Large language models (LLMs) have been widely integrated into information retrieval to advance traditional techniques. However, effectively enabling LLMs to seek accurate knowledge in complex tasks remains a challenge due to the complexity of multi-hop queries as well as the irrelevant retrieved content. To address these limitations, we propose ExSearch, an agentic search framework, where the LLM learns to retrieve useful information as the reasoning unfolds through a self-incentivized process. At each step, the LLM decides what to retrieve (thinking), triggers an external retriever (search), and extracts fine-grained evidence (recording) to support next-step reasoning. To enable LLM with this capability, we adopts a Generalized Expectation-Maximization algorithm. In the E-step, the LLM generates multiple search trajectories and assigns an importance weight to each; the M-step trains the LLM on them with a re-weighted loss function. This creates a self-incentivized loop, where the LLM iteratively learns from its own generated data, progressively improving itself for search. We further theoretically analyze this training process, establishing convergence guarantees. Extensive experiments on four knowledge-intensive benchmarks show that ExSearchS substantially outperforms baselines, e.g., +7.8% improvement on exact match score. Motivated by these promising results, we introduce ExSearch-Zoo, an extension that extends our method to broader scenarios, to facilitate future work.

Theory · Everything Else

Yousef Al-Jazzazi, Haya Diwan, Jinrui Gou, Cameron Musco, Christopher Musco, Torsten Suel

Nearest neighbor search is central in machine learning, information retrieval, and databases. For high-dimensional datasets, graph-based methods such as HNSW, DiskANN, and NSG have become popular thanks to their empirical accuracy and efficiency. These methods construct a directed graph over the dataset and perform beam search on the graph to find nodes close to a given query. While significant work has focused on practical refinements and theoretical understanding of graph-based methods, many questions remain. We propose a new distance-based termination condition for beam search to replace the commonly used condition based on beam width. We prove that, as long as the search graph is navigable, our resulting Adaptive Beam Search method is guaranteed to approximately solve the nearest-neighbor problem, establishing a connection between navigability and the performance of graph-based search. We also provide extensive experiments on our new termination condition for both navigable graphs and approximately navigable graphs used in practice, such as HNSW and Vamana graphs. We find that Adaptive Beam Search outperforms standard beam search over a range of recall values, data sets, graph constructions, and target number of nearest neighbors. It thus provides a simple and practical way to improve the performance of popular methods.

General Machine Learning · Everything Else

Nan Lu, Jian Shi, Xinyu Tian

Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to identify dynamic ranking groups by incorporating temporal penalties into a spectral estimation for the celebrated Bradley-Terry model. To detect structural changes, we introduce an innovative objective function and present a practicable algorithm based on dynamic programming. Theoretically, we establish the consistency of ranking group recognition by exploiting properties of a random 'design matrix' induced by a reversible Markov chain. We also tailor a group inverse technique to quantify the uncertainty in item ability estimates. Additionally, we prove the consistency of structure change recognition, ensuring the robustness of the proposed framework. Experiments on both synthetic and real-world datasets demonstrate the practical utility and interpretability of our approach.

Deep Learning · Everything Else

Haoyu Wang, Wei Dai, Jiawei Zhang, Jialun Ma, Mingyi Huang, Yuguo Yu

Loss of plasticity (LoP) is the primary cause of cognitive decline in normal aging brains next to cell loss. Recent works show that similar LoP also plagues neural networks during deep continual learning (DCL). While it has been shown that random perturbations of learned weights can alleviate LoP, its underlying mechanisms remain insufficiently understood. Here we offer a unique view of LoP and dissect its mechanisms through the lenses of an innovative framework combining the theory of neural collapse and finite-time Lyapunov exponents (FTLE) analysis. We show that LoP actually consists of two contrasting types: (i) type-1 LoP is characterized by highly negative FTLEs, where the network is prevented from learning due to the collapse of representations; (ii) while type-2 LoP is characterized by excessively positive FTLEs, where the network can train well but the growingly chaotic behaviors reduce its test accuracy. Based on these understandings, we introduce Generalized Mixup, designed to relax the representation space for prolonged DCL and demonstrate its superior efficacy vs. existing methods.

Data-centric AI · Everything Else

Hyunseung Lim, Sooyohn Nam, Sungmin Na, Ji Yong Cho, June Yong Yang, Hyungyu Shin, Yoonjoo Lee, Juho Kim, Moontae Lee, Hwajung Hong

Patent examination remains an ongoing challenge in the NLP literature even after the advent of large language models (LLMs), as it requires an extensive yet nuanced human judgment on whether a submitted $\textit{claim}$ meets the statutory standards of $\textit{novelty}$ and $\textit{non-obviousness}$ against previously granted claims—$\textit{prior art}$—in expert domains. Previous NLP studies have approached this challenge as a prediction task (e.g., forecasting grant outcomes) with high-level proxies such as similarity metrics or classifiers trained on historical labels. However, this approach often overlooks the step-by-step evaluations that examiners must make with profound information, including rationales for the decisions provided in $\textit{office actions}$ documents, which also makes it harder to measure the current state of techniques in patent review processes. To fill this gap, we construct PANORAMA, a dataset of 8,143 U.S. patent examination records that preserves the full decision trails, including original applications, all cited references, $\textit{Non-Final Rejections}$, and $\textit{Notices of Allowance}$. Also, PANORAMA decomposes the trails into sequential benchmarks that emulate patent professionals' patent review processes and allow researchers to examine large language models' capabilities at each step of them. Our findings indicate that, although LLMs are relatively effective at retrieving relevant prior art and pinpointing the pertinent paragraphs, they struggle to assess the novelty and non-obviousness of patent claims. We discuss these results and argue that advancing NLP, including LLMs, in the patent domain requires a deeper understanding of real-world patent examination. Our dataset is openly available at https://huggingface.co/datasets/LG-AI-Research/PANORAMA.

Computer Vision · Everything Else

Ali Zafari, Xi Chen, Shirin Jalali

Zero-shot denoising aims to denoise observations without access to training samples or clean reference images. This setting is particularly relevant in practical imaging scenarios involving specialized domains such as medical imaging or biology. In this work, we propose the *Zero-Shot Neural Compression Denoiser* (ZS-NCD), a novel denoising framework based on neural compression. ZS-NCD treats a neural compression network as an untrained model, optimized directly on patches extracted from a single noisy image. The final reconstruction is then obtained by aggregating the outputs of the trained model over overlapping patches. Thanks to the built-in entropy constraints of compression architectures, our method naturally avoids overfitting and does not require manual regularization or early stopping. Through extensive experiments, we show that ZS-NCD achieves state-of-the-art performance among zero-shot denoisers for both Gaussian and Poisson noise, and generalizes well to both natural and non-natural images. Additionally, we provide new finite-sample theoretical results that characterize upper bounds on the achievable reconstruction error of general maximum-likelihood compression-based denoisers. These results further establish the theoretical foundations of compression-based denoising. Our code is available at: https://github.com/Computational-Imaging-RU/ZS-NCDenoiser.

Reinforcement Learning · Everything Else

Kexin ZHENG, Lauriane Teyssier, Yinan Zheng, Yu Luo, Xianyuan Zhan

The recent development of zero-shot reinforcement learning (RL) has opened a new avenue for learning pre-trained generalist policies that can adapt to arbitrary new tasks in a zero-shot manner. While the popular Forward-Backward representations (FB) and related methods have shown promise in zero-shot RL, we empirically found that their modeling lacks expressivity and that extrapolation errors caused by out-of-distribution (OOD) actions during offline learning sometimes lead to biased representations, ultimately resulting in suboptimal performance. To address these issues, we propose Behavior-REgularizEd Zero-shot RL with Expressivity enhancement (BREEZE), an upgraded FB-based framework that simultaneously enhances learning stability, policy extraction capability, and representation learning quality. BREEZE introduces behavioral regularization in zero-shot RL policy learning, transforming policy optimization into a stable in-sample learning paradigm. Additionally, BREEZE extracts the policy using a task-conditioned diffusion model, enabling the generation of high-quality and multimodal action distributions in zero-shot RL settings. Moreover, BREEZE employs expressive attention-based architectures for representation modeling to capture the complex relationships between environmental dynamics. Extensive experiments on ExORL and D4RL Kitchen demonstrate that BREEZE achieves the best or near-the-best performance while exhibiting superior robustness compared to prior offline zero-shot RL methods. The official implementation is available at: https://github.com/Whiterrrrr/BREEZE.

Reinforcement Learning · Everything Else

Jianhao Yan, Yafu Li, Zican Hu, Zhi Wang, Ganqu Cui, Xiaoye Qu, Yu Cheng, Yue Zhang

Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning with verifiable rewards~(RLVR). However, existing RLVR approaches are inherently ``on-policy'', limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. To address this issue, we introduce LUFFY (Learning to reason Under oFF-policY guidance), a framework that augments RLVR with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Specifically, LUFFY combines the Mixed-Policy GRPO framework, which has a theoretically guaranteed convergence rate, alongside policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Compared with previous RLVR methods, LUFFY achieves an over +6.4 average gain across six math benchmarks and an advantage of over +6.2 points in out-of-distribution tasks. Most significantly, we show that LUFFY successfully trains weak models in scenarios where on-policy RLVR completely fails. These results provide compelling evidence that LUFFY transcends the fundamental limitations of on-policy RLVR and demonstrates the great potential of utilizing off-policy guidance in RLVR.

General Machine Learning · Everything Else

Walid Durani, Collin Leiber, Khalid Durani, Claudia Plant, Christian Böhm

Anomaly detection is a crucial task in data mining, focusing on identifying data points that deviate significantly from the main patterns in the data. This paper introduces Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres (ADERH), a new isolation-based technique leveraging two key observations: (i) anomalies are comparatively rare, and (ii) they typically deviate more strongly from general patterns than normal data points. Drawing on a delta-separation argument, ADERH constructs an ensemble of multi-scale hyperspheres built upon randomly paired data points to identify anomalies. To address inevitable overlaps between anomalous and normal regions in the feature space, ADERH integrates two complementary concepts: Pitch, which highlights points near hypersphere boundaries, and NDensity, which down-weights hyperspheres centered on sparse (and often anomalous) regions. By averaging these local, density-adjusted ``isolation'' indicators across many random subsets, ADERH yields robust anomaly scores that clearly separate normal from abnormal samples. Extensive experiments on diverse real-world datasets show that ADERH consistently outperforms state-of-the-art methods while maintaining linear runtime scalability and stable performance across varying hyperparameter settings.

General Machine Learning · Everything Else

Marzi Heidari, Hanping Zhang, Yuhong Guo

The challenge of learning with noisy labels is significant in machine learning, as it can severely degrade the performance of prediction models if not addressed properly. This paper introduces a novel framework that conceptualizes noisy label correction as a reinforcement learning (RL) problem. The proposed approach, Reinforcement Learning for Noisy Label Correction (RLNLC), defines a comprehensive state space representing data and their associated labels, an action space that indicates possible label corrections, and a reward mechanism that evaluates the efficacy of label corrections. RLNLC learns a deep feature representation based policy network to perform label correction through reinforcement learning, utilizing an actor-critic method. The learned policy is subsequently deployed to iteratively correct noisy training labels and facilitate the training of the prediction model. The effectiveness of RLNLC is demonstrated through extensive experiments on multiple benchmark datasets, where it consistently outperforms existing state-of-the-art techniques for learning with noisy labels.

Reinforcement Learning · Everything Else

Yifan Sun, Jingyan Shen, Yibin Wang, Tianyu Chen, Zhendong Wang, Mingyuan Zhou, Huan Zhang

Reinforcement learning (RL) has become an effective approach for fine-tuning large language models (LLMs), particularly to enhance their reasoning capabilities. However, RL fine-tuning remains highly resource-intensive, and existing work has largely overlooked the problem of data efficiency. In this paper, we propose two techniques to improve data efficiency in LLM RL fine-tuning: difficulty-targeted online data selection and rollout replay. We introduce the notion of adaptive difficulty to guide online data selection, prioritizing questions of moderate difficulty that are more likely to yield informative learning signals. To estimate adaptive difficulty efficiently, we develop an attention-based framework that requires rollouts for only a small reference set of questions. The adaptive difficulty of the remaining questions is then estimated based on their similarity to this set. To further reduce rollout cost, we introduce a rollout replay mechanism inspired by experience replay in traditional RL. This technique reuses recent rollouts, lowering per-step computation while maintaining stable updates. Experiments across 6 LLM-dataset combinations show that our method reduces RL fine-tuning time by 23% to 62% while reaching the same level of performance as the original GRPO algorithm. Our code repository is available at https://github.com/ASTRAL-Group/data-efficient-llm-rl/.

Computer Vision · Everything Else

Jinpei Guo, Yifei Ji, Zheng Chen, Kai Liu, Min Liu, Wang Rao, Wenbo Li, Yong Guo, Yulun Zhang

Pretrained latent diffusion models have shown strong potential for lossy image compression, owing to their powerful generative priors. Most existing diffusion-based methods reconstruct images by iteratively denoising from random noise, guided by compressed latent representations. While these approaches have achieved high reconstruction quality, their multi-step sampling process incurs substantial computational overhead. Moreover, they typically require training separate models for different compression bit-rates, leading to significant training and storage costs. To address these challenges, we propose a one-step diffusion codec across multiple bit-rates. termed OSCAR. Specifically, our method views compressed latents as noisy variants of the original latents, where the level of distortion depends on the bit-rate. This perspective allows them to be modeled as intermediate states along a diffusion trajectory. By establishing a mapping from the compression bit-rate to a pseudo diffusion timestep, we condition a single generative model to support reconstructions at multiple bit-rates. Meanwhile, we argue that the compressed latents retain rich structural information, thereby making one-step denoising feasible. Thus, OSCAR replaces iterative sampling with a single denoising pass, significantly improving inference efficiency. Extensive experiments demonstrate that OSCAR achieves superior performance in both quantitative and visual quality metrics. The code and models are available at https://github.com/jp-guo/OSCAR/.

Reinforcement Learning · Everything Else

Fengshuo Bai, Rui Zhao, Hongming Zhang, Sijia Cui, Shao Zhang, bo xu, Lei Han, Ying Wen, Yaodong Yang

Preference-based reinforcement learning (PbRL) bypasses complex reward engineering by learning from human feedback. However, due to the high cost of obtaining feedback, PbRL typically relies on a limited set of preference-labeled samples. This data scarcity introduces two key inefficiencies: (1) the reward model overfits to the limited feedback, leading to poor generalization to unseen samples, and (2) the agent exploits the learned reward model, exacerbating overestimation of action values in temporal difference (TD) learning. To address these issues, we propose STAR, an efficient PbRL method that integrates preference margin regularization and policy regularization. Preference margin regularization mitigates overfitting by introducing a bounded margin in reward optimization, preventing excessive bias toward specific feedback. Policy regularization bootstraps a conservative estimate $\widehat{Q}$ from well-supported state-action pairs in the replay memory, reducing overestimation during policy learning. Experimental results show that STAR improves feedback efficiency, achieving 34.8\% higher performance in online settings and 29.7\% in offline settings compared to state-of-the-art methods. Ablation studies confirm that STAR facilitates more robust reward and value function learning. The videos of this project are released at https://sites.google.com/view/pbrl-star.

Computer Vision · Everything Else

Feng Lu, Tong Jin, Canming Ye, Xiangyuan Lan, Yunpeng Liu, Chun Yuan

Visual place recognition (VPR) is typically regarded as a specific image retrieval task, whose core lies in representing images as global descriptors. Over the past decade, dominant VPR methods (e.g., NetVLAD) have followed a paradigm that first extracts the patch features/tokens of the input image using a backbone, and then aggregates these patch features into a global descriptor via an aggregator. This backbone-plus-aggregator paradigm has achieved overwhelming dominance in the CNN era and remains widely used in transformer-based models. In this paper, however, we argue that a dedicated aggregator is not necessary in the transformer era, that is, we can obtain robust global descriptors only with the backbone. Specifically, we introduce some learnable aggregation tokens, which are prepended to the patch tokens before a particular transformer block. All these tokens will be jointly processed and interact globally via the intrinsic self-attention mechanism, implicitly aggregating useful information within the patch tokens to the aggregation tokens. Finally, we only take these aggregation tokens from the last output tokens and concatenate them as the global representation. Although implicit aggregation can provide robust global descriptors in an extremely simple manner, where and how to insert additional tokens, as well as the initialization of tokens, remains an open issue worthy of further exploration. To this end, we also propose the optimal token insertion strategy and token initialization method derived from empirical studies. Experimental results show that our method outperforms state-of-the-art methods on several VPR datasets with higher efficiency and ranks 1st on the MSLS challenge leaderboard. The code is available at https://github.com/lu-feng/image.

General Machine Learning · Everything Else

Haoyu Li, Xiangru Zhong, Bin Hu, Huan Zhang

Learning-based neural network (NN) control policies have shown impressive empirical performance. However, obtaining stability guarantees and estimates of the region of attraction of these learned neural controllers is challenging due to the lack of stable and scalable training and verification algorithms. Although previous works in this area have achieved great success, much conservatism remains in their frameworks. In this work, we propose a novel two-stage training framework to jointly synthesize a controller a Lyapunov function for continuous-time systems. By leveraging a Zubov‑inspired region of attraction characterization to directly estimate stability boundaries, we propose a novel training-data sampling strategy and a domain-updating mechanism that significantly reduces the conservatism in training. Moreover, unlike existing works on continuous-time systems that rely on an SMT solver to formally verify the Lyapunov condition, we extend state-of-the-art neural network verifier $\alpha,\beta$-CROWN with the capability of performing automatic bound propagation through the Jacobian of dynamical systems and a novel verification scheme that avoids expensive bisection. To demonstrate the effectiveness of our approach, we conduct numerical experiments by synthesizing and verifying controllers on several challenging nonlinear systems across multiple dimensions. We show that our training can yield region of attractions with volume $5 - 1.5\cdot 10^{5}$ times larger compared to the baselines, and our verification on continuous systems can be up to $40-10{,}000$ times faster compared to the traditional SMT solver dReal. Our code is available at https://github.com/Verified-Intelligence/Two-Stage_Neural_Controller_Training.

Probabilistic Methods · Everything Else

Themistoklis Haris, Fabian Spaeh, Spyridon Konstantinos Dragazis, Charalampos Tsourakakis

Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network centrality analysis, ranking and recommendation systems, and epidemiology. In this work, we develop local algorithms for estimating hitting times between a pair of vertices $u,v$ without accessing the full graph, overcoming scalability issues of prior global methods. Our first algorithm uses the key insight that hitting time computations can be truncated at the meeting time of two independent random walks from $u$ and $v$. This leads to an efficient estimator analyzed via the Kronecker product graph and Markov Chain Chernoff bounds. We also present an algorithm extending the work of Peng et al. [2021] that introduces a novel adaptation of the spectral cutoff technique to account for the asymmetry of hitting times. This adaptation captures the directionality of the underlying random walk and requires non-trivial modifications to ensure accuracy and efficiency. In addition to the algorithmic upper bounds, we also provide tight asymptotic lower bounds. Finally, we reveal a connection between hitting time estimation and distribution testing, and we validate our algorithms using experiments on both real and synthetic data.