Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this challenge, we propose CAusal MAthematician (CAMA), a two stage causal framework that equips LLMs with explicit, reusable mathematical structure. In the learning stage, CAMA first constructs the Mathematical Causal Graph (MCG), a high level representation of solution strategies, by combining LLM priors with causal discovery algorithms applied to a corpus of question solution pairs. The resulting MCG encodes essential knowledge points and their causal dependencies. To better align the graph with downstream reasoning tasks, CAMA further refines the MCG through iterative feedback derived from a selected subset of the question solution pairs. In the reasoning stage, given a new question, CAMA dynamically extracts a task relevant subgraph from the MCG, conditioned on both the question content and the LLM’s intermediate reasoning trace. This subgraph, which encodes the most pertinent knowledge points and their causal dependencies, is then injected back into the LLM to guide its reasoning process. Empirical results on real world datasets show that CAMA significantly improves LLM performance on challenging mathematical problems. Furthermore, our experiments demonstrate that structured guidance consistently outperforms unstructured alternatives, and that incorporating asymmetric causal relationships yields greater improvements than using symmetric associations alone.

Large Language Models (LLMs) have achieved remarkable success across various domains.However, a fundamental question remains: Can LLMs effectively utilize causal knowledge for prediction and generation?Through empirical studies, we find that LLMs trained directly on large-scale data often capture spurious correlations rather than true causal relationships, leading to suboptimal performance, especially in out-of-distribution (OOD) scenarios.To address this challenge, we propose Causal Attention Tuning (CAT), a novel approach that injects fine-grained causal knowledge into the attention mechanism.We propose an automated pipeline that leverages human priors to automatically generate token-level causal signals and introduce the Re-Attention mechanism to guide training, helping the model focus on causal structures while mitigating noise and biases in attention scores.Experimental results on our proposed Spurious Token Game (STG) benchmark and multiple downstream tasks demonstrate that our approach effectively leverages causal knowledge for prediction and remains robust in OOD scenarios.The CAT achieves an average improvement of 5.76% on the STG dataset and 1.56% on downstream tasks.Notably, the OOD performance of the Llama-3.1-8Bmodel on STG_M increased from 64.5% to 90.5%, and Qwen's OOD performance on the STG_H dataset improved from 25.4% to 55.9%.Implementation details can be found here.

Time series classification (TSC) is an important task in time series analysis. Existing TSC methods mainly train on each single domain separately, suffering from a degradation in accuracy when the samples for training are insufficient in certain domains. The pre-training and fine-tuning paradigm provides a promising direction for solving this problem. However, time series from different domains are substantially divergent, which challenges the effective pre-training on multi-source data and the generalization ability of pre-trained models. To handle this issue, we introduce Augmented Series and Image Contrastive Learning for Time Series Classification (AimTS), a pre-training framework that learns generalizable representations from multi-source time series data. We propose a two-level prototype-based contrastive learning method to effectively utilize various augmentations in multi-source pre-training, which learns representations for TSC that can be generalized to different domains. In addition, considering augmentations within the single time series modality are insufficient to fully address classification problems with distribution shift, we introduce the image modality to supplement structural information and establish a series-image contrastive learning to improve the generalization of the learned representations for TSC tasks. Extensive experiments show that after multi-source pre-training, AimTS achieves good generalization performance, enabling efficient learning and even few-shot learning on various downstream TSC datasets.

Time series anomaly detection plays a vital role in a wide range of applications. Existing methods require training one specific model for each dataset, which exhibits limited generalization capability across different target datasets, hindering anomaly detection performance in various scenarios with scarce training data. Aiming at this problem, we propose constructing a general time series anomaly detection model, which is pre-trained on extensive multi-domain datasets and can subsequently apply to a multitude of downstream scenarios. The significant divergence of time series data across different domains presents two primary challenges in building such a general model: (1) meeting the diverse requirements of appropriate information bottlenecks tailored to different datasets in one unified model, and (2) enabling distinguishment between multiple normal and abnormal patterns, both are crucial for effective anomaly detection in various target scenarios. To tackle these two challenges, we propose a general time series anomaly Detector with Adaptive Bottlenecks and Dual Adversarial Decoders (DADA), which enables flexible selection of bottlenecks based on different data and explicitly enhances clear differentiation between normal and abnormal series. We conduct extensive experiments on nine target datasets from different domains. After pre-training on multi-domain data, DADA, serving as a zero-shot anomaly detector for these datasets, still achieves competitive or even superior results compared to those models tailored to each specific dataset.

Air pollution significantly threatens human health and ecosystems, necessitating effective air quality prediction to inform public policy. Traditional approaches are generally categorized into physics-based and data-driven models. Physics-based models usually struggle with high computational demands and closed-system assumptions, while data-driven models may overlook essential physical dynamics, confusing the capturing of spatiotemporal correlations. Although some physics-guided approaches combine the strengths of both models, they often face a mismatch between explicit physical equations and implicit learned representations. To address these challenges, we propose Air-DualODE, a novel physics-guided approach that integrates dual branches of Neural ODEs for air quality prediction. The first branch applies open-system physical equations to capture spatiotemporal dependencies for learning physics dynamics, while the second branch identifies the dependencies not addressed by the first in a fully data-driven way. These dual representations are temporally aligned and fused to enhance prediction accuracy. Our experimental results demonstrate that Air-DualODE achieves state-of-the-art performance in predicting pollutant concentrations across various spatial scales, thereby offering a promising solution for real-world air quality challenges.

With the growing availability of multi-domain time series data, there is an increasing demand for general forecasting models pre-trained on multi-source datasets to support diverse downstream prediction scenarios. Existing time series foundation models primarily focus on scaling up pre-training datasets and model sizes to enhance generalization performance. In this paper, we take a different approach by addressing two critical aspects of general forecasting models: (1) how to derive unified representations from heterogeneous multi-domain time series data, and (2) how to effectively capture domain-specific features to enable adaptive transfer across various downstream scenarios. To address the first aspect, we propose Decomposed Frequency Learning as the pre-training task, which leverages frequency-based masking and reconstruction to decompose coupled semantic information in time series, resulting in unified representations across domains. For the second aspect, we introduce the Time Series Register, which captures domain-specific representations during pre-training and enhances adaptive transferability to downstream tasks. Our model achieves the state-of-the-art forecasting performance on seven real-world benchmarks, demonstrating remarkable few-shot and zero-shot capabilities.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pretraining. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverage historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot setting with much better efficiency compared with existing time series foundation models

Multivariate time series forecasting has been widely used in various practical scenarios. Recently, Transformer-based models have shown significant potential in forecasting tasks due to the capture of long-range dependencies. However, recent studies in the vision and NLP fields show that the role of attention modules is not clear, which can be replaced by other token aggregation operations. This paper investigates the contributions and deficiencies of attention mechanisms on the performance of time series forecasting. Specifically, we find that (1) attention is not necessary for capturing temporal dependencies, (2) the entanglement and redundancy in the capture of temporal and channel interaction affect the forecasting performance, and (3) modeling the mapping between the historical and predicting time series is crucial to the forecasting accuracy. To this end, we propose MTS-Mixers, which use two factorized modules to capture temporal and channel dependencies. Experimental results on several real-world datasets show that MTS-Mixers performs promising forecasting results with higher efficiency. Code is available at https://github.com/plumprc/MTS-Mixers.

Current deep learning approaches for lithium-ion battery analysis are often specialized and limited to specific battery types or individual tasks. While recent advances in large language models (LLMs) highlight the potential of pretraining paradigms, existing time-series pretraining models inadequately address the physicochemical complexity and temporal irregularity inherent to battery operational data. We propose LiPM, a pretrained foundation model that unifies multi-dataset learning through physics-aware objectives and irregularity-tolerant temporal modeling. LiPM introduces three key innovations: (1) A Mix-Masked Autoencoder (MMAE) enforcing electrochemical consistency via joint reconstruction of temporally masked patches and cross-channel masked variables(2) A Coulombic Integration Regression (CIR) task explicitly encoding charge conservation laws, and (3) A dual-scale temporal encoder combining irregular intra-patch processing (preserving raw timestamps) with regular inter-patch attention (capturing macroscopic dynamics). Trained on eight heterogeneous battery datasets without cycle-label annotations, LiPM demonstrates universal applicability across partial charge-discharge segments and irregular sampling protocols. Extensive experiments show remarkable improvements over 9 state-of-the-art baselines in critical downstream tasks.

Learning Granger causality from event sequences has important applications in various scenarios. Many methods have been developed based on Hawkes process with a stationarity assumption. However, these methods often fail in real-world scenarios due to violating the stationarity assumption, as an event sequence can be generated under different states at varying times. Although some work tries to model non-stationarity by searching for best segmentation, they still suffer from the lack of robustness and identification guarantee. An intuitive solution is to model the non-stationary generation process in a unified probabilistic generative framework. This presents two significant challenges: how to model the generation process considering both the stationarity of each subsequence and the non-stationarity among the subsequences, and how to identify the Granger causality. To address these challenges, we devise State Hawkes Processes (StateHPs). For the first challenge, StateHPs formulates the state assignments of each subsequence as a Dirichlet distribution and each state as a Hawkes process. For the second challenge, StateHPs introduces a variational Expectation-Maximization algorithm to identify the Granger causal graph. We also develop the identification theories for StateHPs. On real-world data, StateHPs achieves 35.5%, 33.9%, and 36.7% improvement among F1, Precision, and Recall metrics compared to the SOTA baselines.

Graph-based fraud detection has widespread application in modern industry scenarios, such as spam review and malicious account detection. While considerable efforts have been devoted to designing adequate fraud detectors, the interpretability of their results has often been overlooked. Previous works have attempted to generate explanations for specific instances using post-hoc explaining methods such as a GNNExplainer. However, post-hoc explanations can not facilitate the model predictions and the computational cost of these methods cannot meet practical requirements, thus limiting their application in real-world scenarios. To address these issues, we propose SEFraud, a novel graph-based self-explainable fraud detection framework that simultaneously tackles fraud detection and result in interpretability. Concretely, SEFraud first leverages customized heterogeneous graph transformer networks with learnable feature masks and edge masks to learn expressive representations from the informative heterogeneously typed transactions. A new triplet loss is further designed to enhance the performance of mask learning. Empirical results on various datasets demonstrate the effectiveness of SEFraud as it shows considerable advantages in both the fraud detection performance and interpretability of prediction results. Specifically, SEFraud achieves the most significant improvement with 8.6% on AUC and 8.5% on Recall over the second best on fraud detection, as well as an average of 10x speed-up regarding the inference time. Last but not least, SEFraud has been deployed and offers explainable fraud detection service for the largest bank in China, Industrial and Commercial Bank of China Limited (ICBC). Results collected from the production environment of ICBC show that SEFraud can provide accurate detection results and comprehensive explanations that align with the expert business understanding, confirming its efficiency and applicability in large-scale online services.

Real-world data usually present long-tailed distributions. Training on imbalanced data tends to render neural networks perform well on head classes while much worse on tail classes. The severe sparseness of training instances for the tail classes is the main challenge, which results in biased distribution estimation during training. Plenty of efforts have been devoted to ameliorating the challenge, including data resampling and synthesizing new training instances for tail classes. However, no prior research has exploited the transferable knowledge from head classes to tail classes for calibrating the distribution of tail classes. In this article, we suppose that tail classes can be enriched by similar head classes and propose a novel distribution calibration (DC) approach named as label-aware DC (LADC). LADC transfers the statistics from relevant head classes to infer the distribution of tail classes. Sampling from calibrated distribution further facilitates rebalancing the classifier. Experiments on both image and text long-tailed datasets demonstrate that LADC significantly outperforms existing methods. The visualization also shows that LADC provides a more accurate distribution estimation.

Learning with imbalanced data is a challenging problem in deep learning. Over-sampling is a widely used technique to re-balance the sampling distribution of training data. However, most existing over-sampling methods only use intra-class information of minority classes to augment the data but ignore the inter-class relationships with the majority ones, which is prone to overfitting, especially when the imbalance ratio is large. To address this issue, we propose a novel over-sampling model, called Majority-Guided VAE(MGVAE), which generates new minority samples under the guidance of a majority-based prior. In this way, the newly generated minority samples can inherit the diversity and richness of the majority ones, thus mitigating overfitting in downstream tasks. Furthermore, to prevent model collapse under limited data, we first pre-train MGVAE on sufficient majority samples and then fine-tune based on minority samples with Elastic Weight Consolidation(EWC) regularization. Experimental results on benchmark image datasets and real-world tabular data show that MGVAE achieves competitive improvements over other over-sampling methods in downstream classification tasks, demonstrating the effectiveness of our method.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

Graph Edit Distance (GED) is a general and domain-agnostic metric to measure graph similarity, widely used in graph search or retrieving tasks. However, the exact GED computation is known to be NP-complete. For instance, the widely used A* algorithms explore the entire search space to find the optimal solution which inevitably suffers scalability issues. Learning-based methods apply graph representation techniques to learn the GED by formulating a regression task, which can not recover the edit path and lead to inaccurate GED approximation (i.e., the predicted GED is smaller than the exact). To this end, in this work, we present a data-driven hybrid approach MATA* for approximate GED computation based on Graph Neural Networks (GNNs) and A* algorithms, which models from the perspective of learning to match nodes instead of directly regressing GED. Specifically, aware of the structure-dominant operations (i.e., node and edge insertion/deletion) property in GED computation, a structure-enhanced GNN is firstly designed to jointly learn local and high-order structural information for node embeddings for node matchings. Second, top-k candidate nodes are produced via a differentiable top-k operation to enable the training for node matchings, which is adhering to another property of GED, i.e., multiple optimal node matchings. Third, benefiting from the candidate nodes, MATA* only performs on the promising search directions, reaching the solution efficiently. Finally, extensive experiments show the superiority of MATA* as it significantly outperforms the combinatorial search-based, learning-based and hybrid methods and scales well to large-size graphs.

Graph Active Learning (GAL), which aims to find the most informative nodes in graphs for annotation to maximize the Graph Neural Networks (GNNs) performance, has attracted many research efforts but remains non-trivial challenges. One major challenge is that existing GAL strategies may introduce semantic confusion to the selected training set, particularly when graphs are noisy. Specifically, most existing methods assume all aggregating features to be helpful, ignoring the semantically negative effect between inter-class edges under the message-passing mechanism. In this work, we present Semantic-aware Active learning framework for Graphs (SAG) to mitigate the semantic confusion problem. Pairwise similarities and dissimilarities of nodes with semantic features are introduced to jointly evaluate the node influence. A new prototype-based criterion and query policy are also designed to maintain diversity and class balance of the selected nodes, respectively. Extensive experiments on the public benchmark graphs and a real-world financial dataset demonstrate that SAG significantly improves node classification performances and consistently outperforms previous methods. Moreover, comprehensive analysis and ablation study also verify the effectiveness of the proposed framework.

The success of Transformers in long time series forecasting (LTSF) can be attributed to their attention mechanisms and non-autoregressive (NAR) decoder structures, which capture long-range de- pendencies. However, time series data also contain abundant local temporal dependencies, which are often overlooked in the literature and significantly hinder forecasting performance. To address this issue, we introduce SMARTformer, which stands for SeMi-AutoRegressive Transformer. SMARTformer utilizes the Integrated Window Attention (IWA) and Semi-AutoRegressive (SAR) Decoder to capture global and local dependencies from both encoder and decoder perspectives. IWA conducts local self-attention in multi-scale windows and global attention across windows with linear com- plexity to achieve complementary clues in local and enlarged receptive fields. SAR generates subsequences iteratively, similar to autoregressive (AR) decoding, but refines the entire sequence in a NAR manner. This way, SAR benefits from both the global horizon of NAR and the local detail capturing of AR. We also introduce the Time-Independent Embedding (TIE), which better captures local dependencies by avoiding entanglements of various periods that can occur when directly adding po- sitional embedding to value embedding. Our ex- tensive experiments on five benchmark datasets demonstrate the effectiveness of SMARTformer against state-of-the-art models, achieving an improvement of 10.2% and 18.4% in multivariate and univariate long-term forecasting, respectively.

The prevalence of tree-like structures, encompassing hierarchical structures and power law distributions, exists extensively in real-world applications, including recommendation systems, ecosystems, financial networks, social networks, etc. Recently, the exploitation of hyperbolic space for tree-likeness modeling has garnered considerable attention owing to its exponential growth volume. Compared to the flat Euclidean space, the curved hyperbolic space provides a more amenable and embeddable room, especially for datasets exhibiting implicit tree-like architectures. However, the intricate nature of real-world tree-like data presents a considerable challenge, as it frequently displays a heterogeneous composition of tree-like, flat, and circular regions. The direct embedding of such heterogeneous structures into a homogeneous embedding space (i.e., hyperbolic space) inevitably leads to heavy distortions. To mitigate the aforementioned shortage, this study endeavors to explore the curvature between discrete structure and continuous learning space, aiming at encoding the message conveyed by the network topology in the learning process, thereby improving tree-likeness modeling. To the end, a curvature-aware hyperbolic graph convolutional neural network, κHGCN, is proposed, which utilizes the curvature to guide message passing and improve long-range propagation. Extensive experiments on node classification and link prediction tasks verify the superiority of the proposal as it consistently outperforms various competitive models by a large margin.

Recent studies have shown great promise in unsupervised representation learning (URL) for multivariate time series, because URL has the capability in learning generalizable representation for many downstream tasks without using inaccessible labels. However, existing approaches usually adopt the models originally designed for other domains (e.g., computer vision) to encode the time series data and rely on strong assumptions to design learning objectives, which limits their ability to perform well. To deal with these problems, we propose a novel URL framework for multivariate time series by learning time-series-specific shapelet-based representation through a popular contrasting learning paradigm. To the best of our knowledge, this is the first work that explores the shapelet-based embedding in the unsupervised general-purpose representation learning. A unified shapelet-based encoder and a novel learning objective with multi-grained contrasting and multi-scale alignment are particularly designed to achieve our goal, and a data augmentation library is employed to improve the generalization. We conduct extensive experiments using tens of real-world datasets to assess the representation quality on many downstream tasks, including classification, clustering, and anomaly detection. The results demonstrate the superiority of our method against not only URL competitors, but also techniques specially designed for downstream tasks. Our code has been made publicly available at https://github.com/real2fish/CSL.

Graphs are a popular data type found in many domains. Numerous techniques have been proposed to find interesting patterns in graphs to help understand the data and support decision-making. However, there are generally two limitations that hinder their practical use: (1) they have multiple parameters that are hard to set but greatly influence results, (2) and they generally focus on identifying complex subgraphs while ignoring relationships between attributes of nodes. Graphs are a popular data type found in many domains. Numerous techniques have been proposed to find interesting patterns in graphs to help understand the data and support decision-making. However, there are generally two limitations that hinder their practical use: (1) they have multiple parameters that are hard to set but greatly influence results, (2) and they generally focus on identifying complex subgraphs while ignoring relationships between attributes of nodes. To address these problems, we propose a parameter-free algorithm named CSPM (Compressing Star Pattern Miner) which identifies star-shaped patterns that indicate strong correlations among attributes via the concept of conditional entropy and the minimum description length principle. Experiments performed on several benchmark datasets show that CSPM reveals insightful and interpretable patterns and is efficient in runtime. Moreover, quantitative evaluations on two real-world applications show that CSPM has broad applications as it successfully boosts the accuracy of graph attribute completion models by up to 30.68% and uncovers important patterns in telecommunication alarm data.

Recent researches reveal that deep neural networks are sensitive to label noises hence leading to poor generalization performance in some tasks. Although different robust loss functions have been proposed to remedy this issue, they suffer from an underfitting problem, thus are not sufficient to learn accurate models. On the other hand, the commonly used Cross Entropy (CE) loss, which shows high performance in standard supervised learning (with clean supervision), is non-robust to label noise. In this paper, we propose a general framework to learn robust deep neural networks with complementary loss functions. In our framework, CE and robust loss play complementary roles in a joint learning objective as per their learning sufficiency and robustness properties respectively. Specifically, we find that by exploiting the memorization effect of neural networks, we can easily filter out a proportion of hard samples and generate reliable pseudo labels for easy samples, and thus reduce the label noise to a quite low level. Then, we simply learn with CE on pseudo supervision and robust loss on original noisy supervision. In this procedure, CE can guarantee the sufficiency of optimization while the robust loss can be regarded as the supplement. Experimental results on benchmark classification datasets indicate that the proposed method helps achieve robust and sufficient deep neural network training simultaneously.

We present Mask-GVAE, a variational generative model for blind denoising large discrete graphs, in which ”blind denoising” means we don’t require any supervision from clean graphs. We focus on recovering graph structures via deleting irrelevant edges and adding missing edges, which has many applications in real-world scenarios, for example, enhancing the quality of connections in a co-authorship network. Mask-GVAE makes use of the robustness in low eigenvectors of graph Laplacian against random noise and decomposes the input graph into several stable clusters. It then harnesses the huge computations by decoding probabilistic smoothed subgraphs in a variational manner. On a wide variety of benchmarks, Mask-GVAE outperforms competing approaches by a significant margin on PSNR and WL similarity.

In this paper we use a time-evolving graph which consists of a sequence of graph snapshots over time to model many real-world networks. We study the path classification problem in a time-evolving graph, which has many applications in real-world scenarios, for example, predicting path failure in a telecommunication network and predicting path congestion in a traffic network in the near future. In order to capture the temporal dependency and graph structure dynamics, we design a novel deep neural network named Long Short-Term Memory R-GCN (LRGCN). LRGCN considers temporal dependency between time-adjacent graph snapshots as a special relation with memory, and uses relational GCN to jointly process both intra-time and inter-time relations. We also propose a new path representation method named self-attentive path embedding (SAPE), to embed paths of arbitrary length into fixed-length vectors. Through experiments on a real-world telecommunication network and a traffic network in California, we demonstrate the superiority of LRGCN to other competing methods in path failure prediction, and prove the effectiveness of SAPE on path representation.

With the advent of cellular network technologies, mobile Internet access becomes the norm in everyday life. In the meantime, the complaints made by subscribers about unsatisfactory cellular network access also become increasingly frequent. From a network operator's perspective, achieving accurate and timely cellular network diagnosis about the causes of the complaints is critical for both improving subscriber-perceived experience and maintaining network robustness. We present the Intelligent Customer Care Assistant (ICCA), a distributed fault classification system that exploits a data-driven approach to perform large-scale cellular network diagnosis. ICCA takes massive network data as input, and realizes both offline model training and online feature computation to distinguish between user and network faults in real time. ICCA is currently deployed in a metropolitan LTE network in China that is serving around 50 million subscribers. We show via evaluation that ICCA achieves high classification accuracy (85.3%) and fast query response time (less than 2.3 seconds). We also report our experiences learned from the deployment.

Many long-running network analytics applications impose a high-throughput and high reliability requirements on stream processing systems. However, previous stream processing systems cannot sustain high-speed traffic at the core router level. Furthermore, their fault-tolerant schemes cannot provide strong consistency which is essential for network analytics. In this paper, we present the design and implementation of SAND, a fault-tolerant distributed stream processing system for network analytics. SAND is designed to operate under high-speed network traffic, and it uses a novel check pointing protocol which can perform failure recovery based on upstream backup and check pointing. We prove our fault-tolerant scheme provides strong consistency even under multiple node failure. We implement several real-world network analytics applications on SAND, evaluate their performance using network traffic captured from commercial cellular core networks, and demonstrate that SAND can sustain high-speed network traffic and that our fault-tolerant scheme is efficient.