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.

Despite the demonstrated potential of Large Language Models (LLMs) in diverse NLP tasks, their causal reasoning capability appears inadequate when evaluated within the context of the event causality identification (ECI) task. The ECI tasks pose significant complexity for LLMs and necessitate comprehensive causal priors for accurate identification. To improve the performance of LLMs for causal reasoning, we propose a multi-agent Decomposed reasoning framework for Event Causality Identification, designated as Dr.ECI. In the discovery stage, Dr.ECI incorporates specialized agents such as Causal Explorer and Mediator Detector, which capture implicit causality and indirect causality more effectively. In the reasoning stage, Dr.ECI introduces the agents Direct Reasoner and Indirect Reasoner, which leverage the knowledge of the generalized causal structure specific to the ECI. Extensive evaluations demonstrate the state-of-the-art performance of Dr.ECI comparing with baselines based on LLMs and supervised training. Our implementation will be open-sourced at https://github.com/DMIRLAB-Group/Dr.ECI.

Pre-trained vision-language models (VLMs) have revolutionized the field of machine learning, demonstrating exceptional performance across a wide range of tasks. However, their robustness remains vulnerable to the spurious-correlation problem. Existing works often involve fine-tuning the model with labeled data or relying on large language models (LLMs) to generate more complex prompts. Although effective to some extent, these methods introduce new challenges, including additional computational costs and dependence on the quality of prompts without fully utilizing the vision modality. To address these limitations, we propose a novel method named ERICT to Enhance model Robustness by Identifying Concept Tokens. ERICT mitigates spurious correlation directly in the inference stage and comprises two key steps: (1) Identify concept tokens capturing invariant features through auxiliary prompts to generate a token-level mask. (2) Apply the mask to the attention weights of the CLS token in the vision encoder to help the model focus on the relevant image region. Extensive experiments show that ERICT significantly improves the overall performance including that of the worst group, and achieves new state-of-the-art results.

Large language models (LLMs) have shown great potential in decision-making due to the vast amount of knowledge stored within the models.However, these pre-trained models are prone to lack reasoning abilities and are difficult to adapt to new environments, further hindering their application to complex real-world tasks. To address these challenges, inspired by the human cognitive process, we propose Causal-Aware LLMs, which integrate the structural causal model (SCM) into the decision-making process to model, update, and utilize structured knowledge of the environment in a "learning-adapting-acting" paradigm.Specifically, in the learning stage, we first utilize an LLM to extract the environment-specific causal entities and their causal relations to initialize a structured causal model of the environment. Subsequently, in the adapting stage, we update the structured causal model through external feedback about the environment, via an idea of causal intervention. Finally, in the acting stage, Causal-Aware LLMs exploit structured causal knowledge for more efficient policy-making through the reinforcement learning agent. The above processes are performed iteratively to learn causal knowledge, ultimately enabling the causal-aware LLM to achieve a more accurate understanding of the environment and make more efficient decisions. Experimental results across 22 diverse tasks within the open-world game "Crafter" validate the effectiveness of our proposed method.

Missing values are ubiquitous in multivariate time series (MTS) data, posing significant challenges for accurate analysis and downstream applications. In recent years, deep learning-based methods have successfully handled missing data by leveraging complex temporal dependencies and learned data distributions. In this survey, we provide a comprehensive summary of deep learning approaches for multivariate time series imputation (MTSI) tasks. We propose a novel taxonomy that categorizes existing methods based on two key perspectives: imputation uncertainty and neural network architecture. Furthermore, we summarize existing MTSI toolkits with a particular emphasis on the PyPOTS Ecosystem, which provides an integrated and standardized foundation for MTSI research. Finally, we discuss key challenges and future research directions, which give insight for further MTSI research. This survey aims to serve as a valuable resource for researchers and practitioners in the field of time series analysis and missing data imputation tasks. A well-maintained MTSI paper and tool list is available at https://github.com/WenjieDu/Awesome_Imputation.

In this work, we discover that causal inference provides a promising approach to capture heterophilic message-passing in Graph Neural Network (GNN). By leveraging cause-effect analysis, we can discern heterophilic edges based on asymmetric node dependency. The learned causal structure offers more accurate relationships among nodes. To reduce the computational complexity, we introduce intervention-based causal inference in graph learning. We first simplify causal analysis on graphs by formulating it as a structural learning model and define the optimization problem within the Bayesian scheme. We then present an analysis of decomposing the optimization target into a consistency penalty and a structure modification based on cause-effect relations. We then estimate this target by conditional entropy and present insights into how conditional entropy quantifies the heterophily. Accordingly, we propose CausalMP, a causal message-passing discovery network for heterophilic graph learning, that iteratively learns the explicit causal structure of input graphs. We conduct extensive experiments in both heterophilic and homophilic graph settings. The result demonstrates that the our model achieves superior link prediction performance. Training on causal structure can also enhance node representation in classification task across different base models.

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.

The large signal dynamic range affecting the profile recognition of refined structures is one of the major challenges for future spaceborne oceanographic light detection and ranging (lidar) systems. Reduce the intensity of the sea surface signal and ensure that the detector operates in a linear response region, which helps reduce the subsurface signal error and improves the capability to detect weak signals in deep water. As a solution, the off-nadir pointing could reduce the photon counts from the sea surface but leads to depth aliasing. This reduces the vertical resolution and makes it difficult to determine the sea surface’s position and retrieve the thin chlorophyll layer. The lidar signal’s dynamic range is simulated to improve the detection accuracy. Based on the oceanographic lidar simulator, the laser transmission characteristics are analyzed, taking into account various different environmental parameters (including wind speed, sea surface roughness, concentration of whitecaps and bubbles) and lidar specifications (including laser off-nadir angle, divergence angle, and pulsewidth). The results show that increasing the off-nadir angle to 7°–15° can effectively reduce the dynamic range of the sea surface signal by about one order of magnitude, while increasing the aliasing depth by about 4–8 m. Reducing the beam divergence angle is beneficial for accurate inversion of profiles within the limits of engineering realization. Other parameters, such as pulsewidth, wind speed, and sea surface roughness, have little influence on depth aliasing and depth estimation errors.

Conditional independence (CI) testing is an important problem, especially in causal discovery. Most testing methods assume that all variables are fully observable and then test the CI among the observed data. Such an assumption is often untenable beyond applications dealing with, e.g., psychological analysis about the mental health status and medical diagnosing (researchers need to consider the existence of latent variables in these scenarios); and typically adopted latent CI test schemes mainly suffer from robust or efficient issues. Accordingly, this article investigates the problem of testing CI between latent variables. To this end, we offer an auxiliary regression-based CI (AReCI) test by taking the measured variable as the surrogate variable of the latent variables to conduct the regression over the latent variables under the linear causal models, in which each latent variable has some certain measured variables. Specifically, given a pair of latent variables$L_X$and$L_Y$, and a corresponding latent variable set$\mathcal{L}_{O}$,$L_X \CI L_Y | \mathcal{L}_{O}$holds if and only if$A_{\{L_X\}}-\omega_1^\intercal A^{\prime}_{\{\mathcal{L}_{O}\}}$and$A_{\{L_Y\}}-\omega_2^\intercal A^{\prime\prime}_{\{\mathcal{L}_{O}\}}$are statistically independent, where$A^{\prime}$and$A^{\prime\prime}$are the two disjoint subset of the measured variable for the corresponding latent variables,$A^{\prime}_{\{\mathcal{L}_{O}\}} \cap A^{\prime\prime}_{\{\mathcal{L}_{O}\}} =\emptyset$, and$\omega_1$is a parameter vector characterized from the cross covariance between$A_{\{L_X\}}$and$A^{\prime}_{\{\mathcal{L}_{O}\}}$, and$\omega_{2}$is a parameter vector characterized from the cross covariance between$A_{\{L_Y\}}$and$A^{\prime\prime}_{\{\mathcal{L}_{O}\}}$. We theoretically show that the AReCI test is capable of addressing both Gaussian and non-Gaussian data. In addition, we find that the well-known partial correlation test can be seen as a special case of the AReCI test. Finally, we devise a causal discovery method by using the AReCI test as the CI test. The experimental results on synthetic and real-world data illustrate the effectiveness of our method.

Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). However, this i.i.d. assumption is often violated due to the inherent dependencies among the event sequences. Fortunately, in practice, we find these dependencies can be modeled by a topological network, suggesting a potential solution to the non-i.i.d. problem by introducing the prior topological network into Granger causal discovery. This observation prompts us to tackle two ensuing challenges: 1) how to model the event sequences while incorporating both the prior topological network and the latent Granger causal structure, and 2) how to learn the Granger causal structure. To this end, we devise a unified topological neural Poisson auto-regressive model with two processes. In the generation process, we employ a variant of the neural Poisson process to model the event sequences, considering influences from both the topological network and the Granger causal structure. In the inference process, we formulate an amortized inference algorithm to infer the latent Granger causal structure. We encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task. Experiments on simulated and real-world data demonstrate the effectiveness of our approach.

This paper studies the causal relations from subsampled time series, in which measurements are sparse and sampled at a coarser timescale than the causal timescale of the underlying system. In such data, because there are numerous missing time-slices (i.e., cross-sections at each time point) between two consecutive measurements, conventional causal discovery methods designed for standard time series data would produce significant errors. To learn causal relations from subsampled time series, a typical solution is to conduct different interventions and then make a comparison. However, full interventions are often expensive, unethical, or even infeasible, particularly in fields such as health and social science. In this paper, we first explore how readily available two-time-slices data can replace intervention data to improve causal ordering, and propose a novel Descendant Hierarchical Topology algorithm with Conditional Independence Test (DHT-CIT) to learn causal relations from subsampled time series using only two time-slices. Specifically, we develop a conditional independence criterion that can be applied iteratively to test each node from time series and identify all of its descendant nodes. Empirical results on both synthetic and real-world datasets demonstrate the superiority of our DHT-CIT algorithm.

After several decades of development, Chinese marine satellites and corresponding remote sensing applications have made remarkable achievements, and played an important role in Chinese marine information services. However, too little work has been devoted to discussing the progress of China's ocean color observation satellites. In this paper, the typical international ocean color instruments were investigated for a start, and we can trace the development history of international ocean color observation from it. Furthermore, the progress of China’s ocean color satellites was reviewed, especially for the development process of China's 1stgeneration ocean color satellite. Especially, the performance of the newly launched HY-3A spacecraft was also described. Lastly, some measures were discussed for the future of China’s ocean color observation satellites.

Learning causal structure among event types on multitype event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically distributed. However, in many real-world applications, it is commonplace to encounter a topological network behind the event sequences such that an event is excited or inhibited not only by its history but also by its topological neighbors. Consequently, the failure in describing the topological dependency among the event sequences leads to the error detection of the causal structure. By considering the Hawkes processes from the view of temporal convolution, we propose a topological Hawkes process (THP) to draw a connection between the graph convolution in the topology domain and the temporal convolution in time domains. We further propose a causal structure learning method on THP in a likelihood framework. The proposed method is featured with the graph convolution-based likelihood function of THP and a sparse optimization scheme with an Expectation-Maximization of the likelihood function. Theoretical analysis and experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed method.

Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the so-called Granger causality which assumes that the cause event happens strictly prior to its effect event. Such an assumption is often untenable beyond applications, especially when dealing with discrete-time event sequences in low-resolution; and typical discrete Hawkes processes mainly suffer from identifiability issues raised by the instantaneous effect, i.e., the causal relationship that occurred simultaneously due to the low-resolution data will not be captured by Granger causality. In this work, we propose Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for learning the causal structure among events type in discrete-time event sequence. The proposed method is featured with the Expectation-Maximization of the likelihood function and a sparse optimization scheme. Theoretical results show that the instantaneous effect is a blessing rather than a curse, and the causal structure is identifiable under the existence of the instantaneous effect. Experiments on synthetic and real-world data verify the effectiveness of the proposed method.

Domain generalization (DG) is a prevalent problem in real-world applications, which aims to train well-generalized models for unseen target domains by utilizing several source domains. Since domain labels, i.e., which domain each data point is sampled from, naturally exist, most DG algorithms treat them as a kind of supervision information to improve the generalization performance. However, the original domain labels may not be the optimal supervision signal due to the lack of domain heterogeneity, i.e., the diversity among domains. For example, a sample in one domain may be closer to another domain, its original label thus can be the noise to disturb the generalization learning. Although some methods try to solve it by re-dividing domains and applying the newly generated dividing pattern, the pattern they choose may not be the most heterogeneous due to the lack of the metric for heterogeneity. In this paper, we point out that domain heterogeneity mainly lies in variant features under the invariant learning framework. With contrastive learning, we propose a learning potential-guided metric for domain heterogeneity by promoting learning variant features. Then we notice the differences between seeking variance-based heterogeneity and training invariance-based generalizable model. We thus propose a novel method called H eterogeneity-based Two-stage Contrastive Learning (HTCL) for the DG task. In the first stage, we generate the most heterogeneous dividing pattern with our contrastive metric. In the second stage, we employ an invariance-aimed contrastive learning by re-building pairs with the stable relation hinted by domains and classes, which better utilizes generated domain labels for generalization learning. Extensive experiments show HTCL better digs heterogeneity and yields great generalization performance.

Domain adaptation on time series data is an important but challenging task. Most of the existing works in this area are based on the learning of the domain-invariant representation of the data with the help of restrictions like MMD. However, such extraction of the domain-invariant representation is a non-trivial task for time series data, due to the complex dependence among the timestamps. In detail, in the fully dependent time series, a small change of the time lags or the offsets may lead to difficulty in the domain invariant extraction. Fortunately, the stability of the causality inspired us to explore the domain invariant structure of the data. To reduce the difficulty in the discovery of causal structure, we relax it to the sparse associative structure and propose a novel sparse associative structure alignment model for domain adaptation. First, we generate the segment set to exclude the obstacle of offsets. Second, the intra-variables and inter-variables sparse attention mechanisms are devised to extract associative structure time-series data with considering time lags. Finally, the associative structure alignment is used to guide the transfer of knowledge from the source domain to the target one. Experimental studies not only verify the good performance of our methods on three real-world datasets but also provide some insightful discoveries on the transferred knowledge.

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.

Nakagami fading model is widely used in modeling wireless communication systems. In this paper, we present methods to generate Nakagami fading signals with arbitrary cross-correlation and fading parameters by taking the square root of correlated Gamma random variables (RVs) with the corresponding shape parameters. To generate correlated Gamma RVs with different noninteger values of m-parameters, two methods, namely the decomposition method and Sim's method, are proposed. The former is more flexible and efficient. The latter is mathematically exact but carries constraints on the permissible simulation parameters. Simulations show that both methods produce outputs that match well with the specifications.

Certain OFDM channels can be shown to exhibit different fading severity amongst the subcarriers. For such channels, we propose novel adaptive power control and bit loading algorithms to maximize the spectral efficiency of the OFDM system while minimizing the required transmit power at some specified BER level. Unlike its existing counterparts, our adaptive modulation algorithm adapts the subcarrier transmission parameters based on the subcarrier fading statistics rather than the instantaneous channel conditions. A new closed-form expression with good inversion property for QAM BER in Rician fading channel is also developed to facilitate the computation of the optimum adaptive modulation settings. Results show that the proposed scheme can achieve considerable performance enhancement over non-adaptive systems.

Nakagami's (1960) fading model is widely adopted for analyzing wireless communication systems and diversity combining techniques, hence the ability to generate Nakagami fading signals with arbitrary parameters is important for system design and simulations. In the literature, there are only algorithms for generating correlated Nakagami branches with the same fading parameter. We adopt a novel approach to generate Nakagami fading signals with arbitrary fading parameters and any correlation structure. The correlated Nakagami fading variables are generated from the corresponding uncorrelated gamma random variables (RVs). To achieve this, we propose a new decomposition method, and introduce Sim's (1992)method as a complementary approach, to generate correlated gamma RVs. The former is an approximate approach but can deal with any general correlation structures efficiently, while the latter is exact but has some constraints.