Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations

We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we utilize the Physics-Informed Neural Networks (PINNs) framework and design a new adaptive exponentially weighted Asymptotic-Preserving (AP) loss function, which incorporates the macroscopic auxiliary equation that is derived from the original transfer equation directly and explicitly contains the information of the diffusion limit equation. Thus, as the scale parameter tends to zero, the loss function gradually transitions from the transport state to the diffusion limit state. In addition, the initial data, boundary conditions, and conservation laws serve as the regularization terms for the loss. We present several numerical examples to demonstrate the effectiveness of MA-APNNs.

Resprompt: Residual Connection Prompting Advances Multi-Step Reasoning in Large Language Models

Chain-of-thought (CoT) prompting, which offers step-by-step problem-solving rationales, has impressively unlocked the reasoning potential of large language models (LLMs). Yet, the standard CoT is less effective in problems demanding multiple reasoning steps. This limitation arises from the complex reasoning process in multi-step problems: later stages often depend on the results of several steps earlier, not just the results of the immediately preceding step. Such complexities suggest the reasoning process is naturally represented as a graph. The almost linear and straightforward structure of CoT prompting, however, struggles to capture this complex reasoning graph. To address this challenge, we propose Residual Connection Prompting (RESPROMPT), a new prompting strategy that advances multi-step reasoning in LLMs. Our key idea is to reconstruct the reasoning graph within prompts. We achieve this by integrating necessary connections-links present in the reasoning graph but missing in the linear CoT flow-into the prompts. Termed "residual connections", these links are pivotal in morphing the linear CoT structure into a graph representation, effectively capturing the complex reasoning graphs inherent in multi-step problems. We evaluate RESPROMPT on six benchmarks across three diverse domains: math, sequential, and commonsense reasoning. For the open-sourced LLaMA family of models, RESPROMPT yields a significant average reasoning accuracy improvement of 12.5% on LLaMA-65B and 6.8% on LLaMA2-70B. Breakdown analysis further highlights RESPROMPT particularly excels in complex multi-step reasoning: for questions demanding at least five reasoning steps, RESPROMPT outperforms the best CoT based benchmarks by a remarkable average improvement of 21.1% on LLaMA-65B and 14.3% on LLaMA2-70B. Through extensive ablation studies and analyses, we pinpoint how to most effectively build residual connections.

On the Equivalence of Graph Convolution and Mixup

This paper investigates the relationship between graph convolution and Mixup techniques. Graph convolution in a graph neural network involves aggregating features from neighboring samples to learn representative features for a specific node or sample. On the other hand, Mixup is a data augmentation technique that generates new examples by averaging features and one-hot labels from multiple samples. One commonality between these techniques is their utilization of information from multiple samples to derive feature representation. This study aims to explore whether a connection exists between these two approaches. Our investigation reveals that, under two mild conditions, graph convolution can be viewed as a specialized form of Mixup that is applied during both the training and testing phases. The two conditions are: 1) \textit{Homophily Relabel} - assigning the target node's label to all its neighbors, and 2) \textit{Test-Time Mixup} - Mixup the feature during the test time. We establish this equivalence mathematically by demonstrating that graph convolution networks (GCN) and simplified graph convolution (SGC) can be expressed as a form of Mixup. We also empirically verify the equivalence by training an MLP using the two conditions to achieve comparable performance.

LLM-Rec: Personalized Recommendation via Prompting Large Language Models

We investigate various prompting strategies for enhancing personalized recommendation performance with large language models (LLMs) through input augmentation. Our proposed approach, termed LLM-Rec, encompasses four distinct prompting strategies: (1) basic prompting, (2) recommendation-driven prompting, (3) engagement-guided prompting, and (4) recommendation-driven + engagement-guided prompting. Our empirical experiments show that incorporating the augmented input text generated by LLM leads to improved recommendation performance. Recommendation-driven and engagement-guided prompting strategies are found to elicit LLM's understanding of global and local item characteristics. This finding highlights the importance of leveraging diverse prompts and input augmentation techniques to enhance the recommendation capabilities with LLMs.

CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems

Multi-agent dynamical systems refer to scenarios where multiple units interact with each other and evolve collectively over time. To make informed decisions in multi-agent dynamical systems, such as determining the optimal vaccine distribution plan, it is essential for decision-makers to estimate the continuous-time counterfactual outcomes. However, existing studies of causal inference over time rely on the assumption that units are mutually independent, which is not valid for multi-agent dynamical systems. In this paper, we aim to bridge this gap and study how to estimate counterfactual outcomes in multi-agent dynamical systems. Causal inference in a multi-agent dynamical system has unique challenges: 1) Confounders are time-varying and are present in both individual unit covariates and those of other units; 2) Units are affected by not only their own but also others' treatments; 3) The treatments are naturally dynamic, such as receiving vaccines and boosters in a seasonal manner. We model a multi-agent dynamical system as a graph and propose CounterFactual GraphODE (CF-GODE), a causal model that estimates continuous-time counterfactual outcomes in the presence of inter-dependencies between units. To facilitate continuous-time estimation, we propose Treatment-Induced GraphODE, a novel ordinary differential equation based on GNN, which incorporates dynamical treatments as additional inputs to predict potential outcomes over time. To remove confounding bias, we propose two domain adversarial learning based objectives that learn balanced continuous representation trajectories, which are not predictive of treatments and interference. We further provide theoretical justification to prove their effectiveness. Experiments on two semi-synthetic datasets confirm that CF-GODE outperforms baselines on counterfactual estimation. We also provide extensive analyses to understand how our model works.

A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations

We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks(PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving(AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure data-driven networks in the simulation of the nonlinear non-stationary GRTEs.

Tele-Knowledge Pre-training for Fault Analysis

In this work, we share our experience on tele-knowledge pre-training for fault analysis. Fault analysis is a vital task for tele-application, which should be timely and properly handled. Fault analysis is also a complex task, that has many sub-tasks. Solving each task requires diverse tele-knowledge. Machine log data and product documents contain part of the tele-knowledge. We create a Tele-KG to organize other tele-knowledge from experts uniformly. With these valuable tele-knowledge data, in this work, we propose a tele-domain pre-training model KTeleBERT and its knowledge-enhanced version KTeleBERT, which includes effective prompt hints, adaptive numerical data encoding, and two knowledge injection paradigms. We train our model in two stages: pre-training TeleBERT on 20 million telecommunication corpora and re-training TeleBERT on 1 million causal and machine corpora to get the KTeleBERT. Then, we apply our models for three tasks of fault analysis, including root-cause analysis, event association prediction, and fault chain tracing. The results show that with KTeleBERT, the performance of task models has been boosted, demonstrating the effectiveness of pre-trained KTeleBERT as a model containing diverse tele-knowledge.

Learning Probabilities of Causation from Finite Population Data

This paper deals with the problem of learning the probabilities of causation of subpopulations given finite population data. The tight bounds of three basic probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN), were derived by Tian and Pearl. However, obtaining the bounds for each subpopulation requires experimental and observational distributions of each subpopulation, which is usually impractical to estimate given finite population data. We propose a machine learning model that helps to learn the bounds of the probabilities of causation for subpopulations given finite population data. We further show by a simulated study that the machine learning model is able to learn the bounds of PNS for 32768 subpopulations with only knowing roughly 500 of them from the finite population data.

Unit Selection: Learning Benefit Function from Finite Population Data

The unit selection problem is to identify a group of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if incentivized and a different way if not. The unit selection problem consists of evaluation and search subproblems. Li and Pearl defined the "benefit function" to evaluate the average payoff of selecting a certain individual with given characteristics. The search subproblem is then to design an algorithm to identify the characteristics that maximize the above benefit function. The hardness of the search subproblem arises due to the large number of characteristics available for each individual and the sparsity of the data available in each cell of characteristics. In this paper, we present a machine learning framework that uses the bounds of the benefit function that are estimable from the finite population data to learn the bounds of the benefit function for each cell of characteristics. Therefore, we could easily obtain the characteristics that maximize the benefit function.

Relational Message Passing for Fully Inductive Knowledge Graph Completion

In knowledge graph completion (KGC), predicting triples involving emerging entities and/or relations, which are unseen when the KG embeddings are learned, has become a critical challenge. Subgraph reasoning with message passing is a promising and popular solution. Some recent methods have achieved good performance, but they (i) usually can only predict triples involving unseen entities alone, failing to address more realistic fully inductive situations with both unseen entities and unseen relations, and (ii) often conduct message passing over the entities with the relation patterns not fully utilized. In this study, we propose a new method named RMPI which uses a novel Relational Message Passing network for fully Inductive KGC. It passes messages directly between relations to make full use of the relation patterns for subgraph reasoning with new techniques on graph transformation, graph pruning, relation-aware neighborhood attention, addressing empty subgraphs, etc., and can utilize the relation semantics defined in the ontological schema of KG. Extensive evaluation on multiple benchmarks has shown the effectiveness of techniques involved in RMPI and its better performance compared with the existing methods that support fully inductive KGC. RMPI is also comparable to the state-of-the-art partially inductive KGC methods with very promising results achieved. Our codes and data are available at https://github.com/zjukg/RMPI.