Recent studies have raised concerns about the reliability of current mathematical benchmarks, highlighting issues such as simplistic design and potential data contamination. Therefore, creating a reliable benchmark that effectively evaluates the genuine capabilities of large language models (LLMs) in mathematical reasoning remains a significant challenge. To address this, we propose RV-Bench, a framework for Benchmarking LLMs via Random Variables in mathematical reasoning. Specifically, the background content of a random variable question (RV question) mirrors the original problem in existing benchmarks, but the variable combinations are randomized, making it "unseen" by the LLMs. Models must completely understand the question pattern of the original problem to correctly answer RV questions with various variable values. As a result, the LLM's genuine capability in mathematical reasoning is reflected by its accuracy and robustness on RV-Bench. We conducted extensive experiments on over 30 representative LLMs across more than 1000 RV questions. Our findings suggest that LLMs exhibit an imbalance in proficiency between encountered and "unseen" data domains. Proficiency generalization across similar mathematical reasoning tasks is verified to be limited by accuracy and robustness, but it can still be enhanced through test-time scaling.

Graph contrastive learning (GCL) has shown promising performance in semisupervised graph classification. However, existing studies still encounter significant challenges in GCL. First, successive layers in graph neural network (GNN) tend to produce more similar node embeddings, while GCL aims to increase the dissimilarity between negative pairs of node embeddings. This inevitably results in a conflict between the message-passing mechanism of GNNs and the contrastive learning of negative pairs via intraviews. Second, leveraging the diversity and quantity of data provided by graph-structured data augmentations while preserving intrinsic semantic information is challenging. In this paper, we propose a self-supervised conditional distribution learning (SSCDL) method designed to learn graph representations from graph-structured data for semisupervised graph classification. Specifically, we present an end-to-end graph representation learning model to align the conditional distributions of weakly and strongly augmented features over the original features. This alignment effectively reduces the risk of disrupting intrinsic semantic information through graph-structured data augmentation. To avoid conflict between the message-passing mechanism and contrastive learning of negative pairs, positive pairs of node representations are retained for measuring the similarity between the original features and the corresponding weakly augmented features. Extensive experiments with several benchmark graph datasets demonstrate the effectiveness of the proposed SSCDL method.

Graph anomaly detection (GAD) has been widely applied in many areas, e.g., fraud detection in finance and robot accounts in social networks. Existing methods are dedicated to identifying the outlier nodes that deviate from normal ones. While they heavily rely on high-quality annotation, which is hard to obtain in real-world scenarios, this could lead to severely degraded performance based on noisy labels. Thus, we are motivated to cut the edges of suspicious nodes to alleviate the impact of noise. However, it remains difficult to precisely identify the nodes with noisy labels. Moreover, it is hard to quantitatively evaluate the regret of cutting the edges, which may have either positive or negative influences. To this end, we propose a novel framework REGAD, i.e., REinforced Graph Anomaly Detector. Specifically, we aim to maximize the performance improvement (AUC) of a base detector by cutting noisy edges approximated through the nodes with high-confidence labels. (i) We design a tailored action and search space to train a policy network to carefully prune edges step by step, where only a few suspicious edges are prioritized in each step. (ii) We design a policy-in-the-loop mechanism to iteratively optimize the policy based on the feedback from base detector. The overall performance is evaluated by the cumulative rewards. Extensive experiments are conducted on three datasets under different anomaly ratios. The results indicate the superior performance of our proposed REGAD.

Ontology matching (OM) entails the identification of semantic relationships between concepts within two or more knowledge graphs (KGs) and serves as a critical step in integrating KGs from various sources. Recent advancements in deep OM models have harnessed the power of transformer-based language models and the advantages of knowledge graph embedding. Nevertheless, these OM models still face persistent challenges, such as a lack of reference alignments, runtime latency, and unexplored different graph structures within an end-to-end framework. In this study, we introduce a novel self-supervised learning OM framework with input ontologies, called LaKERMap. This framework capitalizes on the contextual and structural information of concepts by integrating implicit knowledge into transformers. Specifically, we aim to capture multiple structural contexts, encompassing both local and global interactions, by employing distinct training objectives. To assess our methods, we utilize the Bio-ML datasets and tasks. The findings from our innovative approach reveal that LaKERMap surpasses state-of-the-art systems in terms of alignment quality and inference time. Our models and codes are available here: https://github.com/ellenzhuwang/lakermap.

Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially depend on the separability of datasets. In fact, even in the most simplest case of binary classification, the rate of convergence depends on two factors: (1) condition number of data matrix, and (2) separability of the dataset. With no further pre-processing techniques such as over-parametrization, data augmentation etc., separability is an intrinsic quantity of the data distribution under consideration. We focus on the landscape design of the logistic function and derive a novel sequence of {\em strictly} convex functions that are at least as strict as logistic loss. The minimizers of these functions coincide with those of the minimum norm solution wherever possible. The strict convexity of the derived function can be extended to finetune state-of-the-art models and applications. In empirical experimental analysis, we apply our proposed rooted logistic objective to multiple deep models, e.g., fully-connected neural networks and transformers, on various of classification benchmarks. Our results illustrate that training with rooted loss function is converged faster and gains performance improvements. Furthermore, we illustrate applications of our novel rooted loss function in generative modeling based downstream applications, such as finetuning StyleGAN model with the rooted loss. The code implementing our losses and models can be found here for open source software development purposes: https://anonymous.4open.science/r/rooted_loss.

Often, deep network models are purely inductive during training and while performing inference on unseen data. Thus, when such models are used for predictions, it is well known that they often fail to capture the semantic information and implicit dependencies that exist among objects (or concepts) on a population level. Moreover, it is still unclear how domain or prior modal knowledge can be specified in a backpropagation friendly manner, especially in large-scale and noisy settings. In this work, we propose an end-to-end vision and language model incorporating explicit knowledge graphs. We also introduce an interactive out-of-distribution (OOD) layer using implicit network operator. The layer is used to filter noise that is brought by external knowledge base. In practice, we apply our model on several vision and language downstream tasks including visual question answering, visual reasoning, and image-text retrieval on different datasets. Our experiments show that it is possible to design models that perform similarly to state-of-art results but with significantly fewer samples and training time.

The accuracy of the estimated stellar atmospheric parameter decreases evidently with the decreasing of spectral signal-to-noise ratio (SNR) and there are a huge amount of this kind observations, especially in case of SNR$<$30. Therefore, it is helpful to improve the parameter estimation performance for these spectra and this work studied the ($T_\texttt{eff}, \log~g$, [Fe/H]) estimation problem for LAMOST DR8 low-resolution spectra with 20$\leq$SNR$<$30. We proposed a data-driven method based on machine learning techniques. Firstly, this scheme detected stellar atmospheric parameter-sensitive features from spectra by the Least Absolute Shrinkage and Selection Operator (LASSO), rejected ineffective data components and irrelevant data. Secondly, a Multi-layer Perceptron (MLP) method was used to estimate stellar atmospheric parameters from the LASSO features. Finally, the performance of the LASSO-MLP was evaluated by computing and analyzing the consistency between its estimation and the reference from the APOGEE (Apache Point Observatory Galactic Evolution Experiment) high-resolution spectra. Experiments show that the Mean Absolute Errors (MAE) of $T_\texttt{eff}, \log~g$, [Fe/H] are reduced from the LASP (137.6 K, 0.195 dex, 0.091 dex) to LASSO-MLP (84.32 K, 0.137 dex, 0.063 dex), which indicate evident improvements on stellar atmospheric parameter estimation. In addition, this work estimated the stellar atmospheric parameters for 1,162,760 low-resolution spectra with 20$\leq$SNR$<$30 from LAMOST DR8 using LASSO-MLP, and released the estimation catalog, learned model, experimental code, trained model, training data and test data for scientific exploration and algorithm study.

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional numerical methods have been developed and widely used for their solutions. Inspired by rapidly growing impact of deep learning on scientific and engineering research, in this paper we propose a novel neural network, GF-Net, for learning the Green's functions of linear reaction-diffusion equations in an unsupervised fashion. The proposed method overcomes the challenges for finding the Green's functions of the equations on arbitrary domains by utilizing physics-informed approach and the symmetry of the Green's function. As a consequence, it particularly leads to an efficient way for solving the target equations under different boundary conditions and sources. We also demonstrate the effectiveness of the proposed approach by experiments in square, annular and L-shape domains.

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit Function Theorem, the proposed algorithm effectively reduces the input dimension to the theoretical lower bound with minor accuracy loss, providing a one-dimensional representation of the function which can be used for regression and sensitivity analysis. Experiments and applications are presented which compare this modified NLL with the original NLL and the Active Subspaces (AS) method. While accommodating sparse input data, the proposed algorithm is shown to train quickly and provide a much more accurate and informative reduction than either AS or the original NLL on two example functions with high-dimensional domains, as well as two state-dependent quantities depending on the solutions to parametric differential equations.