Efficiently Measuring the Cognitive Ability of LLMs: An Adaptive Testing Perspective

Large language models (LLMs), like ChatGPT, have shown some human-like cognitive abilities. For comparing these abilities of different models, several benchmarks (i.e. sets of standard test questions) from different fields (e.g., Literature, Biology and Psychology) are often adopted and the test results under traditional metrics such as accuracy, recall and F1, are reported. However, such way for evaluating LLMs can be inefficient and inaccurate from the cognitive science perspective. Inspired by Computerized Adaptive Testing (CAT) used in psychometrics, we propose an adaptive testing framework for LLM evaluation. Rather than using a standard test set and simply reporting accuracy, this approach dynamically adjusts the characteristics of the test questions, such as difficulty, based on the model's performance. This allows for a more accurate estimation of the model's abilities, using fewer questions. More importantly, it allows LLMs to be compared with humans easily, which is essential for NLP models that aim for human-level ability. Our diagnostic reports have found that ChatGPT often behaves like a ``careless student'', prone to slip and occasionally guessing the questions. We conduct a fine-grained diagnosis and rank the latest 6 instruction-tuned LLMs from three aspects of Subject Knowledge, Mathematical Reasoning, and Programming, where GPT4 can outperform other models significantly and reach the cognitive ability of middle-level students. Different tests for different models using efficient adaptive testing -- we believe this has the potential to become a new norm in evaluating large language models.

Quiz-based Knowledge Tracing

Knowledge tracing (KT) aims to assess individuals' evolving knowledge states according to their learning interactions with different exercises in online learning systems (OIS), which is critical in supporting decision-making for subsequent intelligent services, such as personalized learning source recommendation. Existing researchers have broadly studied KT and developed many effective methods. However, most of them assume that students' historical interactions are uniformly distributed in a continuous sequence, ignoring the fact that actual interaction sequences are organized based on a series of quizzes with clear boundaries, where interactions within a quiz are consecutively completed, but interactions across different quizzes are discrete and may be spaced over days. In this paper, we present the Quiz-based Knowledge Tracing (QKT) model to monitor students' knowledge states according to their quiz-based learning interactions. Specifically, as students' interactions within a quiz are continuous and have the same or similar knowledge concepts, we design the adjacent gate followed by a global average pooling layer to capture the intra-quiz short-term knowledge influence. Then, as various quizzes tend to focus on different knowledge concepts, we respectively measure the inter-quiz knowledge substitution by the gated recurrent unit and the inter-quiz knowledge complementarity by the self-attentive encoder with a novel recency-aware attention mechanism. Finally, we integrate the inter-quiz long-term knowledge substitution and complementarity across different quizzes to output students' evolving knowledge states. Extensive experimental results on three public real-world datasets demonstrate that QKT achieves state-of-the-art performance compared to existing methods. Further analyses confirm that QKT is promising in designing more effective quizzes.

Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning

Mathematical reasoning is one of the crucial abilities of general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus not interpretable) in terms of what knowledge has been learned and applied in the reasoning process. In this paper, we propose a general Learning by Applying (LeAp) framework to enhance existing models (backbones) in a principled way by explicit knowledge learning. In LeAp, we perform knowledge learning in a novel problem-knowledge-expression paradigm, with a Knowledge Encoder to acquire knowledge from problem data and a Knowledge Decoder to apply knowledge for expression reasoning. The learned mathematical knowledge, including word-word relations and word-operator relations, forms an explicit knowledge graph, which bridges the knowledge "learning" and "applying" organically. Moreover, for problem solving, we design a semantics-enhanced module and a reasoning-enhanced module that apply knowledge to improve the problem comprehension and symbol reasoning abilities of any backbone, respectively. We theoretically prove the superiority of LeAp's autonomous learning mechanism. Experiments on three real-world datasets show that LeAp improves all backbones' performances, learns accurate knowledge, and achieves a more interpretable reasoning process.

A Novel Approach for Auto-Formulation of Optimization Problems

In the Natural Language for Optimization (NL4Opt) NeurIPS 2022 competition, competitors focus on improving the accessibility and usability of optimization solvers, with the aim of subtask 1: recognizing the semantic entities that correspond to the components of the optimization problem; subtask 2: generating formulations for the optimization problem. In this paper, we present the solution of our team. First, we treat subtask 1 as a named entity recognition (NER) problem with the solution pipeline including pre-processing methods, adversarial training, post-processing methods and ensemble learning. Besides, we treat subtask 2 as a generation problem with the solution pipeline including specially designed prompts, adversarial training, post-processing methods and ensemble learning. Our proposed methods have achieved the F1-score of 0.931 in subtask 1 and the accuracy of 0.867 in subtask 2, which won the fourth and third places respectively in this competition. Our code is available at https://github.com/bigdata-ustc/nl4opt.

Towards a Holistic Understanding of Mathematical Questions with Contrastive Pre-training

Understanding mathematical questions effectively is a crucial task, which can benefit many applications, such as difficulty estimation. Researchers have drawn much attention to designing pre-training models for question representations due to the scarcity of human annotations (e.g., labeling difficulty). However, unlike general free-format texts (e.g., user comments), mathematical questions are generally designed with explicit purposes and mathematical logic, and usually consist of more complex content, such as formulas, and related mathematical knowledge (e.g., Function). Therefore, the problem of holistically representing mathematical questions remains underexplored. To this end, in this paper, we propose a novel contrastive pre-training approach for mathematical question representations, namely QuesCo, which attempts to bring questions with more similar purposes closer. Specifically, we first design two-level question augmentations, including content-level and structure-level, which generate literally diverse question pairs with similar purposes. Then, to fully exploit hierarchical information of knowledge concepts, we propose a knowledge hierarchy-aware rank strategy (KHAR), which ranks the similarities between questions in a fine-grained manner. Next, we adopt a ranking contrastive learning task to optimize our model based on the augmented and ranked questions. We conduct extensive experiments on two real-world mathematical datasets. The experimental results demonstrate the effectiveness of our model.

Model Inversion Attacks against Graph Neural Networks

Many data mining tasks rely on graphs to model relational structures among individuals (nodes). Since relational data are often sensitive, there is an urgent need to evaluate the privacy risks in graph data. One famous privacy attack against data analysis models is the model inversion attack, which aims to infer sensitive data in the training dataset and leads to great privacy concerns. Despite its success in grid-like domains, directly applying model inversion attacks on non-grid domains such as graph leads to poor attack performance. This is mainly due to the failure to consider the unique properties of graphs. To bridge this gap, we conduct a systematic study on model inversion attacks against Graph Neural Networks (GNNs), one of the state-of-the-art graph analysis tools in this paper. Firstly, in the white-box setting where the attacker has full access to the target GNN model, we present GraphMI to infer the private training graph data. Specifically, in GraphMI, a projected gradient module is proposed to tackle the discreteness of graph edges and preserve the sparsity and smoothness of graph features; a graph auto-encoder module is used to efficiently exploit graph topology, node attributes, and target model parameters for edge inference; a random sampling module can finally sample discrete edges. Furthermore, in the hard-label black-box setting where the attacker can only query the GNN API and receive the classification results, we propose two methods based on gradient estimation and reinforcement learning (RL-GraphMI). Our experimental results show that such defenses are not sufficiently effective and call for more advanced defenses against privacy attacks.

Graph Adaptive Semantic Transfer for Cross-domain Sentiment Classification

Cross-domain sentiment classification (CDSC) aims to use the transferable semantics learned from the source domain to predict the sentiment of reviews in the unlabeled target domain. Existing studies in this task attach more attention to the sequence modeling of sentences while largely ignoring the rich domain-invariant semantics embedded in graph structures (i.e., the part-of-speech tags and dependency relations). As an important aspect of exploring characteristics of language comprehension, adaptive graph representations have played an essential role in recent years. To this end, in the paper, we aim to explore the possibility of learning invariant semantic features from graph-like structures in CDSC. Specifically, we present Graph Adaptive Semantic Transfer (GAST) model, an adaptive syntactic graph embedding method that is able to learn domain-invariant semantics from both word sequences and syntactic graphs. More specifically, we first raise a POS-Transformer module to extract sequential semantic features from the word sequences as well as the part-of-speech tags. Then, we design a Hybrid Graph Attention (HGAT) module to generate syntax-based semantic features by considering the transferable dependency relations. Finally, we devise an Integrated aDaptive Strategy (IDS) to guide the joint learning process of both modules. Extensive experiments on four public datasets indicate that GAST achieves comparable effectiveness to a range of state-of-the-art models.

GraphMI: Extracting Private Graph Data from Graph Neural Networks

As machine learning becomes more widely used for critical applications, the need to study its implications in privacy turns to be urgent. Given access to the target model and auxiliary information, the model inversion attack aims to infer sensitive features of the training dataset, which leads to great privacy concerns. Despite its success in grid-like domains, directly applying model inversion techniques on non-grid domains such as graph achieves poor attack performance due to the difficulty to fully exploit the intrinsic properties of graphs and attributes of nodes used in Graph Neural Networks (GNN). To bridge this gap, we present \textbf{Graph} \textbf{M}odel \textbf{I}nversion attack (GraphMI), which aims to extract private graph data of the training graph by inverting GNN, one of the state-of-the-art graph analysis tools. Specifically, we firstly propose a projected gradient module to tackle the discreteness of graph edges while preserving the sparsity and smoothness of graph features. Then we design a graph auto-encoder module to efficiently exploit graph topology, node attributes, and target model parameters for edge inference. With the proposed methods, we study the connection between model inversion risk and edge influence and show that edges with greater influence are more likely to be recovered. Extensive experiments over several public datasets demonstrate the effectiveness of our method. We also show that differential privacy in its canonical form can hardly defend our attack while preserving decent utility.

A Survey of Knowledge Tracing

High-quality education is one of the keys to achieving a more sustainable world. The recent COVID-19 epidemic has triggered the outbreak of online education, which has enabled both students and teachers to learn and teach at home. Meanwhile, it is now possible to record and research a large amount of learning data using online learning platforms in order to offer better intelligent educational services. Knowledge Tracing (KT), which aims to monitor students' evolving knowledge state, is a fundamental and crucial task to support these intelligent services. Therefore, an increasing amount of research attention has been paid to this emerging area and considerable progress has been made. In this survey, we propose a new taxonomy of existing basic KT models from a technical perspective and provide a comprehensive overview of these models in a systematic manner. In addition, many variants of KT models have been proposed to capture more complete learning process. We then review these variants involved in three phases of the learning process: before, during, and after the student learning, respectively. Moreover, we present several typical applications of KT in different educational scenarios. Finally, we provide some potential directions for future research in this fast-growing field.

Quality meets Diversity: A Model-Agnostic Framework for Computerized Adaptive Testing

Computerized Adaptive Testing (CAT) is emerging as a promising testing application in many scenarios, such as education, game and recruitment, which targets at diagnosing the knowledge mastery levels of examinees on required concepts. It shows the advantage of tailoring a personalized testing procedure for each examinee, which selects questions step by step, depending on her performance. While there are many efforts on developing CAT systems, existing solutions generally follow an inflexible model-specific fashion. That is, they need to observe a specific cognitive model which can estimate examinee's knowledge levels and design the selection strategy according to the model estimation. In this paper, we study a novel model-agnostic CAT problem, where we aim to propose a flexible framework that can adapt to different cognitive models. Meanwhile, this work also figures out CAT solution with addressing the problem of how to generate both high-quality and diverse questions simultaneously, which can give a comprehensive knowledge diagnosis for each examinee. Inspired by Active Learning, we propose a novel framework, namely Model-Agnostic Adaptive Testing (MAAT) for CAT solution, where we design three sophisticated modules including Quality Module, Diversity Module and Importance Module. Extensive experimental results on two real-world datasets clearly demonstrate that our MAAT can support CAT with guaranteeing both quality and diversity perspectives.