Formula recognition endeavors to automatically identify mathematical formulas from images. Currently, the Encoder-Decoder model has significantly advanced the translation from image to corresponding formula markups. Nonetheless, previous research primarily concentrated on single-line formula recognition, ignoring the recognition of multi-line formulas, which presents additional challenges such as more stringent grammatical restrictions and two- dimensional positions. In this work, we present GAP (Grammar And Position-Aware formula recognition), a comprehensive framework designed to tackle the challenges in multi-line mathematical formula recognition. First, to overcome the limitations imposed by grammar, we design a novel Grammar Aware Contrastive Learning (GACL) module, integrating complex grammar rules into the transcription model through a contrastive learning mechanism. Furthermore, primitive contrastive learning lacks clear directions for comprehending grammar rules and can lead to unstable convergence or prolonged training cycles. To enhance training efficiency, we propose Rank-Based Sampling (RBS) specialized for multi-line formulas, which guides the learning process by the importance ranking of different grammar errors. Finally, spatial location information is critical considering the two-dimensional nature of multi-line formulas. To aid the model in keeping track of that global information, we introduced a Visual Coverage (VC) mechanism that incorporates historical attention information into the image features via a parameter-free way. To validate the effectiveness of our GAP framework, we construct a new dataset Multi-Line containing 12,002 multi-line formulas and conduct extensive experiments to show the efficacy of our GAP framework in capturing grammatical rules, enhancing recognition accuracy, and enhancing training efficiency. Codes and datasets are available at https://github.com/Sinon02/GAP.

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.

Computerized Adaptive Testing (CAT) arises as a promising personalized test mode in online education, targeting at revealing students' latent knowledge state by selecting test items adaptively. The item selection strategy is the core component of CAT, which searches for the best suitable test item based on students' current estimated ability at each test step. However, existing selection strategies behave in a brute-force manner, which results in the time complexity being linear to the number of items (N) in the item pool, i.e., O(N). Thus, in reality, the search latency becomes the bottleneck for CAT with a large-scale item pool. To this end, we propose a Search-Efficient Computerized Adaptive Testing framework (SECAT), which aims at enhancing CAT with an efficient selection strategy. Specifically, SECAT contains two main phases: item pool indexing and item search. In the item pool indexing phase, we apply a student-aware spatial partition method on the item pool to divide the test items into many sub-spaces, considering the adaptability of test items. In the item search phase, we optimize the traditional single-round search strategy with the asymptotic theory and propose a multi-round search strategy that can further improve the time efficiency. Compared with existing strategies, the time complexity of SECAT decreases from O(N) to O(logN). Across two real-world datasets, SECAT achieves over 200x speed up with negligible accuracy degradation.

Representation learning of examination papers is significantly crucial for online education systems, as it benefits various applications such as estimating paper difficulty and examination paper retrieval. Previous works mainly explore the representation learning of individual questions in an examination paper, with limited attention given to the examination paper as a whole. In fact, the structure of examination papers is strongly correlated with paper properties such as paper difficulty, which existing paper representation methods fail to capture adequately. To this end, we propose a pre-trained model namely PaperLM to learn the representation of examination papers. Our model integrates both the text content and hierarchical structure of examination papers within a single framework by converting the path of the Examination Organization Tree (EOT) into embedding. Furthermore, we specially design three pre-training objectives for PaperLM, namely EOT Node Relationship Prediction (ENRP), Question Type Prediction (QTP) and Paper Contrastive Learning (PCL), aiming to capture features from text and structure effectively. We pre-train our model on a real-world examination paper dataset, and then evaluate the model with three down-stream tasks: paper difficulty estimation, examination paper retrieval, and paper clustering. The experimental results demonstrate the effectiveness of our method.

Cognitive Diagnosis aims to quantify the proficiency level of students on specific knowledge concepts. Existing studies merely leverage observed historical students-exercise interaction logs to access proficiency levels. Despite effectiveness, observed interactions usually exhibit a power-law distribution, where the long tail consisting of students with few records lacks supervision signals. This phenomenon leads to inferior diagnosis among few records students. In this paper, we propose the Exercise-aware Informative Response Sampling (EIRS) framework to address the long-tail problem. EIRS is a general framework that explores the partial order between observed and unobserved responses as auxiliary ranking-based training signals to supplement cognitive diagnosis. Considering the abundance and complexity of unobserved responses, we first design an Exercise-aware Candidates Selection module, which helps our framework produce reliable potential responses for effective supplementary training. Then, we develop an Expected Ability Change-weighted Informative Sampling strategy to adaptively sample informative potential responses that contribute greatly to model training. Experiments on real-world datasets demonstrate the supremacy of our framework in long-tailed data.

Hierarchical multi-label classification (HMC) deals with the problem of assigning each entity to multiple classes with a taxonomic structure (e.g., tree). Within this structure, classes at different levels tend to have dependencies under the hierarchy constraints. However, most prior studies for HMC tasks tend to ignore the class dependencies within the hierarchy. Moreover, most existing methods generate incoherent predictions and do not satisfy the hierarchy constraint. To this end, based on previously developed HARNN, we propose a general framework, HmcNet, for introducing explicit and implicit class hierarchy constraints to generate coherent predictions. We develop an efficient Prune-based Coherent Prediction (PCP) strategy for the optimal paths selection, which produces coherent predictions in a principled way. HmcNet can be well explained from two perspectives. First, it develops the Hierarchical Attention-based Memory (HAM) unit with implicit class hierarchy constraints to capture class dependencies more intuitively; Second, it subsumes explicit class hierarchy constraints during training and inference phases and generates coherent predictions in a consistent manner. Finally, extensive experimental results on six real-world datasets demonstrate the effectiveness and interpretability of the HmcNet frameworks. To facilitate future research, our code has been made publicly available.

Reading psychology believes text comprehension to involve a complex psychological construction process, with the reader mind being a dynamic associative system that stores an abundance of schemata. For Chinese text, in particular, the unique ideographic writing system allows its lansign to trigger semantic association and schema recalling without the need of phonetics. In contrast to previous research efforts on text classification problems, in this paper we present an interdisciplinary modeling approach that draws inspirations from the cognitive principles of ideography, schema theory and deep learning to study Chinese text classification. Specifically, we first propose a Radical-guided Associative Model (RAM) for preliminary cognitive imitation, which comprises two coupled spaces, namely the Literal Space and Associative Space. Then, taking consideration of the schemata acquired from the mind of a reader which plays a important role in influencing text-dependent information revision, we extend RAM with a systematic Schema-aware Radical-guided Associative Model (SRAM) that embeds label semantics as essential text-independent human knowledge for real-world abstraction. In SRAM, the Schema Space is introduced and a Schema Attention module is proposed with a novel loss paradigm that includes the linkage and interaction between text-dependent prior concepts and text-independent label schemata. Extensive experiments on three real-world datasets demonstrate the effectiveness and rationality of our proposed method.

Similar text search aims to find texts relevant to a given query from a database, which is fundamental in many information retrieval applications, such as question search and exercise search. Since millions of texts always exist behind practical search engine systems, a well-developed text search system usually consists of recall and ranking stages. Specifically, the recall stage serves as the basis in the system, where the main purpose is to find a small set of relevant candidates accurately and efficiently. Towards this goal, deep semantic hashing, which projects original texts into compact hash codes, can support good search performance. However, learning desired textual hash codes is extremely difficult due to the following problems. First, compact hash codes (with short length) can improve retrieval efficiency, but the demand for learning compact hash codes cannot guarantee accuracy due to severe information loss. Second, existing methods always learn the unevenly distributed codes in the space from a local perspective, leading to unsatisfactory code-balance results. Third, a large fraction of textual data contains various types of noise in real-world applications, which causes the deviation of semantics in hash codes. To this end, in this paper, we first propose a general unsupervised encoder-decoder semantic hashing framework, namely MASH (short for Memory-bAsed Semantic Hashing), to learn the balanced and compact hash codes for similar text search. Specifically, with a target of retaining semantic information as much as possible, the encoder introduces a novel relevance constraint among informative high-dimensional representations to guide the compact hash code learning. Then, we design an external memory where the hashing learning can be optimized in the global space to ensure the code balance of the learning results, which can promote search efficiency. Besides, to alleviate the performance degradation problem of the model caused by text noise, we propose an improved SMASH (short for denoiSing Memory-bAsed Semantic Hashing) model by incorporating a noise-aware encoder-decoder framework. This framework considers the noise degree for each text from the semantic deviation aspect, ensuring the robustness of hash codes. Finally, we conduct extensive experiments in three real-world datasets. The experimental results clearly demonstrate the effectiveness and efficiency of MASH and SMASH in generating balanced and compact hash codes, as well as the superior denoising ability of SMASH.

Cognitive diagnosis, aiming at providing an approach to reveal the proficiency level of learners on knowledge concepts, plays an important role in intelligent education area and has recently received more and more attention. Although a number of works have been proposed in recent years, most of contemporary works acquire the traits parameters of learners and items in a transductive way, which are only suitable for stationary data. However, in the real scenario, the data is collected online, where learners, test items and interactions usually grow continuously, which can rarely meet the stationary condition. To this end, we propose a novel framework, Incremental Cognitive Diagnosis (ICD), to tailor cognitive diagnosis into the online scenario of intelligent education. Specifically, we first design a Deep Trait Network (DTN), which acquires the trait parameters in an inductive way rather than a transductive way. Then, we propose an Incremental Update Algorithm (IUA) to balance the effectiveness and training efficiency. We carry out Turning Point (TP) analysis to reduce update frequency, where we derive the minimum update condition based on the monotonicity theory of cognitive diagnosis. Meanwhile, we use a momentum update strategy on the incremental data to decrease update time without sacrificing effectiveness. Moreover, to keep the trait parameters as stable as possible, we refine the loss function in the incremental updating stage. Last but no least, our ICD is a general framework which can be applied to most of contemporary cognitive diagnosis models. To the best of our knowledge, this is the first attempt to investigate the incremental cognitive diagnosis problem with theoretical results about the update condition and a tailored incremental learning strategy. Extensive experiments demonstrate the effectiveness and robustness of our method.

Knowledge tracing (KT) which aims at predicting learner's knowledge mastery plays an important role in the computer-aided educational system. The goal of KT is to provide personalized learning paths for learners by diagnosing the mastery of each knowledge, thus improving the learning efficiency. In recent years, many deep learning models have been applied to tackle the KT task, which has shown promising results. However, most existing methods simplify the exercising records as knowledge sequences, which fail to explore the rich information that existed in exercises. Besides, the existing diagnosis results of knowledge tracing are not convincing enough since they neglect hierarchical relations between exercises. To solve the above problems, we propose a hierarchical graph knowledge tracing model called HGKT to explore the latent complex relations between exercises. Specifically, we introduce the concept of problem schema to construct a hierarchical exercise graph that could model the exercise learning dependencies. Moreover, we employ two attention mechanisms to highlight important historical states of learners. In the testing stage, we present a knowledge&schema diagnosis matrix that could trace the transition of mastery of knowledge and problem schema, which can be more easily applied to different applications. Extensive experiments show the effectiveness and interpretability of our proposed model.

Cognitive psychology research shows that humans have the instinct for abstract thinking, where association plays an essential role in language comprehension. Especially for Chinese, its ideographic writing system allows radicals to trigger semantic association without the need of phonetics. In fact, subconsciously using the associative information guided by radicals is a key for readers to ensure the robustness of semantic understanding. Fortunately, many basic and extended concepts related to radicals are systematically included in Chinese language dictionaries, which leaves a handy but unexplored way for improving Chinese text representation and classification. To this end, we draw inspirations from cognitive principles between ideography and human associative behavior to propose a novel Radical-guided Associative Model (RAM) for Chinese text classification. RAM comprises two coupled spaces, namely Literal Space and Associative Space, which imitates the real process in people's mind when understanding a Chinese text. To be specific, we first devise a serialized modeling structure in Literal Space to thoroughly capture the sequential information of Chinese text. Then, based on the authoritative information provided by Chinese language dictionaries, we design an association module and put forward a strategy called Radical-Word Association to use ideographic radicals as the medium to associate prior concept words in Associative Space. Afterwards, we design an attention module to imitate people's matching and decision between Literal Space and Associative Space, which can balance the importance of each associative words under specific contexts. Finally, extensive experiments on two real-world datasets prove the effectiveness and rationality of RAM, with good cognitive insights for future language modeling.

In intelligent education systems, question difficulty prediction (QDP) is a fundamental task of many applications, such as personalized question recommendation and test paper analysis. Previous work mainly focus on data-driven QDP methods, which are heavily relied on the large-scale labeled dataset of courses. To alleviate the labor intensity, an intuitive method is to introduce domain adaptation into QDP and consider each course as a domain. In educational psychology, there are two factors influencing difficulty common to different courses: the obstacles of comprehending the question and generating a response, namely stimulus and task difficulty. To this end, we propose a novel Stimulus and Task difficulty-based Adversarial Network (STAN) that models question difficulty from the views of stimulus and task. Then, in order to align the difficulty distribution of the source domain and the target domain, we utilize the conditional adversarial learning with readability-enhanced pseudo-labels. Meanwhile, we proposed a sampling method based on density estimation to implicit alignment. Finally, we conduct experiments on the real questions datasets to evaluate the effectiveness of our QDP model and domain adaptation method. Our method significantly improves accuracy over state-of-the-art methods on real-world question data of multiple courses.

Concept extraction aims to find words or phrases describing a concept from massive texts. Recently, researchers propose many neural network-based methods to automatically extract concepts. Although these methods for this task show promising results, they ignore structured information in the raw textual data (e.g., title, topic, and clue words). In this paper, we propose a novel model, named Guided Attention Concept Extraction Network (GACEN), which uses title, topic, and clue words as additional supervision to provide guidance directly. Specifically, GACEN comprises two attention networks, one of them is to gather the relevant title and topic information for each context word in the document. The other one aims to model the implicit connection between informative words (clue words) and concepts. Finally, we aggregate information from two networks as input to Conditional Random Field (CRF) to model dependencies in the output. We collected clue words for three well-studied datasets. Extensive experiments demonstrate that our model outperforms the baseline models with a large margin, especially when the labeled data is insufficient.

Cognitive diagnosis, a fundamental task in education area, aims at providing an approach to reveal the proficiency level of students on knowledge concepts. Actually, monotonicity is one of the basic conditions in cognitive diagnosis theory, which assumes that student's proficiency is monotonic with the probability of giving the right response to a test item. However, few of previous methods consider the monotonicity during optimization. To this end, we propose Item Response Ranking framework (IRR), aiming at introducing pairwise learning into cognitive diagnosis to well model the monotonicity between item responses. Specifically, we first use an item specific sampling method to sample item responses and construct response pairs based on their partial order, where we propose the two-branch sampling methods to handle the unobserved responses. After that, we use a pairwise objective function to exploit the monotonicity in the pair formulation. In fact, IRR is a general framework which can be applied to most of contemporary cognitive diagnosis models. Extensive experiments demonstrate the effectiveness and interpretability of our method.

Representation learning of examination papers is the cornerstone of the Examination Paper Analysis (EPA) in education area including Paper Difficulty Prediction (PDR) and Finding Similar Papers (FSP). Previous works mainly focus on the representation learning of each test item, but few works notice the hierarchical document structure in examination papers. To this end, in this paper, we propose a novel Examination Organization Encoder (EOE) to learn a robust representation of the examination paper with the hierarchical document structure. Specifically, we first propose a syntax parser to recover the hierarchical document structure and convert an examination paper to an Examination Organization Tree (EOT), where the test items are the leaf nodes and the internal nodes are summarization of their child nodes. Then, we applied a two-layer GRU-based module to obtain the representation of each leaf node. After that, we design a subtree encoder module to aggregate the representation of each leaf node, which is used to calculate an embedding for each layer in the EOT. Finally, we feed all the layer embedding into an output module, the process is over and we get the examination paper representation that can be used for downstream tasks. Extensive experiments on real-world data demonstrate the effectiveness and interpretability of our method.

Knowledge Tracing (KT) is a fundamental but challenging task in online education that traces learners' evolving knowledge states. Much attention has been drawn to this area and several works such as Bayesian Knowledge Tracing and Deep Knowledge Tracing are proposed. Recent works have explored the value of relations among concepts and proposed to introduce knowledge structure into KT task. However, the propagated influence among concepts, which has been shown to be a key factor in human learning by the educational theories, is still under-explored. In this paper, we propose a new framework called Structure-based Knowledge Tracing (SKT), which exploits the multiple relations in knowledge structure to model the influence propagation among concepts. In the SKT framework, we not only consider the temporal effect on the exercising sequence but also take the spatial effect on the knowledge structure into account. We take advantages of two novel formulations in modeling the influence propagation on the knowledge structure with multiple relations. For undirected relations such as similarity relations, the synchronization propagation method is adopted, where the influence propagates bidirectionally between neighbor concepts. For directed relations such as prerequisite relations, the partial propagation method is applied, where the influence can only unidirectionally propagate from a predecessor to a successor. Meanwhile, we employ the gated functions to update the states of concepts temporally and spatially. Extensive experiments demonstrate the effectiveness and interpretability of SKT.

In education systems, Finding Similar Exercises (FSE) is the key step for both exercise retrieval and duplicate detection. Recently, more and more attention has been drawn into this area and several works have been proposed, to utilize the exercise content (e.g., texts or images) or the labeled knowledge concepts. Such approaches, however, have failed to take knowledge hierarchy into account. To this end, we advance a novel knowledge-aware multimodal network, namely KnowNet, for finding similar exercises in large-scale online education systems by integrating the knowledge hierarchy into the heterogeneous exercise data and learning a relation-aware semantic representation. Specifically, we first propose a Content Representation Layer (CRL) to learn a unified semantic representation of the heterogeneous exercise content. Then, we design a Hierarchy Fusion Layer (HFL) to exploit the knowledge hierarchy. By combining the knowledge hierarchy, HFL can not only retrieve the relation-aware semantic representation but also provide an interpretable view to investigate the similarity of exercises. Finally, we adopt a Similarity Score Layer (SSL) for returning similar exercises. Extensive experiments demonstrate the effectiveness and interpretability of KnowNet.

Recent years, Chinese text classification has attracted more and more research attention. However, most existing techniques which specifically aim at English materials may lose effectiveness on this task due to the huge difference between Chinese and English. Actually, as a special kind of hieroglyphics, Chinese characters and radicals are semantically useful but still unexplored in the task of text classification. To that end, in this paper, we first analyze the motives of using multiple granularity features to represent a Chinese text by inspecting the characteristics of radicals, characters and words. For better representing the Chinese text and then implementing Chinese text classification, we propose a novel Radicalaware Attention-based Four-Granularity (RAFG) model to take full advantages of Chinese characters, words, characterlevel radicals, word-level radicals simultaneously. Specifically, RAFG applies a serialized BLSTM structure which is context-aware and able to capture the long-range information to model the character sharing property of Chinese and sequence characteristics in texts. Further, we design an attention mechanism to enhance the effects of radicals thus model the radical sharing property when integrating granularities. Finally, we conduct extensive experiments, where the experimental results not only show the superiority of our model, but also validate the effectiveness of radicals in the task of Chinese text classification.

Adaptive learning, also known as adaptive teaching, relies on learning path recommendation, which sequentially recommends personalized learning items (e.g., lectures, exercises) to satisfy the unique needs of each learner. Although it is well known that modeling the cognitive structure including knowledge level of learners and knowledge structure (e.g., the prerequisite relations) of learning items is important for learning path recommendation, existing methods for adaptive learning often separately focus on either knowledge levels of learners or knowledge structure of learning items. To fully exploit the multifaceted cognitive structure for learning path recommendation, we propose a Cognitive Structure Enhanced framework for Adaptive Learning, named CSEAL. By viewing path recommendation as a Markov Decision Process and applying an actor-critic algorithm, CSEAL can sequentially identify the right learning items to different learners. Specifically, we first utilize a recurrent neural network to trace the evolving knowledge levels of learners at each learning step. Then, we design a navigation algorithm on the knowledge structure to ensure the logicality of learning paths, which reduces the search space in the decision process. Finally, the actor-critic algorithm is used to determine what to learn next and whose parameters are dynamically updated along the learning path. Extensive experiments on real-world data demonstrate the effectiveness and robustness of CSEAL.