Large language models (LLMs) have achieved remarkable performance on diverse benchmarks, yet existing evaluation practices largely rely on coarse summary metrics that obscure underlying reasoning abilities. In this work, we propose novel methodologies to adapt cognitive diagnosis models (CDMs) in psychometrics to LLM evaluation, enabling fine-grained diagnosis via multidimensional discrete capability profiles and interpretable characterizations of LLM strengths and weaknesses. First, to enable CDM-based evaluation at benchmark scale (more than 1000 items), we propose a scalable method that jointly estimates LLM mastery profiles and the item-attribute Q-matrix, addressing key challenges posed by high-dimensional latent attributes (K > 20), large item pools, and the prohibitive computational cost of existing marginal maximum likelihood-based estimation. Second, we incorporate item-level textual information to construct AI-embedding-informed priors for the Q-matrix, stabilizing high-dimensional estimation while reducing reliance on costly human specification. We develop an efficient stochastic-approximation algorithm to jointly estimate LLM mastery profiles and the Q-matrix that balances data fit with text-embedding-informed priors. Simulation studies demonstrate accurate parameter recovery. An application to the MATH Level 5 benchmark illustrates the practical utility of our method for LLM evaluation and uncovers useful insights into LLMs' fine-grained capabilities.

Specifically, we utilize students' response records to model student

We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with 4 qubits. This way, the algorithm is able to generate representative states for some of the 49 true SLOCC classes of the four-qubit entanglement states. In particular, it is possible to reach at least one true SLOCC class for each of the nine entanglement families. The quantum circuits synthesized by the algorithm may be useful for the experimental realization of these important classes of entangled states and to draw conclusions about the intrinsic properties of our universe. We introduce a graphical tool called the state-link graph (SLG) to represent the construction of the Quality matrix (Q-matrix) used by the algorithm to build a given objective state belonging to the corresponding entanglement class. This allows us to discover the necessary connections between specific entanglement features and the role of certain quantum gates that the algorithm needs to include in the quantum gate set of actions. The quantum circuits found are optimal by construction with respect to the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive and a useful resource for the automated construction of entangled states with a low number of qubits.

The synchronized flight of bird flocks, exemplified by starling murmurations, is perhaps the most striking example of collective behavior in natural systems, which fascinated scholars for quite a long time [1]. Evolutionary biologists, for instance, have long debated the advantages of living in groups [2], which should offer increased protection from predation by diluting the individual risk and 1 possibly confusing the attackers by the sheer size of the assembly. Flocking behavior involves a high degree of order in the individual directions of motion [3], and has been reproduced by minimal models of self-propelling particles (SPPs), such as Craig Reynolds Boids [4] or the celebrated Vicsek model [5] that has long captivated the attention of statistical physicists and played a pivotal role in the birth of the active matter research field. The essential ingredient of these models is the tendency of individual particles to align their direction of motion with those of their local neighbours, which is enough to promote long range order in systems with finite density (even in two spatial dimensions, due to the non-equilibrium nature of self-propelled particles) such as in toy models with periodic boundary conditions. In open systems, constituted by a finite number of individuals in an open, infinite space, purely alignment interactions are however not enough to maintain group cohesion.

Cognitive diagnosis can infer the students' mastery of specific knowledge concepts based on historical response logs. However, the existing cognitive diagnostic models (CDMs) represent students' proficiency via a unidimensional perspective, which can't assess the students' mastery on each knowledge concept comprehensively. Moreover, the Q-matrix binarizes the relationship between exercises and knowledge concepts, and it can't represent the latent relationship between exercises and knowledge concepts. Especially, when the granularity of knowledge attributes refines increasingly, the Q-matrix becomes incomplete correspondingly and the sparse binary representation (0/1) fails to capture the intricate relationships among knowledge concepts. To address these issues, we propose a Concept-aware Latent and Explicit Knowledge Integration model for cognitive diagnosis (CLEKI-CD). Specifically, a multidimensional vector is constructed according to the students' mastery and exercise difficulty for each knowledge concept from multiple perspectives, which enhances the representation capabilities of the model. Moreover, a latent Q-matrix is generated by our proposed attention-based knowledge aggregation method, and it can uncover the coverage degree of exercises over latent knowledge. The latent Q-matrix can supplement the sparse explicit Q-matrix with the inherent relationships among knowledge concepts, and mitigate the knowledge coverage problem. Furthermore, we employ a combined cognitive diagnosis layer to integrate both latent and explicit knowledge, further enhancing cognitive diagnosis performance. Extensive experiments on real-world datasets demonstrate that CLEKI-CD outperforms the state-of-the-art models. The proposed CLEKI-CD is promising in practical applications in the field of intelligent education, as it exhibits good interpretability with diagnostic results.

Seriation seeks to reconstruct a linear order between variables using unsorted similarity information. It has direct applications in archeology and shotgun gene sequencing for example. We prove the equivalence between the seriation and the combinatorial 2-SUM problem (a quadratic minimization problem over permutations) over a class of similarity matrices. The seriation problem can be solved exactly by a spectral algorithm in the noiseless case and we produce a convex relaxation for the 2-SUM problem to improve the robustness of solutions in a noisy setting. This relaxation also allows us to impose additional structural constraints on the solution, to solve semi-supervised seriation problems.

Recently, knowledge tracing models have been applied in educational data mining such as the Self-attention knowledge tracing model(SAKT), which models the relationship between exercises and Knowledge concepts(Kcs). However, relation modeling in traditional Knowledge tracing models only considers the static question-knowledge relationship and knowledge-knowledge relationship and treats these relationships with equal importance. This kind of relation modeling is difficult to avoid the influence of subjective labeling and considers the relationship between exercises and KCs, or KCs and KCs separately. In this work, a novel knowledge tracing model, named Knowledge Relation Rank Enhanced Heterogeneous Learning Interaction Modeling for Neural Graph Forgetting Knowledge Tracing(NGFKT), is proposed to reduce the impact of the subjective labeling by calibrating the skill relation matrix and the Q-matrix and apply the Graph Convolutional Network(GCN) to model the heterogeneous interactions between students, exercises, and skills. Specifically, the skill relation matrix and Q-matrix are generated by the Knowledge Relation Importance Rank Calibration method(KRIRC). Then the calibrated skill relation matrix, Q-matrix, and the heterogeneous interactions are treated as the input of the GCN to generate the exercise embedding and skill embedding. Next, the exercise embedding, skill embedding, item difficulty, and contingency table are incorporated to generate an exercise relation matrix as the inputs of the Position-Relation-Forgetting attention mechanism. Finally, the Position-Relation-Forgetting attention mechanism is applied to make the predictions. Experiments are conducted on the two public educational datasets and results indicate that the NGFKT model outperforms all baseline models in terms of AUC, ACC, and Performance Stability(PS).

The ever growing abundance of learning traces in the online learning platforms promises unique insights into the learner knowledge assessment (LKA), a fundamental personalized-tutoring technique for enabling various further adaptive tutoring services in these platforms. Precise assessment of learner knowledge requires the fine-grained Q-matrix, which is generally designed by experts to map the items to skills in the domain. Due to the subjective tendency, some misspecifications may degrade the performance of LKA. Some efforts have been made to refine the small-scale Q-matrix, however, it is difficult to extend the scalability and apply these methods to the large-scale online learning context with numerous items and massive skills. Moreover, the existing LKA models employ flexible deep learning models that excel at this task, but the adequacy of LKA is still challenged by the representation capability of the models on the quite sparse item-skill graph and the learners' exercise data. To overcome these issues, in this paper we propose a prerequisite-driven Q-matrix refinement framework for learner knowledge assessment (PQRLKA) in online context. We infer the prerequisites from learners' response data and use it to refine the expert-defined Q-matrix, which enables the interpretability and the scalability to apply it to the large-scale online learning context. Based on the refined Q-matrix, we propose a Metapath2Vec enhanced convolutional representation method to obtain the comprehensive representations of the items with rich information, and feed them to the PQRLKA model to finally assess the learners' knowledge. Experiments conducted on three real-world datasets demonstrate the capability of our model to infer the prerequisites for Q-matrix refinement, and also its superiority for the LKA task.

Value estimation is one key problem in Reinforcement Learning. Albeit many successes have been achieved by Deep Reinforcement Learning (DRL) in different fields, the underlying structure and learning dynamics of value function, especially with complex function approximation, are not fully understood. In this paper, we report that decreasing rank of $Q$-matrix widely exists during learning process across a series of continuous control tasks for different popular algorithms. We hypothesize that the low-rank phenomenon indicates the common learning dynamics of $Q$-matrix from stochastic high dimensional space to smooth low dimensional space. Moreover, we reveal a positive correlation between value matrix rank and value estimation uncertainty. Inspired by above evidence, we propose a novel Uncertainty-Aware Low-rank Q-matrix Estimation (UA-LQE) algorithm as a general framework to facilitate the learning of value function. Through quantifying the uncertainty of state-action value estimation, we selectively erase the entries of highly uncertain values in state-action value matrix and conduct low-rank matrix reconstruction for them to recover their values. Such a reconstruction exploits the underlying structure of value matrix to improve the value approximation, thus leading to a more efficient learning process of value function. In the experiments, we evaluate the efficacy of UA-LQE in several representative OpenAI MuJoCo continuous control tasks.