DOI: 10.5281/zenodo.17667928
title: Mathematical cognitive modeling and knowledge mastery state reasoning method under a multi-task learning framework

description: MultiTaskCognitiveModel

A Multi-Task Mathematical Cognitive Modeling and Adaptive Reasoning FrameworkBased on the study Mathematical cognitive modeling and knowledge mastery state reasoning method under a multi-task learning framework

Overview

MultiTaskCognitiveModel is an integrated and adaptive framework designed to model mathematical cognitive states and infer knowledge mastery within a multi-task learning paradigm. The framework is derived from a unified mathematical and cognitive modeling strategy that addresses the challenges of scalability, interpretability, and adaptability in modern educational AI systems.

By combining probabilistic cognitive representations, graph-based task relationships, temporal mastery evolution, and adaptive reasoning strategies, the system captures how learners interact with mathematical tasks and how their knowledge states evolve over time. The framework unifies the Mathematical Cognitive State Model (MCSM) and the Adaptive Cognitive Reasoning Strategy (ACRS) to provide enhanced predictive accuracy, transparent reasoning, and robust generalization across diverse learning scenarios.

This model provides an end-to-end architecture capable of handling multimodal features, cross-task knowledge transfer, dynamic mastery state updates, and interpretable cognitive analysis.



Features

● Multimodal Cognitive Processing

The framework processes heterogeneous cognitive signals such as behavioral task features, time-series performance, and multimodal physiological indicators.According to the diagram on page 6, the MCSM integrates facial expression features, remote PPG signals, and reduced-dimension representations to build unified latent cognitive states.

● Mathematical Cognitive State Modeling (MCSM)

MCSM represents cognitive mastery as latent probabilistic variables informed by observable features.It models:



Energy-based mappings between features and latent states (Eq. 5–6)

Cross-task cognitive relationships via pairwise potentials (Eq. 7–8)

Temporal mastery evolution through a transition function (Eq. 11–12)


This enables the framework to track cognitive trajectories over time.

● Adaptive Cognitive Reasoning Strategy (ACRS)

ACRS dynamically adjusts reasoning based on evolving mastery states.According to the schematic on page 8, it includes:



Task-specific reasoning functions

A graph-based task-interaction matrix

Dynamic task prioritization

Regularization for interpretability and stability


Attention mechanisms further enhance reasoning accuracy (page 14).

● Multi-Task Learning Integration

Instead of treating tasks independently, the framework learns shared latent structures and inter-task dependencies. This greatly improves generalization and reduces redundancy, as validated in ablation studies (pages 15–16).

● Interpretable Cognitive Insights

The joint graphical and attention-based structure allows transparent inspection of:



Task relationships

Temporal mastery shifts

Influential cognitive features

Salient reasoning segments


This interpretability supports personalized learning decisions.



Evaluation Configuration

Experiments assess the model across:



Cognitive state classification

Mastery estimation

Temporal reasoning

Cross-task and cross-domain generalization


Performance metrics include Accuracy, F1-score, MAE, parameter count, and inference time (pages 12–13).Computational experiments were conducted with PyTorch 2.1 on RTX 3090 GPUs.

Loss functions combine classification, regression, and correlation terms (Eq. 18).



Benchmark Results

● Core Performance

The framework achieves high accuracy and stable generalization across multiple datasets.Examples include:



F1-score: 88.9%

MAE: 0.153

Params: 2.5M(from ablation and comparison tables, pages 14–16)


● Ablation Findings

Removing MCSM or ACRS leads to large performance drops:



Without MCSM: F1 decreases to 79.4%

Without ACRS: F1 decreases to 83.1%(page 15)


● Lightweight Model Comparison

Outperforms MobileNetV3, ShuffleNetV2, GhostNet, EfficientNet-Lite in both accuracy and efficiency (page 16).

● Cognitive Modeling Framework Comparison

Surpasses DKVMN, SAINT, GKT, and DKT in F1-score and MAE(Table 6, page 17)



Datasets

The evaluation uses four benchmark datasets relevant to mathematical cognition and educational technology. Key datasets include:




Dataset Name
Description




Mathematical Cognition Assessment Dataset
Mathematical reasoning tasks, difficulty annotations, timing and accuracy metrics


Knowledge Mastery Progression Dataset
Longitudinal mastery data with contextual metadata


Multi-Task Learning Cognitive States Dataset
EEG, eye-tracking, multimodal signals for multitask cognition


Problem-Solving Reasoning Patterns Dataset
Behavioral logs, reasoning steps, think-aloud transcripts




(page 10–11 + Table 1)

Additional cross-dataset validation uses the MFPT Dataset, focusing on mental fatigue and cognitive load (page 17–18).



Applications

The MultiTaskCognitiveModel framework is suitable for applications such as:



Cognitive state monitoring in adaptive tutoring systems

Mathematical knowledge tracing and mastery prediction

Multi-task educational reasoning models

Temporal cognitive progression analysis

Personalized learning content recommendations

Cognitive fatigue and attention modeling

Human-computer interaction and cognitive workload estimation


The structure supports both research-oriented and real-world intelligent education platforms.



Contributing

Contributions to extend the framework are welcome:



Fork the repository

Create a feature branch

Commit your updates

Open a pull request


Potential contribution areas:



Additional cognitive datasets

Improved attention and reasoning modules

New multimodal feature encoders

Cross-domain cognitive transfer strategies

Real-time adaptive tutoring integrations




Future Work

As highlighted in the study’s conclusion (page 18–19), future improvements may include:



Lightweight approximations for real-time deployment

More domain-independent reasoning mechanisms

Expanded multimodal integration (behavioral, physiological, gaze data)

Enhanced transfer learning for new cognitive domains

Broader scalability in large educational systems


These directions aim to improve efficiency, generalizability, and cognitive insight.



License

The project will adopt the MIT License.



Acknowledgments

This framework is inspired by research in mathematical cognition, probabilistic modeling, graph-based reasoning, and adaptive intelligent tutoring systems. Special thanks to the authors and contributors of the referenced study for foundational insights.