Adaptive Learning Path Recommendation Engine

Design a sophisticated Laravel-based recommendation system that dynamically generates personalized learning paths for students using machine learning algorithms. Create a system that analyzes student performance data, including previous quiz scores, engagement metrics, and learning style indicators. Implement a predictive model using PHP's machine learning libraries that can suggest curriculum adjustments in real-time, with a focus on creating granular, adaptive learning experiences. Include robust caching mechanisms to ensure performance with large student datasets.