Submit your work as a single Jupyter Notebook file. Please use the following naming convention: StudentName_HW#.ipynb (e.g., 王小明_HW1.ipynb).

• Explanations: Use Markdown cells for all text and prose.
• Mathematics: Use LaTeX for mathematical expressions and formulas.

The notebook must be fully reproducible. Before submission, please “Restart & Run All” to ensure the entire notebook executes from start to finish without errors.

If a specific code block requires significant computation time (> 1 minute), please implement a caching mechanism. The script should check for a local data file; if the file exists, the notebook should load the results rather than re-running the lengthy evaluation.

To facilitate efficient grading, the notebook should not take more than 1 minute to execute. If your code requires lengthy computations:

• Implement a caching mechanism (e.g., using pickle or joblib).
• The script should check for the existence of a local data file; if found, it should load the results instead of re-running the evaluation.