Создайте Jupyter Notebook по теме: Диффузионные ге...

Considering lightweight implementation

I want to avoid heavy dependencies since the tool environment could be unpredictable. Typically, Python with common libs like numpy and pandas might be available, but I can rely on numpy only to be safe. I’m planning a small-scale project, like implementing a Denoising Diffusion Probabilistic Model (DDPM) on 2D points, with training steps kept light for efficiency. A simple approach with linear regression or MLPRegressor seems like a good fit while avoiding too much complexity.

Planning a simple model

I’m considering implementing a tiny MLP in numpy, but, since there’s no automatic differentiation, training would be challenging without manually coding gradients. Maybe I should go simpler with linear regression for noise prediction, fitting a different model for each timestep. I could use numpy to generate a synthetic “two moons” dataset and apply a diffusion process, then train the model with linear regression across timesteps, using features like both x_t and timestep embeddings. That should work well for a basic implementation.

Outlining the model and sampling

For the linear regression, the closed-form solution seems fast: $(X^T X)^{-1} X^T y$. I plan to map features like $x_t + \text{embedding}$ to the epsilon vector, training two separate regressions. Alternatively, I could use ridge regression for stability. After that, we'll sample using learned epsilon values and create scatter plots for the "two moons." I'll write up theoretical explanations in markdown with LaTeX math and keep everything in the notebook with synthetic data—no need for external things!

Creating the notebook

I can use nbformat to build the notebook with code and markdown cells. The challenge is ensuring that the code runs correctly, even though we can't execute it in this environment. I’ll ensure the code cells are accurate and include a working model demonstration. Although testing directly may work, targeting a notebook file seems best. I’ll also keep the dataset optional, since we can generate it within the notebook.

Thought for 25s

Fixing the error

The issue seems related to the docstring containing non-escaped backslashes. Python supports Unicode, but the problem occurs when the code tries to interpret text within the triple-quoted string as actual code instead of a string literal. I'll ensure backslashes are properly escaped in the docstring to prevent the SyntaxError. Helping this work smoothly requires focusing on that.

Docstring error investigation

The error seems to arise because of the way the docstring is inside the string defined with dedent(r""" ... """)—not because it's executed, but due to the triple quotes used inside the string. The SyntaxError likely happens when I define the notebook's code cell. Triple quotes within the string might cause it to be misinterpreted. I'll check how we're handling the docstring formatting more closely.

Fixing docstring issue

The issue occurs because the outer string uses triple quotes (r""" ... """), and when I added the inner triple quotes for the function docstring, it prematurely ends the outer string. Python then tries to parse the rest as code, which causes the SyntaxError. I need to escape the inner triple quotes to prevent this from happening.

Thought for 12s