Neural networks can struggle with images they haven't been trained on, highlighting the continued importance of handcrafted models in certain contexts.

The integration of handcrafted models with neural networks presents exciting opportunities for mathematicians to explore and improve image denoising techniques.

Even with handcrafted models, you can still understand and prove things about your solution, ensuring guarantees on the results.

While handcrafted models for image denoising are still relevant, deep neural networks are increasingly outperforming them in various scenarios.

In using neural networks for problems like computer tomography, we are exploring how to combine handcrafted models with neural networks, particularly in how we feed them prior information.

My recent work involves starting with handcrafted models and parameterizing them in a simplified way, rather than using millions of parameters. I learn parameters from actual examples that I want my handcrafted model to produce, which is known as parameter estimation or optimization.

As we scale up classical simulations, we will encounter limitations due to the handcrafted nature of the system, which is why neural world models will exponentially enhance our capabilities.

Experimenting with different AI models is crucial, as their performance can vary significantly across tasks like debugging, planning, and implementing features.

Understanding the distribution of AI model behavior over time is essential for diagnosing performance issues and ensuring consistent outputs.