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4 Qualifying Exam/2 Writing/3. QE Research Approach.md
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@ -39,8 +39,27 @@ Something to justify, why diffusion model as opposed to other generative AI
16. Well we train a neural network as a denoiser.
17. Because the diffusion model forward steps are small and gaussian, we can know the reverse step is also a gaussian distribution.
18. So for our neural network, what we're trying to learn is the mean and standard deviation of the reverse steps for a given timestep.
19. What does this mean for
19. What does this mean for perturbed plants?
20. Well, we can use a diffusion model to generate new perturbed plants that are similar to the original plant
21. How? We train a diffusion model on a structured set.
22. We need to pick a uncertainty function W_2
23. Do this using the usual means. What is the worst we expect to handle?
24. We create a structured set by picking random scalar gains for $\Delta$
25. This is our training data. We train the diffusion model to learn to this data
26. Then, we take the nominal plant, and take some amount of steps forward.
27. We heuristically go a certain amount forward to introduce a certain amount of noise
28. then we go backwards. The diffusion model will try to remove the noise, but not knowing the orignial nominal plant will introduce a perturbation.
29. **This is outcome number 3 and number 2**
30. We can use this frequency response data to find the 'worst case' distance to the critical point -1. We plot this location in the complex plane.
31. Why do we care about the complex plane?
32. This is where the nyquist robust stability and performance criterion live.
33. Our 'valid' perturbations live inside this circle of radius -1
34. We repeat this several times, and only include examples in our set of unstructured perturbations that are within or robustness circle
35. **This is outcome number 1**
36. We generate enough examples to populate this circle until we're comfortable.
## Writin some stuff
The purpose of this proposal is to suggest that using a generative network to create unstructured perturbations can be a viable way to advance the state of the art. But to do this, the current state of diffusion models and their place must be introduced. The generative diffusion model is a recent breakthrough in generative models [@sohl-dicksteinDeepUnsupervisedLearning2015]. Diffusion generative models are the state of the art for image and video generation, and have demonstrated promise for audio generation and noise removal [@kongDiffWaveVersatileDiffusion2020] [@SoraCreatingVideo]. A diffusion generative model, AlphaFold 3, won the Nobel Prize in Chemistry [@AlphaFold3Predicts2024] Diffusion models do this through a forward noise-inducing process, and a learned backwards noise-removing process.
The purpose of this proposal is to suggest that using a generative network to create unstructured perturbations can be a viable way to advance the state of the art. But to do this, the current state of diffusion models and their place must be introduced. The generative diffusion model is a recent breakthrough in generative models [@sohl-dicksteinDeepUnsupervisedLearning2015]. Diffusion generative models are the state of the art for image and video generation, and have demonstrated promise for audio generation and noise removal [@kongDiffWaveVersatileDiffusion2020] [@SoraCreatingVideo]. A diffusion generative model, AlphaFold 3, won the Nobel Prize in Chemistry [@AlphaFold3Predicts2024] Diffusion models do this through a forward noise-inducing process, and a learned backwards noise-removing process.
The forward diffusion process works by introducing small amounts of noise into