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4 Qualifying Exam/2 Writing/3. QE Research Approach.md

@@ -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