From 34347da6caf4fa4393c4359e91cadf762d8f87c8 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Wed, 30 Oct 2024 16:26:59 -0400 Subject: [PATCH] vault backup: 2024-10-30 16:26:59 --- .../2 Writing/3. QE Research Approach.md | 23 +++++++++++++++++-- 1 file changed, 21 insertions(+), 2 deletions(-) diff --git a/4 Qualifying Exam/2 Writing/3. QE Research Approach.md b/4 Qualifying Exam/2 Writing/3. QE Research Approach.md index bc04587c0..64728d00e 100644 --- a/4 Qualifying Exam/2 Writing/3. QE Research Approach.md +++ b/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. \ No newline at end of file +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 \ No newline at end of file