65 lines
4.1 KiB
Markdown
65 lines
4.1 KiB
Markdown
---
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title: Research Approach
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allDay: true
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date: 2024-10-10
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completed:
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type: single
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endDate: 2024-10-22
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---
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5 Pages
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**TARGET: 2800-3000 words**
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# Outline
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1. What are unperturbed perturbations and why are they important?
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2. What is a generative diffusion model?
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3. Where have generative diffusion models been used?
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4. How will generative diffusion models generate new plants?
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5. How can we know if these new plants are in the set of 'controllable' plants?
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6. How are we going to get training data?
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Something to justify, why diffusion model as opposed to other generative AI
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# First Draft
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## Story
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1. Generating unstructured perturbations is pretty hard
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2. They need to be 'random'
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3. diffusion model is good at creating novel examples (cite!)
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4. we can use diffusion models to solve this problem of generating examples
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5. But how does a diffusion model work?
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6. Diffusion model uses two processes
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7. a forward process that introduces noise into an 'input'
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8. this forward process does this using several small steps of noise
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9. These are called timesteps
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10. This noise is a gaussian noise
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11. over time this forward process degrades the input until it is unrecognizable
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12. This takes several several iterations, but is dependent on the amount of noise in each step
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13. The markov chain that this creates is also gaussian at every step, until the noise at the end of the day is some gaussian distribution. Usually mean 0 std. dev beta
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14. A reverse process that tries to remove the noise
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15. But if we destroy the input how can we do this?
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16. Well we train a neural network as a denoiser.
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17. Because the diffusion model forward steps are small and gaussian, we can know the reverse step is also a gaussian distribution.
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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.
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19. What does this mean for perturbed plants?
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20. Well, we can use a diffusion model to generate new perturbed plants that are similar to the original plant
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21. How? We train a diffusion model on a structured set.
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22. We need to pick a uncertainty function W_2
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23. Do this using the usual means. What is the worst we expect to handle?
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24. We create a structured set by picking random scalar gains for $\Delta$
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25. This is our training data. We train the diffusion model to learn to this data
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26. Then, we take the nominal plant, and take some amount of steps forward.
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27. We heuristically go a certain amount forward to introduce a certain amount of noise
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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.
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29. **This is outcome number 3 and number 2**
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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.
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31. Why do we care about the complex plane?
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32. This is where the nyquist robust stability and performance criterion live.
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33. Our 'valid' perturbations live inside this circle of radius -1
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34. We repeat this several times, and only include examples in our set of unstructured perturbations that are within or robustness circle
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35. **This is outcome number 1**
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36. We generate enough examples to populate this circle until we're comfortable.
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## Writin some stuff
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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.
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The forward diffusion process works by introducing small amounts of noise into |