Carol Cuesta-Lazaro
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IAIFI Fellow - Institute for Artificial Intelligence and Fundamental Interactions (MIT)
Deep Generative AI:
Inteligencia Artificial y sus aplicaciones en Física
Latam
Summer School
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Las condiciones iniciales del Universo
Laws of gravity
Distribucion 3D de galaxias
Cuales son las CIs de NUESTRO Universo?
non-Gaussianidad primordial?
Inflacion
Galaxy formation
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Distribucion 3D de materia oscura
Modificar GR en escalas grandes?
Como se forman las galaxias?
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jerarquia de las masas de neutrinos?
AI y Fisica
- Que son los modelos generativos?
- Mis favoritos: likelihood-based
- Normalising flows
- Variational Autoencoders
- Variational Inference
- Diffusion models
Generar vs Discriminar
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https://vitalflux.com/generative-vs-discriminative-models-examples/
El salón de la Fama
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A teddy bear wearing a motorcycle helmet and cape is standing in front of Loch Awe with Kilchurn Castle behind him driving a speed boat near the Golden Gate Bridge
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https://parti.research.google
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Modelos generativos en Fisica
Emular procesos complejos en dimensiones altas
![](https://scitechdaily.com/images/The-IllustrisTNG-Simulations.jpg)
arXiv:2206.04594
Super resolución
![](https://yueyingn.github.io/assets/img/work/SRS-3D.png)
arxiv:2010.06608
Modelos generativos en Fisica
Detectar anomalias
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arxiv:2010.14554
Modelos generativos en Fisica
Comparar datos y simulaciones de forma optima:
Simulation-based Inference
![](https://pbs.twimg.com/media/Fip9la7XgAA5OxG.jpg:large)
Modelos generativos en Fisica
arXiv:1911.01429
Modelar incertidumbres
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arxiv:2010.14554
Modelos generativos en Fisica
Universo actual
Condiciones Iniciales
Representar priors complejos
arxiv:2206.14820
![](https://raw.githubusercontent.com/smsharma/lensing-neural-fields/master/paper/arXiv-v1/figures/hig.png)
Modelos generativos en Fisica
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prior en galaxies?
Lente
gravitacional
Modelos Generativos
![](https://creazilla-store.fra1.digitaloceanspaces.com/cliparts/78147/genie-lamp-clipart-xl.png)
Datos
Una PDF que podamos parametrizar
Maximizar el likelihood!
(o algo que se le parece)
2. Generar muestras
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1. Estimar densidades
Maximizar el likelihood (o algo que se le parezca)
Posterior
Likelihood
Prior
Evidence
![](https://miro.medium.com/v2/resize:fit:1400/1*uLKl0Nz1vFg6bmfiqpCKZQ.png)
Distribucion base
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Distribucion destino (target)
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Normalising flows: Cambio de variables
Transformacion Invertible
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Transformacion Box-Muller: Normalising flows en 1934
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(Image Credit: Phillip Lippe)
z: Variables latentes
Normalising flows
Normalising flows
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No es tan fácil encontrar funciones invertibles!
Splines
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arXiv:2202.05282
Normalising flows en cosmologia
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Normalising flows en cosmologia
arXiv:2202.05282
arXiv:2202.05282
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Normalising flows en cosmologia
Simulation-based Inference
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arXiv:1911.01429
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arxiv:2211.00723
Simulation-based Inference en cosmology
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Las soluciones de ecuaciones diferenciales ordinarias (ODEs) son siempre invertibles!
Problemas NFs: Falta expresividad
- Function invertible
- Jacobiano tratable
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Chen et al. (2018), Grathwohl et al. (2018)
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Variational Auto Encoders
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Complex
Simple
Variational Auto Encoders
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Maximizar el likelihood o algo que se le parezca: Variational Inference
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No es simetrica!
La divergencia de Kullback-Leibler (KL):
Distancia entre dos distribuciones de probabilidad
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Forward KL
Backward KL
Evidence Lower Bound
(ELBO)
Distancia al posterior real
Encontrar
1. ELBO es un lower bound del likelihood
2. Maximizar ELBO = Minimizar KL
Maximizar ELBO maximiza ev/likelihood
Maximizar ELBO para aproximar el posterior
Tutorial 1: Maximizar ELBO para aproximar posteriors en cosmologia
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Variational Auto Encoders
![](https://miro.medium.com/v2/resize:fit:2000/1*ET6FM_KEmwa2N4qgW2MglQ.png)
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Reconstruccion (MSE)
Regularizacion
- Continuo puntos cercanos en espacio latente deberian ser cercanos en el espacio de los datos
- Completo cualquier punto sampleado del espacio latente debe llevar a un ejemplo sensible de los datos
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arxiv:2008.03833
Variational Auto Encoders en Astro
Tutorial 2: Generar galaxias con VAEs
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Reverse diffusion: Quitar ruido al paso previo
Forward diffusion: Ruido Gaussian (fijo)
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Una persona medio Yoda medio Gandalf
Diffusion models
+ dimensiones(z) = dimensiones(x)
+ encoder fijo: ruido gaussiano
Deep VAE
Diffusion =
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Encoder
Ruido Gaussiano
Decoder
(neural network)
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Cosmologia
Diffusion models en cosmologia
Reverse diffusion: Quitar ruido al paso previo
Forward diffusion: Ruido Gaussian (fijo)
![](https://github.com/smsharma/set-diffuser/blob/main/notebooks/plots/animation_both_norotate.gif?raw=true)
arxiv:2104.13478
El zoo de arquitecturas:
déjate llevar por las simetrias
Propiedades de los nodos (posiciones, velocidades...)
Input
Propiedades galaxias ruidosas
Output
Prediccion del ruido
kNN (~20)
Graph neural networks para predecir el ruido
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Prior
Diffusion
Reconstruction
Se un Bayesian de verdad: siempre maximiza el likelihood
arxiv:2107.00630
arxiv:2303.00848
Maximum Likelihood = Denoising
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Tutorial 3: Generar jets de partículas con diffusion models
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Books by Kevin P. Murphy
- Machine learning, a probabilistic perspective
- Probabilistic Machine Learning: advanced topics
- ML4Astro workshop https://ml4astro.github.io/icml2023/
- ProbAI summer school https://github.com/probabilisticai/probai-2023
- IAIFI Summer school
- Blogposts
cuestalz@mit.edu
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Modelos Generativos Summer School Latam
By carol cuesta
Modelos Generativos Summer School Latam
- 272