밤에 쓰는 편지 밤에 쓰는 편지

https://arxiv.org/pdf/2101.09258https://github.com/yang-song/score_flowOct 2021 (NeurIPS 2021)Abstract Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models can be tractably computed through a connection to cont..

https://arxiv.org/pdf/2011.13456https://github.com/yang-song/score_sde(Feb 2021 ICLR 2021)AbstractCreating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms th..

https://arxiv.org/pdf/2006.09011https://github.com/ermongroup/ncsnv2(Oct 2020 NeurIPS 2020)AbstractScore-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32 × 32), and can be unstable under some settings. We provide a new the..

https://arxiv.org/pdf/1907.05600https://github.com/ermongroup/ncsnOct 2020 (NeurIPS 2019)AbstractWe introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different..

충격적일 정도로 난이도가 높아지고 있다.. 작년 1학기에 수업을 들으면서 처음 DGM을 접했다. 거의 컬쳐쇼크에 가까울 정도로 너무 어려웠는데.. 이번 방학에 복습을 하면서,개념을 다시 이해하고 수식을 여러 번 도출해보니,특별한 수학적 기교가 들어간 건 아니라는 건 느꼈다. (단지 손이 좀 고달플 뿐) Concept을 처음으로 받아들이는 과정이 힘들었던 것 같다. 그런데 그 이후의 모델들은..좀 얘기가 달라졌다.. ㅎㅎ ;; 그런데 사실은 진입장벽이 좀 높아서 문제이지differential equation으로 modeling하는 것이 performance 측면에서도 그렇고, computational efficiency 측면에서도 그렇고 월등하다. 무엇보다도.근본적이다. 아무리 non-markovian c..

https://www.youtube.com/playlist?list=PLMrJAkhIeNNT_Xh3Oy0Y4LTj0Oxo8GqsCFourier SeriesInner Products in Hilbert SpaceComplex Fourier SeriesFourier Series and Gibbs PhenomenaThe Fourier TransformThe Fourier Transform and DerivativesThe Fourier Transform and Convolution IntegralsParseval's TheoremSolving the Heat Equation with the Fourier TransformThe Discrete Fourier Transform (DFT)The Fast Fouri..

linear ODE의 solution을 구하기 위해, matrix A를 Eigenvalue decomposition하여, eigenvalue로 diagonize하여 solution을 구하고, basis solution의 linear combination이 boundary condition을 satisfy하는 particular solution을 구했듯이! linear PDE에서는..! orthogonal basis function (cos, sin)의 linear combination으로 boundary condition을 satisfy하는 particular solution을 찾기 위해 Fourier Transform을 하는구나!!

https://www.youtube.com/playlist?list=PLMrJAkhIeNNQromC4WswpU1krLOq5Ro6SPartial Differential Equations OverviewLaplace's Equation and Poisson's EquationDeriving the Heat Equation: A Parabolic Partial Differential Equation for Heat Energy ConservationThe Heat Equation and the Steady State Heat Distribution via Laplace's EquationDeriving the Heat Equation in 2D & 3D (& in N Dimensions!) with Contr..