My Notes
A collection of thoughts, explorations, and research findings in the field of Generative AI.
2025-10
Quaternions and 3D rotations
111
计算机图形学2025-09
3D Gaussian Splatting
Represents a 3D scene as an explicit set of anisotropic 3D Gaussians, each defined by parameters for position, covariance, opacity, and view-dependent color via Spherical Harmonics. Optimizes all parameters from images using stochastic gradient descent, coupled with an adaptive density control mechanism that dynamically clones, splits, and prunes the Gaussians to create a detailed and efficient scene representation.
计算机图形学2025-05
第一性原理分析热力学和统计力学
Statistical mechanics is built upon the postulate of equal probability, which bridges deterministic microscopic mechanics and macroscopic thermodynamics. This foundation allows for the derivation of entropy and temperature, ultimately unifying classical and quantum descriptions through ensemble theory.
热力学和统计力学物理2024-08
An Introduction to Variational Autoencoders
Analyzed the difficulty in deep latent variable models where the marginal likelihood is intractable and cannot be directly optimized, and introduced the framework of variational inference, where an encoder is used to approximate the true posterior distribution, thereby transforming the problem into the optimization of the Evidence Lower Bound (ELBO). Applied the reparameterization trick to enable gradient-based optimization of the ELBO by making the sampling process differentiable, and ultimately achieved end-to-end training of the entire generative model, including both the encoder and the decoder.
generative model