Machine Learning

Analytical Theory of Spectral Bias in Diffusion Sampling and Learning

Mar 26, 2025

Course on biological and artificial intelligence. With tutorials covering self-supervised learning, NLP, and Transformers.

May 1, 2023

TOC {:toc} Motivation Consider a distribution $p(x)$, we could “convolve” it with a kernel $p(\tilde{x}\mid x)=q(\tilde{x}-x)$. The marginal distribution of $\tilde{x}$ is denoted as $p_\sigma(\tilde{x})$. We want to model the score of this convolved distribution and that of the original distribution $\nabla\log p_\sigma(\tilde{x})$ .

Jun 20, 2022

TOC {:toc} Motivation Recently, a line of research emerged in generative image models, diffusion models, which showed a competitive performance with GAN [^1]. More recently, a larger scale version of it gave rise to the ground breaking model DALL-E 2 and its precursor GLIDE.

May 9, 2022

TOC {:toc} Motivation Simply put, “kernel trick” is the finding that sometimes only inner product appears in the formulation of some algorithms. because of this, we could substitute the inner product with some fancier kernel function, i.e. inner product in some other spaces. This post is about another usage of kernel trick. Another usage is Kernel (ridge) Regression.

Mar 21, 2022

TOC {:toc} Motivation Understand the use of kernel in regression problems. For usage in unsupervised learning / dimension reduction, see notes on Kernel PCA. Kernel in Classification Kernel is usually introduced in SVM classification problems. The rationale is that a linearly non-separable dataset could be separable in a high-dimensional feature space using the mapping $\phi:\mathcal X\to\mathcal F$ .

Dec 17, 2021

Comprehensive introduction to computational models in neuroscience covering sensory processing, neural dynamics, and learning

Sep 1, 2021

Motivations Many CNN models have become the bread and butter in modern deep learning pipeline. Here I’m summarizing some famous CNN structure and their key innovations as I use them.

Jan 17, 2021

Student-led tutorial series teaching cutting-edge ML models through hands-on implementation for neuroscience students

Jan 1, 2021

Note on Compiling Torch C Extensions Motivation Sometimes fusing operations in C library without using python can accelerate your model, especially for key operations that occurs a lot and lots of data pass through.

Sep 15, 2020