Some Math behind Neural Tangent Kernel

Neural networks are well known to be over-parameterized and can often easily fit data with near-zero training loss with decent generalization performance on test dataset. Although all these parameters are initialized at random, the optimization process can consistently lead to similarly good outcomes. And this is true even when the number of model parameters exceeds the number of training data points. Neural tangent kernel (NTK) (Jacot et al. 2018) is a kernel to explain the evolution of neural networks during training via gradient descent. It leads to great insights into why neural networks with enough width can consistently converge to a global minimum when trained to minimize an empirical loss. In the post, we will do a deep dive into the motivation and definition of NTK, as well as the proof of a deterministic convergence at different initializations of neural networks with infinite width by characterizing NTK in such a setting. ...

Date: September 8, 2022 | Estimated Reading Time: 17 min | Author: Lilian Weng

Generalized Visual Language Models

Processing images to generate text, such as image captioning and visual question-answering, has been studied for years. Traditionally such systems rely on an object detection network as a vision encoder to capture visual features and then produce text via a text decoder. Given a large amount of existing literature, in this post, I would like to only focus on one approach for solving vision language tasks, which is to extend pre-trained generalized language models to be capable of consuming visual signals. ...

Date: June 9, 2022 | Estimated Reading Time: 24 min | Author: Lilian Weng

Learning with not Enough Data Part 3: Data Generation

Here comes the Part 3 on learning with not enough data (Previous: Part 1 and Part 2). Let’s consider two approaches for generating synthetic data for training. Augmented data. Given a set of existing training samples, we can apply a variety of augmentation, distortion and transformation to derive new data points without losing the key attributes. We have covered a bunch of augmentation methods on text and images in a previous post on contrastive learning. For the sake of post completeness, I duplicate the section on data augmentation here with some edits. New data. Given few or even no data points, we can rely on powerful pretrained models to generate a number of new data points. This is especially true in recent years given the fast progress in large pretrained language models (LM). Few shot prompting is shown to be effective for LM to learn within context without extra training. Data Augmentation The goal of data augmentation is to modify the input format (e.g. text wording, visual appearance) while the semantic meaning stays unchanged. ...

Date: April 15, 2022 | Estimated Reading Time: 28 min | Author: Lilian Weng

Learning with not Enough Data Part 2: Active Learning

This is part 2 of what to do when facing a limited amount of labeled data for supervised learning tasks. This time we will get some amount of human labeling work involved, but within a budget limit, and therefore we need to be smart when selecting which samples to label. ...

Date: February 20, 2022 | Estimated Reading Time: 22 min | Author: Lilian Weng

Learning with not Enough Data Part 1: Semi-Supervised Learning

When facing a limited amount of labeled data for supervised learning tasks, four approaches are commonly discussed. ...

Date: December 5, 2021 | Estimated Reading Time: 26 min | Author: Lilian Weng

How to Train Really Large Models on Many GPUs?

[Updated on 2022-03-13: add expert choice routing.] [Updated on 2022-06-10]: Greg and I wrote a shorted and upgraded version of this post, published on OpenAI Blog: “Techniques for Training Large Neural Networks” ...

Date: September 24, 2021 | Estimated Reading Time: 21 min | Author: Lilian Weng

What are Diffusion Models?

[Updated on 2021-09-19: Highly recommend this blog post on score-based generative modeling by Yang Song (author of several key papers in the references)]. [Updated on 2022-08-27: Added classifier-free guidance, GLIDE, unCLIP and Imagen. [Updated on 2022-08-31: Added latent diffusion model. [Updated on 2024-04-13: Added progressive distillation, consistency models, and the Model Architecture section. ...

Date: July 11, 2021 | Estimated Reading Time: 31 min | Author: Lilian Weng

Contrastive Representation Learning

The goal of contrastive representation learning is to learn such an embedding space in which similar sample pairs stay close to each other while dissimilar ones are far apart. Contrastive learning can be applied to both supervised and unsupervised settings. When working with unsupervised data, contrastive learning is one of the most powerful approaches in self-supervised learning. ...

Date: May 31, 2021 | Estimated Reading Time: 39 min | Author: Lilian Weng

Reducing Toxicity in Language Models

Large pretrained language models are trained over a sizable collection of online data. They unavoidably acquire certain toxic behavior and biases from the Internet. Pretrained language models are very powerful and have shown great success in many NLP tasks. However, to safely deploy them for practical real-world applications demands a strong safety control over the model generation process. ...

Date: March 21, 2021 | Estimated Reading Time: 22 min | Author: Lilian Weng

Controllable Neural Text Generation

[Updated on 2021-02-01: Updated to version 2.0 with several work added and many typos fixed.] [Updated on 2021-05-26: Add P-tuning and Prompt Tuning in the “prompt design” section.] [Updated on 2021-09-19: Add “unlikelihood training”.] ...

Date: January 2, 2021 | Estimated Reading Time: 42 min | Author: Lilian Weng