Lilian Weng

A super long overdue (3+ years?) post on scaling laws. Compute is expensive. Scaling laws are a way to help us reason about the optimal compute allocation between data and model size before committing to a large run. The post covers what scaling laws predict, how

[Updated on 2018-09-30: thanks to Yoonju, we have this post translated in Korean !] [Updated on 2019-04-18: this post is also available on arXiv .] Generative adversarial network (GAN) has shown great results in many generative tasks to replicate the real-world rich content such as images, human language, and music. It is inspired by game theory: two models, a generator and a critic, are competing with each other while making each other stronger at the same time. However, it is rather challengin

Professor Naftali Tishby passed away in 2021. Hope the post can introduce his cool idea of information bottleneck to more people. Recently I watched the talk “Information Theory in Deep Learning” by Prof Naftali Tishby and found it very interesting. He presented how to apply the information theory to study the growth and transformation of deep neural networks during training. Using the Information Bottleneck (IB) method, he proposed a new learning bound for deep neural networks (DNN)

Human vocabulary comes in free text. In order to make a machine learning model understand and process the natural language, we need to transform the free-text words into numeric values. One of the simplest transformation approaches is to do a one-hot encoding in which each distinct word stands for one dimension of the resulting vector and a binary value indicates whether the word presents (1) or not (0).

The algorithms are implemented for Bernoulli bandit in lilianweng/multi-armed-bandit . Exploitation vs Exploration The exploration vs exploitation dilemma exists in many aspects of our life. Say, your favorite restaurant is right around the corner. If you go there every day, you would be confident of what you will get, but miss the chances of discovering an even better option. If you try new places all the time, very likely you are gonna have to eat unpleasant food from time to time. Similarly,

[Updated on 2018-06-30: add two new policy gradient methods, SAC and D4PG .] [Updated on 2018-09-30: add a new policy gradient method, TD3 .] [Updated on 2019-02-09: add SAC with automatically adjusted temperature ]. [Updated on 2019-06-26: Thanks to Chanseok, we have a version of this post in Korean ]. [Updated on 2019-09-12: add a new policy gradient method SVPG .] [Updated on 2019-12-22: add a new policy gradient method IMPALA .] [Updated on 2020-10-15: add a new policy gradient method PPG &

The full implementation is available in lilianweng/deep-reinforcement-learning-gym In the previous two posts, I have introduced the algorithms of many deep reinforcement learning models. Now it is the time to get our hands dirty and practice how to implement the models in the wild. The implementation is gonna be built in Tensorflow and OpenAI gym environment. The full version of the code in this tutorial is available in [lilian/deep-reinforcement-learning-gym] .

[Updated on 2018-10-28: Add Pointer Network and the link to my implementation of Transformer.] [Updated on 2018-11-06: Add a link to the implementation of Transformer model.] [Updated on 2018-11-18: Add Neural Turing Machines .] [Updated on 2019-07-18: Correct the mistake on using the term “self-attention” when introducing the show-attention-tell paper; moved it to Self-Attention section.] [Updated on 2020-04-07: A follow-up post on improved Transformer models is here .]

[Updated on 2019-07-18: add a section on VQ-VAE & VQ-VAE-2 .] [Updated on 2019-07-26: add a section on TD-VAE .] Autocoder is invented to reconstruct high-dimensional data using a neural network model with a narrow bottleneck layer in the middle (oops, this is probably not true for Variational Autoencoder , and we will investigate it in details in later sections). A nice byproduct is dimension reduction: the bottleneck layer captures a compressed latent encoding. Such a low-dimensional represent

So far, I’ve written about two types of generative models, GAN and VAE . Neither of them explicitly learns the probability density function of real data, $p(\mathbf{x})$ (where $\mathbf{x} \in \mathcal{D}$) — because it is really hard! Taking the generative model with latent variables as an example, $p(\mathbf{x}) = \int p(\mathbf{x}\vert\mathbf{z})p(\mathbf{z})d\mathbf{z}$ can hardly be calculated as it is intractable to go through all possible values of the latent code $\mathbf{z}$

[Updated on 2019-10-01: thanks to Tianhao, we have this post translated in Chinese !]

[Updated on 2019-05-27: add the section on Lottery Ticket Hypothesis.] If you are like me, entering into the field of deep learning with experience in traditional machine learning, you may often ponder over this question: Since a typical deep neural network has so many parameters and training error can easily be perfect, it should surely suffer from substantial overfitting. How could it be ever generalized to out-of-sample data points?

[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese ].

In Robotics, one of the hardest problems is how to make your model transfer to the real world. Due to the sample inefficiency of deep RL algorithms and the cost of data collection on real robots, we often need to train models in a simulator which theoretically provides an infinite amount of data. However, the reality gap between the simulator and the physical world often leads to failure when working with physical robots. The gap is triggered by an inconsistency between physical parameters (i.e.

In my earlier post on meta-learning , the problem is mainly defined in the context of few-shot classification. Here I would like to explore more into cases when we try to “meta-learn” Reinforcement Learning (RL) tasks by developing an agent that can solve unseen tasks fast and efficiently.

Stochastic gradient descent is a universal choice for optimizing deep learning models. However, it is not the only option. With black-box optimization algorithms, you can evaluate a target function $f(x): \mathbb{R}^n \to \mathbb{R}$, even when you don’t know the precise analytic form of $f(x)$ and thus cannot compute gradients or the Hessian matrix. Examples of black-box optimization methods include Simulated Annealing , Hill Climbing and Nelder-Mead method .

[Updated on 2020-01-09: add a new section on Contrastive Predictive Coding ]. [Updated on 2020-04-13: add a “Momentum Contrast” section on MoCo, SimCLR and CURL.] [Updated on 2020-07-08: add a “Bisimulation” section on DeepMDP and DBC.] [Updated on 2020-09-12: add MoCo V2 and BYOL in the “Momentum Contrast” section.] [Updated on 2021-05-31: remove section on “Momentum Contrast” and add a pointer to a full post on “Contrastive Representation L

[Updated on 2020-02-03: mentioning PCG in the “Task-Specific Curriculum” section. [Updated on 2020-02-04: Add a new “curriculum through distillation” section.

[Updated on 2020-06-17: Add “exploration via disagreement” in the “Forward Dynamics” section . Exploitation versus exploration is a critical topic in Reinforcement Learning. We’d like the RL agent to find the best solution as fast as possible. However, in the meantime, committing to solutions too quickly without enough exploration sounds pretty bad, as it could lead to local minima or total failure. Modern RL algorithms that optimize for the best returns can achieve

Although most popular and successful model architectures are designed by human experts, it doesn’t mean we have explored the entire network architecture space and settled down with the best option. We would have a better chance to find the optimal solution if we adopt a systematic and automatic way of learning high-performance model architectures.

[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” .]

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.

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 .

[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 .

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

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.

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 d

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 visua

[Updated on 2023-01-24: add a small section on Distillation .] Large transformer models are mainstream nowadays, creating SoTA results for a variety of tasks. They are powerful but very expensive to train and use. The extremely high inference cost, in both time and memory, is a big bottleneck for adopting a powerful transformer for solving real-world tasks at scale. Why is it hard to run inference for large transformer models? Besides the increasing size of SoTA models, there are two main factor

Many new Transformer architecture improvements have been proposed since my last post on “The Transformer Family” about three years ago. Here I did a big refactoring and enrichment of that 2020 post — restructure the hierarchy of sections and improve many sections with more recent papers. Version 2.0 is a superset of the old version, about twice the length. Notations Symbol Meaning $d$ The model size / hidden state dimension / positional encoding size. $h$ The number of heads in

Prompt Engineering , also known as In-Context Prompting , refers to methods for how to communicate with LLM to steer its behavior for desired outcomes without updating the model weights. It is an empirical science and the effect of prompt engineering methods can vary a lot among models, thus requiring heavy experimentation and heuristics. This post only focuses on prompt engineering for autoregressive language models, so nothing with Cloze tests, image generation or multimodality models. At its

Building agents with LLM (large language model) as its core controller is a cool concept. Several proof-of-concepts demos, such as AutoGPT , GPT-Engineer and BabyAGI , serve as inspiring examples. The potentiality of LLM extends beyond generating well-written copies, stories, essays and programs; it can be framed as a powerful general problem solver. Agent System Overview In a LLM-powered autonomous agent system, LLM functions as the agent’s brain, complemented by several key components: P

The use of large language models in the real world has strongly accelerated by the launch of ChatGPT. We (including my team at OpenAI, shoutout to them) have invested a lot of effort to build default safe behavior into the model during the alignment process (e.g. via RLHF ). However, adversarial attacks or jailbreak prompts could potentially trigger the model to output something undesired. A large body of ground work on adversarial attacks is on images, and differently it operates in the continu

[Special thank you to Ian Kivlichan for many useful pointers (E.g. the 100+ year old Nature paper “Vox populi”) and nice feedback. 🙏 ] High-quality data is the fuel for modern data deep learning model training. Most of the task-specific labeled data comes from human annotation, such as classification task or RLHF labeling (which can be constructed as classification format) for LLM alignment training. Lots of ML techniques in the post can help with data quality, but fundamentally hum

Diffusion models have demonstrated strong results on image synthesis in past years. Now the research community has started working on a harder task—using it for video generation. The task itself is a superset of the image case, since an image is a video of 1 frame, and it is much more challenging because: It has extra requirements on temporal consistency across frames in time, which naturally demands more world knowledge to be encoded into the model. In comparison to text or images, it is

Hallucination in large language models usually refers to the model generating unfaithful, fabricated, inconsistent, or nonsensical content. As a term, hallucination has been somewhat generalized to cases when the model makes mistakes. Here, I would like to narrow down the problem of hallucination to cases where the model output is fabricated and not grounded by either the provided context or world knowledge. There are two types of hallucination: In-context hallucination: The model output should

Reward hacking occurs when a reinforcement learning (RL) agent exploits flaws or ambiguities in the reward function to achieve high rewards, without genuinely learning or completing the intended task. Reward hacking exists because RL environments are often imperfect, and it is fundamentally challenging to accurately specify a reward function. With the rise of language models generalizing to a broad spectrum of tasks and RLHF becomes a de facto method for alignment training, reward hacking in RL

Special thanks to John Schulman for a lot of super valuable feedback and direct edits on this post. Test time compute ( Graves et al. 2016 , Ling, et al. 2017 , Cobbe et al. 2021 ) and Chain-of-thought (CoT) ( Wei et al. 2022 , Nye et al. 2021 ), have led to significant improvements in model performance, while raising many research questions. This post aims to review recent developments in how to effectively use test-time compute (i.e. “thinking time”) and why it helps.

Scaling laws are one of the most critical empirical findings in deep learning. The observation is simple in form: the training loss $L$ decreases predictably as we scale up model size $N$, dataset size $D$, and compute $C$, following a power-law curve, which appears as a straight line on a log-log plot. We can view scaling laws as a framework for describing the relationship between compute, loss, model size and data; at its core, it is about how to allocate precious compute optimally between $N$

[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”

The concept of recursive self-improvement (RSI) dates back to I. J. Good (1965) , where he defined an “ultraintelligent machine” as a system that can surpass humans in all intellectual activities and design better machines to improve itself. Yudkowsky (2008) used the phrase “recursive self-improvement” for a specific feedback loop: an AI uses its current intelligence to improve the cognitive machinery that produces its intelligence. This feedback loop in modern AI may ind