Autoregressive Models
The foundation of sequential generation in modern AI
Introduction
Autoregressive models are a class of statistical models that predict future values based on past values in a sequence. In machine learning, they form the backbone of modern language models, music generation, and time series forecasting. These models generate outputs one element at a time, using previously generated elements as context for predicting the next.
Key Insight: Autoregressive models decompose the joint probability distribution of a sequence into a product of conditional distributions, making complex generation tasks tractable.
Core Concept
The fundamental principle of autoregressive modeling is the chain rule of probability:
P(x₁, x₂, ..., xₙ) = P(x₁) × P(x₂|x₁) × P(x₃|x₁,x₂) × ... × P(xₙ|x₁,...,xₙ₋₁)Each element in the sequence is predicted based on all previous elements, creating a natural left-to-right generation process.
Interactive Visualization
Watch how an autoregressive model generates text token by token:
Each new token is predicted based on all previous tokens in the sequence
Types of Autoregressive Models
Language Models
Generate text by predicting the next word/token:
- • GPT series (GPT-3, GPT-4)
- • LSTM language models
- • Character-level RNNs
Time Series Models
Forecast future values from historical data:
- • ARIMA models
- • DeepAR
- • WaveNet for audio
Image Generation
Generate pixels sequentially:
- • PixelRNN/PixelCNN
- • Image GPT
- • DALL-E (partially autoregressive)
Audio Generation
Generate audio samples sequentially:
- • WaveNet
- • SampleRNN
- • Jukebox
Architecture Components
1. Context Window
The number of previous tokens the model can "see" when making predictions:
Fixed Window
Last N tokens
Full History
All previous tokens
Hierarchical
Multiple scales
2. Prediction Head
Converts hidden representations into probability distributions:
# Simplified prediction head hidden_state = model(context) # [batch, hidden_dim] logits = linear(hidden_state) # [batch, vocab_size] probs = softmax(logits) # [batch, vocab_size] next_token = sample(probs) # [batch, 1]
3. Attention Mechanisms
Modern autoregressive models use attention to process long sequences:
Training Autoregressive Models
Teacher Forcing
During training, models use the ground truth previous tokens rather than their own predictions:
Training Time:
Inference Time:
Exposure Bias
Models may struggle when their predictions deviate from training data, as errors compound during generation.
Scheduled Sampling
Gradually transition from teacher forcing to using model predictions during training to reduce exposure bias.
Sampling Strategies
Greedy Decoding
Always select the highest probability token:
✓ Advantages:
- • Deterministic
- • Fast
✗ Disadvantages:
- • Repetitive
- • Less creative
Sampling with Temperature
Control randomness by scaling logits:
Top-k Sampling
Sample from the k most likely tokens only
Top-p (Nucleus) Sampling
Sample from tokens with cumulative probability ≤ p
Applications in Modern AI
Code Generation
GitHub Copilot and similar tools for code completion
Multi-modal Generation
DALL-E 2/3 combining autoregressive and diffusion approaches
Advantages and Limitations
Advantages
- +Tractable likelihood computation and training
- +Natural for sequential data (text, audio, time series)
- +Can generate variable-length outputs
- +Interpretable generation process
Limitations
- -Sequential generation can be slow
- -Error accumulation in long sequences
- -Limited ability to revise earlier predictions
- -May struggle with global coherence
Related Concepts
Next Steps
Continue exploring generative AI architectures: