I’d be happy to continue with the Mini-GPT training code. Let’s finish the implementation:

Now, let’s add a script that allows us to compare the two types of positional embeddings in the context of our Mini-GPT model, to see how they affect performance:

Let me also provide a detailed explanation of the code implementation and key concepts:

Positional Embeddings Implementation

The first artifact implements two types of positional embeddings, which are crucial for transformer models like GPT:

1. Learned Positional Embeddings

• Implementation: An embedding layer that maps position indices to vectors
• Key characteristics:
  • Parameters are learned during training
  • More flexible as they can adapt to specific patterns in the data
  • Requires additional memory for storing parameters
  • Limited to the maximum sequence length seen during training

2. Sinusoidal Positional Embeddings

• Implementation: Mathematical functions (sine and cosine) with different frequencies
• Key characteristics:
  • Fixed pattern that doesn’t require training
  • More memory-efficient (no additional parameters)
  • Can potentially generalize better to sequence lengths not seen during training
  • Uses alternating sine and cosine functions across dimensions

The code includes visualization capabilities to see how these different embeddings look across positions and dimensions.

Mini-GPT Implementation

The second artifact implements a simplified GPT model with these key components:

Key Components:

1. Multi-Head Attention: Allows the model to focus on different parts of the input sequence
   • Splits embeddings into multiple heads for parallel attention computation
   • Computes query, key, and value projections
   • Uses scaled dot-product attention with a causal mask for autoregressive generation
2. Feed-Forward Networks: Processes the attention outputs
   • Two linear transformations with a GELU activation
   • Expands the dimension to d_ff and then back to d_model
3. Decoder Blocks: The fundamental building blocks of GPT
   • Self-attention mechanism
   • Feed-forward network
   • Layer normalization and residual connections
4. Text Generation: Autoregressive sampling with temperature control
   • Supports top-k and nucleus (top-p) sampling for diverse generation
   • Follows the standard autoregressive text generation process
5. Simple Tokenizer: A basic implementation for demonstration purposes
   • Handles word tokenization
   • Builds vocabulary from input texts
   • Provides encode/decode functionality

Training Implementation

The third artifact shows how to train the Mini-GPT model:

• Sets up proper loss function (CrossEntropyLoss with padding ignored)
• Uses the AdamW optimizer with learning rate scheduling
• Implements gradient clipping to prevent exploding gradients
• Tracks and visualizes training metrics
• Demonstrates text generation with different temperature settings

Comparison of Positional Embeddings

The final artifact compares both positional embedding types in a real training scenario:

• Implements both models with identical architectures except for the positional embedding type
• Trains both models on the same data with identical hyperparameters
• Compares training loss curves and training times
• Tests text generation quality
• Assesses generalization to longer sequences (a key advantage of sinusoidal embeddings)

Key Takeaways

1. Architectural Understanding: The code demonstrates the essential components of transformer decoder models like GPT.

2. Positional Embeddings Trade-offs:

   • Learned positional embeddings can adapt to specific patterns but require more parameters and may struggle with longer sequences.
   • Sinusoidal positional embeddings are parameter-efficient and theoretically better for generalization to unseen sequence lengths.

3. Practical Implementation: The implementation includes training, evaluation, and text generation, forming a complete pipeline from data to generated text.

These implementations provide a foundation to understand how modern language models work at their core, with a focus on the critical role of positional information in sequence modeling.

Would you like me to explain any specific part of these implementations in more detail?