# Module 12: Embeddings - Dense Vector Representations for Language Models

## Overview
This module implements the embedding systems that convert discrete tokens into rich vector representations for language processing. You'll build embedding layers, positional encoding systems, and understand how embedding choices affect model memory, performance, and language understanding capabilities.

## What You'll Learn

### Core Implementations
- **Embedding Layer**: Learnable lookup table converting token indices to dense vectors
- **Positional Encoding**: Sinusoidal patterns that add position information to sequences
- **Learned Positional Embeddings**: Trainable position representations
- **Memory-Efficient Systems**: Optimized embedding access and memory management

### ML Systems Concepts
- **Memory Scaling**: How embedding tables scale with vocabulary size and dimensionality
- **Lookup Performance**: Memory bandwidth limitations and cache-friendly access patterns
- **Position Encoding Trade-offs**: Fixed vs learned, extrapolation vs optimization
- **Integration Efficiency**: Embedding pipeline optimization for production systems

### Performance Engineering
- **Embedding Profiling**: Measuring lookup performance and memory usage
- **Scaling Analysis**: Understanding parameter growth and memory requirements
- **Pipeline Optimization**: Efficient token-to-vector transformation workflows
- **Production Patterns**: Large-scale embedding system design and optimization

## Key Learning Outcomes

By completing this module, you'll understand:

1. **Token-to-Vector Pipeline**: How discrete symbols become continuous representations
2. **Embedding Trade-offs**: Vocabulary size vs embedding dimension vs memory usage
3. **Position Encoding**: How transformers gain position awareness for sequences
4. **Systems Optimization**: Memory-efficient embedding lookup and pipeline design
5. **Production Scaling**: How embedding systems scale to billion-parameter models

## Files in This Module

- `embeddings_dev.py` - Main implementation with embedding layer and positional encoding
- `embeddings_dev.ipynb` - Jupyter notebook (auto-generated)
- `module.yaml` - Module configuration and metadata
- `README.md` - This documentation file

## Usage Example

```python
from tinytorch.core.embeddings import Embedding, PositionalEncoding
from tinytorch.core.tokenization import CharTokenizer

# Create tokenizer and embedding layer
tokenizer = CharTokenizer()
embedding = Embedding(vocab_size=tokenizer.vocab_size, embedding_dim=256)

# Add positional encoding
pos_encoding = PositionalEncoding(embedding_dim=256, max_seq_length=512)

# Process text through complete pipeline
tokens = tokenizer.encode("Hello world!")
embeddings = embedding(tokens)
pos_embeddings = pos_encoding(embeddings)
```

## Integration with TinyTorch

This module exports to `tinytorch.core.embeddings` and provides the vector representation foundation for:
- **Attention mechanisms** (Module 13) - Processing sequence representations
- **Transformer models** (Module 14+) - Complete language model architectures
- **Language understanding** - Rich semantic representations for NLP tasks

## Systems Engineering Focus

This module emphasizes the systems engineering aspects of embedding design:

### Memory Characteristics
- **Embedding table**: O(vocab_size × embedding_dim) parameters
- **GPU memory limits**: Large vocabularies require careful memory management
- **Memory bandwidth**: Embedding lookup is often memory-bandwidth bound
- **Distributed storage**: Large embedding tables may require sharding across devices

### Performance Considerations
- **Lookup patterns**: Sequential vs random access affects cache performance
- **Batch efficiency**: Larger batches amortize lookup overhead
- **Position encoding**: Sinusoidal (no parameters) vs learned (more parameters)
- **Pipeline integration**: Embedding lookup must not bottleneck training throughput

## Prerequisites
- Module 02: Tensor (for basic tensor operations)
- Module 11: Tokenization (for token-to-index conversion)
- Understanding of lookup tables and vector operations

## Estimated Time
4-5 hours including implementation, testing, and performance analysis

## Next Steps
After completing this module, you'll be ready for:
- **Module 13: Attention** - Processing sequences with attention mechanisms
- **Module 14: Transformers** - Complete transformer architecture implementation
- Advanced language model architectures and optimization techniques