83 lines
2.5 KiB
Markdown
83 lines
2.5 KiB
Markdown
# LLM KV-Cache Experiment
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## Overview
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This experiment demonstrates space-time tradeoffs in Large Language Model (LLM) attention mechanisms. By varying the KV-cache size, we show how modern AI systems implement Williams' √n pattern through techniques like Flash Attention.
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## Background
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### The Attention Mechanism
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In transformers, attention computes:
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```
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Attention(Q,K,V) = softmax(QK^T/√d)V
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```
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For each new token, we need K and V matrices from all previous tokens.
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### KV-Cache Strategies
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1. **Full Cache O(n)**: Store all past keys/values
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- Maximum memory usage
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- No recomputation needed
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- Used in standard implementations
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2. **Flash Attention O(√n)**: Store recent √n tokens
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- Balanced memory/compute
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- Recompute older tokens as needed
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- Used in production LLMs
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3. **Minimal Cache O(1)**: Store almost nothing
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- Minimum memory usage
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- Maximum recomputation
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- Used in extreme memory-constrained settings
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## Running the Experiment
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```bash
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python llm_kv_cache_experiment.py
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```
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Simulates attention computation for sequences of 512, 1024, and 2048 tokens.
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## Surprising Results
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Our experiment revealed a counterintuitive finding:
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| Cache Size | Memory | Tokens/sec | Speedup |
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|------------|--------|------------|---------|
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| O(n) Full | 12 MB | 197 | 1.0× |
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| O(√n) | 1.1 MB | 1,349 | 6.8× |
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| O(1) | 0.05 MB| 4,169 | 21.2× |
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**Smaller caches are FASTER!** Why?
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1. **Memory bandwidth bottleneck**: Moving 12MB of data is slower than recomputing
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2. **Cache locality**: Small working sets fit in L2/L3 cache
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3. **Modern CPUs**: Computation is cheap, memory access is expensive
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## Real-World Impact
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This pattern is used in:
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- **GPT-4**: Flash Attention enables 32K+ context windows
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- **Claude**: Efficient attention for 100K+ tokens
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- **Llama**: Open models with extended context
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- **Mobile LLMs**: Running models on phones with limited memory
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## Key Insights
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1. Williams' bound assumes uniform memory access
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2. Real systems have memory hierarchies
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3. Sometimes recomputation is faster than memory access
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4. The √n pattern emerges naturally as optimal
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## Production Techniques
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- **Flash Attention**: Fuses operations to minimize memory transfers
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- **Paged Attention**: Virtual memory for KV-cache
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- **Multi-Query Attention**: Shares keys/values across heads
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- **Sliding Window**: Fixed-size attention window
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## Generated Files
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- `llm_attention_tradeoff.png`: Performance visualization
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- `llm_kv_cache_results.json`: Detailed metrics |