# Sparse Head Execution Simulation

This report uses zero-order hold over logged stepwise action/state outputs.
For a sparse scheme, the final output at step 49 is approximated by the most recent checkpoint output.

## Experiment 1.1

### dense

- Head exec count: 50
- Head compute saving ratio: 0.0000
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### sparse_10

- Head exec count: 10
- Head compute saving ratio: 0.8000
- Final action cosine vs dense: mean=0.9341, median=0.9357
- Final state cosine vs dense: mean=0.9130, median=0.9207

### sparse_4

- Head exec count: 4
- Head compute saving ratio: 0.9200
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### sparse_5

- Head exec count: 5
- Head compute saving ratio: 0.9000
- Final action cosine vs dense: mean=0.7747, median=0.7703
- Final state cosine vs dense: mean=0.7463, median=0.7481

### sparse_8

- Head exec count: 8
- Head compute saving ratio: 0.8400
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### tail_heavy_10

- Head exec count: 10
- Head compute saving ratio: 0.8000
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### tail_heavy_6

- Head exec count: 6
- Head compute saving ratio: 0.8800
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### tail_heavy_8

- Head exec count: 8
- Head compute saving ratio: 0.8400
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### tail_only_4

- Head exec count: 4
- Head compute saving ratio: 0.9200
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

### tail_only_6

- Head exec count: 6
- Head compute saving ratio: 0.8800
- Final action cosine vs dense: mean=1.0000, median=1.0000
- Final state cosine vs dense: mean=1.0000, median=1.0000

## Experiment 1.2

- Target threshold: 0.95
- Action earliest checkpoint mean: 46.0179
- State earliest checkpoint mean: 46.5357
- Unique min head steps needed for action: [1.0]
- Unique min head steps needed for state: [1.0]

## Experiment 1.3

### budget_10_uniform_vs_tail

- Tail better action share: 1.0000
- Tail better state share: 1.0000
- Mean tail-minus-uniform action cosine: 0.0659
- Mean tail-minus-uniform state cosine: 0.0870

### budget_4_uniform_vs_tail

- Tail better action share: 0.0000
- Tail better state share: 0.0000
- Mean tail-minus-uniform action cosine: 0.0000
- Mean tail-minus-uniform state cosine: 0.0000

### budget_8_uniform_vs_tail

- Tail better action share: 0.0000
- Tail better state share: 0.0000
- Mean tail-minus-uniform action cosine: 0.0000
- Mean tail-minus-uniform state cosine: 0.0000