unifolm-world-model-action/sparse_head_simulation/report.md

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