Supplementary · Ablation

Structured Physical Chain-of-Thought holds the diagram together

Three text-to-diagram prompts, each rendered by Princigram under two training regimes. Without structured physical annotation, the scene, geometry and topology become incorrect, while the on-figure symbols collapse into illegible gibberish. With SP-CoT, the same architecture generates the entities, relations and values specified by each prompt.

SP-CoT

Structured Physical Chain-of-Thought annotates each training image with an explicit chain of physical entities, quantities and relations. This ablation isolates that single ingredient — everything else in the pipeline is held fixed.

Without SP-CoT — ablated (no structured labeling) With SP-CoT — full model
Case 1

A pulley system with two masses: mass m1 rests on an inclined plane at angle θ, connected by a rope over a pulley to a hanging mass m2.

Without SP-CoTno structured labeling
Case 1 without SP-CoT
  • ✗Scene drifts to a child on a staircase
  • ✗Every annotation is illegible gibberish
  • ✗Pulley and hanging mass misplaced
With SP-CoTfull model
Case 1 with SP-CoT
  • ✓Correct incline with block m1
  • ✓Edge pulley & hanging m2
  • ✓Angle θ labelled at the base
Case 2

An 8.00 kg block on a horizontal table, connected by a rope over a pulley at the table’s edge to a 6.00 kg block hanging vertically.

Without SP-CoTno structured labeling
Case 2 without SP-CoT
  • ✗Meaningless labels “Brw Tal”, “a”, “n”
  • ✗Numeric masses absent
  • ✗Pulley / hanging topology wrong
With SP-CoTfull model
Case 2 with SP-CoT
  • ✓8.00 kg block on the table
  • ✓Edge-mounted pulley
  • ✓6.00 kg mass hanging, masses correct
Case 3

Two blocks 1 and 2 on a horizontal surface: block 1 moves toward block 2 with initial velocity v1, while block 2 connects through a spring to a fixed wall.

Without SP-CoTno structured labeling
Case 3 without SP-CoT
  • ✗Layout corrupted into an L-shaped wall
  • ✗Spring drawn as a detached loop
  • ✗Blocks 1/2 and v1 missing, captions nonsense
With SP-CoTfull model
Case 3 with SP-CoT
  • ✓Block 1 with velocity arrow v1
  • ✓Approaches block 2
  • ✓Spring links block 2 to the fixed wall

Takeaway

Across all three cases the pattern is identical: the ablated model produces plausible-looking artwork whose physics and labels are meaningless, while the SP-CoT model places every mass, pulley, angle and velocity where the prompt demands and renders each symbol (m1, m2, θ, 8.00 kg, 6.00 kg, v1) legibly. Structured physical labeling is what makes the generations physically faithful rather than merely photorealistic.