Cover the instruction factors whose meanings depend on each other.
OOD success
1.3% → 18.5%
Cov4 → Cov12 · higher is better
OOD same-container violation
36.2% → 15.7%
Cov4 → Cov12 · lower is better
Dependent Two-Stage Pick-and-Place · fixed budget of 12 training tasks
The task at one glance
Instruction gives o₁, o₂, and c₂ — but not c₁. Stage 2 reserves the mug, so stage 1 must avoid it.
Object 1o₁ = milk
Object 2o₂ = cube
Container 2c₂ = mug · reserved
Container 1c₁ = ???
Valid
bin
o₁
c₂
mug
o₂
plate
—
o₁ → bin (≠ c₂). Mug stays free for o₂.
Same-container violation
bin
—
c₂
mug
o₁
plate
—
o₁ took the mug reserved for o₂.
Dependent pair (o₁, c₂):
where to put o₁ depends on which container is reserved for stage 2.
Training must cover these joint cases — not arbitrary pairs.
Coverage at one glance
4 × 3 = 12 possible (o₁, c₂) cases. Budget stays at 12 tasks; only how many relation cases appear changes.
c₂=1
c₂=2
c₂=3
o₁
Filled: 12 observed pairs. Ringed: the (milk, mug) example.
Dependent pairs observed
12 / 12
All relation cases appear at least once.
Training budget (fixed)
Always 12 tasks. Broader coverage spreads demos; sparse coverage densifies them on fewer pairs.
OOD result
Broader dependent-pair coverage raises OOD success and lowers same-container violations.