Q3 — Cover Dependent Instruction Factors

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.

Coverage

c₂=1

c₂=2

c₂=3

o₁

Filled cells = an illustrative spread of 12 observed pairs for this Cov level (schematic order, not the true experimental identity). Ringed cell = the (milk, mug) example from the task above.

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.

OOD success

OOD same-container violation

± SE

Selected coverage

Caveat: with a fixed budget, concentrating demos on fewer pairs can favor seen (ID) combinations. Intermediate ID points are noisy — the clean signal is the OOD relational gain above.

36-task Dependent 2S-PP (l4_2s_no_cont0). Means ± SE across seeds. Cov4 / Cov6 / Cov9 / Cov12 keep 12 training tasks while varying observed (o₁, c₂) pairs.