Generality

CoPhy · Blocktower

From a single collision to a falling tower.

Multibody interactions test how the same training principle behaves across scene geometry and different prediction models.

4 learner familiesone multibody setting

Motion preview

Physics demonstration · surface push · ½ speedCoPhy: Fabien Baradel et al. · surface-push demonstration. Source & changes

Across independent experiences

What persists.

Matched objects under the scene-specific relation.

Across distinct realizations

What changes.

Independent support interactions.

Experience → prediction

The task.

Three support histories + three query frames.

→ Multibody motion, including falling and stability.

Evaluated instance

The comparison.

JEPA / CPC / RSSM: Cross. CoPhyNet: Align + Cross.

Controls. Native; Random; Structure where tested.

Interpreting the evidence

What stays fixed in the test.

The common S3/query3 task and frozen visual frontend remain fixed; the matrix preserves learner-specific objectives.

What this setting establishes.

Blocktower contributes a multibody scene to the full learner–environment matrix and reader-design analysis.

Scope of the evidence

Breadth is not a claim of uniform improvement in every matrix cell. The display uses official Blocktower world and cube functions with documented demonstration initial states and a 30 Hz output rate; it is separate from our evaluated trajectories.

Full result record

Measurements and comparisons.

Reported results are kept with their own populations and conditions. Development, held-out and sealed comparisons remain separate.

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Full CoPhy learner × scene matrix

S3/query3 development; source100/head100; source coverage explicit

Trajectory MSE ↓; support and reader-memory probe R² where reported

Full CoPhy learner × scene matrix
Group	Scene	Family	Native	Structure	SPRII	Random
Cross: self-supervised dynamics objectives	Balls	JEPA	1.2563	1.2630	1.2396	1.5827
Cross: self-supervised dynamics objectives	Balls	CPC	1.4399	1.4239	1.5042	1.6228
Cross: self-supervised dynamics objectives	Balls	RSSM	1.3105	1.2582	1.1254	1.3155
Cross: self-supervised dynamics objectives	Collision	JEPA	0.2512	0.2212	0.2297	0.2717
Cross: self-supervised dynamics objectives	Collision	CPC	0.2448	0.2283	0.1778	0.2220
Cross: self-supervised dynamics objectives	Collision	RSSM	0.2731	0.2338	0.1970	0.2192
Cross: self-supervised dynamics objectives	Blocktower	JEPA	0.0931	0.0878	0.0865	0.0863
Cross: self-supervised dynamics objectives	Blocktower	CPC	0.1030	0.0991	0.0995	0.1007
Cross: self-supervised dynamics objectives	Blocktower	RSSM	0.0974	0.0935	0.0943	0.0942
Align + Cross: supervised CoPhyNet objective	Balls	CoPhyNet	1.0534	–	1.0056	1.0698
Align + Cross: supervised CoPhyNet objective	Collision	CoPhyNet	0.2033	–	0.2184	0.2171
Align + Cross: supervised CoPhyNet objective	Blocktower	CoPhyNet	0.0871	–	0.0882	0.0862

Bold marks the lowest reported mean only within each scene × learner row.

Dashed rules separate scenes and the supervised CoPhyNet block.

Align + Cross: supervised CoPhyNet objective · BallsA dash is an unevaluated arm. Development source 0 is not the held-out Collision benchmark.

The full source-0 development matrix retains favorable and adverse comparisons. SPRII uses Cross for JEPA/CPC/RSSM and Align + Cross for CoPhyNet. A dash is an unevaluated arm. These validation cohorts differ from the held-out Collision test.

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Full CoPhy learner × scene matrix

S3/query3 development; source100/head100; source coverage explicit

Trajectory MSE ↓; support and reader-memory probe R² where reported

Full CoPhy learner × scene matrix
Group	Arm	MSE src 0	MSE src 1	MSE src 2	Support R² src 0	Support R² src 1	Support R² src 2	Reader R² src 0	Reader R² src 1	Reader R² src 2
JEPA / Balls	Native	1.2563	1.3185	—	0.7977	0.7981	—	0.7865	0.7778	—
JEPA / Balls	Structure	1.2630	1.2944	—	0.7855	0.7866	—	0.7832	0.7788	—
JEPA / Balls	Cross	1.2396	1.3054	—	0.9162	0.9185	—	0.9051	0.9116	—
JEPA / Balls	Random	1.5827	1.6436	—	0.6777	0.6918	—	0.6884	0.6823	—
JEPA / Collision	Native	0.2512	0.2444	—	0.4431	0.4366	—	0.5657	0.5619	—
JEPA / Collision	Structure	0.2212	0.2238	—	0.5976	0.6246	—	0.6659	0.6706	—
JEPA / Collision	Cross	0.2297	0.2154	—	0.6422	0.6718	—	0.6451	0.6713	—
JEPA / Collision	Random	0.2717	0.2645	—	0.5005	0.5250	—	0.5286	0.5502	—
JEPA / Blocktower	Native	0.0931	0.0895	—	0.1028	0.0902	—	0.0430	0.0467	—
JEPA / Blocktower	Structure	0.0878	0.0876	—	0.1252	0.1301	—	0.0714	0.0879	—
JEPA / Blocktower	Cross	0.0865	0.0876	—	0.1761	0.1564	—	0.1242	0.0860	—
JEPA / Blocktower	Random	0.0863	0.0853	—	0.1673	0.1678	—	0.1256	0.1154	—
CPC / Collision	Native	0.2448	0.2517	—	0.4372	0.4213	—	0.5604	0.5484	—
CPC / Collision	Structure	0.2283	0.2323	—	0.6126	0.5929	—	0.6476	0.6367	—
CPC / Collision	Cross	0.1778	0.1841	—	0.7495	0.7411	—	0.7541	0.7419	—
CPC / Collision	Random	0.2220	0.2212	—	0.6657	0.6588	—	0.6717	0.6711	—
RSSM / Collision	Native	0.2731	0.2674	0.2729	0.334	0.240	0.344	0.497	0.494	0.477
RSSM / Collision	Structure	0.2338	0.2332	0.2273	0.564	0.565	0.570	0.627	0.642	0.634
RSSM / Collision	Cross	0.1970	0.1997	0.2112	0.738	0.723	0.733	0.736	0.719	0.724
RSSM / Collision	Random	0.2192	0.2199	0.2284	0.633	0.643	0.634	0.678	0.669	0.664

Bold identifies Cross prediction errors, including adverse cells; it is not a winner mark.

Dashed rules separate learner × scene groups.

JEPA / Balls · NativeSource columns remain separate. Support R² and reader-memory R² are accessibility assays, not error metrics.

Source coverage is explicit; dashes denote unevaluated cells. Support and reader-memory probes target restitution in Balls, mass in Collision, and vertical gravity in Blocktower. These development cohorts include selection examples and remain separate from the held-out test.

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Frozen-source reader design across scenes

Source-50/head-100; source seed 0; full validation

Relative error reduction versus Native (%) ↑

Frozen-source reader design across scenes
Reader recipe	Balls	Collision	Blocktower
Main initialization, dropout 0.1, initial	-5.448	-4.089	-1.224
Alternative initialization, dropout 0	+7.506	-2.104	-1.477
Alternative initialization, dropout 0.1	+6.074	-4.426	+2.090
New initialization, dropout 0	+0.617	-7.591	+0.621
New initialization, dropout 0.1, every step	+6.646	-2.925	+1.134

Bold marks sign reversals across reader recipes in Balls and Blocktower.

Main initialization, dropout 0.1, initialPositive is an error reduction versus Native. Each row is one shared recipe across scenes; the best cell per scene is not a common selected model.

Every row is one shared reader recipe across all three scenes, using the same frozen source-50 checkpoint. Positive is lower error than Native. The sign varies by scene and recipe; separately selecting each scene’s best cell would change the comparison.

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Complete follow-up outcomes

Separate configurations and populations shown row by row

MSE ↓, except FHN relative L₂ ↓

Complete follow-up outcomes
Configuration	Coverage	Numerical comparison	Finding / scope
JEPA Collision: J2	1,994 test episodes; 3 J2 seeds, 1/control	J2 0.184110 ± 0.005443; Structure 0.214314	Matched-only retest. Four arms and fixed-model interval: Table tab:jepa-collision-followup.
CoPhyNet Collision: Cross	4,000 development recipients; seed 0	Cross 0.203240; prior SPRII 0.210671	Near Native; paired interval against Native includes zero.
CPC Balls: Align	2,000 development recipients; seed 0	Align 1.392711; prior SPRII 1.415352; Structure 1.387643	Lower than prior SPRII, higher than Structure. Full contrasts are indexed in the package.
FHN: tuned SPRII	Report ICs 15/24/45; source 42; selection IC 5 excluded	ID K=4,H=50: SPRII 0.020132; extra-50k NOD 0.021522	Paired-system interval includes zero; other eight split/horizon cells have higher error. Extra-budget control.
Poke object-only: R8 / G2	400 development systems; source 0, reader 0; H=16	R8: M2 0.901091; M1 0.902588; recipient-only 0.911791. M2-M1: -0.001497 [-0.011855,0.008400]. G2: M2 0.913197; M1 0.908531; recipient-only 0.908021	Four-dimensional object-state error; M1 and M2 selected independently.
CoPhyNet Blocktower	8,088 development recipients; seed 0	SPRII 0.088180; Native/Structure 0.087114; Random 0.086230. SPRII-Random: 0.001951 [0.000668,0.003184]	Paired interval versus Structure includes zero; Random has lower mean error.

Bold identifies each follow-up configuration; heterogeneous numerical cells are deliberately not ranked.

Dashed rules separate experiments with different populations and fitted-model coverage.

All completed follow-ups from the configuration round are retained, including null and adverse results. Each row has its own population and model coverage. Paired intervals condition on the reported fitted models; the one-source development rows do not replace the original multi-source comparisons.