4DGS-JEPA: Temporally Compositional Joint-Embedding Prediction for Dynamic Gaussian Splatting

• Reconstruction and interpolation of observed sequences do not necessarily yield reusable dynamics that can roll beyond the observations.Source: §1 · p. 1
• 4DGS-JEPA predicts future embeddings from causal scene prefixes using a hierarchical Gaussian-native state and horizon-conditioned transitions.The state has scene-, motion-group-, and Gaussian-level tokens, supporting both direct prediction and recursive rollout.Source: §1 · p. 2
• Different chronological transition paths to the same endpoint should yield compatible states, with endpoint and path supervision anchoring predictions to future targets.Explicit temporal composition suppresses residual dependence on the path used to reach an endpoint.Source: §1 · p. 2
• A selective geometry decoder and geometry-level composition ground latent dynamics in group motion and Gaussian deformation without requiring complete future appearance reconstruction.Direct and recursively decoded motions are required to agree at motion-group and Gaussian levels.Source: §1 · p. 2
• Unlike recent Gaussian world models centered on future-scene generation, 4DGS-JEPA makes joint-embedding prediction and consistency across temporal paths explicit learning principles.Source: §1 · p. 2
• Hybrid correspondence preserves reliable canonical identities and uses residual optimal transport for ambiguity from reordering or topology change.Source: §1 · p. 2
• The paper characterizes zero-loss path agreement and finite-error rollout bounds, and evaluates temporal composition, decoded geometry composition, and hybrid correspondence separately.Source: §1 · p. 2

2 RELATED WORK

• The positioning distinguishes 4DGS-JEPA by combining Gaussian-native prediction, joint-embedding supervision, and explicit path consistency without making full future reconstruction central.Source: §2 · p. 3

2.1 DYNAMIC GAUSSIAN SCENE REPRESENTATIONS

• 3DGS represents static scenes, while dynamic Gaussian methods model time-varying attributes and often optimize reconstruction or interpolation over observed sequences.4DGS-JEPA instead forecasts from a causal prefix without reconstructing every future pixel or Gaussian attribute.Source: §2.1 · p. 3

2.2 GAUSSIAN WORLD MODELS AND FORECASTING

• Gaussian world models support explicit future prediction, but rely substantially on future-state generation or reconstruction supervision.4DGS-JEPA predicts future target embeddings and uses selective geometry decoding rather than complete future appearance reconstruction.Source: §2.2 · p. 3
• The Structured 4D Latent Predictive Model predicts future 3D structure in a general latent space, whereas 4DGS-JEPA is Gaussian-native and regularizes alternative prediction paths.Source: §2.2 · p. 3

2.3 JOINT-EMBEDDING PREDICTIVE LEARNING

• JEPA methods predict target embeddings across images, video, and robotic planning; VJEPA extends this direction to predictive distributions over future latent states.4DGS-JEPA instead focuses on explicit Gaussian scenes and temporal composition.Source: §2.3 · p. 4

3.1 PROBLEM SETUP AND CAUSAL GAUSSIAN STATES

• The prediction branch uses only observations through context time t; future observations construct training targets, and controlled experiments use generated Gaussian states while learned online front-end evaluation is left to future work.A Gaussian representation fitted jointly over the complete sequence could leak future information into the context state.Source: §3.1 · pp. 4–5

3.2 HIERARCHICAL STUDENT–TEACHER PREDICTIVE STATE

• A hierarchical student encoder represents scene-, motion-group-, and Gaussian-level state, while an EMA teacher encodes future histories for training targets.The teacher is not needed at inference; the encoder is permutation equivariant over primitives and pools Gaussian tokens into group tokens, then a scene token.Source: §3.2 · pp. 5–6

3.3 HORIZON-CONDITIONED LATENT TRANSITION

• The horizon-conditioned transition consumes and returns the same hierarchical predictive state, enabling recursive rollout and temporal composition.Relative horizon conditions each transition; absolute start time can also condition explicitly non-autonomous dynamics, and actions are optional.Source: §3.3 · p. 6

3.4 HIERARCHICAL LATENT DISTANCE

• A hierarchical latent distance compares scene, group, and Gaussian representations using correspondence-weighted matches, capturing global evolution, coherent group motion, and local deformation.Correspondences may be persistent identities or soft matches because Gaussian primitives need not be index-aligned across time.Source: §3.4 · p. 7

3.5 DIRECT MULTI-HORIZON SUPERVISION

• Direct multi-horizon supervision anchors predicted future representations to teacher targets without requiring reconstruction of future appearance.Horizon weights can emphasize nearer or farther futures; experiments cycle uniformly through supervised terminal horizons and do not separately ablate the weighting parameter γ.Source: §3.5 · p. 7

3.6 MULTI-HORIZON PATH SUPERVISION

• Multi-horizon path supervision anchors intermediate recursively predicted states to corresponding future teacher states, exposing transitions to rollout states and reducing the gap between training and recursive inference.A sampled temporal partition divides each terminal horizon into shorter transitions.Source: §3.6 · p. 8

3.7 TEMPORAL COMPOSITION CONSISTENCY

• Temporal composition requires direct and recursively composed predictions reaching the same future endpoint to agree, while target anchoring is needed to connect their agreement to accurate future representations.The constraint applies across admissible decompositions of the same controlled evolution, not as an exact semigroup law; zero path and composition losses establish path agreement on supervised matched support, and rollout errors can accumulate through later transition Lipschitz factors.Source: §3.7 · pp. 8–9

3.8 GEOMETRY-AWARE SELECTIVE DECODER

• The selective geometry decoder grounds latent transitions in explicit Gaussian evolution without reconstructing complete future appearance, decomposing updates into group motion, local deformation, covariance change, and existence.It decodes group rigid-motion increments and Gaussian-level displacement, log-deformation, and endpoint existence probabilities.Source: §3.8 · pp. 9–10
• The selective decoder combines group transforms with Gaussian-specific residual displacement, transports covariance and appearance, and supervises endpoint position, shape, and existence without reconstructing full future appearance.Decoded Gaussian states also serve as the source state for the next segment in a composed rollout.Source: §3.8 · pp. 10–11

3.9 GEOMETRY-LEVEL COMPOSITION AND STRUCTURAL REGULARIZATION

• Geometry-level composition aligns direct and chronologically composed SE(3) transforms and matched Gaussian centers, covariances, and existence, reducing finite-error path discrepancies beyond target-anchored geometry supervision.When both decoded paths exactly match the same target under unambiguous correspondence, their endpoint geometries agree; the consistency term regularizes residual differences when predictions have finite error.Source: §3.9 · pp. 12–13
• Prefix-derived soft priors preserve pairwise distances in rigid groups, smooth only compatible non-rigid residuals, and limit static-region drift, weakening rigidity and static penalties for nonrigidity or topology change.The smoothness prior regularizes residual motion rather than the complete motion, leaving coherent group-level rigid transformations unpenalized.Source: §3.9 · pp. 14–15

3.10 REPRESENTATION REGULARIZATION AND FULL OBJECTIVE

• Variance and covariance regularizers at scene, motion-group, and Gaussian levels discourage collapse and redundant dimensions; the default objective omits pixel-rendering and complete future-appearance reconstruction losses.These regularizers constrain the representation rather than specifying the future state to predict.Source: §3.10 · p. 15

Hybrid correspondence

• The hybrid scheme fixes matches for valid persistent identities, uses motion groups as intermediate constraints, and applies residual optimal transport when identity is uncertain or topology changes.Its design rule is reliable identity → fixed correspondence; uncertain or invalid identity → residual soft matching.Source: §4 · p. 16

Canonical identity

• A prefix-anchored canonical bank preserves slot identities causally, while reserved inactive slots can represent newly emerging geometry.The bank is constructed from observations available through the context endpoint; future observations do not revise earlier bank states.Source: §4 · p. 16

Motion-group correspondence

• Motion groups provide a more stable intermediate correspondence when primitive identities become uncertain under refinement, occlusion, splits, or merges.Group identity can remain stable even when its supporting Gaussian primitives change.Source: §4 · p. 17

Residual optimal transport

• Residual transport uses spatial, semantic, covariance, and group compatibility, with entropy regularization allowing soft matches when correspondence is ambiguous.Semantic cost is omitted when semantic features are unavailable.Source: §4 · pp. 17–18

Topology changes

• Soft residual matching permits one-to-many and many-to-one assignments without claiming to identify the true lineage, while dustbins absorb genuinely unmatched mass.New geometry may first use an available inactive canonical slot; the dustbin is a fallback for geometry that remains unmatched.Source: §4 · pp. 16, 18

Why correspondence is needed

• Because Gaussian array order does not define identity, index-wise comparison can penalize equivalent scenes after reordering, splitting, merging, pruning, or relocation.The resulting comparison is invariant to raw array permutation while remaining sensitive to reliable canonical correspondence.Source: §4 · pp. 15, 16, 19

5.1 CONTROLLED DYNAMIC GAUSSIAN WORLDS

• Procedurally generated Gaussian trajectories provide exact future geometry and motion-group identity, enabling controlled tests; large-scale benchmarks and planning are left to future evaluation.Experiments 1 and 2 retain active primitives with fixed identities, while Experiment 3 introduces correspondence changes separately.Source: §5.1 · p. 19, §5 · p. 19

5.2 EXPERIMENT 1: PATH SUPERVISION AND TEMPORAL COMPOSITION

• Endpoint + Path reduces CompErr from 0.00244 to 0.00065, even without directly minimizing the direct–composed discrepancy through Lcomp, consistent with both routes anchoring toward common future teacher states.On held-out partitions made from seen segment lengths, the full model reduces CompErr from 0.01134 for Endpoint to 0.00260; for harder decompositions with unseen segment lengths, CompErr decreases from 0.00235 to 0.00057.Source: §5.2 · pp. 21–22
• Endpoint + Composition reduces CompErr by 60.6% (0.00244 to 0.00096), while lowering direct FDE from 0.03013 to 0.02905 and rollout FDE from 0.03061 to 0.02940.The horizon-wise results jointly assess target accuracy and path consistency; low CompErr alone does not establish accurate future prediction.Source: §5.2 · p. 21, Figure 2 · p. 22

5.3 EXPERIMENT 2: DOES LATENT COMPOSITION TRANSFER TO GAUSSIAN GEOMETRY?

• At ∆=8, +SE(3) composition lowers Edc_T from 0.00724 to 0.00202, while full geometry composition lowers Dmatch from 0.00192 to 0.00130.Group-level composition most strongly aligns structured motion; adding Gaussian-level matching further reduces primitive-level discrepancy and encourages a common motion explanation across temporal paths.Source: §5.3 · pp. 23–24
• At ∆=8, learned variants obtain FDE between 0.06614 and 0.06728, outperforming constant velocity at 0.07120 while geometry composition changes endpoint FDE only slightly.Relative to latent composition alone, the SE(3) and full variants increase direct FDE by approximately 0.9% and 1.7%, respectively, while improving target-relative structured-motion accuracy by approximately 2.2% and 2.1%.Source: §5.3 · p. 23

5.4 EXPERIMENT 3: HYBRID CORRESPONDENCE UNDER IDENTITY PERTURBATIONS

• Experiment 3 stress-tests matching under permutation, splits, merges, deaths, and births, comparing index matching, OT-only matching, and hybrid identity-preserving residual OT.Hybrid matching fixes valid persistent correspondences and applies residual OT only to unmatched or ambiguous mass; the supplied passages describe the test setup but provide no outcome values.Source: §5.4 · p. 24
• At severity 0.25, Hybrid raises LineageMass from 0.95148 to 0.95988 and lowers geometry discrepancy from 0.06502 to 0.06349 versus OT, with margins narrowing at higher severity.Hybrid maintains higher LineageMass and lower geometry discrepancy than OT at every evaluated severity; the shrinking margin is consistent with more canonical identities becoming invalid and greater reliance on residual OT.Source: Figure 4 · p. 25, §5.4 · pp. 25–26
• Under permutation, Index obtains 0.04056 LineageMass versus OT’s 0.99789 and Hybrid’s 1.00000, and its 0.74311 aggregate geometry discrepancy is over an order of magnitude higher than either correspondence-aware method.The scene is unchanged by permutation, showing that raw primitive array position is not a valid persistent canonical identity.Source: §5.4 · p. 25
• For split/merge events, Hybrid improves LineageMass from OT’s 0.98100 to 0.98715 and reduces aggregate geometry discrepancy from 0.05010 to 0.04906; both methods attain perfect F1 for isolated births and deaths.The Hybrid advantage is concentrated in lineage preservation and induced geometry correspondence, rather than isolated birth/death F1.Source: §5.4 · p. 25
• As hidden identities increase from 0 to 0.5, Hybrid LineageMass falls from 0.95988 to 0.95649 and geometry discrepancy rises from 0.06349 to 0.06409, approaching OT-only values of 0.95148 and 0.06502.This tests the intended fallback: Hybrid uses persistent identity when reliable and shifts toward residual OT as identity information is removed.Source: §5.4 · p. 26

5.5 SUMMARY AND SCOPE

• Across the three experiments, temporal composition reduces latent path dependence, explicit group- and Gaussian-level composition reduces decoded-motion path dependence, and hybrid correspondence handles reordering and topology change.The summary also reports that path supervision further reduces recursive rollout drift and that hybrid correspondence falls back smoothly toward residual OT when persistent identity is unavailable.Source: §5.5 · p. 26
• The results are controlled proof-of-concept evidence on procedurally generated Gaussian dynamics, not evidence of large-scale superiority; evaluation on real scenes, action-conditioned environments, larger Gaussian sets, appearance-sensitive prediction, probes, and planning remains future work.The procedural benchmark provides known future geometry, motion-group transformations, temporal decompositions, and lineage.Source: §5.5 · p. 26

6 DISCUSSION

• The predictive state uses scene-, motion-group-, and Gaussian-level tokens, with endpoint, path, and composition losses supporting direct prediction, rollout, and reduced path dependence.The transition is closed in the predictive state space, and the selective geometry decoder grounds dynamics without requiring complete future-scene reconstruction.Source: §6 · pp. 26–27
• Combining path supervision with temporal composition gives the smallest rollout gap and strongest path consistency, including on held-out temporal decompositions.Composition alone reduces direct–composed discrepancy while preserving target-relative accuracy; it does not by itself establish target correctness.Source: §6 · p. 26
• Explicit geometry composition reduces group-transform path discrepancy by 72.2% at ∆= 8 and Gaussian-level direct–composed discrepancy by 32.5%, with only a small change in endpoint FDE.These findings distinguish latent consistency from decoded geometric consistency.Source: §6 · p. 27
• Hybrid correspondence exactly recovers permutation correspondence in the controlled setting and modestly improves lineage preservation and induced geometry correspondence under split, merge, and mixed perturbations.As persistent identities are removed, Hybrid approaches OT-only behavior smoothly.Source: §6 · p. 27
• The evidence is mechanism-level: Experiments 1–2 use procedurally generated Gaussian states, while Experiment 3 evaluates correspondence independently of the learned transition.The experiments do not establish benefits of the full hierarchy, learned existence dynamics, appearance preservation, or action-conditioned planning; physical correctness and calibrated uncertainty also remain unestablished.Source: §6 · p. 27

7 CONCLUSION

• A hierarchical Gaussian-native predictive state and horizon-conditioned transition support direct prediction and recursive rollout, while selective geometry decoding predicts variables needed for geometric dynamics without complete future appearance reconstruction.The hierarchy spans scene, motion-group, and primitive levels.Source: §7 · p. 27
• Controlled experiments provide proof-of-concept evidence that temporal composition reduces latent path dependence, geometry composition improves decoded-motion consistency, and hybrid correspondence preserves relationships through ordering or topology changes.The conclusion points to reconstructed real scenes, multimodal futures, richer interactions, and action-conditioned prediction as future directions.Source: §7 · p. 27

A.1 INTUITION AND OPERATOR INTERPRETATION

• Temporal composition compares admissible routes over the same elapsed time, penalizing disagreement between direct and composed predictions of the same endpoint.For example, an endpoint at t + 6 can be reached directly or through intermediate horizons.Source: §A.1 · p. 29
• The composition property is approximate, not an assumption that transitions form an exact semigroup.Symmetric stop-gradient terms reverse which route receives gradients without changing their numerical discrepancy.Source: §A.1 · p. 29
• Composition consistency alone does not guarantee target correctness; endpoint and path losses anchor predictions to future targets while composition reduces route dependence.Direct and composed predictions could agree while both remain inaccurate.Source: §A.1 · p. 29

A.2 PROOF OF PROPOSITION 1

• Under zero path loss and zero composition loss with positive composition weights, direct prediction, composed prediction, and the future target agree on supervised matched support.This is the idealized zero-loss case described by Proposition 1.Source: §A.2 · pp. 29–30

A.3 FINITE-ERROR ROLLOUT ACCUMULATION

• The finite-error rollout bound separates initialization mismatch, local transition approximation errors, and their amplification by subsequent Lipschitz factors.It assumes locally Lipschitz segment transitions and bounded local approximation error on the relevant state region.Source: §A.3 · pp. 30–31
• Path supervision primarily addresses recursive target accuracy, whereas composition constrains discrepancy between recurrent states and corresponding direct predictions.The two losses therefore address complementary effects in finite-error rollout.Source: §A.3 · p. 31

B TRAINING PROCEDURE

• Each minibatch samples one terminal horizon and temporal partition; the controlled experiments use restricted versions of the procedure, and Experiment 3 has no optimization.Experiments 1–2 do not backpropagate through Sinkhorn matching; they use fixed persistent correspondence, while Experiment 3 evaluates residual OT independently.Source: B TRAINING PROCEDURE · p. 31

C.1 EXPLICIT GAUSSIAN SCENE REPRESENTATION

• A 3DGS scene is an explicit set of anisotropic Gaussian primitives, whose covariance specifies spatial extent and orientation, opacity controls visibility, and appearance coefficients parameterize view-dependent color.Each primitive represents an oriented ellipsoidal density in 3D.Source: §C.1 · p. 32

C.2 PROJECTION AND ALPHA COMPOSITING

• Gaussian rendering projects primitives through a camera and approximately depth-orders their image-space footprints before front-to-back alpha compositing.Differentiable projection and compositing allow Gaussian parameters to be fitted from image observations.Source: §C.2 · pp. 32–33
• Gaussian reconstruction and rendering are distinct mappings.The supplied passage identifies this distinction but does not specify the mappings further.Source: §C.2 · p. 33

C.3 DYNAMIC GAUSSIAN STATES AND PREDICTIVE DYNAMICS

• The primary learning target is a future representation rather than a rendered future image.The selective geometry decoder provides an interface to future Gaussian motion without complete appearance reconstruction.Source: §C.3 · p. 33
• Experiments 1 and 2 use explicit Gaussian states directly, bypassing reconstruction and rendering to isolate predictive-dynamics errors.Their protocol uses no camera projection, rasterization, RGB reconstruction loss, PSNR, or perceptual image metric.Source: §C.3 · p. 33
• The predictive task is to model causal evolution of a Gaussian-world state, not to reconstruct or query the representation at observed timestamps.The time-indexed Gaussian primitive includes center, covariance, opacity, appearance coefficients, semantic features, and existence.Source: §C.3 · p. 33

D EXPERIMENTAL DETAILS AND ADDITIONAL RESULTS

• Experiments 1 and 2 share a procedural Gaussian-world model and architecture, while each variant is trained independently from initialization.All three experiments ran in Colab with an NVIDIA A100; Experiment 3's NumPy correspondence computations did not require GPU acceleration.Source: D EXPERIMENTAL DETAILS AND ADDITIONAL… · pp. 33–34
• Experiment 3 isolates hybrid correspondence under permutation, split, merge, birth, death, and mixed topology events, with no learned transition or model optimization.Ground-truth lineage is retained for evaluation but hidden from the correspondence procedures.Source: D EXPERIMENTAL DETAILS AND ADDITIONAL… · p. 34
• Experiments 1 and 2 use fixed persistent identities, whereas Experiment 3 tests whether hybrid matching preserves canonical identity when available and degrades toward residual optimal transport as it is removed.Correspondence evaluation uses LineageMass, birth/death detection, and correspondence-induced geometry discrepancy, and is invariant to arbitrary storage ordering.Source: D EXPERIMENTAL DETAILS AND ADDITIONAL… · p. 34

D.1 COMMON CONTROLLED SETUP FOR EXPERIMENTS 1 AND 2

• The generator creates three motion groups with six Gaussians each, combining nonlinear group motion and smooth local deformation; half of scenes include a static group.Train, validation, and test scenes use disjoint seeds, and identities persist without permutation or topology events.Source: §D.1 · p. 34

D.1.1 CAUSAL MOTION-AWARE ENCODER

• The causal motion-aware encoder uses separate geometry and motion-feature branches, then pools Gaussian tokens into group tokens and group tokens into a scene token.The controlled decoder predicts group rotation and translation plus per-Gaussian residual displacement and scale deformation; existence is fixed, with appearance and semantic attributes absent.Source: §D.1.1 · pp. 34–35

D.1.2 REPRESENTATION REGULARIZATION

• Representation regularization is applied at the scene, motion-group, and Gaussian-token levels to both current and direct-predicted representations.Its outer objective weight is 0.02 in both experiments.Source: §D.1.2 · p. 36

D.1.3 CHECKPOINT SELECTION

• Checkpoints are selected by validation target-relative accuracy averaged over direct and rollout FDE across horizons 1, 2, 4, and 8, not by composition metrics.Table 7 covers unseen temporal decompositions, averaged over three seeds, with lower values better.Source: §D.1.3 · p. 36, Table 7 · p. 37

D.2 EXPERIMENT 1: TEMPORAL COMPOSITION

• The four ablation variants share the same data, architecture, EMA teacher, selective decoder, optimization budget, and representation regularization.Geometry supervision is applied only to the direct decoded route, and geometry-level composition is disabled throughout Experiment 1.Source: §D.2 · p. 37
• Training uses horizons 1, 2, 4, and 8, while terminal horizons 3 and 6 are held out and decompositions including segment lengths 3 and 5 test unfamiliar transitions.The evaluation also includes new decompositions formed entirely from familiar segment lengths and held-out routes such as (4,2,2) and (2,2,2,2).Source: §D.2 · p. 37
• 0.00260 from 0.01134 for familiar-length new decompositions, and 0.00057 from 0.00235 with unseen segment lengths: the full path-and-composition model has the lowest CompErr.Table 7 reports generalization to temporal decompositions not used during training, averaged over three random seeds; lower is better.Source: §D.2 · p. 38

D.3 EXPERIMENT 2: GEOMETRY-LEVEL COMPOSITION

• At Δ=2, 4, and 8, explicit SE(3) composition reduces direct–composed transform error by about 72.4%, 76.3%, and 72.2%; the full objective reduces Dmatch by about 18.5%, 40.2%, and 32.5%.The motion-group term gives the strongest transform-level consistency, while the full objective gives the strongest primitive-level Gaussian consistency.Source: Table 8 · p. 39, §D.3 · p. 39
• The three learned geometry-composition variants retain low path discrepancies without predicting negligible motion; at Δ=8, their FDEs are 0.06614–0.06728.Static persistence has FDE 0.32158, while causal constant velocity has FDE 0.07120.Source: §D.3 · p. 39

D.4 EXPERIMENT 3: CORRESPONDENCE STRESS TEST

• Experiment 3 evaluates correspondence independently of the learned transition, using synthetic Gaussian states with known identities and lineage under permutation, topology changes, and semantic noise.The setup uses three Monte Carlo repetitions with 50 trials per perturbation type and severity.Source: §D.4 · p. 39

D.4.1 COUNT-AWARE RESIDUAL MATCHING

• Hybrid assigns valid unique persistent correspondences first, then applies count-aware residual OT to unmatched primitives; split and merge primitives are handled through residual OT.OT-only instead sends the complete source and target sets to the augmented OT problem.Source: §D.4.1 · p. 40

D.4.3 MIXED PERTURBATIONS

• At every evaluated severity, Hybrid retains more lineage mass and lowers geometry discrepancy than OT only, though the margin narrows as perturbations invalidate more persistent identities.Table 10 summarizes mixed permutation, split, merge, birth, and death perturbations across increasing severity.Source: Table 10 · p. 41, §D.4.3 · p. 41

D.4.2 METRICS AND UNCERTAINTY

• Split/merge confidence intervals are separated for OT only and Hybrid on both LineageMass and aggregate geometry discrepancy, consistent with a small systematic Hybrid advantage in this controlled benchmark.The reported intervals are not presented as a separate formal hypothesis test.Source: §D.4.2 · p. 41

D.4.4 PERSISTENT-ID DROPOUT

• As persistent IDs are progressively hidden, Hybrid moves smoothly toward the identity-agnostic OT-only solution rather than failing abruptly.The dropout test leaves geometry and ground-truth lineage unchanged.Source: §D.4.4 · pp. 41–42

E ADDITIONAL DISCUSSION AND LIMITATIONS

• The experiments are controlled mechanism-level tests, not a comprehensive world-model evaluation, and do not establish superiority over reconstruction-based Gaussian or video-space predictive models.Experiments 1 and 2 use procedurally generated Gaussian states; Experiment 3 uses synthetic identity and topology perturbations with known lineage.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 42
• Path agreement alone does not establish future correctness or an exact semigroup law; target-relative supervision and admissible chronological decompositions remain necessary.Actions, absolute time, contacts, and topology changes can alter the relevant transition.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 42
• Robustness to errors from a real online Gaussian front end and performance in action-conditioned prediction, control, or planning are not established.The experiments supply Gaussian states directly and evaluate passive forecasting and correspondence.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · pp. 42, 44
• A deterministic transition returns one future for a fixed context, horizon, and action sequence, so multimodal futures may be averaged or represented by only one trajectory.Probabilistic or multimodal latent prediction is identified as a natural extension.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · pp. 42–43
• Residual correspondence can remain ambiguous for similar primitives, and the finite reserved-slot bank could be exhausted by sufficiently much newly represented geometry.The experiments also do not evaluate residual OT inside end-to-end predictive training.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 43
• Group motion and local residual deformation are not identifiable from endpoint geometry alone, and the structural priors are neither universal physical laws nor separately evaluated in these experiments.Composition encourages a common decomposition across paths but does not establish that it is uniquely or physically correct.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 43
• The experiments focus on geometry rather than appearance and do not establish future view-dependent appearance retention or rendering accuracy.They omit camera projection, rasterization, RGB supervision, PSNR, and perceptual image metrics.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 43
• Large-scene computational efficiency is untested; attention over large Gaussian sets and residual OT matching may become expensive.The controlled experiments use small Gaussian sets and known motion groups.Source: E ADDITIONAL DISCUSSION AND LIMITATIONS · p. 43