Toward Physically Grounded JEPA World Models for Goal-Conditioned Robotic Planning
1. Paper overview
In one sentence: Training a JEPA world model to recover physical state as well as actions improves its reported image-goal planning, while its latent trajectories become less straight on average. e2e4e6e8e10e11
| At a glance | What to know |
|---|---|
| Research problem | Source description Predicting future embeddings avoids pixel reconstruction, but constant embeddings can minimize prediction loss. Recovering actions discourages full collapse without directly specifying which physical configuration and motion information the representation must preserve. The paper asks whether measured-state supervision supplies a useful complementary constraint for image-goal planning. e2e4 |
| Core mechanism | Source description A pair-based state-alignment objective complements latent prediction and inverse dynamics in an end-to-end world model; physical measurements supervise training only. e4 |
| A key reported result | PushT goal-conditioned planning: SA+IDM: 98% Planning success rate (%). Same fixed-problem protocol; auxiliary weights selected using the PushT validation split. Exact evaluation split membership is not restated. IDM 83%; DINO-WM 74%; PLDM 78%; LeWorldModel 96%. Fifteen percentage points above IDM and two above the strongest listed baseline; no uncertainty supports a significance claim. e7e8 |
| Reading caution |
Core contributions
- Source description
A pair-based state-alignment objective complements latent prediction and inverse dynamics in an end-to-end world model; physical measurements supervise training only. e4
- Reader analysis
The IDM-only ablation supports consistent gains from state alignment across four tasks. Transition analysis shows that greater average straightening can accompany lower effective transition dimension and weaker planning; it does not establish dimension as the causal mediator. e8e10e11e12
Figure 1. Three training objectives shape one visual representation; latent prediction supplies the deployment world model. Original paper, p. 2 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start with the middle observation: E maps it to z_t, and the blue F branch combines that embedding with action a_t to predict the next embedding. Its MSE target comes from encoding the next observed image. Follow the red arrows into H: they carry z_t and the observed z_{t+1}, matching Equation (4). Follow the green arrows into G: they carry z_{t-1} and z_t to predict s_t, matching Equation (5). The dashed blue branch depicts prediction at the preceding time step, as the caption states. It is not a stop-gradient or frozen-target marker. All three MSE terms enter the weighted training objective. e3e4e5e6e7
What it supports. State alignment asks an adjacent image pair to preserve configuration and motion information, while inverse dynamics asks a pair to preserve action information. This is a training constraint on E. The deployed planner searches actions through E and F; neither auxiliary head is used to decode a policy action.
Where the evidence stops. The schematic shows one-step prediction; the implementation uses up to three recent latent–action pairs. Full physical-state supervision is available in these experiments. The figure does not establish performance with incomplete or noisy state labels.
2. Motivation
2.1 The problem and the proposed response
Predicting future embeddings avoids pixel reconstruction, but constant embeddings can minimize prediction loss. Recovering actions discourages full collapse without directly specifying which physical configuration and motion information the representation must preserve. The paper asks whether measured-state supervision supplies a useful complementary constraint for image-goal planning. e2e4
2.2 What this reading follows
A robot can plan toward a goal image by comparing imagined future embeddings with the goal embedding. The difficult part is making those embeddings retain useful physical information. This paper trains the representation through three demands: predict what comes next, recover the action that occurred, and recover measured physical state. State measurements are required for training, while deployment uses image encoding and action-conditioned latent rollouts. The four-task results favor adding state alignment to inverse dynamics. The accompanying diagnostics provide a second lesson: a representation can have straighter temporal transitions yet plan less successfully. Read the architecture and success table together before interpreting the geometry plots. e2e4e6e8e10e11
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | Not assigned |
| Architecture | Not assigned |
| Prediction paradigm | Not assigned |
| Quadrant | Not assigned |
This table preserves the labels recorded at reading time. The current major category is WAMs. View the current classification.
3.1 Evidence-based assessment
Insufficient evidence to decide
The recorded classification is entirely unassigned, leaving no existing quadrant to confirm. Architecturally, this is action-conditioned latent future prediction with auxiliary inverse dynamics and state regression. CEM supplies deployment actions through search. Joint training alone does not establish a One Model policy jointly generating futures and actions, and training-time H does not make deployment inverse-dynamics control. e4e5e6
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
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4.2 Equations and their role
5. Method in detail
5.1 Ask an observed pair two different physical questions
The training pair has two distinct roles. For inverse dynamics, H receives the current and next encoded observations and must recover the action chunk between them. If every image collapsed to the same embedding, every pair would look identical and H could only make a constant prediction. The source uses this argument to motivate action-sensitive representations. State alignment adds a different requirement: G receives the previous and current encodings and predicts the current physical measurements. The pair supplies temporal context for velocity in addition to configuration. Both objectives shape E through training, while F learns the action-conditioned transition. Reader interpretation: these constraints can preserve complementary information, but the improvement over IDM alone does not tell us whether pairing, particular state fields, or the extra regression supervision supplies the decisive benefit. e3e4e7e8
5.2 Turn a latent predictor into executed control through search
At deployment the encoder and predictor are fixed. Encode the current image and the goal image, then imagine the consequences of candidate action sequences by applying F recursively. The objective compares only each candidate's terminal latent prediction with the goal embedding using squared distance. CEM improves its candidate distribution using the best-scoring sequences, after which actions are executed and planning resumes from the updated observation. This separates the learned dynamics from the action optimizer: H's training-time action reconstruction is not the control rule. Figure 2 then shows observations from the resulting simulator execution, rather than images generated by a decoder. Reader interpretation: the success table tests the whole combination of representation, predictor and search, so it cannot attribute all gains to representation geometry independently of prediction and planning behavior. e4e6e8e9
5.3 Check how many directions make a trajectory look straight
Temporal straightening compares each displacement with the next using cosine alignment. It summarizes direction consistency, without asking whether the representation retains the physical quantities needed to reach a goal. The authors illustrate the issue with a rank-one limit: nonzero displacements can only point along one direction or its opposite, so infrequent reversals can coexist with a high average score. Their measured LeWorldModel representation is not rank one; Figure 4 instead reports a smaller effective transition dimension than either IDM variant. Table II and Table I show that its larger average straightening also accompanies lower OGBench-Cube success. Reader interpretation: the combined evidence motivates using straightening with transition-energy and planning diagnostics. It does not establish that increasing transition dimension will cause success to improve, or that state alignment's gains are mediated by dimension. e8e10e11e12
5.4 Training and inference
During training
G and H are two-layer MLPs with hidden widths 256 and 512, respectively. All components train jointly with AdamW. Actions and Euclidean state quantities are standardized per dimension using dataset statistics; angular quantities use continuous coordinates to avoid wrap-around. e5
The experiments supervise G with each task's full physical state. Tied weights α = β = 1.0 are selected from {0.01, 0.1, 1.0} using PushT validation planning success and reused across tasks. IDM-only sets α = 0, β = 1.0. e7e8
During inference
Freeze E and F, encode current and goal images, and recursively roll out candidate action sequences. CEM samples sequences, scores terminal latent distance and updates its distribution from elites. Execute the optimized sequence, observe again and replan until success or budget exhaustion. G, H and physical-state measurements are unnecessary at deployment. e4e6
5.5 Implementation flow
- Encode offline trajectories
A behavior-policy dataset pairs observations with physical measurements. Each action chunk contains a fixed number of low-level actions between observations. A randomly initialized ViT-Tiny/14 projects its CLS token to 192 dimensions. e3e5
- Predict latent dynamics
The encoder E produces z_t; predictor F uses actions to predict the next embedding. Its implementation is a six-layer causal Transformer with up to three recent latent–action pairs and 192-dimensional action embeddings injected through zero-initialized AdaLN at every layer. e4e5
- Ground consecutive representations
H receives the encoded pair (z_t, z_{t+1}) to recover action a_t. G receives (z_{t-1}, z_t) to predict physical measurements s_t. The temporal pair supplies context for velocity as well as configuration. These heads use observed embeddings, not F's predicted embeddings. e4
6. Experiments & results
SA+IDM trains an action-conditioned JEPA world model with two auxiliary heads: inverse dynamics recovers executed actions, while state alignment predicts measured physical state from consecutive image representations. Deployment uses only the encoder and latent predictor inside CEM planning. State alignment improves all four reported tasks over IDM alone, while the diagnostics challenge average temporal straightening as a sufficient representation-quality criterion (e2–e12).
6.1 Read the original evidence
Figure 2. A selected successful rollout compares the reference trajectory with observations after executing CEM actions in the simulator. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the top row as the reference connecting the specified start and goal observations. Read the bottom row as the simulator's response to the optimized actions. The intermediate robot poses differ across rows: the planning objective compares the terminal latent representation with the goal representation, rather than requiring frame-by-frame imitation of the reference. The percentage headings mark the displayed progression; they are not task-success percentages. The paper describes this example as reaching the image-defined goal within the evaluation budget. In the method, CEM generates candidate action sequences, F predicts their latent consequences, and actual execution produces the observations displayed here. e6e7e8e9
What it supports. This figure connects latent planning to executed simulator behavior. The images in the lower row are observations following actions, not pixel predictions from the model. It gives a concrete example of successful image-goal control; the aggregate frequency of success must be read from Table I.
Where the evidence stops. This is one selected successful simulator episode. The stills do not establish physical-robot transfer, failure frequency, continuous trajectory safety or planner runtime, and the percentages do not specify exact elapsed environment steps.
Table I. Adding state alignment raises all four reported success rates relative to IDM alone. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Compare the bottom two rows first: they are the paper's direct state-alignment ablation, with inverse-dynamics weight fixed at one. Read columns in order: TwoRoom, Reacher, PushT and OGB-Cube. Every cell is a success percentage. The caption specifies three independently trained seeds and 50 fixed planning problems per seed for the authors' variants. The setup uses goals 25 environment steps ahead and a 50-step interaction budget. Then compare the upper rows, remembering that their means are taken from LeWorldModel's report. Boldface marks the best value per column; TwoRoom includes a tie, and Reacher favors LeWorldModel by one point. e7e8
What it supports. SA+IDM improves over IDM by 6, 22, 15 and 2 percentage points across the four columns, respectively. It reaches 98% on PushT and 87% on OGB-Cube. These results support the usefulness of additional state supervision under the stated protocol, with the largest ablation gain on Reacher.
Where the evidence stops. No success standard deviations or confidence intervals are reported. Baseline means are imported, and PushT validation selected the shared auxiliary weights. Small numerical leads do not establish statistical significance; the table contains no SA-only or single-frame-SA control.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| TwoRoom goal-conditioned planning LeWorldModel benchmark protocol; 50 fixed start–goal problems per seed, three trained seeds; goals 25 environment steps ahead, 50-step interaction budget. | SA+IDM: 100% Planning success rate (%) | IDM 94%; DINO-WM 100%; PLDM 97%; LeWorldModel 87%. Six percentage points above IDM, tied with DINO-WM. Baseline means are imported; success uncertainty is unreported. e7e8 |
| Reacher goal-conditioned planning Same four-task protocol: 50 fixed problems per seed, three trained seeds, 25-step goal offset and 50-step budget. | SA+IDM: 85% Planning success rate (%) | IDM 63%; DINO-WM 79%; PLDM 78%; LeWorldModel 86%. Twenty-two percentage points above IDM; one below LeWorldModel. Comparable point estimates do not establish statistical equivalence. e7e8 |
| PushT goal-conditioned planning Same fixed-problem protocol; auxiliary weights selected using the PushT validation split. Exact evaluation split membership is not restated. | SA+IDM: 98% Planning success rate (%) | IDM 83%; DINO-WM 74%; PLDM 78%; LeWorldModel 96%. Fifteen percentage points above IDM and two above the strongest listed baseline; no uncertainty supports a significance claim. e7e8 |
| OGBench-Cube goal-conditioned planning Same 50 fixed problems per seed and three trained seeds, with a 25-step goal offset and 50-step budget; simulator execution is illustrated in Figure 2. | SA+IDM: 87% Planning success rate (%) | IDM 85%; DINO-WM 86%; PLDM 65%; LeWorldModel 74%. Two percentage points above IDM and thirteen above LeWorldModel. The one-point lead over DINO-WM is a reported mean difference only. e7e8e9 |
| OGBench-Cube temporal straightening 100 sampled observation trajectories held fixed across models; full 192-dimensional latent calculations. | SA+IDM: 0.55 ± 0.034 Mean trajectory straightening score ± standard deviation | IDM: 0.62 ± 0.029; LeWorldModel: 0.69 ± 0.025. Straightening decreases while planning improves; this diagnostic is not a success rate or direct measure of physical accuracy. e10e8 |
| OGBench-Cube transition-subspace analysis Uncentered SVD of latent displacements, separately for the same 100 trajectories. | SA+IDM: 32.8; figure legend reports 32.8 ± 3.0. Mean r95: components retaining 95% of transition energy | IDM 30.2 ± 2.6; LeWorldModel 17.0 ± 1.7, as printed in Figure 4. The ± statistic is not explicitly defined. SA+IDM spreads transition energy across more directions. This association does not prove those directions encode useful physical variables. e11 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 3. A high mean alignment can coexist with occasional sharp reversals in latent motion. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Each column represents one model encoding the same representative OGBench-Cube episode. The top row projects that model's latent states onto its own PCA basis; color tracks time, an open circle marks the start and a cross marks the end. The bottom row computes cosine alignment between successive displacement vectors in the full 192-dimensional space. A score near one indicates similar directions; near minus one indicates reversal. Dashed lines show this episode's means, not the 100-trajectory averages in Table II. LeWorldModel stays highly aligned for much of the trajectory but shows isolated near-reversals, whereas the other columns display more distributed directional changes. e10e11
What it supports. The example helps explain why a large average straightening score need not imply uniformly smooth temporal evolution. LeWorldModel's mean is highest even though it has several pronounced negative excursions. The source uses this mismatch to motivate inspecting how many latent directions carry transition energy.
Where the evidence stops. The PCA bases and axis scales differ, so orientation and apparent path size are not directly comparable across panels. The authors' suggestion that SA reveals physical curvature is a hypothesis, not a measured correspondence between latent turns and physical-state turns.
Table II. The aggregate straightening ranking runs opposite to the OGBench-Cube planning-success ranking for these three models. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read each entry as the mean and standard deviation of trajectory-level straightening scores over 100 sampled OGBench-Cube observation trajectories, held fixed across models. These are dimensionless cosine-based scores, not percentages. Equation (8) first averages local displacement alignment within each trajectory; the table summarizes the resulting trajectory scores. The evaluation uses the full latent representation rather than the two plotted PCA coordinates. Compare the rows with the OGB-Cube column of Table I: LeWorldModel has success 74%, IDM 85%, and SA+IDM 87%. This cross-reference distinguishes a geometric diagnostic from the actual task objective the planner must satisfy. e8e10
What it supports. Adding state alignment reduces the mean score from 0.62 to 0.55 while improving OGBench-Cube success from 85% to 87%. LeWorldModel scores still higher on straightening, at 0.69, but lower on success. The reported comparison therefore does not support maximizing this average as a standalone selection rule.
Where the evidence stops. The ± values here are explicitly standard deviations across trajectories, not uncertainty in planning success or across training seeds. The paper supplies no zero-displacement convention for the cosine denominator, and this diagnostic covers only OGBench-Cube.
Figure 4. LeWorldModel's latent transitions concentrate their energy in fewer directions. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. The horizontal axis counts transition components and the vertical axis shows cumulative transition energy. For each of the same 100 trajectories, the authors apply an uncentered SVD to successive latent displacements; the curves average cumulative energy profiles. The dashed horizontal line marks 95% energy. Read r95 from the legend as the number of components needed to retain that fraction: its reported mean is 17.0 for LeWorldModel, 30.2 for IDM and 32.8 for SA+IDM. The faster-rising green curve therefore indicates stronger concentration, not more physical information. The caption and body do not explicitly identify the statistic following the ± signs. e8e10e11e12
What it supports. The transition analysis supplies a concrete qualification to the straightening result. A model can align successive displacements strongly while varying along relatively few directions. SA+IDM retains a broader effective transition subspace than LeWorldModel in this comparison, accompanying its higher planning success and lower average straightening.
Where the evidence stops. This measures variation along trajectories, not the rank of the full embedding distribution. More transition directions do not by themselves establish better control-relevant information, and the cross-model association does not isolate a causal effect of transition dimension.
7. Analysis & limitations
7.1 What the evidence leaves open
Evidence covers four benchmarks using full physical-state training labels, without a physical-robot study or label-noise/missing-state ablation. The source has no dedicated limitations section; these are boundaries of its reported evaluation. e7e8e9e12
Table I imports baseline means from LeWorldModel and omits seed dispersion. State alignment's gain over IDM is consistent, but small cross-method margins and statistical significance remain unresolved. No SA-only or single-frame-SA control isolates the importance of pairing. e7e8
The authors suggest state supervision exposes physical turns in latent space, lowering straightening. Neither the separate PCA projections nor transition ranks establish that explanation causally; the diagnostic analysis covers OGBench-Cube only. e10e11
7.2 Questions for discussion
- Does the gain survive missing or noisy velocity supervision, and does pair-based G outperform a single-frame control? (e4, e7, e8)
- Would transition dimension still correlate with success after holding latent prediction error and planner settings fixed? (e6, e10, e11)
8. Reproducibility audit
8.1 Requirements and known gaps
Required inputs include the behavior-policy data, measured-state fields, normalization statistics and fixed evaluation problems. The PDF specifies architecture and AdamW, but omits dataset sizes, exact state/angle encodings, action-chunk length, learning rate, batch size, training duration, image preprocessing, hardware and software versions. e3e5e7
CEM population, elite fraction, iterations, horizon value and executed portion before replanning are not specified. Task success thresholds and exact split membership are inherited by reference rather than restated. Code and evaluation configurations are promised upon acceptance; that statement is not evidence of a public release. e5e6e7
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Separate physical-state information from generic auxiliary regression
Reader-proposed check, not performed: on PushT, compare IDM-only, the reported pair-based SA+IDM, a single-frame-SA control using duplicated current embeddings to preserve G's input size, and pair-based SA with state targets shuffled across training samples. Hold training data, initialization seeds, predictor, optimizer budget, normalization and CEM settings fixed; use the same 50 start–goal problems and 50-step interaction budget, with α = β = 1 for SA variants. Report paired success differences and seed dispersion. The physical-grounding account predicts that correctly paired physical targets outperform shuffled targets; the temporal-context account predicts an additional advantage over the single-frame control. Similar gains from shuffled targets, or no pairing advantage, would weaken those particular explanations. Exact missing training and CEM settings must be resolved before claiming a faithful reproduction. e4e5e6e7e8
Check 2: Test whether broader transition variation carries usable state information
Reader-proposed check, not performed: evaluate LeWorldModel, IDM and SA+IDM on the same 100 OGBench-Cube trajectories, computing Equation (8) in full latent space and r95 by uncentered displacement SVD. Declare zero-displacement handling and the meaning of every ± statistic. Add held-out physical-state probes with identical capacity and training budgets, using the same observed latent pairs, and measure planning success under identical CEM settings on the fixed start–goal problems. Repeat across trained seeds. The proposed explanation would gain support if broader transition variation consistently coincides with better held-out state recovery and planning, rather than merely a lower straightening score. Higher r95 without improved probing or planning would show that transition dimension alone is insufficient. This check tests association; it would not establish causal mediation. e4e6e7e8e10e11
8.3 Reading coverage
Visual audit: The complete five-page v1 PDF was rendered and visually inspected: p. 1 verifies title, authors, affiliation and version; p. 2 supplies architecture, data, losses and implementation; p. 3 supplies implementation continuation, planning, evaluation, Figure 2 and Table I including its IDM ablation; p. 4 supplies Equation (8), Figure 3 and Table II; p. 5 supplies Figure 4, conclusion, acknowledgment and references. All six final original crops were separately viewed. Figure 1's arrow inputs and dashed preceding-step branch were checked against its caption and Equations (1)–(6); no claim-relevant inconsistency was found. Table captions and their protocol/uncertainty qualifications were read on the full pages and carried into the guides; table crops contain all cells and rules, with no footnotes omitted. The full text was read in both supplied chunks. No appendix is present; separate supplemental availability remains unverified. External references, code and experiments are outside this reading pass.
PDF pages inspected for this edition: 1, 2, 3, 4, 5. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- PDF p. 1: title, authors, version, abstract and I. Introduction
- PDF p. 2: II.A Offline Data and II.B Model Architecture
- PDF pp. 2–3: II.C Implementation
- PDF p. 3: II.D Latent Planning, III.A Experimental Setup and III.B Planning Performance in Latent Space
- PDF pp. 4–5: III.C Temporal Straightening
- PDF p. 5: IV. Conclusion, Acknowledgment and References
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Both supplied text chunks were read completely; all five PDF pages and all six final figure/table crops were visually inspected.
- Identity: the inspected title and author order match the catalog. The title page identifies arXiv:2609.03565v1 [cs.RO], 3 September 2026. No different revision was supplied or compared; this report covers v1 only (e1).
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout. This acquisition limitation was resolved here by inspecting the supplied PDF images.
- Separate supplemental material availability has not been fully verified.
- No appendix appears in the five-page PDF. No code, external references or separate supplements were inspected, and no experiments were reproduced.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e1PDF p. 1, title/byline/affiliation and arXiv margin stamp
Title matches the supplied catalog. Authors are Muyuan Liu, Yue Huang, Zheng Liang and Xiang Gao; the first two contributed equally, and Xiang Gao is corresponding author. Affiliation is GENISOM AI, Beijing, China. Stamp: arXiv:2609.03565v1 [cs.RO], 3 Sep 2026.
Go to primary source ↓e2PDF p. 1, Abstract and I. Introduction, motivation and contributions
The paper motivates physical-state alignment as complementary to action recovery in a latent-prediction world model. It distinguishes pixel-free planning, collapse prevention and control-relevant physical grounding.
Go to primary source ↓e3PDF p. 2, II.A Offline Data
The fixed behavior-policy dataset contains trajectories of visual observations, physical measurements and action chunks. Each chunk spans a fixed number of low-level actions between adjacent observations; its numerical length and dataset size are not given.
Go to primary source ↓e4PDF p. 2, Figure 1 and caption; II.B Model Architecture, Eqs. (1)–(6)
E encodes observations and F predicts future latents. H(z_t,z_{t+1}) regresses a_t; G(z_{t-1},z_t) regresses s_t. Squared-error losses combine as prediction + α state alignment + β inverse dynamics. The dashed branch is the preceding prediction. Physical measurements and auxiliary heads serve training; deployment uses E and F.
Go to primary source ↓e5PDF pp. 2–3, II.C Implementation
Random ViT-Tiny/14, projected CLS width 192; six-layer causal predictor with up to three latent–action pairs; action width 192 and zero-initialized AdaLN at each layer; two-layer G/H MLPs with hidden widths 256/512. Actions and Euclidean states are standardized, angles use continuous coordinates, and all components use AdamW. Code/configurations are promised upon acceptance. Training schedule, hardware and exact preprocessing/configuration are not supplied.
Go to primary source ↓e6PDF p. 3, II.D Latent Planning, Eq. (7)
Frozen E and F encode current/goal images and recursively predict candidate terminal latents. CEM minimizes terminal squared latent distance by sampling and elite updates; execution is followed by observation and replanning. Numerical CEM settings, horizon and execution interval are not specified.
Go to primary source ↓e7PDF p. 3, III.A Experimental Setup and Table I caption
Four LeWorldModel benchmark tasks use full physical-state SA labels, 50 fixed problems per seed, goals 25 environment steps ahead and a 50-step interaction budget. Own results average three independently trained seeds; baseline means come from LeWorldModel. PushT validation selects tied α = β = 1.0 from 0.01, 0.1 and 1.0. Exact split membership and task success thresholds are not restated.
Go to primary source ↓e8PDF p. 3, Table I, all method rows and task columns; III.B ablation paragraph
Success percentages in TwoRoom/Reacher/PushT/OGB-Cube order: DINO-WM 100/79/74/86; PLDM 97/78/78/65; LeWorldModel 87/86/96/74; IDM 94/63/83/85; SA+IDM 100/85/98/87. IDM-only uses α = 0 and β = 1.0. No success uncertainty, SA-only or single-frame-SA result is reported.
Go to primary source ↓e9PDF p. 3, Figure 2 and caption; III.B final paragraph
Top row is an OGBench-Cube reference trajectory; bottom row shows actual simulator observations after executing CEM actions. The text describes one successful trial within the evaluation budget, not predicted images or physical-robot execution.
Go to primary source ↓e10PDF p. 4, III.C Temporal Straightening, Eq. (8), Table II and Figure 3/caption
Consecutive-displacement cosine scores are calculated in the full 192-dimensional space. Table II gives mean ± SD over 100 fixed OGBench-Cube trajectories: LeWorldModel 0.69 ± 0.025, IDM 0.62 ± 0.029, SA+IDM 0.55 ± 0.034. Figure 3 independently fits each PCA projection; representative means are 0.718, 0.602 and 0.555. Physical-turn sensitivity is a suggested explanation, and zero-displacement handling is not specified.
Go to primary source ↓e11PDF p. 4, III.C final paragraph; PDF p. 5, Figure 4/caption and III.C continuation
Uncentered SVD analyzes displacements from the same 100 trajectories; r95 counts components retaining 95% of transition energy. Figure 4 plots mean cumulative energy and labels LeWorldModel 17.0 ± 1.7, IDM 30.2 ± 2.6, SA+IDM 32.8 ± 3.0. The text identifies mean r95 but does not explicitly define the ± statistic. The rank-one parallel/antiparallel argument explains how high average alignment can coexist with restricted transition variation.
Go to primary source ↓e12PDF p. 5, IV. Conclusion
The authors conclude that state alignment complements inverse dynamics and that average straightening can conceal concentrated transition variation. Combining SIGReg's distributional safeguard with physical grounding is future work. The conclusion adds no physical-robot experiment or dedicated limitations analysis.
Go to primary source ↓8.5 Primary sources
Toward Physically Grounded JEPA World Models for Goal-Conditioned Robotic Planning ↗
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