Latent Energy Action Planning with World Models
1. Paper overview
In one sentence: LEAP improves action planning through a frozen latent world model by requiring decoded terminal-state agreement, at the cost of numerical goal supervision and additional online optimization. e-motivatione-energye-rolloute-proposale-maine-ablatione-agreemente-limits
| At a glance | What to know |
|---|---|
| Research problem | Source description Optimizing predicted goal error can select model mistakes. In one Push-T CEM trace, final latent cost is 4.40 versus an expert reference of 4.75, while action distance reaches 11.19 and maximum magnitude reaches 2.32 times the expert reference. This illustrates a failure mode, not its population frequency. e-motivation |
| Core mechanism | Source description LEAP keeps the pretrained encoder and predictor fixed, differentiates through autoregressive rollouts to optimize actions with L-BFGS, then projects and rescores candidates. e-rolloute-optimization |
| A key reported result | Four-domain goal-reaching success: LEAP: Push-T 90.0±3.0; OGBench-Cube 100.0±0.0; Reacher 89.0±3.1; TwoRooms 100.0±0.0; unweighted mean 94.8±1.1. Success (%), ± one reported binomial standard error. Matched 100 trials/task; same starts, checkpoints, evaluation code and 50-step budget. LeWM+CEM: 88.0±3.2, 62.0±4.9, 75.0±4.3, 85.0±3.6; mean 77.5±2.0. Reported gain: 17.3 percentage points between complete systems. The 50-trial means are 96.5±1.3 versus 77.0±2.9. e-maine-protocol |
| Reading caution | Source description The authors identify inherited long-horizon and out-of-distribution model errors and dependence on numerical goal descriptors. Image-derived geometry and broader physical evaluation are future directions, not demonstrated capabilities. e-limits |
Core contributions
- Source description
LEAP keeps the pretrained encoder and predictor fixed, differentiates through autoregressive rollouts to optimize actions with L-BFGS, then projects and rescores candidates. e-rolloute-optimization
- Reader analysis
A shared energy demands both latent and decoded goal agreement. Paired component ablations provide stronger mechanism evidence than the complete-system CEM comparison. e-energye-ablatione-main
Figure 2. Two goal signals share one predicted rollout and update the action sequence. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read left to right: the current frame enters the frozen LeWM encoder, and its latent initializes the purple autoregressive chain. Orange arrows show each action block conditioning a rollout step. On the right, the predicted terminal latent feeds both a latent-goal comparison and a frozen descriptor decoder. Their costs meet in the energy box; the magenta feedback arrow returns to candidate actions. Snowflakes mark fixed model parameters, not a detached action computation graph. Although the drawing exposes only the final descriptor, Equation (12) scores the last two predictions. The proposal initializes the action box; it contributes no extra penalty to the energy. e-architecturee-rolloute-energye-proposale-optimization
What it supports. The architecture makes action optimization the online computation. LEAP does not retrain the world model during planning. Its decoder supplies a second goal representation, while both goal costs remain functions of the same predicted trajectory. Lower total energy therefore means stronger predicted agreement across the two representations.
Where the evidence stops. The action box labels t:t+H, whereas the text defines H blocks through t+H−1. The one-descriptor drawing also omits the two-step window in Equation (12). Projection and rescoring occur afterward in Algorithm 1; neither bounded actions nor accurate execution follows from the diagram alone.
2. Motivation
2.1 The problem and the proposed response
Optimizing predicted goal error can select model mistakes. In one Push-T CEM trace, final latent cost is 4.40 versus an expert reference of 4.75, while action distance reaches 11.19 and maximum magnitude reaches 2.32 times the expert reference. This illustrates a failure mode, not its population frequency. e-motivation
2.2 What this reading follows
A world model can predict useful features yet still mislead an optimizer that searches those features aggressively. LEAP addresses this problem at action-selection time: it refines a proposed action sequence through frozen LeWorldModel dynamics, scoring both visual latent similarity and agreement with a numerical goal descriptor. This edition follows the action gradient, examines the controlled success comparison, and then asks what the energy ablations actually isolate. The central distinction is between better predicted agreement and better executed behavior. The paper measures both, but its decoded-state diagnostic is not an independent certificate that the learned dynamics are physically correct. e-motivatione-energye-rolloute-proposale-maine-ablatione-agreemente-limits
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 unassigned catalog supplies no quadrant assertion to confirm. Architecture evidence supports action-conditioned latent prediction with external action optimization and separately fitted proposal/readout networks. Actions are optimized variables, not jointly predicted future/action outputs or an inverse-dynamics readout. Figure 2 does not establish a unified One Model system; the snapshot remains unchanged. e-rolloute-proposale-architecture
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 Why corroborating a predicted goal can change the plan
Begin with the paper’s optimization-loop problem: a planner deliberately seeks action sequences where its learned objective is small, so average predictive accuracy does not establish accuracy on the sequences it selects. LEAP keeps the native terminal-latent distance and adds a decoder-based error averaged across the last two predicted states. Each decoder coordinate is standardized using training statistics, and the error is divided by descriptor dimension and window length. Both costs are nonnegative, so a small total cannot conceal a large disagreement in either representation. This is the paper’s predicted-agreement argument. It does not guarantee that either prediction matches the eventual environment state, or that the candidate trajectory remains within offline-data support. e-motivatione-energye-decoder
5.2 Follow a candidate from a learned guess to executed controls
The learned action proposal is an initializer, not a third energy term. Its deterministic output forms the first candidate; seeded perturbations provide additional local starts when the configured candidate count exceeds one. L-BFGS then changes the action tensor through the frozen rollout’s computation graph. Fixed network parameters still permit derivatives with respect to actions. After the solve, LEAP clamps every candidate to the normalized environment range and recomputes its energy, because projection can change the trajectory being evaluated. Selection uses these new finite scores. The selected plan executes five action blocks, equivalent to 25 primitive steps, before replanning within the 50-step budget. Freezing the world model therefore separates offline fitting from online action refinement, not prediction from execution. e-proposale-rolloute-optimizatione-protocol
5.3 Separate system performance, mechanism evidence and local explanation
Reader analysis: Table I compares complete planners under matched evaluation, whereas Table III fixes the proposal, solver, projection and starts to isolate the energy. Its 5.5-point gain therefore answers a narrower question than the 17.3-point headline improvement, under a different trial protocol. Figure 3 illustrates local descent geometry; Table IV measures decoded agreement, not independent execution accuracy. Table VI shows nonmonotonic weight sensitivity, and Table VIII shows that extra optimizer iterations need not help. However, the latter contains an unresolved arithmetic inconsistency: L-BFGS/5 visibly lists 92, 88, 88 and 98 percent, whose reader-calculated mean is 91.5%, while the printed Mean is 94.0%. Neither should be silently substituted for the other as the authors’ intended result. L-BFGS/10 remains highest at 96.5% under either reading, but the exact gap to L-BFGS/5 requires clarification. e-maine-ablatione-landscapee-agreemente-weightse-optimizer
5.4 Training and inference
During training
Official LeWM checkpoints remain frozen. Per domain, a 256–256 descriptor MLP trains for 50 epochs on 9,000 examples, with 1,000 held out. Training-set coordinate statistics standardize descriptors. Benchmark state descriptors supervise fitting; success labels are unused. e-decoder
A three-hidden-layer SiLU proposal predicts five normalized action blocks from benchmark context. It minimizes expert-action MSE with a 95/5 training/validation split, retaining minimum validation loss. Both auxiliary networks are frozen for evaluation. e-proposale-decoder
During inference
L-BFGS uses learning rate 1.0, ten iterations, history 100, strong-Wolfe search and tolerances 10^{-7}/10^{-9}. Five latent transitions cover 25 primitive steps before replanning; the budget is 50 steps. Candidate counts are 32/1/4/4 for Push-T/Cube/Reacher/TwoRooms. Bounds are [-2,2], except TwoRooms [-1.6,1.6]. Shared energy/optimizer settings are chosen on paired 50-trial sweeps before a different 100-trial start schedule. e-optimizatione-protocol
5.5 Implementation flow
- Encode and initialize
The frozen encoder produces current and goal latents. A goal-conditioned proposal supplies the first candidate; seeded perturbations supply additional starts. The proposal has zero weight in the optimized energy. e-rolloute-proposal
- Differentiate the imagined trajectory
Each action block conditions its corresponding autoregressive transition. Retaining the action-to-latent computation graph lets terminal costs update the entire horizon without changing model parameters. e-rolloute-optimization
- Require complementary goal agreement
Compare the final latent with the encoded goal. Decode both final predicted latents and compare their standardized descriptors with the numerical goal. Nonnegative terms cannot cancel each other’s disagreement. e-energy
- Project, rescore, execute
Clamp refined candidates to admissible bounds, recompute energy, and choose the lowest finite score per environment. Algorithm 1 rejects an all-nonfinite plan but specifies no recovery controller. e-optimization
6. Experiments & results
LEAP refines an action horizon through frozen LeWorldModel dynamics, combining latent-goal matching with a learned decoder’s terminal-state error. A trained proposal initializes search; projection bounds executed controls. Four-domain mean success rises from 77.5% to 94.8% against matched LeWM+CEM. The narrower energy ablation improves from 91.0% to 96.5%, separating the extra objective’s contribution from the complete planner change. Numerical goal descriptors and trustworthy learned rollouts remain prerequisites (e-energy, e-proposal, e-optimization, e-main, e-ablation, e-limits).
6.1 Read the original evidence
Table I. The matched final evaluation favors LEAP, especially on OGBench-Cube. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use the leftmost column to keep the two protocols separate. The lower pair of rows is the final 100-trial comparison; the upper pair contains 50-trial results. Within each pair, compare LEAP and LeWM+CEM across the same task columns, then read the unweighted mean. The small values after the plus/minus signs are reported binomial standard errors, not variation across retraining seeds. Both planners use the official frozen checkpoints, matched starts and the same interaction budget. Shared energy and optimizer settings were selected using 50-trial sweeps before the final evaluation used a different start schedule. e-maine-protocole-proposal
What it supports. At 100 trials, LEAP’s mean is 94.8% versus 77.5%, a reported 17.3-percentage-point gain. The largest task difference is OGBench-Cube: 100% versus 62%. Push-T changes from 88% to 90%, so the mean improvement should not be read as an equal gain in every domain.
Where the evidence stops. This is a complete-system comparison: proposal initialization, refinement and terminal readout differ from native CEM. It cannot assign the entire gain to one energy term. A printed zero standard error at 100% is not proof of certain success on new trials.
Figure 5. Selected executed rollouts show both earlier success and cases where only LEAP attains the goal. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read each task as a pair: LeWM+CEM is above, and the row labeled Ours is LEAP below. Move across the irregularly spaced time columns; T counts primitive environment steps, not optimization iterations or latent transitions. Compare each state with the goal image at the right. Red crosses mark states before goal attainment and green checks mark states at or after it. The source repeats terminal frames for later display times after a rollout terminates. Thus the repeated green frames should be read as a display convention, not additional observations demonstrating continued successful control after termination. e-qualitativee-main
What it supports. These selected examples show LEAP reaching Push-T in 23 versus 25 steps and TwoRooms in 9 versus 24. LEAP reaches OGBench-Cube by step 23 and Reacher by 28, while the paired CEM rows remain unsuccessful across the displayed frames. They illustrate behaviors behind the aggregate task comparison.
Where the evidence stops. Selected stills cannot estimate success frequency, establish continuous trajectories between columns, or demonstrate physical-robot deployment. Later repeated terminal frames supply no independent evidence of stability. Use Table I for aggregate outcomes and Section V-F for the timing and repetition conventions.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Four-domain goal-reaching success Matched 100 trials/task; same starts, checkpoints, evaluation code and 50-step budget. | LEAP: Push-T 90.0±3.0; OGBench-Cube 100.0±0.0; Reacher 89.0±3.1; TwoRooms 100.0±0.0; unweighted mean 94.8±1.1. Success (%), ± one reported binomial standard error | LeWM+CEM: 88.0±3.2, 62.0±4.9, 75.0±4.3, 85.0±3.6; mean 77.5±2.0. Reported gain: 17.3 percentage points between complete systems. The 50-trial means are 96.5±1.3 versus 77.0±2.9. e-maine-protocol |
| Planning cost and budgeted interaction One environment at a time on the same task-assigned GPU. | LEAP: 1.28 s; 21.06 steps. Planning seconds/trial; budgeted primitive steps/trial | LeWM+CEM: 1.20 s; 26.41 steps. Timing includes initialization/optimization, excluding loading, stepping and visualization. Failures receive the full step budget. These are not end-to-end latency measurements. e-efficiency |
| Paired energy-component ablation 50 paired trials; checkpoint, proposal, optimizer, candidates and projection fixed. | Full LEAP 96.5. Unweighted mean success (%) | Latent-only 91.0; terminal-state-only 52.0. Terminal matching adds 5.5 points over latent-only refinement. Full LEAP is best in every domain. e-ablation |
| First-decision terminal-descriptor agreement First selected plans on paired starts; LEAP versus latent-only. | Task-mean ratio 0.933; paired-lower mean 89%. Predicted terminal-error ratio; starts with lower error | Ratios: Push-T 0.940, Cube 0.917, Reacher 0.921, TwoRooms 0.954. The 6.7% reduction concerns decoder predictions, not independently measured physical error. e-agreement |
| Terminal-state weight sensitivity Paired 50-trial sweep; damping disabled. | Weight 10: 96.5. Unweighted mean success (%) | Weights 0/0.1/0.3/1/3: 91.0/93.5/93.0/88.5/89.0. Reacher falls to 68% at weights 1 and 3, then reaches 92% at 10. Improvement is nonmonotonic. e-weights |
| Damping composition Paired 50-trial protocol. | Latent plus terminal-state: 96.5. Unweighted mean success (%) | Latent plus damping at weight 3: 94.5; all three terms: 94.0. The penalties do not add constructively here. Final LEAP excludes damping. e-damping |
| Optimizer selection Final energy; paired 50-trial study. | L-BFGS/10: 96.5. Success (%); printed unweighted means, with the L-BFGS/5 inconsistency disclosed | Printed means: Adam/20 93.0; Adam/40 92.5; L-BFGS/5 94.0; L-BFGS/20 91.0. However, the visible L-BFGS/5 task cells are 92/88/88/98, whose reader-calculated mean is 91.5%. L-BFGS/5 is internally inconsistent: its printed 94.0% mean and −2.5-point superscript disagree with the task cells, which imply 91.5% and −5.0 points versus L-BFGS/10. The intended result is unresolved. L-BFGS/10 remains highest under either reading; more iterations need not help. No matched wall-clock comparison is provided. e-optimizer |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 3. A second terminal objective changes the preferred local descent path. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start with the white diamond shared by both panels. The horizontal and vertical axes are action offsets, not physical object positions. In the left panel, follow the red descent path toward the cyan cross marking a misleading latent basin. In the right panel, the magenta path instead approaches the yellow star representing the expert action. The other energy changes the local landscape rather than simply multiplying all costs by a constant. Read the color bar carefully: it shows normalized energy above each panel’s minimum. It does not supply absolute total-energy values that can be compared directly between panels. e-landscapee-energye-proposal
What it supports. The local example illustrates the proposed mechanism: descriptor matching can penalize a region that looks attractive under the latent objective and redirect action refinement. The visible contours and paths explain why the extra term can alter the selected action, rather than merely change the numerical scale of its score.
Where the evidence stops. This is one two-dimensional Push-T slice, not the full action tensor or a frequency estimate. The figure does not establish global convergence, uniform improvement, or immunity to model error. Its expert-action reference is a diagnostic, not an online energy term.
Table III. The terminal readout helps most when it complements the latent goal. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the first row as the paired reference, then remove one goal signal at a time. The proposal, checkpoint, optimizer, candidate count, projection and sampled starts stay fixed across these rows. This makes the table a more direct test of the objective than the CEM comparison. The superscripts are percentage-point changes from full LEAP, not uncertainty intervals. Notice the asymmetry: the latent-only row stays comparatively strong, whereas terminal-state-only drops sharply on manipulation and reaching. TwoRooms is the exception to that severe drop, with terminal-state-only reaching 96%, but the combined objective remains the best row there too. e-ablatione-protocole-agreement
What it supports. Full LEAP reaches a 96.5% mean, compared with 91.0% for latent-only and 52.0% for terminal-state-only. The 5.5-point improvement over latent-only is the directly controlled evidence for adding descriptor matching within this planner. It supports complementarity rather than replacing the latent visual goal.
Where the evidence stops. The table uses the 50-trial protocol employed for configuration selection and supplies no multi-seed uncertainty. Better decoder agreement is also measured in Table IV, but that diagnostic evaluates a quantity LEAP optimizes; it is not independent physical validation.
Table VI. A shared terminal-state weight helps only after navigating nonmonotonic sensitivity. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read down the first column as the terminal-state weight increases. Damping is disabled throughout, so the zero-weight row is the latent-only reference. The colored superscripts compare each entry with that reference in percentage points. Follow Reacher before looking at the mean: its success is 86% without the state term, falls to 68% at weights 1 and 3, and rises to 92% at weight 10. The other task columns partly hide that deterioration when averaged. This is why the paper fixes one selected weight across domains instead of interpreting the second energy as automatically beneficial at every strength. e-weightse-energye-protocol
What it supports. The best tested shared weight is 10, giving a 96.5% mean and improving every task over the zero-weight row. Weights 1 and 3 instead yield means of 88.5% and 89.0%. These results establish sensitivity within the sweep, not a monotonic relationship between descriptor emphasis and success.
Where the evidence stops. The authors suggest competing gradients and local basins explain Reacher’s dip; this table measures success, not gradient directions. It cannot establish optimality beyond the tested weights, nor whether the same weight transfers to longer horizons or different descriptor calibration.
7. Analysis & limitations
7.1 What the evidence leaves open
The authors identify inherited long-horizon and out-of-distribution model errors and dependence on numerical goal descriptors. Image-derived geometry and broader physical evaluation are future directions, not demonstrated capabilities. e-limits
Two learned readouts of the same rollout cannot certify physical accuracy or offline-data support. Projection establishes action-range admissibility only. The decoder-error diagnostic measures a quantity explicitly optimized by LEAP. e-energye-agreement
Figure 5 shows selected benchmark rollouts with repeated terminal frames. It cannot establish population success or physical deployment. PLDM, DINO-WM and Random in Figure 4 are contextual LeWM rates, not rerun comparisons. e-qualitativee-main
Table VIII contains an unresolved internal inconsistency: L-BFGS/5 prints a 94.0% mean, but its visible task rates average 91.5%. This affects its comparison with other optimizer settings, although L-BFGS/10 remains highest under either reading. Raw trial outcomes or an author correction are needed to resolve it. e-optimizer
7.2 Questions for discussion
- Would decoded agreement predict executed success under descriptor noise or domain shift?
- How much of the complete-system gain comes from proposal initialization and projection?
- Does the shared terminal weight remain useful at longer horizons?
8. Reproducibility audit
8.1 Requirements and known gaps
Reproduction requires official checkpoints/evaluation code, offline descriptors and expert sequences, training-only normalization and paired starts. The PDF does not enumerate descriptor coordinates, proposal context fields/hidden widths, perturbation scale, exact split identities, auxiliary training optimizers, CEM settings or task success thresholds. e-decodere-proposale-protocol
GPU model/count and software versions are unspecified. Record these, closure counts and synchronized timing: strong-Wolfe search may exceed nominal iterations. Runtime scales as O(QKH) predictor steps for Q objective/gradient evaluations, K candidates and horizon H; retaining rollout activations increases memory. e-optimizatione-efficiency
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: Test whether predicted agreement tracks executed state error
Reader-proposed check, not run: on paired held-out starts, compare full LEAP with latent-only refinement while fixing checkpoints, proposal candidates, optimizer, projection and interaction budget. Record each first selected plan’s decoded terminal error, then execute it and measure goal-descriptor error from benchmark state signals at the corresponding block boundaries. Use those state signals only for evaluation. Report paired changes in predicted error, executed error and task success, including cases where the signs disagree. Repeat with controlled noise added to the numerical goal descriptor after applying the same training normalization. If decoded error consistently improves while executed error or success does not, the diagnostic in Table IV would overstate physical grounding under that condition. e-agreemente-ablatione-energye-decodere-protocole-limits
Check 2: Isolate dependence on the learned proposal
Reader-proposed check, not run: cross two objectives, latent-only and full LEAP, with two initialization centers, the trained proposal and a fixed zero-action sequence within the stated bounds. Keep each task’s candidate count, shared perturbation draws, horizon, L-BFGS settings and post-solve projection/rescoring identical. Predeclare the perturbation scale because the PDF does not specify it. Use held-out paired starts, measure success differences and paired uncertainty, and record closure counts plus synchronized planning time. A full-energy gain under both centers would support an objective contribution beyond proposal quality; a gain confined to proposal-centered starts would reveal initialization dependence. Comparing proposal versus zero-center within each objective would quantify a component that the headline CEM comparison does not isolate. e-proposale-ablatione-maine-protocole-optimizatione-efficiency
8.3 Reading coverage
Visual audit: All nine original PDF pages were rendered at 200 DPI and visually inspected, covering title/authors/version, complete method and equations, Algorithm 1, all five figures, all eight tables, limitations and references. Six final crops were separately inspected: Figures 2, 3 and 5; Tables I, III and VI. Narrow originals were rendered at 400 DPI rather than upscaled. Figure 2’s single terminal descriptor and action-index label were checked against Equations (1) and (12) and Algorithm 1; the differences are disclosed in its guide/caution. Figure 5’s repeated terminal frames follow Section V-F. No appendix is present. Separate supplements, external references, code and continuous videos were not inspected; no reproduction was performed. Table VIII on page 7 was re-inspected: L-BFGS/5 visibly prints 92/88/88/98, while its Mean column prints 94.0 and its superscript −2.5. The base result, evidence, limitation and tutorial disclose the reader-calculated 91.5% mean and −5.0-point difference without claiming an author correction. The extraction’s Cube value of 98 is not used as the PDF value.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9. 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
- Abstract; I. Introduction
- II. Related Work
- III. Problem Formulation, A–B
- IV. Methodology, A–C; Algorithm 1
- V. Experimental Evaluation, A–F
- VI. Discussion and Conclusion, including Limitations and Future Directions
- References [1]–[21], PDF pp. 7–9
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- Revision scope: title and both authors match the catalog. The inspected title page identifies arXiv:2609.03294v1 [cs.LG], 3 September 2026; no other edition or revision was supplied or compared (e-identity).
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout. This acquisition omission was addressed by visually inspecting all nine PDF pages and all six final crops.
- Separate supplemental material availability has not been fully verified. No separate supplement was supplied; the nine-page PDF contains no appendix.
- Code and external linked references were not inspected. No experiments were run or reproduced.
- The supplied text extraction reads the Table VIII L-BFGS/5 OGBench-Cube cell as 98, whereas the inspected PDF visibly prints 88. This report follows the PDF cell and separately discloses its conflict with the printed row mean (e-optimizer).
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e-identityPDF p. 1, title, author line, affiliation footnote and arXiv margin
Observed title: Latent Energy Action Planning with World Models. Authors: Phu Pham and Aniket Bera. Both are with the Department of Computer Science, Purdue University, USA. Margin: arXiv:2609.03294v1 [cs.LG], 3 Sep 2026.
Go to primary source ↓e-motivationPDF p. 1, Figure 1 and Introduction; p. 2, Section III-A, Eqs. (3)–(4)
The representative CEM trace ends at latent cost 4.40 versus expert 4.75, action distance 11.19 and magnitude ratio 2.32. The support argument distinguishes optimizer-selected error from average prediction accuracy without claiming every plan leaves support.
Go to primary source ↓e-rolloutPDF p. 2, Section III, Eq. (1); p. 3, Section IV-A, Eqs. (7)–(8)
Frozen LeWM encodes current and goal images. Each embedded action conditions an autoregressive latent transition. LEAP retains gradients to the H-block action tensor while model parameters remain frozen.
Go to primary source ↓e-energyPDF p. 3, Section III-B and Section IV-B, Eqs. (6), (9)–(12)
Total energy combines final squared latent distance with descriptor MSE averaged over the last L=2 predictions and D coordinates, with lambda_s=10. Nonnegative terms require complementary predicted agreement, but establish neither action bounds nor offline support.
Go to primary source ↓e-decoderPDF p. 3, Section IV-B, paragraph following Eq. (11)
The readout uses benchmark descriptors and frozen embeddings: 9,000 training examples, 1,000 held out, 50 epochs, MLP hidden widths 256–256, training-statistic coordinate standardization, no success labels. Coordinate schemas and training optimizer settings are not enumerated.
Go to primary source ↓e-proposalPDF p. 4, Section IV-C, initialization paragraphs in both columns
A three-hidden-layer SiLU proposal predicts five normalized blocks from benchmark context, trains with expert-sequence MSE and a 95/5 split, and retains minimum validation loss. Its deterministic output is the first start; other starts use seeded perturbations. It has zero energy weight. Context fields, hidden widths and perturbation scale are unspecified.
Go to primary source ↓e-optimizationPDF p. 3, Eq. (5); p. 4, Section IV-C, Eq. (13) and solver/complexity/execution paragraphs; p. 5, Algorithm 1
L-BFGS: learning rate 1.0, ten iterations, history 100, tolerances 10^-7/10^-9, strong-Wolfe search. Projection follows solving; rescoring precedes finite-score selection. Five blocks execute before replanning. Complexity is O(QKH); line search can add closures. No all-nonfinite recovery policy is supplied.
Go to primary source ↓e-architecturePDF p. 4, Figure 2 and caption; p. 3, Eq. (12); p. 2, action-horizon definition; p. 5, Algorithm 1
The diagram separates frozen encoding, action-conditioned rollout and two energies, with gradient feedback to candidates. It depicts only the final descriptor, whereas Eq. (12) scores two terminal predictions. The action-box t:t+H label differs from the text definition of H blocks through t+H-1; this edition follows the text. Projection and rescoring are in the algorithm, not the diagram.
Go to primary source ↓e-landscapePDF p. 4, Figure 3, caption and accompanying Section IV-B discussion
A local 2-D Push-T action slice shows latent-only descent toward an off-center basin and total-energy descent toward the expert action. The color bar is normalized energy above each panel minimum; axes are action offsets. This is local geometry, not aggregate success.
Go to primary source ↓e-protocolPDF p. 5, Section V-A, left-column paragraphs and paragraph below Table I
Four official checkpoints use frozen encoder/predictor. Start/goal observations are 25 steps apart in offline trajectories; H=5, execution=25 primitive steps, budget=50. K=32/1/4/4. Bounds are [-2,2], except TwoRooms [-1.6,1.6]. Settings are selected on 50-trial sweeps before a different 100-trial schedule. Exact sample indices and success thresholds are not listed.
Go to primary source ↓e-mainPDF p. 5, Table I, all rows/columns; Figure 4 caption; Section V-B
At 100 trials, LEAP/CEM task success is 90/88, 100/62, 89/75, 100/85 percent; means 94.8±1.1/77.5±2.0. Table I gives task binomial standard errors and 50-trial means 96.5±1.3/77.0±2.9. Other Figure 4 baselines are copied contextual results. LEAP–CEM is explicitly a complete-system comparison.
Go to primary source ↓e-efficiencyPDF p. 5, Section V-A timing paragraph; p. 6, Table II and Section V-B continuation
LEAP/CEM: planning 1.28/1.20 seconds per trial; budgeted steps 21.06/26.41. Timing includes initialization/optimization and excludes loading/stepping/visualization, with one environment on the same task-assigned GPU. Hardware model/count and software versions are not supplied.
Go to primary source ↓e-ablationPDF p. 6, Table III and Section V-C, first two paragraphs
Paired 50-trial ablations fix checkpoint, proposal, optimizer, candidates, projection and starts. Full/latent-only/terminal-only means are 96.5/91.0/52.0 percent. Full rates are 94/100/92/100; latent-only 90/94/86/94; terminal-only 34/56/22/96.
Go to primary source ↓e-agreementPDF p. 6, Table IV and Section V-C selected-plan discussion
First-decision decoded terminal-error ratios are 0.940/0.917/0.921/0.954, mean 0.933. Paired-lower rates are 89/98/96/73%, mean 89%. These decoder-predicted errors support predicted agreement, not independent physical accuracy.
Go to primary source ↓e-weightsPDF p. 7, Table VI; p. 6, Section V-D, terminal-state weight discussion
With damping disabled, lambda_s=0/0.1/0.3/1/3/10 gives means 91.0/93.5/93.0/88.5/89.0/96.5. Reacher rates are 86/86/84/68/68/92. Competing local descent directions are the authors’ interpretation; the table does not directly measure them.
Go to primary source ↓e-dampingPDF p. 6, Eq. (14), Table V and Section V-D; p. 7, Table VII and Section V-D continuation
Damping penalizes differences between terminal descriptors independent of goal error. Its best tested weight without state matching is 3, giving mean 94.5; terminal matching gives 96.5; combining them gives 94.0. Final LEAP excludes damping.
Go to primary source ↓e-optimizerPDF p. 7, Table VIII, all rows, especially L-BFGS/5 task cells, Mean and superscript; Section V-E
Printed paired 50-trial optimizer means: L-BFGS/10 96.5, Adam/20 93.0, Adam/40 92.5, L-BFGS/5 94.0, L-BFGS/20 91.0. The rendered L-BFGS/5 row visibly lists Push-T 92, OGBench-Cube 88, Reacher 88 and TwoRooms 98. Reader arithmetic gives (92+88+88+98)/4=91.5%, hence −5.0 percentage points versus 96.5%, conflicting with the printed mean 94.0 and superscript −2.5. The intended correction cannot be established from this source. The table reports success, not optimizer-specific wall-clock times.
Go to primary source ↓e-qualitativePDF p. 7, Section V-F; p. 8, Figure 5 and caption
Rows pair CEM and LEAP under displayed goals. T counts primitive steps; red crosses precede attainment and green checks mark attained goals. LEAP/CEM finish Push-T at 23/25 and TwoRooms at 9/24; LEAP reaches Cube by 23 and Reacher by 28 while displayed CEM frames remain unsuccessful. Terminal frames repeat after termination.
Go to primary source ↓e-limitsPDF p. 7, Section VI, Limitations and Future Directions
The authors identify inherited long-horizon/out-of-distribution model limitations and numerical-goal dependence. Image-derived geometry, occlusion/domain-shift robustness and broader physical evaluation remain future work.
Go to primary source ↓8.5 Primary sources
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