Learning Counterfactual World Models for Embodied Reasoning under Partial Observability
1. Paper overview
In one sentence: CLWM improves simulated planning by supervising the outcome geometry of imagined action sequences, at the cost of privileged training labels and additional branching. e-probleme-rolloute-maine-controlse-limite-impl
| At a glance | What to know |
|---|---|
| Research problem | Source description Under partial observability, a visually plausible future may conceal an intervention that changes later feasibility. The paper calls this counterfactual collapse: imagined summaries are close under latent distance although their intervention outcomes are far apart. History-dependent beliefs must retain distinctions useful for control, rather than only current appearance. The causal language denotes alternative executed action sequences; it does not assert structural causal identification. e-problem |
| Core mechanism | Source description CLWM adds outcome-supervised contrastive learning over open-loop latent branches, with same-belief, perceptual-alias, and value-disagreement negatives. The contribution is the intervention-based pair construction rather than a new planning architecture. e-contraste-rollout |
| A key reported result | Aliased Maze: CLWM: 78.9 ± 1.4; CFS 0.86. Episode success (%) and CFS AUROC. Default layout and aliasing intensity 0.0; final checkpoints, 100 fixed test episodes, five seeds (0–4). TD-MPC-style: 67.3 ± 1.5; CFS 0.70. The largest reported success gain is 11.6 percentage points. ± denotes seed-level standard error. e-maine-tasks |
| Reading caution | Source description Reliable outcome signals and extra branching/mining are required. Long-horizon compounding error, exploration, distribution shift, and reward misspecification remain unsolved. Pretrained-encoder applicability is conceptual, and the reported benchmarks do not establish physical robot deployment. e-limite-tasks |
Core contributions
- Source description
CLWM adds outcome-supervised contrastive learning over open-loop latent branches, with same-belief, perceptual-alias, and value-disagreement negatives. The contribution is the intervention-based pair construction rather than a new planning architecture. e-contraste-rollout
Table 4. The auxiliary machinery shapes latent dynamics during training; the projection head is discarded for evaluation. Original paper, p. 11 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start with the branching row: each anchor supplies 64 interventions, divided among policy, random, and replay proposals. The next two rows explain how those alternatives become supervision: LPIPS identifies visually similar windows, while task-specific outcomes describe hidden object position, topological cell, or later-subtask feasibility. Then read the encoder and head rows together. The projection head maps a 256-dimensional rollout summary through 128 units to 64; the outcome head predicts outcome classes. These head dimensions agree with the table's arrows, but the open-loop recurrence itself is specified in Equations (8)–(9), not drawn here. The compute row describes reported training costs. e-imple-confige-rolloute-losse-limit
What it supports. CLWM adds structured training examples and auxiliary heads around a recurrent latent model. The source reports about 24 hours per CLWM run versus 12 hours per baseline on one NVIDIA A100. Its deployment claim rests on removing the contrastive machinery, not on a measured latency comparison.
Where the evidence stops. The table does not define rollout-summary aggregation or explain how continuous outcome descriptors become outcome classes. It also does not specify adapters between encoder features and prior latents in the recurrence. Software versions and compute are source reports, not independently tested configurations.
2. Motivation
2.1 The problem and the proposed response
Under partial observability, a visually plausible future may conceal an intervention that changes later feasibility. The paper calls this counterfactual collapse: imagined summaries are close under latent distance although their intervention outcomes are far apart. History-dependent beliefs must retain distinctions useful for control, rather than only current appearance. The causal language denotes alternative executed action sequences; it does not assert structural causal identification. e-problem
2.2 What this reading follows
A planner can fail even when its world model predicts convincing observations: two actions may look alike immediately but leave different hidden possibilities for later control. CLWM addresses this with a recurrent belief model and a training objective that distinguishes intervention outcomes. The five excerpts below connect its implementation to three benchmark comparisons, a component ablation, and two diagnostics. Read the gains together with their limits: the evaluation uses simulation-trained models, the strongest causal attribution still needs controls with matched outcome-label access, and the proposed extension to pretrained encoders remains unmeasured. e-probleme-rolloute-maine-controlse-limite-impl
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 catalog snapshot is unassigned, so no existing quadrant judgment can be confirmed. Architecture evidence supports a recurrent stochastic latent dynamics model with an MPC action selector. Actions condition future prediction and are selected by search; the source specifies neither joint future/action generation nor inverse dynamics. Jointly trained losses alone do not justify a One Model classification. e-beliefe-rolloute-mpc
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 Use memory to anchor genuinely open-loop alternatives
Begin with an agent whose current image cannot reveal the full control state. The observation encoder and previous action update a recurrent belief; a Gaussian posterior then supplies the stochastic latent. That belief anchors several candidate action sequences. The crucial distinction appears in Equation (9): once a branch enters imagination, the model has no future observation to encode, so it feeds a sampled prior latent into the recurrent update. This prevents future ground-truth observations from quietly correcting the branch during training. Appendix A uses eight-step counterfactual branches and 64 proposals per anchor. Only after these alternatives exist can the training objective compare their outcomes. The resulting imagined futures are predictions; they are not evidence that all candidate actions were executed at deployment. e-beliefe-rolloute-confige-imple-mpc
5.2 Make intervention outcomes define the contrast
A conventional contrastive objective may distinguish unrelated trajectories without teaching the model which similar-looking actions lead to different consequences. CLWM instead assigns pairs using intervention outcomes. A hidden object's position, a topological cell, or a vector of future subtask feasibility can separate cases that pixels alone confuse. Equation (11) rewards similarity to positive outcomes relative to the combined positive and negative set. The three hard-negative strategies target alternative actions from one belief, perceptually aliased outcomes, and value disagreement despite low reconstruction error. An auxiliary outcome head can stabilize this training, but removing that head does not remove the labels used to construct pairs. This explains why Table 2 is informative about components yet cannot fully resolve the privileged-supervision confound. e-contraste-losse-imple-ablatione-controls
5.3 Plan in the learned dynamics, then audit their geometry
At deployment, MPC scores 512 action sequences over a 12-step horizon using predicted rewards and a terminal value. The agent executes the first action of the best sequence and replans after feedback. Neither hard-negative mining nor the projection head is required for that control loop. The diagnostic asks a separate question: do distances between imagined dynamics summaries distinguish interventions with different outcomes? CFS computes this AUROC with the projection head discarded, using simulator outcome labels during evaluation. Table 1 combines the diagnostic with actual simulated task performance, and Figure 1 restricts its independent association claim to baseline classes. CLWM's own point is consistent with that trend, but its aligned training objective prevents treating it as an independent validation sample. e-mpce-confige-cfse-maine-correlation
5.4 Training and inference
During training
The full loss combines observation reconstruction or representation prediction, posterior/prior KL, reward prediction, value prediction, counterfactual contrast, and optional outcome prediction. Weights are βKL=0.5 with free bits, βr=1.0, βv=0.1, λcf=0.1, and λinv=0.01. No frozen pretrained encoder is part of the reported experiments. e-losse-confige-limit
Runs use AdamW, batch size 256, one million environment steps, and learning rate 3×10⁻⁴ with 10,000-step warmup and cosine decay to 10⁻⁶. Temperature is 0.07. Mining uses LPIPS image-patch similarity over five steps, 16 negatives per anchor, and outcome-distance threshold 0.1. e-confige-impl
During inference
MPC evaluates N=512 candidate sequences over H=12 steps using discounted predicted rewards plus terminal value. It executes only the first action of the best sequence, observes feedback, and replans. The projection head and contrastive computation are absent from deployment; privileged outcome labels are still needed for the evaluation diagnostic. e-mpce-confige-cfs
5.5 Implementation flow
- Infer a belief
A modality encoder feeds recurrent belief b with the previous action. A Gaussian posterior infers stochastic latent z; an action-conditioned Gaussian prior predicts its successor. Appendix A specifies belief/latent dimensions 200/32 and a four-layer CNN plus a proprioceptive/tactile MLP. e-beliefe-confige-impl
- Branch without future observations
From each anchor, sample 64 intervention sequences: 50% policy rollouts, 25% random shooting, and 25% replay. Roll out K=8 steps. During imagination the sampled prior latent replaces observation-encoder features in the recurrent update; future ground-truth observations are never posterior-fed. e-rolloute-confige-impl
- Align outcomes and separate hard alternatives
The projection head maps a rollout summary to a contrastive embedding. Positives share an outcome class or small outcome distance. Negatives differ in outcome; hard cases share a belief, look similar, or disagree in predicted value despite low reconstruction loss. Privileged labels define pairs as well as supervise the optional outcome head. e-contraste-losse-controls
6. Experiments & results
Counterfactual Latent World Models (CLWM) train action-conditioned imagined futures to preserve differences in intervention outcomes even when observations look alike. A recurrent world model supplies latent rollouts to model-predictive control; privileged outcome labels supervise an additional contrastive objective during training. Reported simulation gains reach 11.6 percentage points in navigation success. The evidence supports targeted representation training, while supervision-matched controls and audits of pretrained encoders remain open.
The supplied paper contains two diagnostic figures and four tables, but no architecture or method schematic. Table 4 supplies the original implementation visual, while the recurrent information flow is explained from Sections 4.1–4.5. Five original crops cover implementation, quantitative results, ablations, and both diagnostics; Table 3 was inspected in full without an additional crop. The referenced supplement with per-seed values was not supplied, so it contributes no visuals or checked statistics. e-beliefe-rolloute-mpce-imple-confige-correlatione-aliase-supplement
6.1 Read the original evidence
Table 1. CLWM improves task performance and counterfactual separability across the three reported simulated benchmarks. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read each task's paired columns together. Push and Maze report episode success and counterfactual separability (CFS AUROC); Kitchen reports normalized return and exploitation, whose downward arrow indicates lower is better. The first five rows compare reconstruction, reward-aware, generic contrastive, Dreamer-style, and TD-MPC-style models; these are the paper's baseline labels. Compare CLWM primarily with TD-MPC-style, the strongest displayed baseline. The caption specifies final checkpoints, 100 fixed test episodes, and five seeds, with ± denoting standard error for success and return. Maze uses its default layout at aliasing intensity 0.0. CFS and exploitation use the same seeds but have no displayed error terms. e-maine-baselinese-taskse-exploite-controls
What it supports. CLWM raises Push success from 65.1% to 74.6% and Maze success from 67.3% to 78.9%, gains of 9.5 and 11.6 percentage points. Kitchen return rises from 62.8 to 72.3. These results support improved simulated control under the reported protocols and accompany higher CFS.
Where the evidence stops. Exploitation falls from 18.4 to 9.7 on the reported percentage scale. However, the caption and Section 5.1 define a fraction of failures, while Section 6.1 describes episodes. That denominator remains unresolved; the table also lacks supervision-matched controls.
Figure 1. CFS tracks success across a small set of baseline model classes; CLWM provides a consistency check. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Follow the horizontal axis from less to more separable imagined futures, then compare the corresponding vertical success rates. Blue circles denote Occluded Push and red squares Aliased Maze. Although individual model names are absent, the caption identifies each series' rightmost point as CLWM. The dashed line is a least-squares fit to the ten baseline points pooled across tasks, whereas the reported correlations are computed separately across five baseline classes per task. Equation (14) measures CFS on the dynamics summaries after discarding the projection head. Thus the diagnostic examines the representation used by the planner, rather than only the embedding directly trained by contrastive loss. e-correlatione-cfse-limit
What it supports. The paper reports correlations of 0.94 for Push and 0.95 for Maze across the five baseline classes. Because those baselines do not optimize CFS, their association is more informative for metric validation than CLWM's high-scoring points. This is initial evidence that the diagnostic tracks a control-relevant property.
Where the evidence stops. The plot has few model-class observations and no uncertainty bars. Correlation does not establish causation or a universal threshold for trustworthy planning. CLWM explicitly trains an aligned objective, and no large-scale pretrained encoder is evaluated here.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Occluded Push Simulator tabletop pushing with occlusion; final checkpoints, 100 fixed test episodes, five seeds (0–4). | CLWM: 74.6 ± 1.5; CFS 0.84. Episode success (%) and CFS AUROC | TD-MPC-style: 65.1 ± 1.6; CFS 0.71. Success improves by 9.5 percentage points. ± is standard error over seeds; CFS has no displayed uncertainty. e-maine-tasks |
| Aliased Maze Default layout and aliasing intensity 0.0; final checkpoints, 100 fixed test episodes, five seeds (0–4). | CLWM: 78.9 ± 1.4; CFS 0.86. Episode success (%) and CFS AUROC | TD-MPC-style: 67.3 ± 1.5; CFS 0.70. The largest reported success gain is 11.6 percentage points. ± denotes seed-level standard error. e-maine-tasks |
| Deferred Kitchen Simulated long-horizon manipulation with hidden subtask preconditions; same final-checkpoint, 100-episode, five-seed protocol. | CLWM: return 72.3 ± 1.6; exploitation 9.7. Normalized return; reported exploitation rate (%) | TD-MPC-style: return 62.8 ± 2.0; exploitation 18.4. Return rises by 9.5 units. Exploitation falls on the reported scale, but its denominator is inconsistent: Section 5.1/Table 1 say planning failures, whereas Section 6.1 says episodes. e-maine-taskse-exploit |
| Counterfactual-negative ablation Table 2 variants trained/evaluated identically across all three benchmarks; bottom row is a reference baseline. | Without perceptual-alias negatives: 67.5 / 69.1; 0.74; 16.8. Push/Maze success (%); mean CFS; Kitchen exploitation (%) | Full CLWM: 74.6 / 78.9; 0.85; 9.7. Random negatives: 68.1 / 70.6; 0.76; 15.4. Alias-negative removal causes the largest displayed success losses. No ablation error bars are supplied, and label access remains a confound. e-ablatione-controls |
| CFS association with control Five baseline model classes per task; CLWM excluded from correlation validation. | 0.94 on Occluded Push; 0.95 on Aliased Maze. Reported correlation r between CFS and success | Figure 1 fits its dashed trend to ten pooled baseline points. Small model-class associations support an initial diagnostic, not causal proof or independent validation using CLWM itself. e-correlation |
| Aliased Maze at maximum aliasing Intensity 1.0; same final checkpoints and default layout, 100 test episodes, means over five seeds. | CLWM: 66. Episode success (%) | TD-MPC-style: 55; RSSM-Recon: 38. An 11-point margin persists as observations become less informative. Figure 2 lacks uncertainty bars and does not test new layouts. e-alias |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Table 2. Perceptual-alias negatives have the largest displayed effect, but outcome-label access is not fully controlled. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use Full CLWM as the within-method reference. Each subsequent variant removes a particular source of supervision or changes the negative pool. Push and Maze columns report separate success percentages; average CFS combines those two tasks, while Kitchen exploitation belongs to a different benchmark. The separated bottom row repeats TD-MPC-style from Table 1 and is not an ablation. Removing perceptual-alias negatives produces the lowest success among these variants. Random negatives recover some benefit over the reference baseline but fall short of full CLWM. Removing the outcome head still leaves privileged labels in contrastive pair construction, so this row does not measure learning without outcome labels. e-ablatione-controls
What it supports. Without perceptual-alias negatives, Push/Maze success falls from 74.6/78.9 to 67.5/69.1, and mean CFS drops from 0.85 to 0.74. This supports the importance of distinguishing visually similar outcomes. It does not determine how much of the overall advantage comes from labels versus the loss geometry.
Where the evidence stops. Section 6.3 calls the outcome head the least contributing component, but removing value-disagreement negatives causes smaller success losses in this table. No uncertainty is displayed. The authors also acknowledge missing outcome-head-only and supervision-matched baseline controls.
Figure 2. The planning advantage persists across increased perceptual aliasing in the same maze layout. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read left to right as local observations become less informative about topological state. The leftmost points correspond to the default intensity 0.0 used in Table 1. Black diamonds show CLWM, brown triangles TD-MPC-style, red squares Dreamer-style, and blue circles RSSM-Recon. The caption states that all points reuse the same final checkpoints and evaluation protocol, with 100 test episodes and means over five seeds. This makes the figure a stress test of already trained models under altered observations. It is not evidence of retraining at each intensity. At the right boundary, compare both absolute success and the remaining gap between the top two methods. e-aliase-maine-config
What it supports. At intensity 1.0, CLWM retains 66% success, versus 55% for TD-MPC-style and 38% for RSSM-Recon. The strongest-baseline gap remains 11 percentage points, close to the default-setting 11.6-point gap. Thus the reported advantage persists as the benchmark's visual ambiguity increases.
Where the evidence stops. The source supplies neither error bars nor a precise operational recipe for transforming observations at each intensity. The caption retains the default maze layout, so this figure does not establish generalization to new topologies, physical navigation, or broader distribution shifts.
7. Analysis & limitations
7.1 What the evidence leaves open
Reliable outcome signals and extra branching/mining are required. Long-horizon compounding error, exploration, distribution shift, and reward misspecification remain unsolved. Pretrained-encoder applicability is conceptual, and the reported benchmarks do not establish physical robot deployment. e-limite-tasks
The paper explicitly lacks an outcome-head-only variant with λcf=0 and a baseline receiving identical outcome labels. Therefore the existing ablations cannot fully separate privileged supervision from the contrastive geometry. e-controls
Section 6.3 calls the outcome head the least contributing component, but Table 2 shows smaller success losses when value-disagreement negatives are removed (3.3/4.9 points versus 3.8/5.4). The numerical rows support a more qualified ranking. e-ablatione-controls
7.2 Questions for discussion
- Would matched outcome-label access preserve the advantage of hard counterfactual negatives?
- Does CFS predict planning quality across held-out layouts and frozen pretrained encoders?
8. Reproducibility audit
8.1 Requirements and known gaps
Appendix A reports a single NVIDIA A100, approximately 24 hours per CLWM run versus 12 hours per baseline. Listed simulators are MuJoCo (MJX) v1.2.1, a Gymnasium-based grid world v0.1.0, and adapted RoboSuite v2.0. These are source-reported configurations, not verified installations. e-impl
Reproduction still needs the referenced per-seed supplement, exact benchmark adaptations/splits, rollout-summary construction, and input adapters for the open-loop recurrence. Continuous outcome descriptors versus the class-based outcome head, distance/similarity choices and mining cutoffs, free-bits threshold, reward normalization, aliasing transformation, and exploitation thresholds/denominator are insufficiently specified. e-supplemente-rolloute-contraste-imple-confige-cfse-aliase-exploit
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: Match outcome-label access before attributing the gain to geometry
Reader-proposed check, not performed: on Occluded Push and Aliased Maze, compare full CLWM with (1) the same model retaining the outcome head but setting λcf=0, (2) TD-MPC-style with an outcome head trained on the same labels, and (3) CLWM with random negatives at a matched negative count. Reuse training data, anchor interventions, outcome labels, model capacity where applicable, environment-step budget, seeds, and final-checkpoint evaluation episodes. Record compute as well as success, CFS with the projection head removed, and outcome accuracy. A persistent hard-negative advantage after matching label access would support the geometry explanation; parity with outcome-only supervision would weaken it. Report seed-level differences and uncertainty. e-controlse-ablatione-confige-imple-cfs
Check 2: Test whether CFS predicts control on held-out ambiguities
Reader-proposed check, not performed: freeze the reported model classes and collect a separate set of common simulator anchors, with verified alternative-intervention outcomes. Evaluate both the documented maze layout and held-out layouts, stratifying anchors by perceptual aliasing. Fix the intervention pool, rollout horizon, latent-distance definition, planner budget, and outcome-labeling rule across models; resolve the source's unspecified distance and aliasing recipes before comparing numbers. Compute CFS without the projection head and measure MPC success on separate episodes. Assess baseline-only associations within each layout and report uncertainty. If CFS remains high while success falls, or the association vanishes outside the original layout, its usefulness as a transferable planning audit would be limited. e-cfse-correlatione-aliase-confige-limit
8.3 Reading coverage
Visual audit: All 11 PDF pages were rendered and visually inspected, including the title/byline/version, complete method equations, evaluation definitions, both figures, Tables 1–4, limitations, references, and Appendix A. Every final crop was viewed; the main-results and ablation crops were tightened to exclude fragments of preceding captions while retaining every header and row. Table 4 head dimensions were cross-checked with the method; there is no architecture diagram to inspect. Supporting pages for every retained method, numerical, training, evaluation, and reproduction claim are included. Source inconsistencies in exploitation accounting and the outcome-head ranking are disclosed in the report and visual cautions. No supplemental pages or external code were inspected.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Appendix coverage: reviewed.
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
- 1 Introduction
- 2 Related Work
- 3 Problem Setting
- 4 Counterfactual Latent World Models
- 4.1 Belief-State Encoder
- 4.2 Action-Conditioned Counterfactual Rollouts
- 4.3 Counterfactual Contrastive Objective
- 4.4 Full Training Objective
- 4.5 Planning with CLWM
- 5 Experimental Design
- 5.1 Benchmarks
- 5.2 Baselines
- 5.3 Metrics
- 6 Results
- 6.1 CLWM Improves Planning in the Regime Where Prediction Is Ambiguous
- 6.2 Counterfactual Separability Tracks Downstream Control
- 6.3 Ablations Show That the Gains Come from Counterfactual Structure
- 6.4 Robustness under Perceptual Aliasing
- 7 Discussion
- 8 Limitations and Broader Impact
- 9 Conclusion
- References
- A Experimental Details
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.
- Identity: PDF p. 1 matches the supplied title and both authors, Todd Y. Zhou and Daniel Zhang, each credited to Harvard University. The observed edition is arXiv:2609.05834v1 [cs.AI], 5 September 2026. No title, author, or date discrepancy was observed; no other edition was supplied or compared.
- Text extraction does not reconstruct figure images; this reading therefore also inspected all 11 original PDF pages, both figures, and Tables 1–4. All four supplied text chunks were read in full, including References and Appendix A.
- Separate supplemental material availability has not been fully verified. Appendix A refers to per-seed results in supplementary material, but no supplement was supplied, so those values could not be checked.
- Code was not inspected and experiments were not reproduced. External references were not opened.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e-identityPDF p. 1, title/byline and arXiv margin
Exact supplied title; Todd Y. Zhou and Daniel Zhang; Harvard University for each; arXiv:2609.05834v1 [cs.AI], 5 Sep 2026.
Go to primary source ↓e-problemPDF pp. 2–3, Sections 1–3, especially Eq. (3) and causal-reasoning paragraph
Counterfactual collapse means nearby imagined summaries despite distinct intervention outcomes. Interventional terminology does not imply identifiability.
Go to primary source ↓e-beliefPDF pp. 3–4, Section 4.1, Eqs. (4)–(6)
Observation encoder and previous action update recurrent belief; posterior and action-conditioned prior are Gaussian.
Go to primary source ↓e-rolloutPDF p. 4, Section 4.2, Eqs. (7)–(10)
Alternative action sequences produce open-loop prior rollouts; sampled latent replaces observation features for belief advancement. Projection embeddings are training-only.
Go to primary source ↓e-contrastPDF p. 4, Section 4.3, Eq. (11) and negative-mining paragraph
Outcome labels define positives and negatives. The loss pools exponentiated positive similarities; three hard-negative types target action alternatives, visual aliasing, and value disagreement.
Go to primary source ↓e-lossPDF pp. 4–5, Section 4.4, Eqs. (12)–(13)
Training combines prediction, KL, reward, value, contrastive, and optional outcome losses.
Go to primary source ↓e-mpcPDF p. 5, Section 4.5
MPC scores discounted reward plus terminal value, executes the first action, and replans; deployment needs no contrastive computation.
Go to primary source ↓e-tasksPDF p. 5, Section 5.1; PDF p. 11, Table 4, Outcome descriptors and Simulators rows
Benchmarks involve occluded pushing, topologically aliased navigation, and delayed manipulation feasibility. Table 4 specifies simulation implementations and privileged task outcomes.
Go to primary source ↓e-baselinesPDF pp. 5–6, Section 5.2
Five baselines cover reconstruction RSSM, reward-aware RSSM, generic contrastive CPC-RSSM, Dreamer-style latent actor-critic learning, and TD-MPC-style value-guided planning.
Go to primary source ↓e-mainPDF p. 6, Table 1, all rows/columns and caption
CLWM and TD-MPC-style: Push success 74.6±1.5 vs 65.1±1.6 and CFS .84 vs .71; Maze success 78.9±1.4 vs 67.3±1.5 and CFS .86 vs .70; Kitchen return 72.3±1.6 vs 62.8±2.0 and exploitation 9.7 vs 18.4. Five seeds, SEM, final checkpoints, 100 fixed episodes; Maze intensity 0.0.
Go to primary source ↓e-cfsPDF p. 6, Section 5.3, Eq. (14) and following paragraph
CFS is AUROC of imagined latent distance for different intervention outcomes, with projection head discarded and privileged simulator labels used at evaluation.
Go to primary source ↓e-correlationPDF p. 7, Figure 1/caption and Section 6.2
Reported baseline-only correlations are .94 for Push and .95 for Maze; dashed fit pools ten baseline points. CLWM points are explicitly excluded as independent validation.
Go to primary source ↓e-ablationPDF p. 7, Table 2, all rows and caption; Section 6.3
Full CLWM, negative removals, no outcome head, and random negatives are compared; CFS averages Push and Maze. No value-disagreement: 71.3/74.0 success; no outcome head: 70.8/73.5. The final TD-MPC-style row is a reference, not an ablation.
Go to primary source ↓e-controlsPDF p. 8, continuation of Section 6.3, outcome-head paragraph
Authors characterize the outcome-head cost as least, explain labels enter both objectives, and acknowledge absent λcf=0 and supervision-matched baseline controls.
Go to primary source ↓e-aliasPDF p. 8, Figure 2/caption and Section 6.4
Same checkpoints/default layout and 100-episode protocol across aliasing intensities; five-seed means. At intensity 1.0, success is 66% CLWM, 55% TD-MPC-style, and 38% RSSM-Recon; uncertainty bars are absent.
Go to primary source ↓e-limitPDF p. 9, Sections 7–9, especially Section 8
Models were trained from scratch; pretrained-encoder CFS is unmeasured. Reliable labels and extra training cost are limitations, as are unsolved compounding error, exploration, shift, and reward misspecification.
Go to primary source ↓e-configPDF p. 11, Table 3, all rows
Five seeds 0–4; belief/latent 200/32; MPC N=512, H=12; K=8; τ=.07; specified loss weights, AdamW schedule, batch 256, one million environment steps, and final-checkpoint evaluation.
Go to primary source ↓e-implPDF p. 11, Table 4, all rows
M=64 branching mix 50/25/25; LPIPS five-step mining, 16 negatives, outcome-distance threshold .1. Lists outcome descriptors, simulator versions, CNN/MLP architecture, mirrored decoder, 256→128→64 projection discarded at evaluation, class outcome head, sensitivity ranges, and single-A100 approximate 24h/12h costs.
Go to primary source ↓e-supplementPDF p. 11, Appendix A opening paragraph
Appendix A directs readers to supplementary per-seed values underlying Tables 1 and 2; those values are not printed in the supplied PDF.
Go to primary source ↓e-exploitPDF p. 5, Section 5.1; PDF p. 6, Table 1 caption and Section 6.1 final paragraph
Definition/caption use the percentage of planning failures, while the results prose describes 18.4% of episodes. The denominator and high/low value thresholds are unresolved in this edition.
Go to primary source ↓8.5 Primary sources
Learning Counterfactual World Models for Embodied Reasoning under Partial Observability ↗
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