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INTACT: Isomorphic Intent-to-Action Learning for Search-Free World Models

Junhan Sun, Hao Zhao, Guofeng Zhang

arXiv:2607.26056v1cs.RO

TL;DR

Forward world models predict action effects but do not directly identify actions for desired changes, leaving deployment dependent on expensive search. INTACT learns an intent-to-action interface from reward-free, action-labeled trajectories, achieving strong multi-task success with zero-search inference and making search optional.

  • Problem

    Forward world models predict action effects, but goal-conditioned control still numerically searches for actions because inverse action–latent semantics remain uncalibrated.

  • Method

    INTACT aligns physical successor and deployable goal intents through shared action-law semantics, jointly learning a conditional action interface without pointwise latent matching.

  • Results

    89.39±0.77% macro Direct SR is achieved by one shared four-task INTACT encoder, improving all four tasks over matched shared-encoder LeWM.

  • Takeaways & Limitations

    INTACT exposes amortized action selection directly at deployment, making search an optional verifier rather than the mandatory world-model interface.

  • Takeaways & Limitations

    The action quotient is identified only on demonstrated support, and cross-task transfer still fails without explicit alignment or broader coverage.

Abstract

from arXiv · show

Forward latent world models predict how actions change a scene, but recover actions for a desired change only through expensive test-time search. We introduce INTACT (INtent-To-ACTion), an end-to-end JEPA that turns action-labeled, reward-free trajectories into a deployable intent-to-action interface. Each transition supplies physical intent $z_{t+1}-z_t$, while a future goal supplies deployment intent $\operatorname{sg}(z_g)-z_t$. The architecture is isomorphic between the local and goal motion-intent backbone-input graphs through an identical four-slot grammar and shared parameters, and between supported local and goal motion-intent families through action-law semantics induced by the same predictor rather than pointwise latent equality. INTACT also provides intact transfer from RGB evidence to action-effective latent intent coordinates and from intent families to their corresponding action-law families. Asymmetric endpoint gradients ground physical successors and fix future goals as anchors, joining representation learning and control without pointwise latent matching or globally linear dynamics. The resulting coordinates support a robust distributional action law: its conditional mean serves directly as a search-free policy, while sampling remains available for diversity or optional verification. On the four official LeWM tasks, one-epoch, zero-search models reach 85.78\%, 100.00\%, 97.67\%, and 97.89\% success. Optional local CEM centered on the Direct plan reaches 96.86\% macro success using 384 instead of 9,000 candidate sequences, reducing sampling by $23.44\times$ while improving pure CEM by 16.00 points. One shared four-task encoder reaches 89.39\% E5 Direct macro and improves every task over jointly trained LeWM, while predicted--expert action-family kNN tracks Direct success at $r=0.954$. Direct inference takes 2.9--5.5 ms.

SUCCESS GAP +31.7 pp

INTACT turns action-aligned latent intent into search-free control, outperforming LeWM by 31.7 points on a fixed E5 Cube audit. The results also indicate that its gains involve shared-operator structure and a unified multi-task intent space, rather than goal-only behavioral cloning.

  • Interpretation: The observed advantage is not reducible to goal-only BC, according to the reported novelty analysis.The section separately identifies this distinction as a contribution.
  • Representation: INTACT’s representation preserves shared-operator conjugacy and a unified multi-task intent space.The lower panels are described as showing prevention of representational collapse and preservation of this unified space.
  • Success gap: 98.7% versus 67.0% success (+31.7 points): INTACT Direct outperforms LeWM CEM 300×30 from 300 matched starts.The audit uses a fixed E5 Cube evaluation.
  • Success gap: 97 favorable and only two adverse success flips characterize the INTACT-versus-LeWM comparison from the same starts.The flip summary is reported as INTACT ✓ / LeWM ✗ 97 and INTACT ✗ / LeWM ✓ 2.
  • Control: At inference, a goal-conditioned call emits one action chunk for search-free Direct control, while rollout is retained for optional verification and replanning.The Forward Predictor retains latent-dynamics and SIGReg supervision during training.

1 Introduction

INTACT turns reward-free, action-labeled trajectories into an isomorphic latent intent-to-action interface that supports direct control without pointwise latent matching or test-time search. It preserves controllable action-family structure while retaining predictive information, achieving strong single-task and multi-task benchmark results.

  • Core approach: INTACT learns state-conditioned motion intents from action-labelled transitions and converts deployment goal displacements into actions through a shared proper likelihood.The local and goal branches use isomorphic typed predictor graphs with asymmetric gradient routing, while future-goal anchors receive stop-gradient treatment.
  • Representation: INTACT preserves predictive latent information while organizing action-equivalent requests into a conditional action quotient for rapid control readout.The quotient applies to action conditions, not the complete JEPA latent, which must retain contacts, obstacles, and future visual information.
  • Design principles: INTACT avoids regressing goal intents onto physical successors, instead preserving their conditional family relation through probabilistic action likelihood.This prevents pointwise matching from discarding velocity, contact, or action-identifiable information.
  • Results: 85.78%, 100.00%, 97.67%, and 97.89% success are reached on PushT, Cube, Reacher, and TwoRoom by final one-epoch, no-search single-task models.The result uses three training seeds per task on the official four-task LeWM benchmark.
  • Results: 42.69±7.19% Direct macro SR is achieved by Full INTACT at E1, versus 35.75±7.58% for waypoint-intent-only and 33.47±3.98% for inverse-only.Adding physical inversion to goal-intent-only raises PushT and TwoRoom by 12.89 and 15.33 points.
  • Evaluation: 0.954 is the Pearson correlation between predicted–expert action-family kNN and official SR, compared with 0.815 for pointwise action R2.After controlling epoch and cohort, kNN remains r = 0.902.

2 Related Work

Prior work spans latent JEPA world models, inverse and hindsight-imitation objectives, skill discovery, action-induced representation equivalence, and planner-guided control. INTACT combines these lines while distinguishing its jointly trained, forward-model-based, deployment action conditional from prior methods.

  • Latent world models and JEPAs: JEPA world models predict in representation space, with DINO-WM, PLDM, and LeWM differing in encoder freezing and regularization choices.PlaNet, Dreamer, and TD-MPC2 provide related latent-dynamics and control foundations.
  • Inverse dynamics and skill discovery: Inverse dynamics, empowerment, options, and unsupervised skill methods organize controllable visual structure, temporally extended actions, reachable outcomes, or predictable skill-conditioned dynamics.Prior examples include inverse-supervised JEPA regularization, DIAYN, DADS, and CIC.
  • Hindsight goal-conditioned imitation: INTACT’s deployment branch has a GCSL-like hindsight action-likelihood form but retains JEPA forward prediction and SIGReg on fixed offline expert trajectories.It is therefore distinct from original GCSL, which alternates policy-driven collection with supervised updates.
  • Metric learning and action-induced equivalence: Action-induced equivalence relates to metric learning, bisimulation, and action quotients, but INTACT’s quotient acts on local and goal motion intents at fixed JEPA state.Its representation geometry is tied to output distributions and coexists with an explicit forward world model rather than operating on complete VLM prompts.

3 INTACT: Theory and Method

INTACT closes the forward–action gap by applying one shared conditional action operator to both realized physical transitions and deployable goal conditions. Its isomorphic typed-slot construction, asymmetric endpoint gradients, and conditional action-law semantics produce a search-free recurrent action interface without requiring globally linear dynamics or pointwise latent equality.

  • Shared operator: INTACT applies one shared conditional action operator to realized physical transitions and pre-action goal conditions, while retaining a separate forward predictor.The physical call uses the observed successor displacement; the goal call uses a future-goal displacement available before acting.
  • Endpoint gradients: Asymmetric endpoint gradients keep physical successors attached for representation learning while stop-gradient fixes future goals as deployment intent anchors.The goal endpoint is fixed only in the deployment loss; current-state latents, the conditional operator, and physical branches remain trainable.
  • Isomorphic intent: Its two calls are isomorphic through typed input slots and shared parameters, while their motion-intent families correspond through conditional action laws rather than numerical latent equality.The construction explicitly avoids pointwise latent matching and does not assert globally linear latent dynamics.
  • Action-law identification: Proper conditional likelihood training recovers the expert action law on every supported condition, giving action-equivalent endpoints the same predicted action law.This supported quotient recovery does not identify behavior for deployable goal conditions outside the realized-successor support.
  • Deployment interface: At deployment, the conditional Gaussian mean recurrently generates an H-block plan through the unchanged Forward Predictor, and Direct executes without sampled candidates or terminal cost.Optional Guarded A instead centers a 128 × 3 local raw-action search on the Direct plan with σ0 = 0.25.

4 Experimental Design

The experiments evaluate INTACT across four official LeWM domains under standardized RGB-based protocols, controlled training settings, and explicit zero-search and search-based controls. Ablations, probes, and mechanism analyses separate representation shaping from action-conditional control benefits.

  • Tasks and evaluation: Evaluation covers PushT, OGBench Cube, DMC Reacher, and TwoRoom using RGB observations and five-step action blocks, with 100 episodes per seed across seeds {0, 1, 42}.Simulator state is restricted to probes and success predicates, while headline SR follows the official evaluator.
  • Training protocol: Task-specific models train from scratch for one epoch with batch size 256, AdamW learning rate 5 × 10−4, and three training seeds.The final goal-displacement model uses SIGReg 0.02 and the shared grammar in Eq. (16).
  • Planning controls: Direct uses zero candidate sequences and zero terminal-cost calls, while pure CEM optimizes raw actions and Guarded A evaluates 128 sequences for three iterations around Direct.Pure CEM is a functional control rather than an encoder-only statistic.
  • Mechanism analysis: Frozen probes measure physical-state and transition-action R2, effective rank, per-dimension standard deviation, collapsed-dimension fraction, and mean cosine similarity on episode-disjoint episodes.Together with actor-disabled CEM, these analyses distinguish representation shaping from learned action-conditional execution.
  • Ablations: The controlled factorial compares forward-only LeWM, physical inverse-only, intent-only, and Full INTACT across six cells, evaluated at E1–E5 with Direct, pure CEM, Guarded A, probes, and diagnostics.Intent-only and Full use waypoint and goal-displacement coordinates; all cells use training seeds {0, 42, 3072}.
  • Mechanism analysis: Mechanism analysis computes predicted–expert linear CKA, local kNN overlap, action R2, and NLL within native task action coordinates, averaging equally without zero-padding heterogeneous spaces.The primary cohort contains both Full INTACT interfaces, three seeds, and E1–E5.

5 Results

INTACT delivers strong zero-search control with one end-to-end training epoch, while low-budget search serves mainly as optional verification. Its goal-displacement coordinate, shared encoder, and learned intent–action family relation improve task performance, representation quality, and transferability.

  • Efficiency: 95.33 macro SR is achieved by Direct with zero candidates and 2.9–5.5 ms planner-side latency after one end-to-end epoch.INTACT uses no frozen-encoder phase or separately trained phase-2 controller.
  • Task results: 85.78/100.00/97.67/97.89% Direct SR is obtained on PushT/Cube/Reacher/TwoRoom, using one tenth as many full-data passes as published LeWM.Goal displacement outperforms the waypoint coordinate under every matched interface.
  • Shared training: 89.39±.77 macro Direct SR is reached by one shared encoder at E5, versus 66.17±2.67 for matched shared-encoder LeWM with CEM 300 × 30.INTACT improves LeWM by 5.66/32.23/12.56/42.44 points on PushT/Cube/Reacher/TwoRoom and exceeds the 85.75 published task-specific LeWM macro.
  • Coordinate comparison: 89.39±.77 versus 76.42±2.32 macro Direct SR shows goal displacement overtakes waypoint by E5, although waypoint leads 42.69±7.19 versus 36.83±5.63 at E1.The E1 comparison measures optimization speed, whereas E5 reveals the stronger converged intent coordinate.
  • Family transfer: .954 is the predicted–expert action-family kNN correlation with official Direct SR in the strict replication cohort.Across primary checkpoints, CKA and local kNN overlap correlate with Direct SR at .861 and .926; adjusted kNN remains .902.

6 Limitations

INTACT’s evidence is limited to demonstrated support, simulated benchmark settings, and diagnostics that provide necessary checks rather than formal guarantees. Its direct Gaussian policy can obscure multimodal actions, while gauge-equivalence and transfer findings do not establish exact conjugacy, global affine coordinates, or exclusive representation properties.

  • Evidence scale: Three training seeds and three evaluation seeds per checkpoint provide only a coarse scaling estimate, despite complete coverage of the controlled multi-task matrix and conversion audit.The audit covers six objective cells, E1–E5, and both Full INTACT interfaces under Math-SDPA.
  • Identifiability: The action quotient is identified only on demonstrated support and does not determine arbitrary counterfactual goals or whether alternative actions are equally valid.Full goal displacement preserves direction and distance but remains approximate around obstacles, contact switches, and multimodal demonstrations.
  • Diagnostics: Current diagnostics are necessary checks, not certificates: effective rank and SRS can reward isotropic noise, Gsep is only an action-distinctness proxy, and Expert NLL is not independent.A stronger evaluation would use action-equivalent and action-distinct counterfactual conditions and report normalized causal measures.
  • Policy multimodality: The deployed Direct action is the mean of a diagonal Gaussian, so it can fall between valid modes at junctions or contact transitions.Search can verify proposals but forfeits the zero-candidate identity; mixture actors, uncertainty-triggered verification, and quotient-aware mode selection are proposed alternatives.
  • Representation claims: Gauge-equivalence evidence is task-manifold conditioned and does not establish exact conjugacy or a single global affine chart.Alignability is not INTACT-exclusive because LeWM and inverse-only backbones can also align into a trained Full actor; reverse swaps show gauges cannot create an absent deployment map.
  • Scope and evaluation: Experiments cover four simulated tasks with fixed image goals, task-specific action heads, and offline expert trajectories, leaving real-robot, out-of-distribution, distractor, and cross-embodiment generalization unestablished.The headline uses the official LeWM benchmark for comparability, while the stricter legality-aware audit is reported separately and requires independent validation.

7 Conclusion · Appendix

INTACT frames physical successors and deployable goals through the expert action law they induce at a fixed world state, enabling a direct conditional control interface. Controlled audits report strong one-epoch, zero-search performance and show that optional plan-centered search improves efficiency while retaining high success.

  • 7 Conclusion: INTACT identifies physical successors and deployable goal intents through the expert action law they induce at a fixed world state.The method rejects endpoint identity and Euclidean proximity as the useful commonality.
  • 7 Conclusion: 85.78%, 100.00%, 97.67%, and 97.89% official Direct SR are achieved after one epoch with no candidate search.The result uses three training seeds on every task.
  • 7 Conclusion: 96.86% with 384 sequences exceeds 93.78% with 9,000 sequences in the final coordinate comparison.The former is plan-centered Guarded A, while the latter is actor-on CEM; 95.33% is the corresponding Direct macro result.
  • 7 Conclusion: 68.04% CLEAR Moderate SR under correct pairing falls to 9.46% after pair shuffling in the 21,600-episode gauge audit.The calibration curve saturates near 64/full episodes, and reverse Full-backbone-to-LeWM-actor alignment remains at 5.08%.
  • 7 Conclusion: 96.86% macro and 92.22% worst-task SR are reached by Guarded A with 23.44× fewer sampled candidate sequences than matched pure CEM 300×30.Guarded A uses a 128×3 raw-action residual search centered on the deterministic INTACT plan and exceeds pure CEM by 16.00 macro points.
  • 7 Conclusion: 0.08 macro point separates ordinary σ0 = 0.25 from the recommended inference result, while an L2-trust variant raises PushT to 92.78% but is less uniform.The L2-trust variant is therefore not part of the recommended inference interface.
  • 7 Conclusion: Search becomes an optional verifier rather than the mandatory model interface because a single JEPA can retain predictive state and expose a conditional action law at deployment.The broader construction is presented as not tied to JEPA, although the supplied passage truncates before completing that generalization.

A Proofs and Statistical Interpretation

The proofs show that successor-only training cannot identify behavior for unsupported deployment intents, whereas proper likelihood preserves distinct expert action laws on supported endpoints. The statistical analysis further distinguishes population equivalence from finite-batch effects of paired sampling under adaptive optimization.

  • Proposition 2: Successor-only risk cannot identify deployment behavior for goal intents outside the supported successor set S.Changing an actor at an unsupported goal intent leaves the successor-only integral unchanged.
  • Proposition 3: Proper likelihood uniquely recovers the expert conditional action law almost everywhere on every supported endpoint.The proof uses an entropy-plus-KL decomposition, with equality only when modeled and expert conditional laws agree.
  • Proposition 3: If two endpoints share the same expert action law, both recovered laws coincide; differing expert laws remain distinguishable under proper likelihood.This conclusion follows by applying the KL argument to each supported endpoint.
  • Statistical interpretation: Paired estimation preserves the same population expectation as independent Bernoulli endpoint sampling, but changes finite-batch gradient covariance under adaptive optimization.It also keeps one conditional observation per transition and fixes the action-loss scale; paired controls test this finite-sample prediction.

B Implementation and Evaluation Identities … D.1 Which intent coordinate should the shared operator receive?

The appendix specifies INTACT’s implementation, endpoint routes, interaction grammar, and design-selection evidence. Across matched one-pass studies, full goal displacement and a state-dependent interaction sub-grammar are selected for the shared operator.

  • B Implementation and Evaluation Identities: The encoder is ViT-Tiny/14 projected to 192 dimensions, while a six-layer causal transformer predicts histories of length three and groups five environment actions per model action.The shared Predictor is a three-layer width-1024 MLP with Layer-Norm and GELU, emitting diagonal-Gaussian mean and log standard deviation clipped to [−5, 2].
  • C.1 Waypoint route and equal-progress assumption: Waypoint attribution narrows train–deployment support but removes remaining-distance magnitude, whereas the raw-goal route uses m_goal,t = sg(z_g) − z_t and permits state-dependent progress.The future endpoint is detached only in deployment; it remains attached as the real successor of the last physical transition, and neither a complete batch nor the encoder is detached.
  • C.2 Why intent coordinates do not straighten trajectories: Goal-conditioned transitions may include detours, contact changes, and multimodal residuals, so intent coordinates do not impose a Euclidean trajectory penalty.The Forward Predictor updates reachability and the goal residual.
  • C.3 Alternative endpoint sampling and end-to-end necessity: Endpoint sampling can draw one transition endpoint from a Bernoulli choice, but end-to-end likelihood training is necessary when identical observations require different action laws under the same intent.Backpropagation through the encoder exposes the controllable distinction that a frozen downstream actor cannot recover from aliasing.
  • C.4 Endpoint grammar and interaction prediction: The A–G grammar tests matched displacement/product slots against product-only changes, and SC > SG rejects centering the product alone as sufficient.The interaction is interpreted as a state–intent interaction in the controlled endpoint study.
  • C.5 General endpoint conditioning: The general endpoint design may expose an optional relation r, while the final raw-goal policy trains across remaining offsets r = 1, …, 5 without explicitly receiving horizon.Its inputs are the current state, raw goal displacement, interaction feature, and previous action.
  • D Design Selection and Ablation Logic: The ablation appendix fixes design choices through matched interventions while keeping the headline evaluation protocol unchanged.Studies use one full-data pass, three training seeds, the same evaluation episodes, and deterministic Math-SDPA.
  • D.1 Which intent coordinate should the shared operator receive?: +7.00 points is the A→E gain from waypoint endpoint to full goal displacement, with exact p = 4.17 × 10−9; the matched interaction difference-in-differences is +3.89 points.The matched endpoint-to-centered change A→C is +4.33 points, centered-to-full-goal C→E is +2.67 points, SE − SF = +2.56, and SC − SG = +3.44; G shows that deleting z_t⊙z_t alone is insufficient.

D.2 Does the result require trajectory straightening or a particular optimizer? … E.4 Representation and conversion diagnostics

The controlled results show that INTACT’s action-aligned interface does not require globally straight latent trajectories or a particular optimizer, while bounded verification and audited representation diagnostics preserve reliable performance. Across single-task, shared-encoder, and conversion analyses, action-law quality tracks success more closely than geometric spread alone.

  • D.2 Does the result require trajectory straightening or a particular optimizer?: 85.67/86.00/86.67% for E and 81.50/81.67/83.00% for F across re-encoding intervals 1/2/5 show no significant endpoint differences.The reported p-values are 0.392/0.253, while the waypoint curve is confounded by reset-restarted 1/h phases.
  • D.2 Does the result require trajectory straightening or a particular optimizer?: A 0.3 flexible-linearity weight collapses Direct SR to 14.11%, whereas a 0.01 chord penalty lowers validation chord MSE from 0.2173 to 0.2064 but yields 79.22% SR.The result separates visibly straighter geometry from better control performance.
  • D.2 Does the result require trajectory straightening or a particular optimizer?: 77.67±0.88% and 68.22±1.26% from formal probabilistic NLL settings do not establish pointwise regression as preferable, while forward weights 1.0/0.3/0.1/0 give 77.67/73.11/59.56/25.22%.A single-seed Huber screening run obtains 55.0%, and the forward predictor complements rather than replaces world prediction.
  • D.3 Why is Guarded A the optional verifier?: 85.78% Direct rises to 92.33% for PushT at σ0 = 0.25, while larger correction radii degrade Reacher; Guarded A reaches 96.86% macro with 384 sequences.Guarded A is statistically near unguarded σ0 = 0.25 at 96.78%, and doubling to K = 256 reaches 96.83% without a resolved gain.
  • E.4 Representation and conversion diagnostics: Healthy SIGReg-supported high-dimensional clouds may appear shell-like or interleaved in t-SNE, so projection morphology is qualitative and neither computes nor ranks SR.Quantitative analyses instead use original-space rank, standard deviation, forward error, probes, and predicted–expert action-family relations.
  • D.4 Qualitative multi-task geometry: The selection rule preserves the world objective, exposes a distance-preserving intent coordinate with matched state interaction, learns both condition families through one probabilistic operator, and adds only bounded local search.This summarizes the controlled geometry and verifier design choices.
  • E.1 Single-task evaluator and attribution details: 77.67±.88% at the selected one-epoch setting exceeds 77.00±2.03% at 7.5 × 10−4 and 77.22±1.07% after a second epoch, despite effective rank rising from about 43.7 to 58.8.The second epoch separates geometric spread from action-aligned representation quality.
  • E.4 Representation and conversion diagnostics: .954 pooled predicted–expert action-family kNN correlation tracks official Direct SR across 45 formula-eligible checkpoints, compared with .897 for CKA, .815 for pointwise action R2, and −.786 for NLL.Leave-one-epoch-out kNN values remain [.946, .963], and analyses use one point per checkpoint rather than one point per transition.

E.5 Task-conditioned gauge controls · F Actor-Sharing Mechanism Audit

Task-conditioned gauge controls show that correct pairing substantially improves CLEAR Moderate success while cross-task transfer remains negative, supporting task-local action charts. The actor-sharing audit links stronger sharing and gradient coordination to goal use and success, while showing that consistency alone does not establish physical correctness.

  • E.5 Task-conditioned gauge controls: 68.04% CLEAR Moderate SR follows correct pairing, versus 9.46% with shuffled pairing, a +58.58 point gain positive across all 24 protocol units.The 8-cluster bootstrap 95% CI is [48.83, 67.58].
  • E.5 Task-conditioned gauge controls: 64.83% SR is reached with full-episode calibration, compared with 26.67%, 56.00%, and 64.42% using 4, 16, and 64 episodes.Same-objective cross-seed swaps define the alignment ceiling; LeWM and inverse backbones aligned into a trained Full actor are positive alignability controls.
  • E.5 Task-conditioned gauge controls: 5.08% SR remains for Full-backbone-to-LeWM-actor transfer, while the inverse actor recovers only inverse-level function.These reverse-transfer results contrast with the positive alignability controls.
  • E.5 Task-conditioned gauge controls: Cross-task and leave-one-task-out actor-output transfer remain negative, while pooled calibration reaches only .484/.539 R2.The shared visual backbone can support several task-local charts without requiring one global canonical action space.
  • F Actor-Sharing Mechanism Audit: The actor-sharing audit measures shared action-network parameters, complete-coordinate gradient cosine, goal-shuffle response, and Forward-Predictor consistency on fixed PushT waypoint batches.Shared fraction counts parameters touched by both local and deployment losses; gradient cosine is zero by construction for disjoint actors.
  • F Actor-Sharing Mechanism Audit: 0.575 gradient cosine indicates positive physical/deployment gradient alignment in the fully shared model, and gradient coordination and SR decline together as sharing weakens.Across six designs, shuffle-goal response has exploratory Spearman ρ = 0.943 with SR (n = 6), while the small design count precludes a universal claim.
  • F Actor-Sharing Mechanism Audit: Goal-intent-only has the lowest consistency MSE but the worst SR, showing that Forward-Predictor self-consistency does not establish physical correctness.The passage introduces this as one of two especially informative negative controls.

G Exploratory Diagnostic Definitions and Correlations

This section defines exploratory diagnostics for latent geometry and goal-conditioned actor response, then relates them to predictive and action-distribution metrics. SRS tracks Direct success strongly in a small endpoint analysis, but these diagnostics are intended for mechanism auditing rather than universal thresholds or ranking.

  • Diagnostic definitions: SRS combines entropy effective rank with how closely latent sample radii match the Gaussian shell expected at that effective dimension.It measures geometric spread, not the information encoded by those dimensions.
  • Diagnostic definitions: Gsep measures an actor’s response to a changed goal relative to its own predictive uncertainty.It does not test whether the goal change requires a different expert action or whether the response direction is correct.
  • Correlation analysis: The exploratory analysis pairs rank, SRS, and Gsep with forward MSE, deployment NLL/RMSE, symmetric KL, and shuffled-goal ∆NLL using matched sampling across 56 method–task cells.Correlations subtract each task mean before pooling; endpoint runs predate the controlled Math-SDPA factorial, so SR values are not used for ranking.
  • Correlation analysis: 0.978 Pearson r links SRS with CLEAR v0.3 E5 Moderate Direct SR, while 0.977 links it with Strict Direct SR across ten semantic endpoint configurations.The corresponding Spearman correlations are 0.652 and 0.809, respectively; the smaller analysis supports geometry auditing rather than a universal threshold.

H Single-Task Latent-Linearity Stress Test … L.3 Pinned references and public checkpoint bundles

The appendices stress-test INTACT’s latent construction, historical alternatives, planning matrix, anti-retrieval robustness, and evaluation protocols. They also distinguish official, Moderate, and Strict claims while pinning public benchmark and checkpoint references.

  • H Single-Task Latent-Linearity Stress Test: Strict latent-linearity losses reduce waypoint error but do not improve Direct or actor-disabled planning, supporting INTACT’s use of Euclidean construction only as an actor condition.At flexible weight 0.30, effective rank falls to 41.96 and the frozen action probe reaches R2 = 0.111.
  • I Historical Latent-Perturbation Diagnostic: Figure A5’s gauge controls show that correctly paired calibration restores control, recovery saturates near 64 episodes, and coordinate maps cannot create an untrained deployment conditional.The audit contains 21,600 CLEAR Moderate episodes and excludes evaluation episodes from calibration.
  • I Historical Latent-Perturbation Diagnostic: 96% official SR at E15 was achieved by the deterministic predictor, versus 92% for the strongest flow model, while flow inference cost 18.4% more per matched optimizer step.The deterministic model also led at E1, E5, and E10; the strongest flow run changed SIGReg from 0.09 to 0.03, so this is a narrow historical control.
  • J Complete Goal-Displacement Planner Matrix: Table A12 reports all 576 planner jobs, covering 12 base rules and four guarded rules under separate PASS audits, with macro defined as the unweighted task mean.Each method has 36 jobs: three checkpoints per task, evaluation seeds {0, 1, 42}, and 100 episodes.
  • K Episode-Disjoint Anti-Retrieval Audit: 77.56% on 900 paired episodes was reached by the full model, only 0.12 point below the 77.67% standard-protocol estimate, with gains surviving unseen expert episodes and independent runs.The goal-intent model solved 358 episodes uniquely versus 22 for transition inverse; all three training-seed means improved.
  • L Evaluation Protocol Scope: The official LeWM benchmark remains the headline protocol, while CLEAR-LeWM is a separate versioned software benchmark pinned to v0.5.1 commit 32f4416c and auditable artifacts.Official and CLEAR scores are never pooled; the audit also pins manifests, Math-only SDPA, deterministic algorithms, checkpoint hashes, and episode outcomes.
  • L.1 Why a corrected protocol is informative: Moderate removes automatic success and implementation defects with minimal semantic change, whereas Strict requires stronger physical completion and is reported separately rather than averaged.Historical sampling creates automatic-success mass, including 38.38% of valid Cube pairs and 8.82% of TwoRoom +25 pairs already within the endpoint threshold.
  • L.2 Moderate and Strict are different claims: INTACT has completed Moderate only, so no Strict score is imputed; under Moderate, single-task Direct changes Reacher from 97.67% official SR to 49.56%.The public reference table reports Moderate/Strict task cells, with INTACT using audited Direct inference and official LeWM using pinned CEM 300×30.
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