Causal Retention in Interactive Agents: Interface Factorization and Selective Adaptation

Motivation

• A task-sufficient state may fail intervention probes because objectives can leave action, context, direct target, value, or delay unspecified.Causal retention evaluates the frozen state against probe semantics fixed independently of learning.Source: §1 · pp. 1–2

Related work

• Causal retention differs from behavioral sufficiency: a learner may optimize return, transition prediction, or action quality without exposing every later-probed mechanism coordinate.The paper distinguishes this question from invariant prediction, causal representation learning, and intervention extrapolation, which target different estimands.Source: §1 · p. 2

Contributions

• For finite SCM classes, optimal probe error is an explicit Bayes risk, zero exactly when interface fibers refine probe-answer fibers, and any post-processed state inherits its lower bound.The paper also characterizes budgeted retesting by posterior coverage and exact selective updates by their unique shifted-entry support.Source: §1 · p. 3
• Causal Core writes mechanism entries only with evidence and combines readout filtering, temporal credit, hidden-context setup, and local diagnostic updates.Experiments include continuous responses, an official pretrained TD-MPC2 checkpoint, and frozen Qwen hidden states evaluated under independently fixed probe semantics.Source: §1 · p. 3

2 Problem Formulation

• An intervention replaces the protocol action while leaving the remaining rollout policy fixed; the evaluator may include latent context unavailable to the learner.The setup allows observation, reward, rankings, prediction errors, diagnostics, or mechanism probes as learning interfaces.Source: §2 · p. 3, §2.5 · p. 7

2.1 Mechanism Space

• Mechanism answers track action, context, direct target, effect value, and delay; deterministic descendants or sensor readouts are not direct targets.The evaluator fixes the answer semantics independently of the learned state, and a mechanism memory is one possible representation.Source: §2 · p. 4, §2.1 · p. 4

2.2 Mechanism Risk

• Graph error, reward regret, top-action accuracy, and prediction error can miss mechanism errors, while coordinate risks diagnose which answer component failed.The exact risk is the main target; coordinate risks distinguish errors in context, target, value, or delay.Source: §2.2 · pp. 4–5

2.3 Selective Adaptation

• Selective adaptation requires zero loss on both stable and shifted entries under a small target budget; pure transfer can miss shifts, while broad relearning can corrupt stable entries.A single missed shifted mechanism may be invisible in average loss when the shifted set is small.Source: §2.3 · pp. 5–6

2.4 Standing Conditions

• Constructive guarantees assume aligned source and target keys, independent fixed probes, measurable observed coordinates, and separated finite decisions; latent predicates require assigned setup and control regimes.Conditions C2–C3 are sufficient, not necessary: if they fail, quotient and decision lower bounds remain, but finite-sample upper bounds need not hold.Source: §2.4 · p. 6

2.5 Population Interfaces

• The interface’s probe Bayes risk is the smallest error available from that interface, and it is zero only when the interface separates all probe-distinct SCMs.No estimator using an interface can guarantee zero mechanism risk when two SCMs share its law but have different probe answers.Source: §2.5 · p. 7, §2.6 · p. 8
• Metric-valued answers extend the risk analysis by changing the loss geometry rather than the semantics of retention.For Hamming loss, the metric risk coincides with the ordinary probe risk.Source: §2.5 · p. 7

2.6 Exact Causal Retention

• Exact causal retention requires a single decoder to recover the evaluator-fixed answer map from the learned state after learning stops.The criterion is implementation-independent: a memory table, recurrent state, or external module qualifies only if it supports that decoder.Source: §2.6 · p. 7

3 Causal Core

• Causal Core writes action-context-target-value-delay entries only when intervention evidence supports every coordinate, keeping mechanism memory independent of the policy optimizer.The memory transition preserves keys and allows at most one value for each action-context-target-delay key.Source: §3 · p. 8

3.1 Readout Filtering

• Synchronized readouts are excluded from direct-target writing unless an intervention separates them.A candidate classified as a readout can re-enter the direct-target set only through a separating intervention.Source: §3.1 · p. 9

3.2 Temporal Credit

• Delayed entries are written only when the selected lag beats competing recent actions by a margin, using matured paired trials.This is intended to prevent a waiting action or post-effect observation from being written as the cause.Source: §3.2 · p. 9

3.3 Diagnostic Adaptation

• Diagnostic surprise selects entries for retesting and local updating, while entries outside the selected shifted set remain fixed.Stable corruption can occur only through an incorrect set-selection event under the stated condition.Source: §3.3 · p. 10

3.4 Hidden-Context Setup

• Hidden-context labels require an actively searched setup regime, matched controls, and a contrast not explained by a visible separator.With passive eligibility probability qi, even an oracle needs m/qi attempts on average to collect m eligible outcomes.Source: §3.4 · pp. 10–11

• The optimal probe error is a Bayes risk, zero exactly when interface fibers refine probe-answer fibers, and post-processing cannot lower it.Source: §4 · pp. 11–12
• A size-k retest list achieves zero omission exactly when the union of posterior-supported shifted sets fits within k entries.When shifted sets are uniform and independent of the diagnostic signal, optimal coverage is given by the fraction of possible shifted sets contained in a size-k list.Source: §4 · p. 14
• With per-entry diagnostic samples, shifted-set recovery uses m=O(∆^-2 log(n/δ)) samples per entry, with matching scaling necessary up to constants.The result assumes shifted and stable entries have diagnostic means separated by ∆>0.Source: §4 · pp. 14–15
• An exact target update must edit every shifted entry to its target value and no stable entry, making the shifted set its unique edit support.The result is relative to the mapped source memory.Source: §4 · p. 16
• For compact metric-valued responses, zero risk has the same fiber criterion, while separation by 2ε on probe mass q forces worst-case risk of at least qε.Source: §4 · p. 17

5.1 Protocols and Baselines

• The evaluation freezes learned states before scoring fixed probes across finite SCMs, hidden-context variants, continuous responses, and language-model states.Baselines match their available interfaces, including passive and reward learners, ranking loss, conditional discovery, latent world models, and the official TD-MPC2 checkpoint.Source: §5 · p. 18, §5.1 · p. 18

5.2 Coarse Interfaces

• In noisy-hidden worlds, Causal Core reached target-edge F1 0.764 on the ranking task and 0.79 with zero readout and hidden-label false positives on the expanded matched run.A latent world model had next-bit accuracy 0.905 but target-edge F1 0.24; task or predictive performance could coexist with poor fixed-probe recovery.Source: §5.2 · p. 19

5.3 Write Validity and Local Adaptation

• Causal Core achieved AdaptScore 1.00 in renamed and semantic-readout adaptation, while non-diagnostic and readout-unsafe baselines scored 0.Ungated Qwen exploration produced 92.3 false entries and 37.0 readout false positives; context-search and control-planner gates reduced these counts.Source: §5.3 · p. 20

5.4 Hidden Contexts and Continuous Responses

• Active setup raised hidden recall from 0.125 after 80 interactions to 0.625 after 160, with zero hidden false positives in the four-family horizon sweep.In a continuous metric SCM, metric Causal Core reached F1 1.000 with no readout false positives, whereas global linear regression reached F1 0.667.Source: §5.4 · p. 20
• Selective TD-MPC2 adaptation raised shifted-actuator sign accuracy from 0.057 to 0.948, with stable-response NRMSE remaining 0.673.The selective update used five target states per actuator and localized the shift in all nine runs.Source: §5.4 · p. 20, Figure 3 · p. 21

5.5 Language-Model States and Proposal Policies

• Gated Qwen mechanism states reached 1.000 changed-delay accuracy and 0.056 readout FPR, while frozen final-layer probes reached 0.583 on changed delays.The frozen probes scored 0.958 balanced accuracy on source mechanisms; the admissible-write gate preserved changed-delay accuracy while reducing readout false positives.Source: §5.5 · p. 21, Figure 4 · p. 21
• The proposal-policy gate raised Qwen target-edge F1 from 0.163 to 0.678–0.727 and eliminated readout false positives.Causal prompting alone produced 32.0 readout false positives.Source: §5.5 · p. 21

5.6 Reproducibility

• The authors provide code, source-data tables, raw results, and appendices documenting seeds, budgets, model variants, probe definitions, and implementation details.The code covers SCM generation, baselines, MuJoCo and language-model experiments, and figure rebuilding.Source: §5.6 · p. 22

6 Conclusion

• Causal retention concerns whether a frozen learned state preserves an interventional answer map beyond what task success requires.The paper connects probe Bayes risk, posterior retest coverage, and exact edit decomposition to selective adaptation; continuous results concern a fixed query distribution, not unrestricted latent-SCM recovery.Source: §6 · p. 22

A.1 Coarse Behavioral and Predictive Interfaces

• Finite SCM classes exhibit reward, optimal-policy, ranking, graph, synchronized-readout, and passive hidden-context interfaces that are strictly coarser than the exact mechanism-probe interface.For each interface, a point-mass probe distribution has minimax mechanism risk at least 1/2.Source: §A.1 · p. 22
• Matching rewards or rankings can conceal different direct targets, while identical graphs can conceal different effect values.Synchronized readouts can agree on observed outcomes despite different direct targets; passive observations can also conceal hidden eligibility context.Source: §A.1 · pp. 22–23
• These coarsenings do not make reward, graph estimation, or ranking uninformative; additional intervention contrasts can resolve a particular ambiguity.The proposition says these population objects need not determine every coordinate of the mechanism answer.Source: §A.1 · p. 23

A.2 Finite-Sample Contrast Gates

• With K adaptive gates and average contrasts separated from thresholds by γ, joint error probability is at most 2K exp{−Nϵ2γ2/2}.A separate finite-class readout rule bounds false negatives by e−2mγ2 and false positives by |F|e−2mγ2 when population accuracies are separated from the threshold by γ.Source: §A.2 · pp. 24–25

A.3 Hidden-Context Acquisition

• A setup policy that reaches an eligible state within h actions with probability at least β gives a finite attempted-action budget for collecting m eligible outcomes with probability at least 1−δ.Under passive access, the expected number of attempts is m/q, where q is the ambient eligibility probability.Source: §A.3 · p. 25

A.4 Randomized Lists and Adaptive Stopping

• Under a hard cap of k distinct retests, adaptive ordering cannot increase the probability that the list covers every shifted entry beyond the posterior-coverage bound EΓk(Z).Exact final memory requires testing every shifted entry unless an untested entry is supplied by an external oracle.Source: §A.4 · p. 26

A.5 Diagnostic Localization Lower Bound

• For a symmetric one-shift family, the lower-bound argument compares coordinate-specific sample laws and applies Fano’s inequality to shifted-entry localization.The two laws differ at the shifted coordinates, with pairwise divergences bounded using the Bernoulli contrast.Source: §A.5 · pp. 26–27

A.6 Top-s Diagnostic Selection

• Exact top-s recovery succeeds with probability at least 1−δ when m ≥2∆−2 log(n/δ).Here shifted entries have means at least p, stable entries at most q, and ∆=p−q.Source: §A.6 · p. 27

A.7 Coordinate Loss and End-to-End Sample Composition

• Entry errors decompose across context, target, value, and delay coordinates, with source error further divided into target, context, readout, temporal, and hidden components.Hidden error splits into set-localization and hidden-label error.Source: §A.7 · pp. 27–28
• Diagnostic selection determines which target entry is tested, while local retesting determines its replacement coordinates.This is the component factorization used by Theorem 7.Source: §A.7 · p. 28
• When source, schema, diagnostic, and update failure budgets sum to at most δ, the probability of nonzero adaptation loss is at most δ.The component bounds include readout and hidden-label tests, with the attempted-action budget for shifted-set localization supplied by Proposition 13.Source: §A.7 · p. 28

B.1 Fixed-Memory Evaluation

• After interaction stops, the evaluator queries each method’s frozen answer map on held-out probes and compares it with the SCM answer.Ground-truth mechanisms construct probes and scores after the run and are never supplied to the writer during interaction.Source: §B.1 · pp. 28–29
• Exact mechanism accuracy requires tuple matches, while finite-discovery and language tables report target-edge precision, recall, and F1.Separate probes measure context, value, delay, and readout; AdaptScore requires correcting every shifted entry while preserving every stable entry.Source: §B.1 · p. 29

B.2 Baselines

• Baselines vary the learning objective and interface, including reward-associated effects, passive correlations, conditional transition differences, frozen source-transition models, and gated or ungated writers.These controls separate objective and interface effects from output-format effects.Source: §B.2 · p. 29
• Mean target-edge F1 is 0.793 for Causal Core, 0.640 for conditional discovery, 0.789 for oracle tuple lift, 0.239 for latent modeling, and 0.396 for the transition probe.The latent world model attains next-bit accuracy 0.905 (0.907 with the readout oracle), so its probe error is not explained by failed source prediction.Source: §B.2 · p. 29, Table 1 · p. 29

B.3 Continuous Metric Cells

• A continuous pulse counts as correct only when its direct target, sign, and context cell match the reference answer.The evaluator fixes the metric cells before training.Source: §B.3 · p. 30
• Metric Causal Core retains F1 1.000 at noise levels 0.02, 0.05, 0.10, and 0.15.Random-correlation F1 scores are 0.402, 0.321, 0.265, and 0.252; global linear scores are 0.667, 0.667, 0.667, and 0.695.Source: §B.3 · p. 30

B.4 Distributional World-Model Probes

• The actuator-remapping experiment uses five states per actuator and changes an entry only when an alternative actuator hypothesis halves paired loss.The selective and unrestricted global updates receive identical target pairs.Source: §B.4 · p. 31
• On random target directions, NRMSE is 0.630 for the selective update, versus 1.138 for the frozen model and 1.548 for the global update.On directions excluding the shifted actuator, stable-response errors are 0.673, 1.460, and 0.673, respectively; the selective update matches the oracle actuator map at reported precision without changing stable responses.Source: §B.4 · p. 31, Table 4 · p. 31

• The hidden-state evaluation uses controlled intervention records and binary direct-target or delay probes, with disjoint procedural families for training and testing.The 504 balanced training probes and 360 balanced test probes use fresh random permutations of neutral action and state tokens across families and conditions.Source: §B.5 · p. 31
• The frozen model’s hidden vectors are decoded at five layers, with additional last-layer decoders and query-only, logit-margin, and paired-evidence controls.Decoders and thresholds are frozen before evaluation on the six test families.Source: §B.5 · pp. 31–32
• The last-layer linear decoder scores 0.583 on shifted delays, while the gated mechanism state reaches a perfect shifted-delay score and accepts only 5.6% of synchronized-readout candidates.Paired evidence recovers changed delays but accepts 94.4% of synchronized readouts; the RBF decoder scores 0.250 on shifted delays.Source: §B.5 · p. 32
• The causal prompt does not remove readout contamination; gated variants apply an evidence gate after observing transitions, so their advantage comes from memory updates rather than generated explanations as causal labels.Qwen2.5-7B-Instruct proposes the next legal intervention from the current transcript; explanations and reward predictions receive no probe credit.Source: §B.5 · p. 32

• Small, default, and wide candidate schedules yield target-edge F1 of 0.698 at 80 steps and 0.763 at 160 steps, with zero readout false positives.Hidden recall rises from 0.125 to 0.625.Source: §B.6 · p. 32
• Candidate caps determine which contrasts are attempted, not how frozen probes are scored.Metric cells, target budgets, saved MuJoCo states, language prompts, and parsers are fixed before held-out scoring; malformed language proposals count as failures.Source: §B.6 · pp. 32–33
• Because finite-SCM trajectories are adaptive, iid bounds are not reported as confidence intervals for the empirical tables.Lemma 11 covers randomized adaptive logging, while continuous protocols use the paired design directly.Source: §B.6 · pp. 32–33