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Beyond Update Counts: A Control Map for Evaluating Test-Time Model Updates
Zehao Zhao, Shangjian Yin, Rui Liu, Chongyang Bai, Mark Ibrahim, Kavosh Asadi, Yuchen Lu, Hang Cui, Hamed Firooz
TL;DR
Update counts and immediate scores do not capture which updates were available before each answer or whether learned information lasts and remains localized. The Control Map records pre-answer histories and evaluates behavior, acquisition, retention, locality, and new settings separately. Results show setting-dependent schedule and editor performance, while learning does not guarantee retention or locality.
Problem
Evaluations often summarize test-time updates by policy labels, frequency, or total counts, although these omit what is updated, where, when, and in what order.
Source: §1 · p. 1Method
The Control Map records ordered committed updates preceding each answer and separately evaluates behavioral change, acquisition, retention, locality, and performance in a new setting.
Source: §1 · p. 2Results
Editor rankings vary across evaluated model–benchmark–question bundles; on prospective WikiRecent, MEMIT’s gain over ROME was +0.2142 nats per target token on canonical prompts, while both failed locality.
Source: §6.2 · pp. 8–9Takeaways & Limitations
Evaluations should report ordered pre-answer updates and assess acquisition, later retention, and locality separately, with new-setting outcomes measured directly.
Source: §7 · p. 9The guarantees depend on the tracing rule capturing relevant paths, and the cross-setting grid changes model, benchmark, and test questions together, so it does not identify the cause of heterogeneity.
Source: §6.3 · p. 9
Abstract
from arXiv · showhide
Test-time updating lets a language model change persistent state after training---such as model weights, adapter parameters, or a memory module---before or while answering queries. Existing evaluations often compare systems using update count or frequency and performance measured immediately afterward. These summaries omit what is updated, where, when, and in what order. The same total can therefore hide an important difference: one system may answer after one update while another answers after two. We introduce the Control Map, an evaluation framework that records the committed updates preceding each scored answer and separately evaluates behavioral changes, immediate learning (acquisition), later recall (retention), preservation of unrelated behavior (locality), and performance in new settings. We prove when counts alone determine final state and show, under stated assumptions, how differences between pre-answer histories limit differences in average scores. Using ControlMap, our experiments reveal three insights. First, update scheduling matters: at a 760M-parameter checkpoint, 24 schedules with the same update count yield 19.7%--34.2% accuracy. Second, learning an edit does not guarantee that it lasts or remains contained: all six selected CounterFact LoRA settings learn the new information, while ROME retains edits at all 13 operating points but fails locality at each. Third, no editor performs best consistently across models, benchmarks, and tests. Evaluations should therefore report update histories and assess acquisition, retention, and locality separately.
1 Introduction
Update counts and policy labels can obscure which updates were available before each answer. The Control Map records those histories and separates behavioral change, memory quality, and cross-setting results; experiments and formal results show why those distinctions matter.
1.1 Related work and positioning
- The framework complements update mechanisms and editing evaluations by asking which ordered updates actually preceded each evaluated answer.Source: §1.1 · p. 2
- The Control Map records ordered updates completed before each answer and separately evaluates histories, behavioral change, acquisition, retention, locality, and performance in a new setting.Source: §1.1 · pp. 2–3
- Under stated assumptions, greater overlap between recorded histories tightens bounds on average-score differences; the paper also characterizes when update counts determine final state.Source: §1.1 · p. 3
- 24 equal-count schedules span 19.7%–34.2% accuracy, while six CounterFact settings pass acquisition but none pass retention or locality.Method rankings also vary across models, benchmarks, and tests.Source: §1.1 · p. 3
2 The Control Map and Problem Formulation
The Control Map formalizes update policies, the committed histories declared relevant to an answer, and separate records for behavioral and memory outcomes. Its guarantees depend on assumptions about history sufficiency and tracing.
2.1 Stateful policies and operating points
- An operating point pairs a setting—model, task and interface, evaluated output, and optional cost budget—with a fully specified update policy and configuration.Source: §2.1 · pp. 3–4
- A policy specifies update actions plus cadence, query-relative phase, and commit rule; actions select update admission, content, parameter support, writer, and strength.Source: §2.1 · p. 4
- The mutable model and writer state changes when an update is committed and remains unchanged when it is not.Source: §2.1 · p. 4
- A declared pre-answer history is the ordered sequence of committed transitions that a dependency specification identifies as able to influence the score; policies are history-equivalent when these sequences match.Source: §2.1 · p. 4
2.2 Pre-answer histories and comparison resolution
- For fixed deterministic update types, counts of each type determine the final state for every ordering exactly when their update maps commute pairwise; intermediate answers may still depend on order.Source: §2.2 · p. 4
- History resolution ranges from 0 to 1: zero implies equal average scores under the theorem’s assumptions, while one leaves the bound spanning the full score range.Source: §2.2 · p. 5
- The bounds require a defensible bound on scoring-process mismatch and do not verify that the tracing rule captures every relevant path.Source: §2.2 · p. 5
2.3 Control Map records
- The Control Map keeps history, behavioral-change estimates and uncertainty, acquisition, retention, locality, and cost separate; evidence for distinguishable histories alone does not establish effect direction.Source: §2.3 · p. 5
3 Which Updates Reach Each Answer?
The section distinguishes schedules by the committed updates available before each answer. Short inputs can collapse nominally different schedules into the same history, while experiments illustrate both history-based bounds and the importance of matching complete event order.
3 Which Updates Reach Each Answer?
- Short inputs permit fewer updates and collapse more nominal schedules to the same pre-answer history; longer inputs expose more of the schedule grid.Source: §3 · p. 5
3.1 Formulation
- For the MAC schedule experiment, exact enumeration gives 1, 4, 12, and 24 history classes when H is 0, 1, 2–3, and at least 4, respectively.Source: §3.1 · p. 5
3.2 Experimental protocol and results
- On SocialIQA, each period-4 versus period-8 swap changes history on 1/1,954 rows, bounding any binary-accuracy contrast at 0.0512 percentage points; all six observed contrasts are zero.Source: §3.2 · p. 6
- In a controlled LoRA test, the tracing procedure recovered the prespecified sZ = 1/2 and rejected all 16 injected trace corruptions, validating conformance in that setup rather than complete coverage of published editor internals.Source: §3.2 · p. 6
- After matching complete event order and other listed factors, all 1,600 pairs have identical terminal model states and locality scores, so the apparent dose–locality curve disappears.Source: §3.2 · p. 6
4 Behavioral Effects of Control Choices
The section examines how placement, timing, and dose relate to behavioral outcomes. Its placement findings are specific to the tested checkpoint and are presented as a local response surface, not a universal schedule rule.
4 Behavioral Effects of Control Choices
- For supported policy comparisons, the analysis reports mean behavioral difference, uncertainty, inference unit, and when the analysis was specified.Unless stated otherwise, 95% ranges use paired family- or block-level reweighting of one fixed evaluation set.Source: §4 · p. 6
4.1 Experimental protocol and results
- At this checkpoint, fitted additive effects of frequent updates are positive in the earliest and latest layer groups and negative in the middle groups.The authors treat this as a local placement–frequency interaction, not a universal layer rule.Source: §4.1 · p. 6
- The additive assignment map explains 95.3% of between-schedule variation descriptively, with leave-one-schedule-out R2 = 0.863 and root-mean-square error = 1.59 percentage points.The analysis covers all 24 assignments on the same 6,000-example Single-NIAH evaluation set; the result is a local response surface.Source: Figure 2 · p. 7
- Table 1 presents controlled comparisons of placement, timing, and dose, with each row changing one choice while preserving listed controls.Source: Table 1 · p. 7
5 Feasibility of Acquired Memory
The section applies separate thresholds to acquisition, retention, and locality, showing that immediate learning alone does not establish memory quality. Results vary across editor settings, and passing requires every required component to meet its criterion.
5.1 Decision rules
- The overall memory-quality decision passes only when every required check passes; strong acquisition cannot compensate for failed retention or locality.The retention check also requires at least 20% of edit pairs to meet installation and at least half of those installed edits to be retained.Source: §5.1 · p. 8
5.2 Experimental protocol and results
- 6/6 selected CounterFact LoRA settings pass acquisition, but retention and locality each pass 0/6; ROME passes retention at all 13 operating points but locality at none.The prespecified four-setting LoRA screen passes in 0/4 and triggers its stopping rule.Source: §5.2 · p. 8
- On the 160-family positive-control set, MEMIT-high passes with acquisition 8.30 nats and locality damage 2.08 percentage points; ROME-low is inconclusive.In a separate setting-specific eight-edit sequence, AlphaEdit meets all declared memory-quality criteria at each of four tested doses.Source: §5.2 · p. 8
- The five-percentage-point locality boundary is prespecified, but CounterFact pass breakpoints are 3.20 points for MEMIT-high and 6.42 for ROME-low.On WikiRecent, the corresponding breakpoints are 52.73 and 50.78; relaxing locality cannot rescue LoRA because retention passes in 0/6 settings.Source: §5.2 · p. 8
6 Generalization Across Models and Benchmarks
The section compares results across model–benchmark settings and finds that editor rankings do not reliably carry over. Direct evaluation in new settings is needed to establish whether a result recurs, while the cross-setting grid cannot identify why outcomes differ.
6.1 Comparing settings
- A bundle is a fixed model and editor configuration; cross-setting comparisons prespecify how update plans correspond and preserve the positive side of the comparison.Endpoint-specific measurements are reported separately; one setting does not determine an unevaluated setting without an additional invariance assumption.Source: §6.1 · p. 8
6.2 Results across two model bundles
- On GPT-2XL, the MEMIT-minus-ROME acquisition contrast is positive on all three endpoints (+0.7850, +0.5772, +1.2930 nats), while locality-success contrast reverses across benchmarks.The locality-success contrast is +2.5625 percentage points on CounterFact, −7.5000 on zsRE, and −15.9180 on WikiData-CounterFact.Source: §6.2 · pp. 8–9
- On Llama-3.2-3B, acquisition favors ROME on all three endpoints (−0.3017, −0.2116, −0.2247 nats), and both editors fail every locality requirement.The predicted locality pattern (+, −, −) does not recur; the result is (+, +, ?).Source: §6.2 · p. 9
- On prospective WikiRecent, MEMIT’s gain over ROME after four edits is +0.2142 nats per target token on canonical prompts and +0.7178 on a rephrase, yet both fail locality.The 512 editor-call sequences match their specifications, but the overall evidence requirement fails.Source: §6.2 · p. 9
- At the source setting, binary success, full-vocabulary Kullback–Leibler divergence, and greedy-token change all favor MEMIT when oriented so positive means better performance.Across evaluated model–benchmark–question bundles, tested-editor relative performance varies, so a source-setting ranking should not be assumed to carry over.Source: §6.2 · pp. 8–9
6.3 What the combined evidence supports
- The cross-setting grid changes model, benchmark, and test questions together, demonstrating heterogeneity without identifying its cause.The paper concludes that update histories and direct new-setting evaluation address different questions: what differed before scoring and whether a result recurs.Source: §6.3 · p. 9
7 Conclusion
The paper recommends evaluating test-time updates by their ordered pre-answer histories and separately measuring behavior, acquisition, retention, locality, costs, and outcomes in new settings. Its formal results clarify when counts suffice, how trace differences constrain score differences, and why separate coordinate studies do not identify untested combinations.
7 Conclusion
- Evaluations should record ordered pre-answer updates, mechanisms, configurations, and measurement times, while reporting acquisition, retention, locality, uncertainty, costs, and new-setting outcomes separately.For comparisons across settings, the update-plan correspondence should be specified and outcomes measured directly there.Source: §7 · p. 9
AI use statement; Ethics statement; Reproducibility statement
- The authors report AI assistance across research and manuscript tasks, no human participants or deployment, and reproducibility materials that omit legacy family-level measurements, raw data, checkpoints, and third-party editor internals.The public bundle supports only a stated subset of recomputations, and release remains subject to privacy, redistribution, and licensing checks.Source: AI use statement · p. 10, Ethics statement · p. 10, Reproducibility statement · p. 10
A.1 Secondary resolution guarantees; A.4 Why counts can fail, and when they are sufficient
- Across all finite update sequences, per-atom counts determine the final-state map if and only if update maps commute pairwise; intermediate queries can still depend on the update prefix.Scalar write counts discard atom identities, and counts can suffice accidentally on a restricted catalogue.Source: §A.1 · p. 14, §A.4 · p. 18
A.1 Secondary resolution guarantees
- Under the stated theorem assumptions, a target assignment effect of at least δ requires history resolution of at least δ/(b − a).Below that threshold, the target effect is unattainable under those assumptions.Source: §A.1 · p. 15
A.2 Evidence records and decision rules
- The evidence record keeps histories and their resolution, effect estimates and uncertainty, absolute behavioral gates, costs, and any transport result distinct.The evaluation procedure freezes the design before outcomes, compiles traces, estimates supported effects, tests acquisition, retention, and locality separately, and evaluates any declared transport rule in the target setting.Source: §A.2 · pp. 15, 17
- Tested LoRA settings acquire targets without passing the joint retention-and-locality gate, while fixed MEMIT’s locality advantage over ROME reverses at both tested KnowEdit endpoints.These examples distinguish acquisition, feasibility, and cross-endpoint verdict stability.Source: §A.2 · p. 17
A.3 Trace-resolution consequences
- Observed-summary resolution is bounded by full trace resolution, with equality requiring the summary to retain the relevant contrast information.No finite score-magnitude cap follows for unbounded log probability or negative log likelihood without clipping, a bounded transform, or additional tail conditions.Source: §A.3 · p. 18
A.5 Why separate coordinate studies do not identify a joint controller
- Separate coordinate effects do not identify an untested context-policy-endpoint combination over unrestricted bounded response surfaces without added structural restrictions.For the two-coordinate example, the missing outcome cell may take any value in its allowed range; the paper also limits its context-choice result to commensurable utilities, not endpoint-native metrics with incomparable scales.Source: §A.5 · pp. 18–19
A.6 Adapter robustness, coverage evidence, and gate sensitivity
The section tests how incomplete traces and changing locality thresholds affect the Control Map’s conclusions. A live neural check validates recorded-path conformance, but does not establish complete ancestry coverage.
A.6 Adapter robustness, coverage evidence, and gate sensitivity
- The hidden-cache state machine shows that omitting a score ancestor can make the declared exact bound miss by exactly k/N, while including that ancestor restores the bound.Across 16 cells, the non-ancestral bound and restored coverage were verified in 16/16; the omitted-ancestor failure occurred in all 12 cells with k > 0.Source: §A.6 · pp. 19–20
- The live neural check validates recorded nonzero-gradient paths in one randomly initialized model, but leaves coverage of unrecorded or zero-gradient dependencies unverified.The compiler validated 16 chronological chains, rejected 16 specified corruptions, and accepted the restored trace.Source: §A.6 · p. 20
- For SocialIQA, the 1/1954 history resolution makes the binary-outcome cap conditional on an unmeasured aggregate deviation budget, not an empirical effect estimate.The study supplies no empirical value for that budget.Source: §A.6 · p. 20, Table 3 · p. 20
- The six selected LoRA settings have locality damage of 30.625–53.203 points, and retention passes in 0/6, so relaxing locality alone cannot produce a full pass.The joint-rule convention makes equality at either interval boundary inconclusive; all observed WikiRecent intervals lie wholly below the five-point threshold, preserving its four verdicts under either convention.Source: §A.6 · p. 21
- On WikiRecent, ROME’s rephrase installation point is 0.20703125, just above the 0.20 cutoff; changing that gate would not alter the existing locality-failure verdict.All four WikiRecent acquisition and continuous-retention ranges clear zero, and every retained-among-installs point clears 0.50.Source: §A.6 · p. 21
- Across three locality readouts, MEMIT-minus-ROME ordering is robust, but the post-hoc comparison does not isolate causes or establish absolute feasibility without separately frozen gates.The readouts reuse the same probes; gate values should reflect an explicit deployment tolerance and be frozen per endpoint, rather than treating five points as universal.Source: §A.6 · pp. 21–22
B.1 Outcome-blind trace atlas
The trace atlas and associated experiments examine how pre-answer histories, update placement, and dose relate to model behavior and memory quality. Results vary by schedule and setting, while acquisition alone does not establish retention or locality.
B.1 Outcome-blind trace atlas
- 1, 4, 12, or 24 distinct histories arise as the number of complete pre-answer writes increases; across 27,072 rows, mean schedule-pair history aliasing is 0.128517.On SocialIQA, each of six period-4/period-8 swaps changes history on one of 1,954 rows, with identical predictions and accuracies.Source: §B.1 · pp. 22–23, Figure 3 · p. 23
B.2 Complete-order locality correction
- Across 1,600 cross-dose pairs, terminal parameters and locality match when editor, strength, replicate, family, and complete event order are fixed; dose-indexed locality movement therefore reflects an order-mixture association.The comparison covers 160 MEMIT, 480 ROME, and 960 LoRA pairs.Source: §B.2 · p. 24
B.3 Immediate-versus-deferred effect
- Immediate-minus-deferred held-out means are positive for all four GPT-2 sizes, but the prospective Pythia-410M interval includes zero and does not confirm the effect.The GPT-2 means range from +0.059816 to +0.432027 nats; the Pythia estimate is +0.1592 nats with interval [−0.4484, +0.7667].Source: §B.3 · p. 24
B.4 Equal-count placement response
- Accuracy ranged from 19.733% for schedule (4, 1, 2, 8) to 34.233% for (1, 8, 4, 2) across all 24 assignments on the same 6,000 Single-NIAH rows.The additive band–period description accounts for 95.322% of between-schedule variation; these are descriptive results for one checkpoint and evaluation set.Source: §B.4 · p. 24
B.5 Selected-setting dose summary
- Across 18 selected LoRA/SGD settings, empirical peaks occur at doses 1/2/4/8 in 9/7/2/0 settings, and the prespecified best-dose prediction is confirmed in 7/18.These counts summarize a selected grid, not population prevalence or a universal dose rule.Source: §B.5 · p. 24
B.6 Effect record and uncertainty; C.1 Feasibility decision rules
- The Control Map records effects only for comparisons supported by recorded histories, while feasibility rules keep acquisition, retention, and locality as separate gates and report cost separately.A full pass requires every behavioral condition specified for that study; cost is a gate only when a budget is declared.Source: §B.6 · p. 24, §C.1 · p. 25, Table 7 · p. 25
C.2 Matched factual-recall Stage-0 protocol and full decision
- In Stage 0, acquisition passes 4/4 settings, but retention and locality each fail 4/4, so no setting passes the conjunction and Stage 1 is not run.The test does not establish a safe writer, population-level predictor accuracy, or an online controller.Source: §C.2 · pp. 25, 28
C.3 Natural factual-recall family extension
- Across six selected settings, the frozen dose-selection rule yields 5/6 exact calls versus 3/6 for always-dose-1 (two wins, four ties, zero losses), a descriptive tally with no significance or population claim.The two added settings passed acquisition gates, but neither retention nor locality passed.Source: §C.3 · pp. 28–29
C.4 Partially outcome-blind published-editor schedule grids
The published-editor grids show that acquisition and locality can vary differently across schedule and editor settings. A separate shared-eight-event test finds MEMIT-high passes all stated gates across measured doses, but the extension has limited scope.
C.4 Partially outcome-blind published-editor schedule grids
- Across the GPT-2XL grids, MEMIT-high passes acquisition, retention, locality, and the full gate at all three doses, while ROME passes acquisition and retention in all nine cells but certifies neither locality nor the full conjunction.ROME’s acquisition dose response is inconclusive at low strength and dose-insensitive at default and high strength; its locality-response classifications are inconclusive for default and high.Source: §C.4 · p. 29, Table 11 · p. 29
- Across 1,600 matched cross-dose pairs, terminal parameters and locality are identical when complete event order is fixed, so dose-indexed locality movement is an order-mixture association, not an identified query-boundary effect.The comparison comprises 160 MEMIT, 480 ROME, and 960 LoRA pairs.Source: §C.4 · p. 29
C.5 Prospective shared-eight-event MEMIT facet
- On the shared eight-event MEMIT-high facet, dose 8 exceeds dose 4 by +0.05481 nats, but the contrast is small relative to the 0.5-nat practical threshold and the full dose range is classified dose-insensitive.Retention, locality, and every full-gate component pass at all four doses.Source: §C.5 · p. 30, Table 12 · p. 30
- The shared-eight-event extension is prospective for its new executions but was designed after the four-event dose-insensitive result, so it is not an independent confirmation or evidence that dose insensitivity diagnoses writer quality.It is not pooled with Stage 0.Source: §C.5 · p. 30
C.6 Fresh published-editor confirmation
Across the editor studies, acquisition, retention, and locality do not move together, and locality comparisons depend on the evaluated setting. The results range from an inconclusive fresh comparison to a confirmed advantage on one fixed panel, without establishing a universal editor ranking.
C.6 Fresh published-editor confirmation
- In the fresh 64-family confirmation, both editors passed acquisition and retention, but the +3.398 percentage-point locality-success contrast was inconclusive.Its 95% range crossed zero, so the prespecified prediction of less MEMIT locality damage remained unresolved.Source: Table 13 · p. 30, §C.6 · pp. 30–31
C.7 Disjoint pre-outcome-frozen 160-family extension
- On the disjoint 160-family CounterFact panel, MEMIT-high passed the full gate and exceeded ROME-low in locality success by +2.5625 percentage points (95% range [+1.0625, +4.2656]).ROME passed acquisition and retention, but its locality range crossed the threshold, leaving its locality and full conjunction inconclusive.Source: Table 14 · p. 31, §C.7 · pp. 31–32
C.8 Adaptive ROME-low eight-event facet
- Across all four doses, ROME-low passed acquisition and retention, while locality and the full conjunction remained inconclusive.The ordered event sequence and terminal state were identical across doses, so locality was identical; the acquisition range and dose-winner contrast did not resolve the prespecified dose-sensitive test.Source: Table 15 · p. 32, §C.8 · p. 32
C.9 Post-hoc relation-cluster sensitivity
- Two post-hoc relation-cluster checks left the observed MEMIT locality advantage above zero, but did not establish a universal editor ranking.The checks do not generalize beyond the selected model, benchmark, strengths, and endpoint.Source: §C.9 · pp. 32–33
C.10 Additional-editor dose breadth
- AlphaEdit passed the behavioral criteria and was insensitive to dose, while FT-L failed the behavioral criteria and had inconclusive dose sensitivity.The joint prediction was not confirmed; these classifications apply to the tested configurations and declared CounterFact neighborhood protocol.Source: §C.10 · p. 33, Table 17 · p. 33
D.1 Formal comparison across settings
- Across evaluated endpoint–bundle cells, MEMIT-minus-ROME contrasts vary, but the trajectories do not isolate the cause of that heterogeneity.A source ordering outside evaluated support requires an explicit invariance condition or new target evidence; endpoint-specific metrics are not a common utility ranking.Source: Figure 6 · p. 34, §D.1 · p. 34
D.2 Prospective WikiRecent evaluation
The prospective WikiRecent study tested whether a fixed editor comparison transported to a new knowledge-insertion panel. Mean direction transport passed, but locality failures prevented the absolute feasibility claims from passing.
D.2 Prospective WikiRecent evaluation
- The frozen comparison used 64 families, four cyclic edit orders, and GPT-2XL policies MEMIT-high and ROME-low; all executed rows matched the precomputed score-ancestral sequence.The outcome-blind panel selection enforced globally unique subjects, target strings, token sequences, and prompts.Source: §D.2 · p. 35
- Mean-direction transport passed, but large negative locality changes made all four policy–context feasibility conjunctions, the designated MEMIT target-feasibility claim, and EvidenceComplete fail.The transported mean direction did not imply that either editor met the absolute locality requirement.Source: §D.2 · pp. 35–36
- The post-hoc KL-divergence and greedy-token diagnostics reused the same two probes, added no probe breadth, and supported no population claim.The diagnostics were not frozen gates.Source: §D.2 · p. 36
- The reproducibility bundle omits remote scheduler records, so it cannot independently reconstruct submission and completion chronology.An independent analysis reproduced the results, and all 15 prespecified protocol checks passed.Source: §D.2 · p. 36
D.3 GPT-2XL endpoint-native transport
On GPT-2XL, MEMIT had higher acquisition than ROME in all three endpoint-native settings, while locality rankings reversed across endpoints. A prospective Llama test did not reproduce the frozen locality signature; adjusted and cluster-based checks preserved that mixed pattern.
D.3 GPT-2XL endpoint-native transport
- MEMIT’s acquisition advantage was positive in all three GPT-2XL settings, but locality contrasts were +2.5625, −7.5000, and −15.9180 points, reversing the locality ranking on two endpoints.The acquisition contrasts were +0.7850266 nats on CounterFact, +0.5772456 on zsRE, and +1.2929676 on WikiData-CounterFact.Source: Table 20 · p. 37, §D.3 · p. 37
D.4 Prospective Llama-3.2-3B recurrence test
- The predicted Llama locality signature (+, −, −) was not reproduced: the observed signature was (+, +, ?), making the primary pattern test inconclusive.All six method–endpoint points passed acquisition and adjacent terminal retention but failed locality and the full conjunction; model and native-configuration changes prevent architecture-specific attribution.Source: Table 21 · p. 38, §D.4 · pp. 38–39
D.5 Combined results for the GPT-2XL comparison
- The combined GPT-2XL record had all required evidence fields populated, but EvidenceComplete did not pass.Transport and the claim ladder failed, and MEMIT failed target locality twice; dataset and locality instrument co-varied, precluding a dataset-only causal effect.Source: Table 22 · p. 39, §D.5 · p. 39
D.6 Post-hoc across-endpoint sensitivity for the Llama signs
- After post-hoc Bonferroni adjustment, locality remained (+, +, ?) and acquisition was (−, −, ?); the frozen locality recurrence still failed.The Bonferroni analysis tested simultaneous sign stability and did not claim population coverage.Source: §D.6 · p. 39, Table 23 · p. 39
D.7 Post-hoc cluster-pairs sensitivity
- Post-hoc relation-cluster checks retained the GPT-2XL sign pairs and left Llama zsRE locality positive and WikiData unresolved.The checks address exact relation-form dependence, not arbitrary semantic-relation or model-population inference.Source: §D.7 · pp. 39–40, Table 24 · p. 39
D.8 Summary of invalid shortcuts
- Table 25 catalogs four unsupported shortcuts alongside evidence-based alternatives.The paper argues that relative performance and absolute memory quality should be reported separately.Source: Table 25 · p. 40
E Reproducibility materials and scope
The framework connects intervention, provenance, editing-metric, and transportability ideas in a single evaluation record. Its tracing and cross-setting conclusions remain bounded by declared score dependencies and evidence or assumptions for unevaluated settings.
E Reproducibility materials and scope
- The planned release omits raw or restricted data, model checkpoints, private execution records, and legacy family-level measurements.Aggregate results alone do not allow independent recomputation of legacy family-level intervals.Source: E Reproducibility materials and scope · p. 40
- The Control Map connects existing evaluation ideas in one record, while tracing guarantees depend on declared score dependencies and conclusions in unevaluated settings require assumptions or target evidence.The record separates update histories, behavioral change and uncertainty, acquisition, retention, locality, and cost; missing or invalid evidence remains undefined.Source: E Reproducibility materials and scope · p. 40
F Complete proofs of the formal results
The proofs establish when update counts determine composed maps, how history summaries constrain observable differences, and where estimability or off-support conclusions require additional conditions.
F.1 Deterministic history-resolution formula; F.2 Count factorization
- Pairwise commutativity makes final maps factor through atom counts; on restricted catalogues, equal-count words need only induce equal maps.Scalar counts are coarser than atom counts, and intermediate reads can depend on update prefixes.Source: §F.2 · p. 41, §F.1 · p. 41
F.3 History-resolution certificate
- A common conditional outcome kernel contracts total-variation differences, with equality possible when the summary preserves the sign partition.The common-kernel premise fails if omitted paths leave outcome laws policy-dependent after conditioning on the recorded history.Source: §F.3 · pp. 41–42
F.4 Resolution floor
- A lower bound on score difference yields a resolution floor: history resolution must be at least δ/(b −a).Source: §F.4 · p. 42
F.5 Conditional-kernel mismatch
- Conditional-kernel mismatch adds error to the common-kernel bound, while bounded outcomes yield a corresponding mean-score bound.The displayed proof combines the mismatch terms by the triangle inequality and caps total variation at one.Source: §F.5 · pp. 42–43
F.6 Schedule-class staircase
- The schedule-class count rises from one history at H=0 to four at H=1, twelve at H=2 or 3, and 24 for H≥4.For deterministic schedule pairs, rows with differing histories contribute their row mass to total variation.Source: §F.6 · p. 43
F.7 Working-basis estimability
- Observationally invisible basis perturbations have zero intercept change and lie in ker(I_U); a linear functional is estimable exactly when its coefficient lies in range(I_U).Source: §F.7 · p. 43
F.8 Dimension of the band–period working basis
- The space of 4×4 matrices with zero row and column sums has dimension nine, and differences of permutation matrices span it.Source: §F.8 · p. 44
F.9 Off-support non-identification
- Evaluated records do not identify off-support responses without an additional restriction or target evidence; unresolved intervals cannot establish a common sign.In the two-coordinate illustration, the unobserved value can vary across its bounded range, and opposite-sign within-context utility differences defeat either constant policy choice in the stated set.Source: §F.9 · p. 44