When Should We Intervene at Test Time?

Jiahao Zhang; Xinling Wen; Liangliang Li; Yu Chen

cs.LGOct 27, 2026

When Should We Intervene at Test Time?

Authors: Jiahao Zhang, Xinling Wen, Liangliang Li, Yu Chen

Organizations: Zhengzhou University of Aeronautics · Xi’an University of Technology

Abstract

Test-time adaptation helps a deployed model respond to changing inputs, but the same intervention can rescue one batch and damage the next. Updating normalization statistics, for example, can improve corrupted images yet fail when a batch contains mostly one class. Average accuracy hides these failures and cannot tell a model when to use an intervention. Target labels can guide this decision, but they are scarce and some choices are already clear. We introduce PORTAL, a controller that chooses when to deploy an intervention, which inputs to label, and when to stop querying. Each available prediction rule is a candidate, and its predictions are fixed before current feedback arrives. Every acquired label therefore evaluates all candidates on the same input. PORTAL combines these shared comparisons and directs queries toward candidates that can still overtake the current leader. It stops when the remaining labels cannot change the choice or when the possible accuracy gain no longer justifies another query. Our analysis links the required feedback to accuracy gaps and shared mistakes, explaining why some choices need much less evidence. Experiments show that this control turns an intervention that loses accuracy overall into a useful choice on selected batches. It prevents severe failures caused by changes in arrival order and preserves gains across complete corruption streams. When a fixed rule already works well, PORTAL uses little feedback to retain its performance. Periodic label checks reveal when past evidence needs refreshing and help the controller recover as conditions change. The acquired labels also train stronger candidates for future batches, and selection brings nearly all of their accuracy gains into deployment. The same feedback therefore improves both the choice made now and the predictions available to later batches.

Figures & tables

Figure 1: Portal compares fixed candidates through shared labels. It deploys the leader when no rival can overtake it or when the value bound falls below the label price. Otherwise, it queries to improve the decision. Snowflakes mark fixed predictions; flames mark updates to the class-probability estimates.

Figure 2: A strong fixed intervention fails when classes arrive together. On class-block PACS, BN+flip reaches 22.58% accuracy and Portal reaches 51.28%. Net batch harm falls from 32.41 to 0.34 percentage points. Domain, Mixed and Class denote domain blocks, mixed domains and class blocks. Results use a Photo source and batch size 64. Bars average three orders; accuracy error bars show order standard deviation (SD). The inset enlarges the selectors’ harm values.

Figure 3: Accuracy gains over the incumbent on the recorded PACS trajectory, including queried inputs. Portal uses symmetric-KL queries and paired ERM. Random gate matches its admission rate; random queries use three labels. Oracle uses full-batch labels. Appendix R.2 gives the full protocol.

	Noise			Blur				Weather				Digital				Summary
Model / rule	Gau.	Shot	Imp.	Def.	Gla.	Mot.	Zoom	Snow	Frost	Fog	Bri.	Con.	Ela.	Pix.	JPEG	Avg.	Labels
CIFAR-10-C / ResNet-18
Source	25.8	32.8	25.0	56.6	51.5	67.6	65.0	77.3	66.4	73.5	91.2	33.9	76.8	45.6	73.1	57.48 $\pm$ 1.12	0
BN	66.2	68.5	59.5	87.2	65.0	86.1	87.3	81.2	80.1	84.7	90.6	86.9	76.6	79.0	71.4	78.02 $\pm$ 0.50	0
Flip	26.3	33.2	25.2	57.1	52.5	68.3	65.9	78.2	67.2	74.0	92.1	33.9	78.1	45.7	74.4	58.14 $\pm$ 1.00	0
BN+flip	68.7	71.2	62.7	88.6	67.2	86.9	88.4	83.0	81.6	85.8	91.1	87.5	78.4	80.1	73.4	79.65 $\pm$ 0.56	0

Table 2: Severity-five CIFAR accuracy (%) on shared held-out images, averaged over three source models. Summary: mean

\pm

standard deviation (SD) and labels per suite. Bold marks the best deployable rule; the oracle is an evaluation reference.

Figure 4: Exact selection-error probabilities for brightness (left) and JPEG (right). Curves use uniform sampling without replacement; markers use 2,000 independent subset draws per setting. Means cover three checkpoints. Schedules use distinct image blocks.

Figure 5: Five PACS orders. Error bars show order SD; numbers give credits per batch. Coincident curves share a legend entry.

A. Common-posterior acquisition
Acquisition	Accuracy (%)	Labels	Harm (pp)
Uniform	59.35 $\pm$ 0.13	132.8	1.78
Disagreement	59.31 $\pm$ 0.23	96.8	1.86
Maximum-pair KL	59.33 $\pm$ 0.26	118.8	1.85
PORTAL value	59.32 $\pm$ 0.34	85.6	1.86
B. Labels purchased after stopping

Table 3: Four-candidate PACS controls. A shares the posterior, history, budget and stopping rule. B adds labels after stopping. Harm averages positive batch accuracy losses relative to the unchanged model over evaluation inputs; pp denotes percentage points.

Figure 6: A change in the label law with fixed candidate predictions and stratum frequencies. Vertical lines mark the transition. Decay multiplies past counts by 0.9. The original five-seed experiment and its costs appear in Table 70 .

Stream	Label ceiling	Post-change gain (pp)	Recovery, delay $\leq 10$
Two-pattern abrupt	120	$+9.52\ [8.83,10.21]$	0.92
Two-pattern gradual	120	$+4.87\ [4.16,5.58]$	0.80
Two-pattern gradual, larger budget	160	$+6.44\ [5.92,6.96]$	0.94
300-mode recurrent, priority audit	100	$+3.28\ [0.61,5.95]$	0.685 / 0.798 / 0.642
300-mode recurrent, larger-budget variant	160	$+8.55\ [7.68,9.41]$	0.907 / 0.933 / 0.893

Table 4: Post-change gains over our reconstructed EW selector at equal label ceilings; brackets give paired intervals. Recovery is the fraction with delay

\leq 10

. Sparse rows give changes 25/50/75 under prioritized queries. The sparse 160-label variant changes both budget and settings.

Rule	Selected	Learned	Decision
Fixed BN+flip	59.68 ±0.28	—	0
Uniform ERM	65.91 ±0.49	73.03	393.0
Disagreement ERM	70.29 ±0.76	72.98	393.0
Portal	72.64 ±1.05	73.03	70.8

Table 5: PACS accuracy (%). Selected is deployed accuracy, given as mean

\pm

SD over five stream orders. Learned always uses each policy’s learned candidate. Decision labels form part of the 393 total labels per stream. The fixed rule uses zero labels.

Appendix figures & tables72 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{A}_{t}$ , $I$	Available batch interventions and incumbent at time $t$ .
$Q_{t}$ , $E_{t}$	Permanent eligible query and deployment/evaluation inputs.
$R_{a}$ , $D_{a}$	Candidate correctness and its difference from incumbent correctness.
$s$ , $w_{s}$ , $p_{sa}$	Joint prediction stratum, target frequency and candidate class.
$\theta_{s}$ , $A_{a}(\theta)$	Conditional label law and expected target accuracy.
$\Delta_{a}$ , $v_{s,a}$	Best-candidate gap and within-stratum paired reward variance.

Appendix

Table 6: Statistical objects used throughout the paper.

Analysis	Required observation structure	Result and validation
Shared-label complexity	Independent categorical labels within known, queryable strata; fixed prediction signatures	Information lower bound, paired-variance upper bound and local allocation coefficient.
Posterior querying	Positive independent Dirichlet priors and shared stratum label laws	Joint accuracy covariance, one-label value and sufficient local stopping conditions.
Gaussian finite budget	Common-factor joint Gaussian feedback with fixed risks and biases	Exact winner probabilities, budget and correlation responses; independent score simulation.
Frozen neural pools	Uniform subsets of a specified finite query pool; frozen predictions and evaluation outcomes	Exact discrete selection and deployment loss; independent subset simulation.
Persistent state	Shared future inputs, query labels and affine head/cache updates	Exact state recurrence, directional loss interval and margin bound; explicit branch replay.

Appendix

Table 7: Result dependencies and the quantity each result predicts.

Figure 7: Four-candidate selection under varying accuracy gaps (columns), query bias (rows) and error correlation

\rho

(curves). Lines integrate Gaussian winner probabilities. Markers and 95% error bars use 100,000 independent score vectors per condition. Canceling shared noise strengthens the query ranking, including when bias makes that ranking wrong. Appendix E gives parameters and neural-network validation.

Figure 8: Exact finite-budget predictions on all 655 PACS batches with incumbent-default ties. Solid lines use the hypergeometric law; dashed lines use its finite-population Gaussian approximation; points and 95% error bars use independent subset simulation. The left panel evaluates the same full population for both pools. The middle and right panels condition on agreement or opposition between realized pool and evaluation advantage signs. Uniform and top-half-KL pools have 404/397 aligned and 153/154 opposed batches, respectively. Seven top-half pools use fewer than ten labels at cap ten. Error bars measure simulation error.

Figure 9: The same finite-budget experiment with BN+flip selected on ties. All-batch gain uses all 20,775 evaluation occurrences across five orders; conditional panels retain their pool-specific aligned and opposed groups. The strong fixed default changes the small-budget response while leaving the exact sampling calculation unchanged. Curves and uncertainty follow the preceding figure.

Figure 10: Retain versus undo an update. (a,b) Immediate and future accuracy changes with order SD. (c,d) Normalized loss changes

(\Delta\mathrm{CE}-L)/R

: quartiles, medians and full-range whiskers within the predicted interval

[0,1]

	Checkpoint 0				Checkpoint 1				Checkpoint 2
Corruption	I	B	F	BF	I	B	F	BF	I	B	F	BF
Gaussian	22.13	66.36	22.03	68.41	27.73	67.01	28.48	69.52	28.06	67.37	28.30	69.90
Shot	29.25	67.61	29.26	70.43	34.26	69.00	34.81	71.78	36.06	69.52	36.32	72.13
Impulse	22.53	58.86	22.97	62.09	22.02	60.92	22.04	63.55	29.56	60.85	30.38	63.89
Defocus	54.54	87.34	55.31	88.61	55.88	87.73	56.48	88.93	59.74	87.70	60.19	88.99
Glass	55.10	65.17	56.08	67.32	50.14	64.88	51.63	67.06	50.83	65.94	51.99	67.76

Appendix

Table 8: Complete CIFAR10-C fixed-intervention accuracy (%). Each checkpoint evaluates all 10,000 images in every severity-5 corruption; all columns use zero feedback.

	Checkpoint 0				Checkpoint 1				Checkpoint 2
Corruption	I	B	F	BF	I	B	F	BF	I	B	F	BF
Gaussian	10.21	39.76	10.19	41.13	9.53	39.58	9.83	41.09	12.13	38.31	12.01	40.48
Shot	11.99	41.11	12.21	42.85	11.03	40.19	11.38	42.05	13.41	40.20	13.56	42.22
Impulse	6.64	34.72	6.77	36.32	6.63	33.61	6.62	35.27	8.23	33.57	8.23	35.83
Defocus	34.80	66.18	35.00	67.23	34.49	66.08	34.85	66.98	35.22	65.67	35.47	66.23
Glass	20.19	42.66	19.93	43.56	19.06	42.69	19.49	43.66	19.48	41.91	19.56	43.46

Appendix

Table 9: Complete CIFAR100-C fixed-intervention accuracy (%). Each checkpoint evaluates all 10,000 images in every severity-5 corruption; all columns use zero feedback.

Dataset	Method	Accuracy (%)	$\Delta$ BF (pp)	Labels
CIFAR10-C	Fixed BF	$79.646\pm 0.561$	0.000	0.0
CIFAR10-C	Mean logits	$76.548\pm 1.295$	-3.099	0.0
CIFAR10-C	Uniform ERM	$78.275\pm 0.583$	-1.371	7065.0
CIFAR10-C	Disagreement ERM	$78.361\pm 0.591$	-1.285	7065.0
CIFAR10-C	Symmetric-KL ERM	$79.202\pm 0.499$	-0.444	7065.0
CIFAR10-C	Portal	$79.259\pm 0.506$	-0.388	612.3

Appendix

Table 10: Complete-suite comparison on the common evaluation population. Accuracy is averaged over three checkpoints; the accompanying value is the sample SD. Label counts are per 15-corruption suite.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	21.78	65.92	21.86	67.56	56.70	65.08	65.58	67.58	67.56	68.76	53
Shot	29.04	68.12	29.14	70.48	63.04	68.62	68.84	70.24	70.24	71.42	50
Impulse	23.06	57.74	23.04	61.38	55.34	57.96	58.04	61.28	61.38	62.24	54
Defocus	54.62	87.14	54.90	88.26	83.20	86.80	87.34	88.26	87.96	89.06	44
Glass	54.60	65.04	55.58	67.44	65.86	65.08	64.74	66.24	65.72	68.72	72
Motion	67.50	86.20	68.22	86.64	84.72	84.94	85.64	86.42	86.34	87.72	42

Appendix

Table 11: CIFAR10-C, checkpoint 0: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	27.50	66.08	28.64	69.28	56.76	66.60	67.16	69.24	68.80	70.14	58
Shot	33.60	68.32	34.50	71.30	61.78	67.86	70.12	71.20	70.94	72.00	55
Impulse	22.04	60.30	22.04	62.82	50.36	60.20	60.86	62.48	62.74	63.92	62
Defocus	55.72	87.28	56.48	88.66	82.80	87.38	87.94	88.64	88.66	89.26	34
Glass	49.28	64.18	50.62	66.74	62.28	63.88	64.18	64.86	66.34	67.72	34
Motion	66.32	85.60	66.86	86.44	83.02	85.74	85.52	86.32	86.34	87.46	28

Appendix

Table 12: CIFAR10-C, checkpoint 1: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	28.14	66.70	28.40	69.34	62.20	66.70	67.04	69.24	69.16	70.28	56
Shot	35.88	69.10	35.84	71.80	67.14	70.26	70.92	71.64	71.38	72.74	66
Impulse	29.98	60.48	30.44	64.04	57.80	62.32	62.50	63.24	63.14	64.96	64
Defocus	59.58	87.24	60.00	88.74	85.76	87.16	87.80	88.66	88.34	89.38	43
Glass	50.66	65.82	51.42	67.44	64.54	65.18	64.60	66.42	67.02	68.76	47
Motion	68.98	86.62	69.86	87.68	85.48	86.28	86.52	87.66	87.14	88.40	38

Appendix

Table 13: CIFAR10-C, checkpoint 2: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	10.70	39.66	10.54	40.84	32.32	39.46	39.84	40.34	40.84	41.88	52
Shot	12.26	41.08	12.52	42.68	34.58	41.06	40.72	41.94	42.36	44.00	63
Impulse	7.16	35.04	7.22	36.34	29.18	35.34	35.32	36.16	34.74	37.74	46
Defocus	34.18	65.30	34.00	66.22	62.44	64.24	64.84	66.22	65.50	67.24	27
Glass	20.32	42.12	19.92	42.86	39.44	40.30	40.46	42.30	42.56	44.30	36
Motion	43.28	62.58	44.28	63.28	61.76	61.46	60.86	62.64	63.08	64.48	12

Appendix

Table 14: CIFAR100-C, checkpoint 0: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	9.92	39.70	10.20	40.94	31.30	39.64	39.60	40.72	40.94	42.08	58
Shot	11.12	40.30	11.56	41.78	33.60	38.40	38.68	41.48	41.78	42.82	57
Impulse	7.36	34.02	7.36	35.30	30.76	34.56	34.90	34.96	35.10	36.50	41
Defocus	33.86	64.76	33.88	65.88	62.60	63.38	64.46	65.76	65.48	66.84	25
Glass	19.10	42.24	19.78	43.16	39.14	41.76	42.14	42.54	42.32	44.28	34
Motion	43.52	62.80	44.54	63.64	62.12	61.80	62.38	63.46	62.42	64.96	11

Appendix

Table 15: CIFAR100-C, checkpoint 1: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Corruption	I	B	F	BF	Mean	U	D	K	J	O	$Q_{J}$
Gaussian	12.32	38.18	12.06	39.90	34.02	38.80	38.66	39.38	39.66	40.76	53
Shot	13.68	40.16	13.62	41.86	36.10	40.10	39.98	41.20	41.56	43.06	36
Impulse	8.64	33.44	8.66	35.58	30.74	33.60	33.52	34.60	35.58	36.60	32
Defocus	34.64	65.46	34.90	65.72	62.14	64.62	64.76	65.70	65.62	67.06	29
Glass	19.90	40.74	19.88	42.22	39.28	40.30	40.22	41.24	41.12	43.30	27
Motion	42.68	62.22	43.58	62.74	60.96	60.78	60.90	62.42	62.28	63.72	14

Appendix

Table 16: CIFAR100-C, checkpoint 2: accuracy (%) on the same 5,000 evaluation images per corruption. U, D and K are uniform, disagreement-first and symmetric-KL empirical selection; J is joint selection; O is the batch oracle. The last column counts J labels, with a suite total in the Mean row.

Dataset	Domain	$n$	S	T	V2	V8
PACS	Art Painting	2048	98.68	99.02	99.17	99.17
PACS	Cartoon	2344	99.45	99.57	99.57	99.62
PACS	Photo	1670	99.88	99.94	99.94	99.94
PACS	Sketch	3929	95.47	95.04	95.19	95.34
PACS	Equal-domain	9991	98.369	98.393	98.468	98.517
PACS	Pooled	9991	97.798	97.738	97.828	97.898

Appendix

Table 17: Whole-dataset CLIP ViT-L/14 readouts with zero feedback. S uses one template and one view; T uses eight templates on the original view; V2 and V8 average universal-template log probabilities over two and eight views. OfficeHome uses the saved prediction stream evaluated by its controller.

Rule	PACS	OfficeHome	VLCS
Fixed eight views	98.44/0	89.01/0	84.10/0
Uniform ERM	98.43/473.6	88.90/738.0	84.07/354.8
Mean-pair KL	98.44/473.6	88.63/738.0	83.91/354.8
Portal , four	98.44/1.4	89.01/7.4	83.92/89.4
Fixed StatA	98.40/0	—	85.11/0
Portal + StatA	98.44/2.4	—	84.58/96.0

Appendix

Table 18: CLIP accuracy (%) / labels on shared evaluation images. Accuracy averages domains; labels average five orders. Mean-pair KL ranks inputs by average pairwise divergence. A dash marks an unmeasured entry. Appendix I gives full readouts.

Dataset	Method	Equal-domain (%)	Pooled	$\Delta$ V8	Labels
PACS	Fixed S	$98.1906\pm 0.0000$	97.5412	-0.2462	0.0
PACS	Fixed T	$98.2791\pm 0.0000$	97.5615	-0.1578	0.0
PACS	Fixed V2	$98.4249\pm 0.0000$	97.7037	-0.0120	0.0
PACS	Fixed V8	$98.4369\pm 0.0000$	97.7444	0.0000	0.0
PACS	Uniform ERM	$98.4343\pm 0.0056$	97.7403	-0.0025	473.6
PACS	Disagreement ERM	$98.4343\pm 0.0314$	97.7403	-0.0025	473.6

Appendix

Table 19: VLM evaluation on a permanent common E population. Accuracy is an equal-domain mean over five stream orders; SD measures stream/query variation on one checkpoint and set of image transformations. Pooled accuracy weights images. Labels are actual per-stream annotations.

Dataset	Domain	V8	U	D	K	J	$Q_{J}$
PACS	Art Painting	99.069	99.069	99.069	99.069	99.069	0.0
PACS	Cartoon	99.570	99.570	99.570	99.570	99.570	0.0
PACS	Photo	100.000	100.000	100.000	100.000	100.000	0.0
PACS	Sketch	95.108	95.098	95.098	95.119	95.129	1.4
OfficeHome	Art	88.898	88.865	88.405	88.388	88.898	0.0
OfficeHome	Clipart	78.016	77.668	77.239	77.426	78.034	6.0

Appendix

Table 20: VLM common-E domain-level accuracy (%) averaged over five stream orders. U, D and K denote uniform, disagreement-first and symmetric-KL empirical selection. J denotes Portal , and

Q_{J}

counts its labels. V8 is the fixed default.

Estimator	Accuracy (%)	$\Delta$ fixed (pp)
Unqueried fixed V8	92.8201	0.0000
Unqueried selected output	92.8839	0.0639
Whole current batch	90.1952	1.3689
Next microbatch	88.7376	-0.0887

Appendix

Table 21: OfficeHome with three labels per eight-image microbatch. Each timing rule is compared with the fixed output on the same scored inputs. Fixed accuracy is 88.8263% on whole or next batches and 92.8201% on unqueried inputs.

Corruption	E	U	UM	UD	US	UMD	Blend	Avg	$U_{M.25}$	$U_{D.25}$
Gaussian	62.61	60.33	60.23	61.86	64.26	60.71	60.54	61.36	59.77	60.73
Shot	55.25	53.35	54.04	54.60	57.33	54.01	53.71	54.48	53.34	53.69
Impulse	54.88	53.12	50.12	53.86	57.03	52.21	51.93	52.19	51.31	53.29
Defocus	64.08	62.50	63.02	62.79	65.30	62.75	62.61	63.08	62.66	62.54
Glass	61.54	60.28	60.54	60.58	63.43	60.53	60.26	60.61	60.34	60.32
Motion	53.52	53.51	53.61	53.01	54.85	53.11	52.60	52.61	53.38	53.14

Appendix

Table 22: ImageNet-C error (%) for fixed logit compositions on all 15 severity-5 corruptions, 50,000 images each. E is the EATTA readout; U is the two-view batch-statistic readout; M, D and S are median restoration, unsharp restoration and a source-reset branch. Weights are defined in the text.

	Additional-query stream			Independent repeat			Shared-prefix stream
Corruption	P	F	A	P	F	A	P	F	A	q
Gaussian	62.82	60.32	61.26	62.98	60.36	61.14	61.77	59.90	61.10	3.92
Shot	55.32	53.33	53.98	55.38	53.58	54.22	54.69	53.37	54.06	3.99
Impulse	54.90	53.02	53.66	54.88	53.08	53.63	54.24	51.38	53.23	3.49
Defocus	64.11	62.44	63.05	64.26	62.56	63.08	63.12	61.85	62.66	4.19
Glass	61.39	60.00	60.51	61.46	60.26	60.72	60.47	59.37	59.99	4.30

Appendix

Table 23: ImageNet-C current-batch error (%) under two feedback protocols. The first two streams use three adaptation labels plus three separate selection labels per batch. The shared-prefix stream reuses selection labels for the committed update; q counts its committed prefix, excluding additional provisional supervised reads. P, F and A denote EATTA, fixed challenger and selected output.

Benchmark	Backbone	Reference	Metric	Reported	Fixed	$\Delta$
ImageNet-C	ResNet-50	EATTA	Error	50.90	49.3395	1.5605
ImageNet-K	ResNet-50	EATTA	Error	61.40	61.1252	0.2748
ImageNet-A	ViT-B/16	TDA	Acc.	60.11	60.2000	0.0900
PACS	ViT-L/14	WATT	Acc.	97.51	98.5171	1.0071
OfficeHome	ViT-L/14	TPT	Acc.	86.72	88.8435	2.1235
VLCS	ViT-L/14	TENT	Acc.	80.20	83.7927	3.5927

Appendix

Table 24: Direct fixed-intervention endpoints and reported literature values. ImageNet-C/K use EATTA with three labels per batch; the visual-language rows use zero target labels. Margins orient improvement positively. The ImageNet-A endpoint averages two declared runs. CIFAR fixed endpoints use zero labels, while their SimATTA references use active feedback.

Query	Output	Accuracy (%)	$\Delta$ BF	CE	Decision Q	Total Q
Uniform	Fixed BF	$59.677\pm 0.278$	0.000	1.2205	0.0	0
Uniform	Always learned	$73.030\pm 0.695$	13.353	0.9430	393.0	393
Uniform	Selected output	$65.911\pm 0.493$	6.233	1.0918	393.0	393
Disagreement	Fixed BF	$59.677\pm 0.278$	0.000	1.2205	0.0	0
Disagreement	Always learned	$72.982\pm 0.779$	13.304	0.9424	393.0	393
Disagreement	Selected output	$70.286\pm 0.759$	10.609	0.9999	393.0	393

Appendix

Table 25: Causal PACS residual-head learning with ridge coefficient 1 and logit scale 4. Each query policy generates its own full learning trajectory over five orders. Decision labels are part of the total 393 labels, and unused joint-decision slots train the next-batch head. Fixed BF alone uses zero target labels.

$\lambda$	Scale	Query	Always learned	Selected	$\Delta$ learned
1	4	Uniform	73.030	65.911	-7.119
1	4	Disagreement	72.982	70.286	-2.696
1	4	Portal	73.025	72.640	-0.385
0.1	4	Uniform	75.321	68.125	-7.196
0.1	4	Disagreement	75.576	71.981	-3.596
0.1	4	Portal	75.302	74.729	-0.573

Appendix

Table 26: All residual-head sensitivity settings fixed before evaluation on PACS. Every row uses five complete orders and 393 total labels per order. The primary setting remains lambda=1 and scale=4.

State	$H$	$\Delta$ now	$\Delta$ future	$\Delta$ CE	$L$	$R$	Changes
Head commit	1	0.2296	-0.1972	-0.5907	-2.6530	8.1582	174.2
Head commit	4	0.2038	-0.0578	-0.7994	-1.5634	3.0299	333.6
Head commit	16	0.2313	-0.0169	-0.4486	-0.6574	0.8191	302.8
Cache commit	1	0.0293	0.0148	-0.2187	-0.2212	0.0115	7.6
Cache commit	4	0.0366	0.0118	-0.1917	-0.1935	0.0086	23.4
Cache commit	16	0.0372	0.0023	-0.1503	-0.1510	0.0036	40.4

Appendix

Table 27: Persistent-state continuation on PACS. Accuracy changes are in percentage points. Future cross-entropy (CE) change, directional linear term L and remainder ceiling R are multiplied by 1,000. The actual CE change lies in [L,L+R] before averaging. Changes counts hard-prediction differences over all valid overlapping comparisons per order.

Domain	Single	Eight-view	Decision	Eight-view MiB
Art	2.354	16.669	0.507	2616.9
Clipart	2.084	16.732	0.546	2617.6
Product	2.093	16.784	0.633	2617.6
Real World	2.100	16.809	0.451	2617.6
Mean	2.158	16.749	0.534	2617.4

Appendix

Table 28: Measured OfficeHome CLIP ViT-L/14 component costs, batch size 8. Forward columns are ms/image; decision is ms/batch after action logits exist. Each domain contributes 64 measured images. Memory is peak allocation in MiB.

Acquisition	$k$	$G$	$H_{B}$	$S$
Always candidate	-	7.49	2.47	11.85
Uniform	1	4.54	0.84	4.33
Uniform	2	1.58	0.26	1.17
Uniform	3	0.30	0.00	0.05
Disagreement	1	5.77	1.25	5.81
Disagreement	2	3.50	0.53	2.47

Appendix

Table 29: Normalization on the frozen Photo-source PACS model. Each acquisition rule uses three query labels and the distinct minimum signed count k. The default is running-statistic I. G and

H_{B}

are percentage points; S is the percentage of newly introduced errors.

Acquisition	$k$	$G$	$H_{B}$	$S$
Always candidate	-	0.02	1.19	2.07
Uniform	1	0.01	0.05	0.12
Uniform	2	0.00	0.00	0.00
Uniform	3	0.00	0.00	0.00
Disagreement	1	-0.04	0.43	0.68
Disagreement	2	0.03	0.07	0.12

Appendix

Table 30: Horizontal views on the frozen Photo-source PACS model. Each acquisition rule uses three query labels and the distinct minimum signed count k. The default is running-statistic I. G and

H_{B}

are percentage points; S is the percentage of newly introduced errors.

Acquisition	$k$	$G$	$H_{B}$	$S$
Always candidate	-	8.80	2.00	11.18
Uniform	1	5.15	0.72	4.30
Uniform	2	1.86	0.19	1.18
Uniform	3	0.33	0.00	0.10
Disagreement	1	7.03	0.69	5.16
Disagreement	2	4.26	0.24	2.31

Appendix

Table 31: Normalization and views on the frozen Photo-source PACS model. Each acquisition rule uses three query labels and the distinct minimum signed count k. The default is running-statistic I. G and

H_{B}

are percentage points; S is the percentage of newly introduced errors.

$T$	$G$	$H_{B}$	$S$	Overlap (%)	Changed (%)
0.25	7.50	1.40	7.54	68.40	19.54
0.5	7.37	1.34	7.22	77.51	13.74
1	7.25	1.15	6.15	100.00	0.00
2	7.10	1.01	5.78	82.49	9.31
4	6.85	1.05	5.90	76.18	13.59

Appendix

Table 32: Positive-temperature acquisition control with fixed hard predictions. The candidate is BF, the budget is three, and k=1. Overlap and decision changes use temperature one as the reference.

Binning	Bin	Batches	$n_{E}$	Query gain	E gain	Negative (%)
All domains	1	27	849.4	14.07	6.10	17.04
All domains	2	26	829.2	45.64	17.16	10.00
All domains	3	26	829.2	33.08	10.60	26.92
All domains	4	26	842.4	21.79	4.75	38.46
All domains	5	26	804.8	33.85	5.34	33.08
Within domain	1	28	900.4	25.71	9.23	22.86

Appendix

Table 33: Symmetric-KL score quintiles for BF, from low to high. Query and evaluation gains use their own image populations. Negative is the percentage of batches where BF increases evaluation errors. Bin membership depends on the label-free query score.

		Uniform			Disagreement			Symmetric KL
$m$	$k$	$G$	$H_{B}$	$S$	$G$	$H_{B}$	$S$	$G$	$H_{B}$	$S$
1	1	2.42	0.40	2.22	5.05	0.51	3.89	5.85	1.00	5.36
3	1	5.15	0.72	4.30	7.03	0.69	5.16	7.25	1.15	6.15
3	2	1.86	0.19	1.18	4.26	0.24	2.31	5.20	0.51	2.66
3	3	0.33	0.00	0.10	1.53	0.03	0.62	2.78	0.12	0.90
5	1	6.51	0.74	4.87	7.56	1.01	6.26	7.63	1.20	6.80

Appendix

Table 34: All distinct measured frozen-PACS budget/count rules. Each acquisition block reports gain G, negative batch contribution

H_{B}

, and sample-new-error percentage S. Thresholds that induce the same signed count are represented once.

Mixture family	Output	$G$	$H_{B}$	$S$	Labels/batch
Disagreement + fixed BF	Mixture	7.6495	1.1456	7.2663	1.9522
Disagreement + fixed BF	Symmetric KL	7.2491	1.1456	6.1468	3.0000
Two disagreement counts	Mixture	5.9117	0.5054	4.0110	3.0000
Two disagreement counts	Symmetric KL	5.1986	0.5054	2.6619	3.0000

Appendix

Table 35: Expected outcomes of two fitted rule mixtures and their symmetric-KL targets at matched negative batch cost. The mixtures use high-endpoint probabilities 0.3492647 and 0.5957447, respectively.

Cost	$k$	Point gap	2.5%	97.5%
Batch net cost	1	-0.4004	-0.5453	-0.2555
Batch net cost	2	-0.7131	-1.5901	0.7030
Batch net cost	3	0.1090	-2.5777	1.2591
New errors	1	-0.0717	-0.2560	0.1362
New errors	2	0.5973	-0.1205	1.1252
New errors	3	0.7927	0.0611	1.2920

Appendix

Table 36: Symmetric-KL gain minus the empirical frontier without symmetric-KL rules, including K-Margin in the alternative library. Every one of the 3,125 ordered stream resamples refits the frontier. Bounds are the 2.5th and 97.5th descriptive percentiles, in percentage points.

Output	Image	Batch	2 batches	4 batches	8 batches	Domain
Always BF	11.1817	1.9976	1.2130	0.7220	0.3995	0.0000
Disagreement	5.1649	0.6883	0.5247	0.3418	0.1877	0.0000
Symmetric KL	6.1468	1.1456	0.8857	0.6691	0.4043	0.0193

Appendix

Table 37: Negative contribution when the same selected outputs are scored at different grouping scales. Only the scoring partition changes. Individual-image groups yield S, and original-batch groups yield

H_{B}

Domain	Class	$n_{E}$	Always BF	Disagreement	Symmetric KL
Art	dog	183	-6.23	-3.72	-2.40
Art	elephant	123	9.43	5.20	4.88
Art	giraffe	131	-10.08	-5.19	-3.66
Art	guitar	91	-4.84	-2.86	-2.42
Art	horse	92	-3.26	-2.17	-2.17
Art	house	149	1.48	0.94	0.81

Appendix

Table 38: All domain-by-class gains on the permanent PACS evaluation population. Each group denominator is fixed across the five orders. The two query rules use three labels and k=1.

Dataset	Readout	Full data (%)	Common $E$ (%)	Labels
PACS	Prompt average	98.393 $\pm$ 0.000	98.279 $\pm$ 0.000	0
PACS	Eight views	98.517 $\pm$ 0.000	98.437 $\pm$ 0.000	0
PACS	Mean logits	98.502 $\pm$ 0.000	98.390 $\pm$ 0.000	0
PACS	StatA	98.445 $\pm$ 0.051	98.404 $\pm$ 0.063	0
VLCS	Prompt average	83.099 $\pm$ 0.000	83.523 $\pm$ 0.000	0
VLCS	Eight views	83.793 $\pm$ 0.000	84.097 $\pm$ 0.000	0

Appendix

Table 39: Episodic StatA and fixed CLIP readouts. Accuracy is equal-domain mean

\pm

stream-order SD. Fixed readouts have no order variation; all rows use zero target labels.

Dataset	Domain	Readout	Accuracy (%)
PACS	Art	Eight views	99.170 $\pm$ 0.000
PACS	Art	StatA	99.219 $\pm$ 0.035
PACS	Cartoon	Eight views	99.616 $\pm$ 0.000
PACS	Cartoon	StatA	99.727 $\pm$ 0.038
PACS	Photo	Eight views	99.940 $\pm$ 0.000
PACS	Photo	StatA	100.000 $\pm$ 0.000

Appendix

Table 40: Domain-level StatA comparison on full data. Values are accuracy means

\pm

stream-order SD over five orders.

Dataset	Domain	Readout	Accuracy (%)
PACS	Art	Eight views	99.069 $\pm$ 0.000
PACS	Art	StatA	99.255 $\pm$ 0.046
PACS	Cartoon	Eight views	99.570 $\pm$ 0.000
PACS	Cartoon	StatA	99.725 $\pm$ 0.094
PACS	Photo	Eight views	100.000 $\pm$ 0.000
PACS	Photo	StatA	100.000 $\pm$ 0.000

Appendix

Table 41: Domain-level StatA comparison on common

E

. Values are accuracy means

\pm

stream-order SD over five orders.

Dataset	Time (s)	Peak MiB	Final-batch adjustments	Initialization $\|\Delta p\|$
PACS	7.95 $\pm$ 0.24	24.51	0	1.75e-06
VLCS	5.92 $\pm$ 0.03	20.33	5	1.83e-06

Appendix

Table 42: StatA resource measurements from an isolated rerun. Time is seconds per four-domain stream; memory is peak allocated GPU memory. The final three-image batch uses two neighbors. Initialization

|\Delta p|

is the largest difference between the solver’s initial probabilities and the stored prompt-average probabilities.

	Four readouts		Add StatA
Rule	Accuracy (%)	Labels	Accuracy (%)	Labels
Original view	98.191 $\pm$ 0.000	0.0	98.191 $\pm$ 0.000	0.0
Prompt average	98.279 $\pm$ 0.000	0.0	98.279 $\pm$ 0.000	0.0
Two views	98.425 $\pm$ 0.000	0.0	98.425 $\pm$ 0.000	0.0
Eight views	98.437 $\pm$ 0.000	0.0	98.437 $\pm$ 0.000	0.0
StatA	—	—	98.404 $\pm$ 0.063	0.0

Appendix

Table 43: PACS portfolio expansion on common

E

. Accuracy is equal-domain mean

\pm

stream-order SD. The four-action portfolio contains the original, prompt-average, two-view and eight-view readouts; the fifth action is episodic StatA. Empirical-query rows are paired reruns for this expansion.

	Four readouts		Add StatA
Rule	Accuracy (%)	Labels	Accuracy (%)	Labels
Original view	80.845 $\pm$ 0.000	0.0	80.845 $\pm$ 0.000	0.0
Prompt average	83.523 $\pm$ 0.000	0.0	83.523 $\pm$ 0.000	0.0
Two views	83.861 $\pm$ 0.000	0.0	83.861 $\pm$ 0.000	0.0
Eight views	84.097 $\pm$ 0.000	0.0	84.097 $\pm$ 0.000	0.0
StatA	—	—	85.106 $\pm$ 0.137	0.0

Appendix

Table 44: VLCS portfolio expansion on common

E

. Accuracy is equal-domain mean

\pm

	PACS		OfficeHome		VLCS
Rule	Acc.	Labels	Acc.	Labels	Acc.	Labels
Eight views	98.437 $\pm$ 0.000	0.0	89.008 $\pm$ 0.000	0.0	84.097 $\pm$ 0.000	0.0
Mean logits	98.390 $\pm$ 0.000	0.0	88.237 $\pm$ 0.000	0.0	83.650 $\pm$ 0.000	0.0
Portal	98.442 $\pm$ 0.007	1.4	89.010 $\pm$ 0.012	7.4	83.919 $\pm$ 0.170	89.4
Uniform / mixture	98.398 $\pm$ 0.014	473.6	88.415 $\pm$ 0.098	737.4	83.868 $\pm$ 0.228	354.8
Disagreement / mixture	98.415 $\pm$ 0.009	473.6	88.636 $\pm$ 0.068	737.4	84.005 $\pm$ 0.139	354.8

Appendix

Table 45: Primary convex-readout results (

\lambda=1

) on common

E

. Accuracy is equal-domain mean

\pm

stream-order SD; labels average five orders. Discrete ERM rows use the same queries as the corresponding mixture.

			Accuracy (%)		CE		Brier
$\lambda$	Acquisition	Labels	D	M	D	M	D	M	Fit (s)
0.1	Uniform	473.6	98.429 $\pm$ 0.007	98.382 $\pm$ 0.021	0.0580	0.0604	0.0252	0.0264	0.821
0.1	Disagreement	473.6	98.434 $\pm$ 0.031	98.393 $\pm$ 0.033	0.0584	0.0603	0.0253	0.0262	0.825
0.1	Maximum KL	473.6	98.439 $\pm$ 0.029	98.407 $\pm$ 0.049	0.0584	0.0597	0.0253	0.0259	1.028
0.1	Target Fisher	473.6	98.434 $\pm$ 0.034	98.417 $\pm$ 0.069	0.0583	0.0595	0.0253	0.0258	1.167
1	Uniform	473.6	98.429 $\pm$ 0.007	98.398 $\pm$ 0.014	0.0580	0.0604	0.0252	0.0264	0.503

Appendix

Table 46: Complete convex-readout grid on PACS common

E

. Every acquisition uses up to three current-batch labels; means and SDs cover five stream orders. Accuracy, cross-entropy and Brier columns pair discrete ERM (D) with the fitted mixture (M). Runtime is CPU mixture-fitting/replay time per stream.

			Accuracy (%)		CE		Brier
$\lambda$	Acquisition	Labels	D	M	D	M	D	M	Fit (s)
0.1	Uniform	737.4	88.863 $\pm$ 0.121	88.523 $\pm$ 0.144	0.3952	0.4105	0.1580	0.1623	1.464
0.1	Disagreement	737.4	88.637 $\pm$ 0.118	88.579 $\pm$ 0.094	0.4080	0.4060	0.1617	0.1609	1.283
0.1	Maximum KL	737.4	88.688 $\pm$ 0.122	88.726 $\pm$ 0.112	0.4018	0.4000	0.1601	0.1592	1.401
0.1	Target Fisher	737.4	88.687 $\pm$ 0.088	88.724 $\pm$ 0.077	0.4029	0.4006	0.1604	0.1595	1.570
1	Uniform	737.4	88.863 $\pm$ 0.121	88.415 $\pm$ 0.098	0.3952	0.4084	0.1580	0.1619	0.938

Appendix

Table 47: Complete convex-readout grid on OFFICEHOME common

E

			Accuracy (%)		CE		Brier
$\lambda$	Acquisition	Labels	D	M	D	M	D	M	Fit (s)
0.1	Uniform	354.8	83.907 $\pm$ 0.202	83.819 $\pm$ 0.248	0.4629	0.4648	0.2402	0.2392	0.681
0.1	Disagreement	354.8	83.869 $\pm$ 0.126	83.956 $\pm$ 0.164	0.4651	0.4625	0.2404	0.2390	0.630
0.1	Maximum KL	354.8	83.918 $\pm$ 0.158	84.068 $\pm$ 0.151	0.4661	0.4603	0.2408	0.2371	0.666
0.1	Target Fisher	354.8	83.887 $\pm$ 0.181	83.901 $\pm$ 0.241	0.4659	0.4613	0.2409	0.2381	0.775
1	Uniform	354.8	83.907 $\pm$ 0.202	83.868 $\pm$ 0.228	0.4629	0.4615	0.2402	0.2382	0.462

Appendix

Table 48: Complete convex-readout grid on VLCS common

E

Figure 11: Actual batch/source changes and label-channel stress tests. Panels (a)–(d) use regenerated predictions under three stream orders per condition; (e)–(f) use the primary five frozen-prediction orders with multiclass annotation replacement. Accuracy error bars are order standard deviations; label curves show mean actual acquisitions. Fixed output and mean-logit references retain zero feedback cost. Class-block arrivals change the normalization predictions, while label corruption leaves every candidate prediction fixed.

	Source checkpoint			Photo source: batch size				Photo source: arrival order
Rule	Art	Cart.	Sketch	16	32	64	128	Rev.	Mixed	Grad.	Class
Source	68.42	76.91	38.32	50.85	50.85	50.88	50.88	50.88	50.88	50.88	50.88
BN	77.33	80.35	62.45	57.18	58.07	58.17	58.80	58.17	59.67	59.08	22.65
Flip	68.94	77.51	38.02	50.90	50.90	50.90	50.90	50.90	50.90	50.90	50.90
BN+flip	78.39	81.41	63.02	58.49	59.39	59.53	59.87	59.53	60.56	60.63	22.58
Mean logits	78.89	82.20	55.22	60.79	61.54	61.34	61.47	61.34	59.15	60.92	45.25

Appendix

Table 49: PACS under changes in source checkpoint, batch size and arrival order. Every entry averages three regenerated stream orders.

	Source checkpoint			Photo source: batch size				Photo source: arrival order
Rule	Art	Cart.	Sketch	16	32	64	128	Rev.	Mixed	Grad.	Class
Source	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
BN	0.59	1.73	0.01	5.97	3.83	2.58	1.48	2.58	0.87	1.53	32.41
Flip	1.00	1.13	1.46	1.75	1.52	1.21	0.91	1.21	1.28	1.29	1.12
BN+flip	0.55	1.21	0.00	5.21	3.28	1.93	1.12	1.93	0.70	1.08	32.41
Mean logits	0.12	0.37	0.01	1.14	0.58	0.19	0.04	0.19	0.14	0.13	8.10

Appendix

Table 50: Net batch harm and sample-level new errors under the same PACS conditions as Table 49 .

Figure 12: Outcome decomposition under dynamic arrival conditions. Color identifies the selected rule and texture identifies whether a sample is rescued, newly harmed, correct under both outputs, or incorrect under both. The components are a linear decomposition of the reported source accuracy, selected accuracy and sample-level new errors on the common evaluation population.

$\eta$	Rule	Accuracy (%)	Labels	New errors (pp)
0	Uniform	58.97 $\pm$ 0.72	393.0	8.53
0	Disagreement	58.93 $\pm$ 0.47	393.0	8.66
0	Maximum KL	58.73 $\pm$ 0.23	393.0	8.55
0	Portal	59.31 $\pm$ 0.36	130.8	10.53
0.1	Uniform	59.00 $\pm$ 0.65	393.0	8.52
0.1	Disagreement	58.81 $\pm$ 0.47	393.0	8.45

Appendix

Table 51: Class-label corruption on the complete frozen PACS portfolio, five stream orders. A queried class is replaced uniformly by a different class with probability

\eta

. Accuracy is mean

\pm

order SD; labels and newly introduced errors are means. Predictions and evaluation labels are unchanged.

Controller	Expanded-set error (%)	Expansion effect (pp)
HILTTA-style	36.1698	+14.3203
Portal	18.9375	-1.2422
Harmonized SimATTA-style	15.2719	—
Committee	18.3438	—

Appendix

Table 52: Locked controller comparison across ten confirmation seeds. Errors include every scored episode input. Positive expansion effects mean that adding candidates increases error. A dash indicates that no expansion contrast is reported for that comparator.

Controller	All inputs	Current-query-excluded
Always challenger	-5.7965	-5.4337
Random gate	$-1.6997\ [-2.2946,-1.1256]$	$-1.5937\ [-2.1556,-1.0389]$
Uniform three-query admission	$+1.1508\ [0.8320,1.4689]$	$+0.9441\ [0.6104,1.2663]$
Portal paired admission	+2.2583	+1.7863
Full-batch oracle	+3.3280	+3.1247

Appendix

Table 53: PACS gains in percentage points over the matched incumbent. All inputs include current queried examples. Query-excluded removes current query positions, not historical labels or source-domain reuse. Brackets give 95% random-policy replay intervals where available.

Step	Operation
1	Freeze all candidate logits and merge exact hard-output copies. Form joint prediction strata and target frequencies.
2	Initialize each stratum from Equation ( 86 ), adding eligible historical acquired-label counts.
3	Compute the posterior means/covariance, default-tied leader and all-candidate bound $U$ .
4	Stop if the local query allowance is exhausted or $U\leq 0.002$ . Stop if no available target-stratum query remains.
5	Compute capped rival reachability. Stop if every rival is unreachable within the remaining local allowance.
6	Compute one-label decision values. On a zero-value plateau, use Equation ( 89 ). Stop if no available query has positive score.

Appendix

Table 54: Finite-batch joint selection. Predictions, current target composition and available query locations are inputs; acquired class labels are the feedback.

Acquisition	Accuracy (%)	Labels	Batch harm (pp)
Uniform	59.35 $\pm$ 0.13	132.8	1.78
Disagreement	59.31 $\pm$ 0.23	96.8	1.86
Maximum-pair KL	59.33 $\pm$ 0.26	118.8	1.85
PORTAL value	59.32 $\pm$ 0.34	85.6	1.86

Appendix

Table 55: Acquisition with a common posterior, history, available budget and stopping rule. Only the current query locations change. Means

\pm

SD cover five PACS stream orders.

Setting	Stop reason	Stops	Extra	Choice change	$\Delta$ accuracy (pp)
Primary	Unreachable	653	1.0	0.00%	+0.000 $\pm$ 0.000
Primary	Unreachable	653	3.0	0.00%	+0.000 $\pm$ 0.000
Primary	Unreachable	653	5.0	0.31%	+0.000 $\pm$ 0.051
Price 0.05	EVPI bound	498	1.0	1.20%	-0.075 $\pm$ 0.052
Price 0.05	EVPI bound	498	3.0	2.21%	-0.019 $\pm$ 0.100
Price 0.05	EVPI bound	498	5.0	2.81%	-0.012 $\pm$ 0.141

Appendix

Table 56: Counterfactual labels after stopping. Extra labels follow a fixed maximum-pair-KL order and never enter future history. Accuracy change is positive when continuation reduces held-out errors.

Variant	Accuracy (%)	Labels	Batch harm	New errors
Primary	59.31 $\pm$ 0.36	130.8	1.92	10.53
Label price 0.01	59.31 $\pm$ 0.36	129.8	1.92	10.53
Label price 0.025	59.32 $\pm$ 0.39	123.8	1.91	10.46
Label price 0.05	59.37 $\pm$ 0.34	108.0	1.91	10.52
Prior mass 0.25	59.31 $\pm$ 0.34	137.0	1.89	10.42
Prior mass 4	59.34 $\pm$ 0.24	156.4	1.88	10.36

Appendix

Table 57: Prior, stopping-price and history sensitivity on five PACS stream orders. All settings were fixed before this grid was evaluated.

Setting	$C$	$K$	Strata mean	P95	History mass	Queries/batch
PACS RN50	7	4	27.17	37.00	34.30%	1.00
CIFAR-10-C	10	4	30.62	42.00	20.20%	0.26
CIFAR-100-C	100	4	60.43	64.00	3.51%	0.16
PACS CLIP	7	4	7.53	9.00	0.01%	0.01
OfficeHome CLIP	65	4	42.28	48.55	0.31%	0.03
VLCS CLIP	5	4	8.34	12.00	8.74%	0.75

Appendix

Table 58: Observed prediction patterns.

C

counts classes and

K

counts candidates. Stratum counts are per batch; P95 is their 95th percentile. History mass is the fraction of deployment inputs whose pattern has acquired labels from earlier batches. RN50 denotes ResNet-50. Query rate is labels per batch.

Query policy	Output	Accuracy (%)	$\Delta$ BF	Total labels	Decision labels
CIFAR-10-C
—	Fixed BN+flip	$79.65\pm 0.56$	$0.00$	$0$	$0$
Uniform	Learned	$79.74\pm 0.54$	$+0.09$	$7065$	$7065.0$
Uniform	Selected	$79.64\pm 0.56$	$0.00$	$7065$	$7065.0$
Disagreement	Learned	$79.74\pm 0.52$	$+0.10$	$7065$	$7065.0$
Disagreement	Selected	$79.65\pm 0.58$	$0.00$	$7065$	$7065.0$

Appendix

Table 59: Causal residual-readout transfer on complete severity-five corruption suites. Accuracy is mean

\pm

SD over three source checkpoints. Each learned trajectory uses 7,065 labels; decision labels are the subset used for current output comparison. All methods score the same 75,000 evaluation occurrences per checkpoint suite.

Nominal labels/batch	Total cap	Actual labels	Accuracy (%)
1	131	112.8	55.28 $\pm$ 0.45
3	393	128.6	55.28 $\pm$ 0.44
5	655	128.6	55.28 $\pm$ 0.44

Appendix

Table 60: Full stochastic CAMS with four single-candidate advice policies, permanent query eligibility and per-example predictions. Mean

\pm

SD over five PACS stream orders. Cap allocation is proportional to domain batch counts; realized requests follow CAMS.

Order	Incoming	BN+flip	Shared gate	Post-update	Initial-only
201	79.06	79.95	79.21	79.28	79.04
202	78.87	79.37	78.92	79.16	78.87
203	79.78	80.31	80.05	79.88	79.78
204	81.35	81.85	81.47	81.76	81.35
205	80.00	80.82	80.26	80.17	80.05
Mean $\pm$ SD	79.81 $\pm$ 0.98	80.46 $\pm$ 0.94	79.98 $\pm$ 1.00	80.05 $\pm$ 1.04	79.82 $\pm$ 0.99

Appendix

Table 61: Shared-label HILTTA on the same 4,155 permanent evaluation images per order. Every row uses 393 total labels. Incoming and BN+flip predictions are fixed before current labels; post-update predictions are available later. Initial-only uses BN+flip on the first batch and incoming output thereafter.

	Two candidates		Four candidates
Rule	Accuracy	Labels	Accuracy	Labels
Identity	50.88 $\pm$ 0.00	0.0	50.88 $\pm$ 0.00	0.0
BN	—	—	58.37 $\pm$ 0.14	0.0
Flip	—	—	50.90 $\pm$ 0.00	0.0
BN+flip	59.68 $\pm$ 0.28	0.0	59.68 $\pm$ 0.28	0.0
Mean logits	60.96 $\pm$ 0.12	0.0	61.63 $\pm$ 0.16	0.0

Appendix

Table 62: Fixed-bank portfolio and selector ablations on PACS, five complete stream orders. Default-tied ERM uses BN+flip on empirical ties; first-tied ERM uses the first action. Accuracy is mean

\pm

SD, and labels are actual per-stream means. Mean logits is an additional output function.

History	Credit	Stop rule	Accuracy	Labels	Harm
Independent	1	Portal	$59.34\pm 0.11$	90.4	1.74
Independent	1	Reachability only	$59.34\pm 0.11$	90.4	1.74
Independent	1	Value bound only	$59.06\pm 0.26$	131.0	1.69
Independent	1	Confidence proxy	$59.06\pm 0.26$	131.0	1.69
Independent	1	Mean-gap threshold	$59.06\pm 0.26$	131.0	1.69
Independent	3	Portal	$59.35\pm 0.34$	140.0	1.88

Appendix

Table 63: Stopping controls on five PACS stream orders. Accuracy is mean

\pm

order SD in percent. Labels count actual purchases. Harm is the positive batch-level accuracy loss relative to the unchanged model, averaged over all evaluation inputs, in percentage points.

Data ( $K$ )	Fixed	Portal	Top-KL
CIFAR-10-C (4)	79.65	79.26/612.3	79.20/7065
CIFAR-100-C (4)	54.32	53.87/381.7	53.76/7065
PACS (5)	61.63	62.07/144.2	60.57/393
CIFAR-10.1 (5)	89.87	89.59/1.9	89.06/96

Appendix

Table 64: Fixed accuracy and selector accuracy (%) / labels on common evaluation inputs.

K

counts selectable candidates. Labels are actual totals per suite or stream.

Rule	Accuracy (%)	Labels	Harm
Fixed BN+flip	$59.68\pm 0.28$	0.0	5.05
Fixed mean logits	$61.63\pm 0.16$	0.0	0.00
Uniform empirical selection	$60.45\pm 0.72$	393.0	2.08
Top-KL empirical selection	$60.57\pm 0.43$	393.0	2.24
Portal , cumulative	$62.07\pm 0.71$	144.2	1.55
Portal , decay 0.9	$62.11\pm 0.67$	250.4	1.62

Appendix

Table 65: Five-candidate PACS replay, five stream orders. The fixed ensemble is available to every selector and resolves ties. Harm is measured against that ensemble in percentage points. The audited detector is a separate exploratory variant.

Condition	Best fixed	Ensemble	Cumulative	Decay	KL-5	KL-4
Art, domain, 64	78.89	78.89	78.01/79.0	77.90/138.7	77.89/377.3	77.45
Cartoon, domain, 64	82.20	82.20	81.79/51.3	81.65/72.3	81.72/362.7	80.97
Photo, domain, 16	60.79	60.79	60.50/98.7	60.66/156.3	60.20/1561.7	58.12
Photo, domain, 32	61.54	61.54	61.30/111.0	61.39/202.3	60.52/783.0	59.25
Photo, domain, 128	61.47	61.47	61.94/156.7	61.76/182.3	60.71/198.0	59.29
Photo, class, 64	50.90	45.25	51.74/211.3	53.60/330.0	49.58/393.0	54.11

Appendix

Table 66: All five-candidate PACS dynamic conditions, averaged over three orders. Condition lists source, arrival order, and batch size. Paired entries are accuracy (%)/labels. Best fixed is the hindsight best single fixed output for that condition. KL-4 is the original four-candidate Top-KL accuracy from Table 49 ; KL-5 uses the expanded portfolio.

Rule	Accuracy (%)	Labels
Fixed identity	$89.23\pm 0.97$	0.0
Fixed BN	$85.84\pm 0.68$	0.0
Fixed flip	$89.87\pm 0.81$	0.0
Fixed BN+flip	$86.22\pm 0.42$	0.0
Fixed mean logits	$89.69\pm 0.70$	0.0
Uniform empirical selection	$89.56\pm 0.72$	96.0

Appendix

Table 67: CIFAR-10.1 with three checkpoints and three orders per checkpoint. Each order has 1,000 evaluation images. Accuracy is mean

\pm

checkpoint SD after averaging orders within a checkpoint. Audit labels are included in cost.

Schedule	Rule	Accuracy (%)	Labels
Noise first	Fixed BN+flip	$76.67\pm 0.63$	0.0
Noise first	Fixed mean logits	$72.52\pm 1.40$	0.0
Noise first	Uniform empirical selection	$73.55\pm 0.65$	300.0
Noise first	Top-KL empirical selection	$74.07\pm 0.76$	300.0
Noise first	Portal , cumulative	$74.96\pm 1.00$	57.3
Noise first	Portal , decay 0.9	$74.98\pm 1.05$	80.7

Appendix

Table 68: Sequential corruption-switch selection. Accuracy is mean

\pm

checkpoint SD on the common evaluation images. Each stream has 100 batches and disjoint base images across segments. The fixed BN+flip output is the strongest fixed candidate in every complete schedule.

Schedule	Corruption	3 labels	15 labels	75 labels	300 labels
Noise first	Brightness	90.82	64.90	24.05	2.35
Noise first	Gaussian noise	11.53	11.59	1.73	0.00
Noise first	Jpeg compression	86.02	59.90	35.03	14.52
Noise first	Shot noise	11.66	16.63	7.61	1.06
Alternating	Brightness	91.41	67.66	30.35	4.71
Alternating	Impulse noise	12.40	15.79	5.53	0.06

Appendix

Table 69: Exact probability (%) of selecting the worse of BN+flip and mean logits. Means cover three checkpoints. Columns give the number of labels sampled uniformly without replacement from one corruption segment. Tie decisions use BN+flip. Differences between schedules also reflect their distinct image-index blocks.

History	Stable		Abrupt		Gradual
	Acc.	Labels	Acc.	Labels	Acc.	Labels
Cumulative	72.21	0.0	22.54	0.0	22.92	0.0
No history	62.60	150.4	64.10	150.2	63.42	90.0
Decay 0.9	72.21	150.4	67.66	149.8	70.88	85.4
One audit per batch	72.21	50.0	27.24	72.8	22.92	30.0
Audit/reset 0.05	72.21	54.2	38.34	74.4	33.71	38.2

Appendix

Table 70: Conditional-label change with fixed predictions and stratum weights. Accuracy is in percent; labels count purchases within the displayed period, including audits. Stable and abrupt columns cover the final 50 batches. Gradual columns cover the final 30, after the transition. Means cover five synthetic seeds.

Change	Prioritized audit	Uniform audit
Abrupt	$+3.94\ [0.59,7.28]$	$+4.75\ [1.36,8.14]$
Gradual	$+1.69\ [-3.24,6.62]$	$+1.58\ [-3.36,6.51]$
Recurrent	$+3.28\ [0.61,5.95]$	$+3.84\ [1.24,6.43]$

Appendix

Table 71: Post-change accuracy difference from reconstructed EW in percentage points on the 300-mode sparse protocol. Priority oversamples atypical examples within a mode; uniform draws do not. Each cell contains 28 blocks and 840 seed streams, with the same scored examples and 100-label ceiling for both methods.

Inference-Time Intervention

Inference-time intervention changes model inputs, internal signals, or decisions during use to improve safety, reliability, or task performance.

See all 33 papers

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Sungkyunkwan University · Nanyang Technological University

Sep 10, 2026J/K move · Enter open · S save

When is Test-Time Adaptation Identifiable From Unlabeled Evidence?

Kartik Jhawar, Lipo Wang

Institute for Digital Molecular Analytics and Science School of Electrical and Electronic Engineering Nanyang Technological University, Singapore

Test-Time Adaptation

Open paper AskPDF arXiv

Test-time adaptation (TTA) offers many ways to update a deployed model without labels, but choosing the wrong update can make a strong source model worse. Recent methods therefore try to predict which adaptation will work from unlabeled test data. We ask a prior question: does the evidence given to the selector contain enough information to determine the best action at all? We show that this is not guaranteed, even with a perfect selector. If an observation channel makes two deployments look the same while their TTA rankings differ, reliable selection is impossible from that channel; richer evidence can restore the decision only when it resolves the relevant ambiguity. We make this boundary exact in a finite-batch Gaussian TTA model, where doing nothing beats mean recentering for small shifts, recentering wins beyond a unique critical shift, and the boundary shrinks as

1/\sqrt n

. Public benchmark studies on CIFAR-100-C and DomainNet-126 show the same failure mode with modern TTA methods: changing only deployment structure can reverse the oracle action while global order-blind evidence remains unchanged. The result is a practical way to separate two failure modes that are usually mixed together: a weak selector versus an information channel that cannot support the desired decision in the first place.

Abstract

Inference-Time Intervention

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