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 ± 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 ± 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 ± 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 ± 0.56
0
Table 2: Severity-five CIFAR accuracy (%) on shared held-out images, averaged over three source models. Summary: mean ± 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 ± 0.13
132.8
1.78
Disagreement
59.31 ± 0.23
96.8
1.86
Maximum-pair KL
59.33 ± 0.26
118.8
1.85
PORTAL value
59.32 ± 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 ≤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 ≤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 ± 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
At , I
Available batch interventions and incumbent at time t .
Qt , Et
Permanent eligible query and deployment/evaluation inputs.
Ra , Da
Candidate correctness and its difference from incumbent correctness.
s , ws , psa
Joint prediction stratum, target frequency and candidate class.
θs , Aa(θ)
Conditional label law and expected target accuracy.
Δa , vs,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 ρ (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 (ΔCE−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 (%)
Δ BF (pp)
Labels
CIFAR10-C
Fixed BF
79.646±0.561
0.000
0.0
CIFAR10-C
Mean logits
76.548±1.295
-3.099
0.0
CIFAR10-C
Uniform ERM
78.275±0.583
-1.371
7065.0
CIFAR10-C
Disagreement ERM
78.361±0.591
-1.285
7065.0
CIFAR10-C
Symmetric-KL ERM
79.202±0.499
-0.444
7065.0
CIFAR10-C
Portal
79.259±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
QJ
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
QJ
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
QJ
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
QJ
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
QJ
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
QJ
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
Δ V8
Labels
PACS
Fixed S
98.1906±0.0000
97.5412
-0.2462
0.0
PACS
Fixed T
98.2791±0.0000
97.5615
-0.1578
0.0
PACS
Fixed V2
98.4249±0.0000
97.7037
-0.0120
0.0
PACS
Fixed V8
98.4369±0.0000
97.7444
0.0000
0.0
PACS
Uniform ERM
98.4343±0.0056
97.7403
-0.0025
473.6
PACS
Disagreement ERM
98.4343±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
QJ
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 QJ counts its labels. V8 is the fixed default.
Estimator
Accuracy (%)
Δ 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
UM.25
UD.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
Δ
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 (%)
Δ BF
CE
Decision Q
Total Q
Uniform
Fixed BF
59.677±0.278
0.000
1.2205
0.0
0
Uniform
Always learned
73.030±0.695
13.353
0.9430
393.0
393
Uniform
Selected output
65.911±0.493
6.233
1.0918
393.0
393
Disagreement
Fixed BF
59.677±0.278
0.000
1.2205
0.0
0
Disagreement
Always learned
72.982±0.779
13.304
0.9424
393.0
393
Disagreement
Selected output
70.286±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.
λ
Scale
Query
Always learned
Selected
Δ 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
Δ now
Δ future
Δ 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
HB
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 HB are percentage points; S is the percentage of newly introduced errors.
Acquisition
k
G
HB
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 HB are percentage points; S is the percentage of newly introduced errors.
Acquisition
k
G
HB
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 HB are percentage points; S is the percentage of newly introduced errors.
T
G
HB
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
nE
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
HB
S
G
HB
S
G
HB
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 HB , and sample-new-error percentage S. Thresholds that induce the same signed count are represented once.
Mixture family
Output
G
HB
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
Stream
Always BF
11.1817
1.9976
1.2130
0.7220
0.3995
0.0000
0.0000
Disagreement
5.1649
0.6883
0.5247
0.3418
0.1877
0.0000
0.0000
Symmetric KL
6.1468
1.1456
0.8857
0.6691
0.4043
0.0193
0.0000
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 HB .
Domain
Class
nE
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 ± 0.000
98.279 ± 0.000
0
PACS
Eight views
98.517 ± 0.000
98.437 ± 0.000
0
PACS
Mean logits
98.502 ± 0.000
98.390 ± 0.000
0
PACS
StatA
98.445 ± 0.051
98.404 ± 0.063
0
VLCS
Prompt average
83.099 ± 0.000
83.523 ± 0.000
0
VLCS
Eight views
83.793 ± 0.000
84.097 ± 0.000
0
Appendix
Table 39: Episodic StatA and fixed CLIP readouts. Accuracy is equal-domain mean ± 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 ± 0.000
PACS
Art
StatA
99.219 ± 0.035
PACS
Cartoon
Eight views
99.616 ± 0.000
PACS
Cartoon
StatA
99.727 ± 0.038
PACS
Photo
Eight views
99.940 ± 0.000
PACS
Photo
StatA
100.000 ± 0.000
Appendix
Table 40: Domain-level StatA comparison on full data. Values are accuracy means ± stream-order SD over five orders.
Dataset
Domain
Readout
Accuracy (%)
PACS
Art
Eight views
99.069 ± 0.000
PACS
Art
StatA
99.255 ± 0.046
PACS
Cartoon
Eight views
99.570 ± 0.000
PACS
Cartoon
StatA
99.725 ± 0.094
PACS
Photo
Eight views
100.000 ± 0.000
PACS
Photo
StatA
100.000 ± 0.000
Appendix
Table 41: Domain-level StatA comparison on common E . Values are accuracy means ± stream-order SD over five orders.
Dataset
Time (s)
Peak MiB
Final-batch adjustments
Initialization ∣Δp∣
PACS
7.95 ± 0.24
24.51
0
1.75e-06
VLCS
5.92 ± 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 ∣Δp∣ 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 ± 0.000
0.0
98.191 ± 0.000
0.0
Prompt average
98.279 ± 0.000
0.0
98.279 ± 0.000
0.0
Two views
98.425 ± 0.000
0.0
98.425 ± 0.000
0.0
Eight views
98.437 ± 0.000
0.0
98.437 ± 0.000
0.0
StatA
—
—
98.404 ± 0.063
0.0
Appendix
Table 43: PACS portfolio expansion on common E . Accuracy is equal-domain mean ± 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 ± 0.000
0.0
80.845 ± 0.000
0.0
Prompt average
83.523 ± 0.000
0.0
83.523 ± 0.000
0.0
Two views
83.861 ± 0.000
0.0
83.861 ± 0.000
0.0
Eight views
84.097 ± 0.000
0.0
84.097 ± 0.000
0.0
StatA
—
—
85.106 ± 0.137
0.0
Appendix
Table 44: VLCS portfolio expansion on common E . Accuracy is equal-domain mean ± 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.
PACS
OfficeHome
VLCS
Rule
Acc.
Labels
Acc.
Labels
Acc.
Labels
Eight views
98.437 ± 0.000
0.0
89.008 ± 0.000
0.0
84.097 ± 0.000
0.0
Mean logits
98.390 ± 0.000
0.0
88.237 ± 0.000
0.0
83.650 ± 0.000
0.0
Portal
98.442 ± 0.007
1.4
89.010 ± 0.012
7.4
83.919 ± 0.170
89.4
Uniform / mixture
98.398 ± 0.014
473.6
88.415 ± 0.098
737.4
83.868 ± 0.228
354.8
Disagreement / mixture
98.415 ± 0.009
473.6
88.636 ± 0.068
737.4
84.005 ± 0.139
354.8
Appendix
Table 45: Primary convex-readout results ( λ=1 ) on common E . Accuracy is equal-domain mean ± stream-order SD; labels average five orders. Discrete ERM rows use the same queries as the corresponding mixture.
Accuracy (%)
CE
Brier
λ
Acquisition
Labels
D
M
D
M
D
M
Fit (s)
0.1
Uniform
473.6
98.429 ± 0.007
98.382 ± 0.021
0.0580
0.0604
0.0252
0.0264
0.821
0.1
Disagreement
473.6
98.434 ± 0.031
98.393 ± 0.033
0.0584
0.0603
0.0253
0.0262
0.825
0.1
Maximum KL
473.6
98.439 ± 0.029
98.407 ± 0.049
0.0584
0.0597
0.0253
0.0259
1.028
0.1
Target Fisher
473.6
98.434 ± 0.034
98.417 ± 0.069
0.0583
0.0595
0.0253
0.0258
1.167
1
Uniform
473.6
98.429 ± 0.007
98.398 ± 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
λ
Acquisition
Labels
D
M
D
M
D
M
Fit (s)
0.1
Uniform
737.4
88.863 ± 0.121
88.523 ± 0.144
0.3952
0.4105
0.1580
0.1623
1.464
0.1
Disagreement
737.4
88.637 ± 0.118
88.579 ± 0.094
0.4080
0.4060
0.1617
0.1609
1.283
0.1
Maximum KL
737.4
88.688 ± 0.122
88.726 ± 0.112
0.4018
0.4000
0.1601
0.1592
1.401
0.1
Target Fisher
737.4
88.687 ± 0.088
88.724 ± 0.077
0.4029
0.4006
0.1604
0.1595
1.570
1
Uniform
737.4
88.863 ± 0.121
88.415 ± 0.098
0.3952
0.4084
0.1580
0.1619
0.938
Appendix
Table 47: Complete convex-readout grid on OFFICEHOME 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
λ
Acquisition
Labels
D
M
D
M
D
M
Fit (s)
0.1
Uniform
354.8
83.907 ± 0.202
83.819 ± 0.248
0.4629
0.4648
0.2402
0.2392
0.681
0.1
Disagreement
354.8
83.869 ± 0.126
83.956 ± 0.164
0.4651
0.4625
0.2404
0.2390
0.630
0.1
Maximum KL
354.8
83.918 ± 0.158
84.068 ± 0.151
0.4661
0.4603
0.2408
0.2371
0.666
0.1
Target Fisher
354.8
83.887 ± 0.181
83.901 ± 0.241
0.4659
0.4613
0.2409
0.2381
0.775
1
Uniform
354.8
83.907 ± 0.202
83.868 ± 0.228
0.4629
0.4615
0.2402
0.2382
0.462
Appendix
Table 48: Complete convex-readout grid on VLCS 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.
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.
η
Rule
Accuracy (%)
Labels
New errors (pp)
0
Uniform
58.97 ± 0.72
393.0
8.53
0
Disagreement
58.93 ± 0.47
393.0
8.66
0
Maximum KL
58.73 ± 0.23
393.0
8.55
0
Portal
59.31 ± 0.36
130.8
10.53
0.1
Uniform
59.00 ± 0.65
393.0
8.52
0.1
Disagreement
58.81 ± 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 η . Accuracy is mean ± 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≤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 ± 0.13
132.8
1.78
Disagreement
59.31 ± 0.23
96.8
1.86
Maximum-pair KL
59.33 ± 0.26
118.8
1.85
PORTAL value
59.32 ± 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 ± SD cover five PACS stream orders.
Setting
Stop reason
Stops
Extra
Choice change
Δ accuracy (pp)
Primary
Unreachable
653
1.0
0.00%
+0.000 ± 0.000
Primary
Unreachable
653
3.0
0.00%
+0.000 ± 0.000
Primary
Unreachable
653
5.0
0.31%
+0.000 ± 0.051
Price 0.05
EVPI bound
498
1.0
1.20%
-0.075 ± 0.052
Price 0.05
EVPI bound
498
3.0
2.21%
-0.019 ± 0.100
Price 0.05
EVPI bound
498
5.0
2.81%
-0.012 ± 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 ± 0.36
130.8
1.92
10.53
Label price 0.01
59.31 ± 0.36
129.8
1.92
10.53
Label price 0.025
59.32 ± 0.39
123.8
1.91
10.46
Label price 0.05
59.37 ± 0.34
108.0
1.91
10.52
Prior mass 0.25
59.31 ± 0.34
137.0
1.89
10.42
Prior mass 4
59.34 ± 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 (%)
Δ BF
Total labels
Decision labels
CIFAR-10-C
—
Fixed BN+flip
79.65±0.56
0.00
0
0
Uniform
Learned
79.74±0.54
+0.09
7065
7065.0
Uniform
Selected
79.64±0.56
0.00
7065
7065.0
Disagreement
Learned
79.74±0.52
+0.10
7065
7065.0
Disagreement
Selected
79.65±0.58
0.00
7065
7065.0
Appendix
Table 59: Causal residual-readout transfer on complete severity-five corruption suites. Accuracy is mean ± 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 ± 0.45
3
393
128.6
55.28 ± 0.44
5
655
128.6
55.28 ± 0.44
Appendix
Table 60: Full stochastic CAMS with four single-candidate advice policies, permanent query eligibility and per-example predictions. Mean ± 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 ± SD
79.81 ± 0.98
80.46 ± 0.94
79.98 ± 1.00
80.05 ± 1.04
79.82 ± 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 ± 0.00
0.0
50.88 ± 0.00
0.0
BN
—
—
58.37 ± 0.14
0.0
Flip
—
—
50.90 ± 0.00
0.0
BN+flip
59.68 ± 0.28
0.0
59.68 ± 0.28
0.0
Mean logits
60.96 ± 0.12
0.0
61.63 ± 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 ± 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±0.11
90.4
1.74
Independent
1
Reachability only
59.34±0.11
90.4
1.74
Independent
1
Value bound only
59.06±0.26
131.0
1.69
Independent
1
Confidence proxy
59.06±0.26
131.0
1.69
Independent
1
Mean-gap threshold
59.06±0.26
131.0
1.69
Independent
3
Portal
59.35±0.34
140.0
1.88
Appendix
Table 63: Stopping controls on five PACS stream orders. Accuracy is mean ± 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±0.28
0.0
5.05
Fixed mean logits
61.63±0.16
0.0
0.00
Uniform empirical selection
60.45±0.72
393.0
2.08
Top-KL empirical selection
60.57±0.43
393.0
2.24
Portal , cumulative
62.07±0.71
144.2
1.55
Portal , decay 0.9
62.11±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±0.97
0.0
Fixed BN
85.84±0.68
0.0
Fixed flip
89.87±0.81
0.0
Fixed BN+flip
86.22±0.42
0.0
Fixed mean logits
89.69±0.70
0.0
Uniform empirical selection
89.56±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 ± 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±0.63
0.0
Noise first
Fixed mean logits
72.52±1.40
0.0
Noise first
Uniform empirical selection
73.55±0.65
300.0
Noise first
Top-KL empirical selection
74.07±0.76
300.0
Noise first
Portal , cumulative
74.96±1.00
57.3
Noise first
Portal , decay 0.9
74.98±1.05
80.7
Appendix
Table 68: Sequential corruption-switch selection. Accuracy is mean ± 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.
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/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.
Kartik Jhawar, Lipo Wang
Institute for Digital Molecular Analytics and Science School of Electrical and Electronic Engineering Nanyang Technological University, Singapore
Active test-time adaptation (ATTA) improves robustness under distribution shift by updating a deployed model during inference while selectively querying supervision. However, most existing ATTA methods implicitly assume that supervision can be requested for every incoming test batch, which can incur substantial annotation cost over long test streams. In this work, we introduce budgeted ATTA in which labels are available for only a fraction of test batches. This formulation shifts the central challenge from deciding what to label within a batch to deciding when supervision should be applied over time. To address this challenge, we propose a budget-aware approach WISE-ATTA that allocates supervision over the test stream based on lightweight signals computed online, prioritizing periods where supervision is likely to be most useful. When a batch is selected for supervision, we further employ a drift-based sample selection criterion that targets samples exhibiting ongoing, unconverged adaptation dynamics, enabling effective updates from a single labeled example. We evaluate this approach on synthetic corruptions (ImageNet-C) and natural distribution shifts (ImageNet-R/K/A). Across settings, WISE-ATTA achieves competitive or improved performance compared to recent ATTA methods while requiring substantially fewer labels. Overall, we find that the timing of supervision is a key, yet underexplored, aspect of active test-time adaptation. Code: https://github.com/Muhammad-Huzaifaa/WISE-ATTA
Muhammad Huzaifa, Lea Schönherr, Thorsten Eisenhofer
Continual test-time adaptation (CTTA) adapts a source model to an unlabeled test stream whose distribution may change over time. Existing TTA methods often assess prediction reliability using confidence or entropy, which primarily reflect the model's self-certainty for the current sample. In CTTA, accumulated target observations can provide complementary evidence for correcting the source prediction, but this history may become misaligned as the target distribution changes. The key question is therefore not how much the correction differs from the source prediction, but whether and how strongly it should be applied. This paper proposes Gain-Aware INtervention (GAIN), a backpropagation-free CTTA framework guided by a simple principle: history proposes, gain decides. GAIN maintains compact target statistics to form a correction proposal and a posterior-predictive evaluator that accounts for estimation uncertainty. The resulting source-relative gain estimates the proposal's benefit and determines a sample-specific intervention strength along a continuous path through efficient one-dimensional optimization. Gain-controlled predictions then update the target statistics online, limiting the propagation of unreliable corrections, all without backpropagation, sample storage, or replay. Across five benchmarks, our method achieves strong predictive performance, with favorable accuracy--calibration--efficiency trade-offs in continual adaptation. On ImageNet-C, for example, GAIN achieves 61.9% accuracy with near-source calibration. It remains stable under diverse and challenging continual shifts while running 15.9x faster than a representative optimization-based CTTA baseline.
Youjia Zhang, Huiling Liu, Soyun Choi +2
Sungkyunkwan University · Nanyang Technological University