Selection-Safe Conformal Early Exit: Distribution-Free Coverage under Adaptive Depth

Adria Binte Habib; Ibne Farabi Shihab

cs.LGOct 14, 2026

Selection-Safe Conformal Early Exit: Distribution-Free Coverage under Adaptive Depth

Authors: Adria Binte Habib, Ibne Farabi Shihab

Organizations: Department of Computer Science, BRAC University · Department of Computer Science, Iowa State University

Abstract

Calibrating a conformal prediction set at each early exit does not preserve coverage once a data-dependent exit is selected. We construct one terminal path score from prefix maxima, calibrate a single split-conformal quantile, and return nested prefix sets that all contain the valid terminal set. The guarantee is selection-safe without an alpha/L correction and holds simultaneously for every post-calibration label-free stopping policy that preserves terminal-set containment. We also bound the efficiency cost of the path maximum by the empirical tail of the early-over-terminal score excess. Across eight encoder task-backbone cells, pathwise selection attains macro coverage 0.901 versus 0.814 for naive layerwise selection, with average set size 1.41 and latency fraction 0.71. On CIFAR-100 with a 24-exit ViT-L/16 (n_cal=500), first-eligible stopping at budget b=4 attains coverage 0.902, set size 2.76, and latency fraction 0.57, and the same calibration supports deployment-time budget changes without refitting. In a joint exit-count/calibration-size sweep at n=100, pathwise set size moves only from 3.02 to 3.11 as exits increase from 4 to 24, while Bonferroni degenerates to the full label space for 12 or more exits. Paired comparison against MinSE valid selection at (n,L)=(100,24) gives a set-size difference of 0.80 [0.47, 1.13]. Full-vocabulary decoder experiments remain a negative boundary, with sets of 7,162-9,620 tokens. Pathwise calibration is most useful when candidate exits are many relative to calibration size, when budgets change after calibration, and when shallow heads return actionable sets.

Figures & tables

Method	Controlled target	Selected validity	Avg. set	Latency/full	Exit/full
Naive layerwise CP	fixed-layer coverage	$0.814$	$1.22$	$0.51$	$0.50$
Bonferroni CP	simultaneous coverage	$0.954$	$1.71$	$0.79$	$0.79$
EENN-AVCS ( Jazbec et al., 2024a )	AVCS coverage	$0.911$	$1.54$	$0.76$	$0.75$
MinSE valid selection ( Hegazy et al., 2025 )	selected-set coverage	$0.903$	$1.40$	$0.70$	$0.69$
FyS supervised ( Jazbec et al., 2024b )	$0$ – $1$ risk	$0.900$	n/a	$0.67$	$0.66$
Pathwise conformal	selected-set coverage	$0.901$	$1.41$	$0.71$	$0.71$

Table 1: Matched five-seed encoder comparison at target coverage

0.90

. Every numerical entry is the macro average over the same eight task–backbone cells. Fast-yet-Safe controls supervised

0

–

1

risk rather than conformal set coverage; paired uncertainty is reported separately in Tables 11 and 12 .

Panel of Figure 1 — Figure 1: Per-cell selected-coverage distributions. Points are cell means. For SST-2, MNLI, and BoolQ, bars are the $10$ th– $90$ th percentiles across paired calibration–test roles. RTE uses one fixed calibration/test partition; its bars are the corresponding percentiles across the $5$ head-training seeds. Exact means, model accuracies, and familywise paired intervals appear in Appendix L .

Panel of Figure 2 — Figure 2: CIFAR-100 latency–set-size tradeoff for the explicit $(n,L)=(500,24)$ configuration used in the scaling grid. Bars are paired $95\%$ hierarchical-bootstrap intervals over head seeds and calibration subsamples. For each budget $b\in\{1,2,4,8,16\}$ , first-eligible is the earliest admissible stop; the design-chosen slack policy is a restriction and therefore lies weakly to its right in latency while returning smaller sets. The MinSE, EENN-AVCS, and Bonferroni markers are exactly the $(500,24)$ entries of Appendix N . Exact coverage, empty-terminal rate, and frontier values are reported in Appendix M .

Panel of Figure 3 — Figure 3: Scaling with the number of candidate exits on CIFAR-100. Bars show marginal paired-bootstrap intervals for each method; they are descriptive and are not used to test pathwise against MinSE. The left panel uses $n=100$ and a log $y$ -axis because Bonferroni has rank $n+1$ at $L=12$ and $L=24$ , forcing the returned set to all $100$ classes. The right panel uses $n=2000$ . Paired pathwise–MinSE difference intervals, which exploit the shared calibration subsample and test set, appear in Appendix N .

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Protected object	Guarantee	Main requirement
Layerwise CP	set at fixed exit	marginal coverage per exit	exit fixed in advance
EENN-AVCS ( Jazbec et al., 2024a )	nested exit sequence	anytime-valid predictive set	posterior-stability construction
Fast-yet-Safe ( Jazbec et al., 2024b )	adaptive point or distribution	expected or high-probability risk	specified loss and calibrated policy
Valid selection ( Hegazy et al., 2025 )	chosen conformal set	post-selection coverage	stability correction
Pathwise CP	returned prefix set	exact marginal coverage	exchangeability and frozen path

Appendix

Table 2: Relationship to the closest approaches. “Exact” refers to the stated finite-sample guarantee under each method’s assumptions, not to equality of empirical coverage.

Task	Backbone	$t_{\star}$	$m_{t_{\star}}/n$	$B$ gap	$w_{t_{\star}}$	$\sum_{y}\widehat{M}_{y}$	RHS	observed inflation	RHS / observed
SST-2	BERT	$0.145$	$0.089$	$0.026$	$0.171$	$0.095$	$0.016$	$0.01$	$1.62$
SST-2	DistilBERT	$0.149$	$0.086$	$0.022$	$0.171$	$0.101$	$0.017$	$0.01$	$1.73$
MNLI	BERT	$0.082$	$0.088$	$0.029$	$0.111$	$0.620$	$0.069$	$0.06$	$1.15$
MNLI	DistilBERT	$0.086$	$0.087$	$0.034$	$0.120$	$0.720$	$0.086$	$0.08$	$1.08$
RTE	BERT	$0.052$	$0.081$	$0.021$	$0.073$	$0.780$	$0.057$	$0.05$	$1.14$
RTE	DistilBERT	$0.055$	$0.084$	$0.025$	$0.080$	$0.940$	$0.075$	$0.07$	$1.07$

Appendix

Table 3: Theorem 2 in measured units.

t_{\star}

is the smallest threshold satisfying

m_{t}\leq n-k

; “

B

gap” is

B_{(k+m_{t})}-B_{(k)}

; RHS is

w_{t}\sum_{y}\widehat{M}_{y}

from the independent design role; observed inflation is the paired test mean of

(|\mathcal{C}_{L}^{\rm path}|-|\mathcal{C}_{L}^{\rm last}|)_{+}

. The design-role slope column is fixed independently of the test-role cardinality summaries.

Stage	Operation
Train	Fit the backbone and exit heads on training data.
Design	Choose exits and increasing score maps without using final calibration or test labels; a provisional budget may guide this search.
Calibrate	Compute $S_{i}=\max_{\ell\leq L}r_{\ell}(X_{i},Y_{i})$ and the single quantile $\widehat{q}$ on $\mathcal{D}_{\mathrm{cal}}$ .
Execute	Update $A_{\ell}(x,y)$ candidatewise and construct $\mathcal{C}_{\ell}(x)$ after every executed exit.
Stop	Return an eligible prefix set; if none is eligible, return $\mathcal{C}_{L}(x)$ , or $\mathcal{Y}$ when $\mathcal{C}_{L}(x)$ is empty.

Appendix

Table 4: Execution order. Only the design stage may optimize the score or exit schedule; the final calibration labels are used once to compute the terminal rank.

Target	Guarantee	Required condition	Not implied
Selected set	marginal coverage $\geq 1-\alpha$	exchangeable terminal scores; frozen path	feature-conditional validity
Realized calibration	Beta or DKW lower floor	independent calibration draw; stated continuity or conservative ties	per-input coverage
Group shift	coverage within each fixed group	within-group exchangeability and valid $n_{g}$ quantile	arbitrary covariate shift
Hybrid output	error $\leq\alpha_{\rm pt}+\alpha_{\rm set}$	joint point-error control and valid fallback	error $\leq\alpha$ when both branches use $\alpha$

Appendix

Table 5: Guarantees and their load-bearing assumptions. Each row concerns a different probability statement; satisfying one row does not imply the others.

PAC size	$n=200$	$n=500$	$n=1500$	required minimum
Fraction above floor	$0.9985$	$0.9992$	$0.9992$	$0.90$ – $0.99$
Group method	easy	medium	hard	shifted marginal
Pooled	$1.0000$	$0.9913$	$0.6887$	$0.8112$
Mondrian	$0.9177$	$0.9054$	$0.9149$	$0.9129$

Appendix

Table 6: Controlled PAC and Mondrian verification at

\alpha=0.1

. PAC entries give the minimum fraction of

4000

calibration draws above the DKW floor over

\delta\in\{0.1,0.05,0.01\}

. The group rows give coverage after shifting the mixture toward the hard group.

$n$	coverage (mean $\pm$ SD)	Beta floor	DKW floor	set size	worst draw
$100$	$0.905\pm 0.028$	$0.848$	$0.778$	$1.47$	$0.841$
$200$	$0.900\pm 0.018$	$0.864$	$0.813$	$1.44$	$0.871$
$500$	$0.905\pm 0.011$	$0.877$	$0.845$	$1.46$	$0.884$
$1000$	$0.902\pm 0.009$	$0.884$	$0.861$	$1.44$	$0.885$
$1500$	$0.903\pm 0.006$	$0.887$	$0.868$	$1.44$	$0.888$

Appendix

Table 7: Calibration-size scaling on MNLI/BERT over repeated calibration draws at

\alpha=0.1

and

\delta=0.05

. Coverage is mean

\pm

SD; Beta and DKW columns are training-conditional lower floors.

Shift	calibration	hard $n_{\rm cal}$	hard cov.	shifted cov.	set	exit/full
MNLI label	pooled	$1719$	$0.894$	$0.900$	$1.44$	$0.73$
MNLI label	Mondrian	$1719$	$0.911$	$0.906$	$1.42$	$0.72$
BoolQ label	pooled	$618$	$0.811$	$0.860$	$1.56$	$0.86$
BoolQ label	Mondrian	$618$	$0.895$	$0.888$	$1.51$	$0.85$
SST-2 difficulty	pooled	$72$	$0.669$	$0.817$	$1.04$	$0.32$
SST-2 difficulty	Mondrian	$72$	$0.805$	$0.881$	$1.23$	$0.48$

Appendix

Table 8: Group-prior shift with the hardest group’s test weight tripled while within-group examples and score laws remain unchanged.

$\alpha_{\rm pt}/\alpha_{\rm set}$	commit $c$	cond. commit err. $e_{c}$	joint point err. $ce_{c}$	fallback share $1-c$	fallback cov. $q_{f}$	joint fallback miss	overall cov.	latency/full
$0.02/0.08$	$0.180$	$0.041$	$0.0074$	$0.820$	$0.923$	$0.0631$	$0.9295$	$0.690$
$0.05/0.05$	$0.340$	$0.061$	$0.0207$	$0.660$	$0.951$	$0.0323$	$0.9470$	$0.660$
$0.08/0.02$	$0.470$	$0.079$	$0.0371$	$0.530$	$0.983$	$0.0090$	$0.9539$	$0.640$

Appendix

Table 9: Risk-budgeted point-prediction hybrid. Conditional commit error uses only committed examples; fallback coverage uses only the

E^{c}

denominator. The two joint error columns are measured on all inputs and sum directly to one minus overall coverage.

Task	Backbone	returned path set	empty terminal	mean positive inflation
SST-2	BERT	$1.03$	$0.1\text{--}0.2\%$	$0.01$
SST-2	DistilBERT	$1.04$	$0.1\text{--}0.2\%$	$0.01$
MNLI	BERT	$1.44$	–	$0.06$
MNLI	DistilBERT	$1.62$	–	$0.08$
RTE	BERT	$1.49$	$0.1\text{--}0.2\%$	$0.05$
RTE	DistilBERT	$1.68$	$0.1\text{--}0.2\%$	$0.07$

Appendix

Table 10: Cost diagnostic for the terminal path maximum. Returned-set size is a direct test-role measurement; the binary empty-terminal column reports the run-level range supplied for these cells. Positive inflation is the paired statistic bounded by Theorem 2 ,

\mathbb{E}[(|\mathcal{C}_{L}^{\rm path}|-|\mathcal{C}_{L}^{\rm last}|)_{+}]

. No terminal or last-layer mean cardinality is reconstructed from a coverage lower bound.

Task	Backbone	$\Delta_{c}$	familywise $95\%$ interval
SST-2	BERT	$0.057$	$[0.036,\,0.078]$
SST-2	DistilBERT	$0.046$	$[0.022,\,0.070]$
MNLI	BERT	$0.080$	$[0.062,\,0.098]$
MNLI	DistilBERT	$0.060$	$[0.039,\,0.081]$
RTE	BERT	$0.105$	$[0.061,\,0.149]$
RTE	DistilBERT	$0.134$	$[0.083,\,0.185]$

Appendix

Table 11: Paired selection-gap inference. Intervals are familywise

95\%

hierarchical paired-bootstrap intervals obtained from the maximum absolute studentized statistic across the eight declared cells.

Comparator	$\Delta$ validity	$\Delta$ latency/full	$\Delta$ avg. set
MinSE valid selection	$-0.002\ [-0.011,\,0.007]$	$0.010\ [-0.012,\,0.032]$	$0.010\ [-0.036,\,0.056]$
EENN-AVCS	$-0.012\ [-0.022,\,-0.002]$	$-0.040\ [-0.064,\,-0.016]$	$-0.130\ [-0.188,\,-0.072]$
Bonferroni CP	$-0.055\ [-0.066,\,-0.044]$	$-0.070\ [-0.095,\,-0.045]$	$-0.300\ [-0.363,\,-0.237]$

Appendix

Table 12: Paired differences relative to pathwise conformal at the primary operating point. All point estimates subtract macro averages over the same eight cells in Table 1 ; positive latency and set differences mean pathwise is larger. Brackets give

95\%

hierarchical paired-bootstrap intervals.

Task	$\Pr(J\leq L/4)$	$\mathbb{E}[J/L]$	$\Pr(J=L)$	$\Pr(D>0)$	$Q_{.95}(D)$	false removal at $L/2$
SST-2	$0.62$	$0.29$	$0.10$	$0.64$	$0.18$	$0.88$
MNLI	$0.21$	$0.61$	$0.33$	$0.37$	$0.11$	$0.61$
RTE	$0.13$	$0.71$	$0.45$	$0.23$	$0.07$	$0.55$
BoolQ	$0.17$	$0.68$	$0.39$	$0.32$	$0.09$	$0.58$

Appendix

Table 13: Mechanism diagnostics pooled across backbones.

D=[\max_{j<L}r_{j}-r_{L}]_{+}

is the excess entering Theorem 2 ;

Q_{.95}(D)

is its

95

th percentile on true labels.

Score or schedule	coverage range	avg. set	exit/full	latency/full
$-\log p$	$0.890$ – $0.906$	$1.41$	$0.71$	$0.71$
Design affine	$0.887$ – $0.915$	$1.45$	$0.68$	$0.68$
Design ECDF	$0.890$ – $0.950$	$1.54$	$0.70$	$0.71$
APS	$0.885$ – $0.935$	$1.75$	$0.84$	$0.84$
RAPS	$0.887$ – $0.934$	$1.71$	$0.82$	$0.83$
Sparse schedule	$0.892$ – $0.929$	$1.39$	$0.65$	$0.66$

Appendix

Table 14: Score and schedule ablations under common pathwise calibration and data roles. Coverage ranges span the eight encoder task–backbone cells.

$n$	$\delta$	mean cov.	path floor	fraction above	12-exit floor
$200$	$0.10$	$0.9004$	$0.8241$	$0.9985$	$0.7906$
$200$	$0.05$	$0.9004$	$0.8135$	$1.0000$	$0.7829$
$200$	$0.01$	$0.9004$	$0.7927$	$1.0000$	$0.7669$
$500$	$0.10$	$0.9001$	$0.8520$	$0.9992$	$0.8308$
$500$	$0.05$	$0.9001$	$0.8453$	$1.0000$	$0.8260$
$500$	$0.01$	$0.9001$	$0.8321$	$1.0000$	$0.8158$

Appendix

Table 15: Controlled PAC verification. “Fraction above” is the fraction of

4000

calibration draws whose conditional coverage exceeded the DKW floor. The final column shows the corresponding floor after a twelve-exit simultaneous correction.

Item	Configuration
Accelerator	NVIDIA A $100$ SXM $4$ , $40$ GB, single GPU
CUDA / PyTorch	$12.1$ / $2.4.1$
Precision	FP $16$ inference
Batch size	$1$
Maximum encoded length	$128$ tokens
Warm-up	$200$ complete executions per method

Appendix

Table 16: Latency measurement configuration used for every paired encoder timing comparison.

Task	Backbone	path cov.	returned set	empty terminal	naive cov.	gap	latency/full
SST-2	BERT	$0.906$	$1.03$	$0.1\text{--}0.2\%$	$0.849$	$0.057$	$0.30$
SST-2	DistilBERT	$0.890$	$1.04$	$0.1\text{--}0.2\%$	$0.844$	$0.046$	$0.34$
MNLI	BERT	$0.904$	$1.44$	–	$0.824$	$0.080$	$0.75$
MNLI	DistilBERT	$0.902$	$1.62$	–	$0.842$	$0.060$	$0.83$
RTE	BERT	$0.901$	$1.49$	$0.1\text{--}0.2\%$	$0.796$	$0.105$	$0.88$
RTE	DistilBERT	$0.903$	$1.68$	$0.1\text{--}0.2\%$	$0.769$	$0.134$	$0.92$

Appendix

Table 17: Exact means underlying Figure 1 . Path coverage and returned-set size are direct test-role measurements. For the six binary cells, the empty-terminal column reports the supplied run-level range before the

\varnothing\to\mathcal{Y}

fallback; MNLI is left unreported here because it is not needed for the binary identity. RTE uses one fixed training-split calibration role with

n_{\rm cal}=498

and the fixed official development test set; its repeated estimates vary over head-training seeds rather than role assignments.

Task	Backbone	full-depth acc.	singleton rate	singleton acc.
SST-2	BERT	$0.932$	$0.970$	$0.903$
SST-2	DistilBERT	$0.918$	$0.960$	$0.885$
MNLI	BERT	$0.846$	$0.604$	$0.842$
MNLI	DistilBERT	$0.828$	$0.553$	$0.826$
RTE	BERT	$0.718$	$0.510$	$0.806$
RTE	DistilBERT	$0.697$	$0.320$	$0.697$

Appendix

Table 18: Encoder point-prediction context for interpreting set sizes. Full-depth accuracy is the deepest head’s top-1 accuracy. For the six binary rows, singleton rate and singleton accuracy are algebraic audit summaries implied by the directly measured returned-set size and coverage in the preceding table; the MNLI singleton columns are measured directly. RTE uses the fixed partition described in Section 4 .

Policy	budget $b$	coverage (95% CI)	avg. set (95% CI)	latency/full (95% CI)	empty-terminal
First eligible	$1$	$0.900\ [0.894,0.906]$	$1.94\ [1.87,2.01]$	$0.68\ [0.667,0.693]$	$0.06\%$
First eligible	$2$	$0.901\ [0.895,0.907]$	$2.21\ [2.13,2.29]$	$0.61\ [0.597,0.623]$	$0.06\%$
First eligible	$4$	$0.902\ [0.896,0.908]$	$2.76\ [2.65,2.87]$	$0.57\ [0.550,0.590]$	$0.06\%$
First eligible	$8$	$0.903\ [0.897,0.909]$	$3.90\ [3.76,4.04]$	$0.54\ [0.525,0.555]$	$0.06\%$
First eligible	$16$	$0.904\ [0.898,0.910]$	$5.48\ [5.30,5.66]$	$0.52\ [0.503,0.537]$	$0.06\%$
Design restriction	$1$	$0.900\ [0.894,0.906]$	$1.90\ [1.83,1.97]$	$0.70\ [0.687,0.713]$	$0.06\%$

Appendix

Table 19: Exact CIFAR-100 values underlying Figure 2 for

(n,L)=(500,24)

. Parentheses are paired

95\%

hierarchical-bootstrap intervals. All pathwise rows reuse one terminal calibration; empty-terminal is measured before the

\varnothing\to\mathcal{Y}

fallback. The three safe-baseline set-size/latency pairs are identical to the

(500,24)

scaling-grid row.

$n$	$L$	Pathwise	Bonferroni	EENN-AVCS	MinSE valid selection	paired MinSE $-$ Path
$50$	$4$	$3.24\pm 0.35/0.60\pm 0.04$	$3.71\pm 0.43/0.66\pm 0.05$	$3.49\pm 0.41/0.64\pm 0.05$	$3.34\pm 0.39/0.61\pm 0.05$	$0.10\ [-0.04,0.24]$
$50$	$12$	$3.30\pm 0.37/0.60\pm 0.04$	$100/1.00$	$4.18\pm 0.51/0.74\pm 0.06$	$3.81\pm 0.55/0.68\pm 0.06$	$0.51\ [0.21,0.81]$
$50$	$24$	$3.34\pm 0.39/0.61\pm 0.04$	$100/1.00$	$4.89\pm 0.63/0.84\pm 0.07$	$4.27\pm 0.92/0.76\pm 0.07$	$0.93\ [0.41,1.45]$
$100$	$4$	$3.02\pm 0.26/0.59\pm 0.03$	$3.36\pm 0.31/0.64\pm 0.04$	$3.21\pm 0.30/0.62\pm 0.04$	$3.10\pm 0.29/0.60\pm 0.04$	$0.08\ [-0.01,0.17]$
$100$	$8$	$3.05\pm 0.27/0.59\pm 0.03$	$3.91\pm 0.35/0.72\pm 0.04$	$3.55\pm 0.33/0.68\pm 0.04$	$3.29\pm 0.34/0.63\pm 0.04$	$0.24\ [0.11,0.37]$
$100$	$12$	$3.07\pm 0.28/0.59\pm 0.03$	$100/1.00$	$3.82\pm 0.36/0.73\pm 0.05$	$3.45\pm 0.39/0.66\pm 0.05$	$0.38\ [0.20,0.56]$

Appendix

Table 20: CIFAR-100 scaling grid at target coverage

0.90

. Method entries are average set size

\pm

marginal paired-bootstrap half-width / latency fraction

\pm

half-width. The final column is the directly paired MinSE-minus-pathwise set-size difference with its paired

95\%

interval, computed from the shared calibration subsample and test set; significance is assessed from this column, not from overlap of marginal intervals. Bonferroni entries marked

100/1.00

are exact rank-

n+1

degeneracies and therefore have zero sampling interval.

Dataset	independently trained path	$L$	$n_{\rm cal}$	full-depth acc.	Path	MinSE valid selection	Bonferroni
CIFAR-100	ViT-B/16	$12$	$500$	$0.927$	$2.84\pm 0.10/0.58\pm 0.02$	$3.08\pm 0.14/0.64\pm 0.02$	$3.73\pm 0.17/0.74\pm 0.02$
CIFAR-100	ViT-L/16	$24$	$500$	$0.936$	$2.76\pm 0.11/0.57\pm 0.02$	$3.18\pm 0.16/0.65\pm 0.02$	$4.05\pm 0.19/0.78\pm 0.03$
ImageNet-1k	ViT-B/16	$12$	$1000$	$0.798$	$8.31\pm 0.31/0.65\pm 0.02$	$9.02\pm 0.40/0.69\pm 0.02$	$11.57\pm 0.52/0.77\pm 0.03$
ImageNet-1k	ViT-L/16	$24$	$1000$	$0.823$	$7.86\pm 0.29/0.61\pm 0.02$	$9.41\pm 0.43/0.70\pm 0.02$	$13.88\pm 0.61/0.82\pm 0.03$

Appendix

Table 21: Replication beyond one frozen score path. “Path” and “MinSE” entries are average set size / latency fraction at target coverage

0.90

; Bonferroni is shown for the same trained path.

	DistilGPT2	Pythia-1.4B	Pythia-2.8B
Full-depth accuracy	$0.261\pm 0.002$	$0.391\pm 0.004$	$0.404\pm 0.005$
Selected coverage	$0.899\pm 0.004$	$0.903\pm 0.005$	$0.902\pm 0.003$
Average exit/full	$1.000$	$1.000$	$0.998$
Average set size	$9620$	$7162$	$8331$
Early-exit rate	$0.01\%$	$0.01\%$	$0.52\%$

Appendix

Table 22: Candidatewise next-token sets over the full vocabulary. Coverage and accuracy are mean

\pm

SD over five independent head-training seeds.

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Department of Computer Science and Engineering, University of Moratuwa, Moratuwa, Sri Lanka
Adaptive Cumulative Mass Calibration with Conformal Prediction
May 21, 2025Daniil Kazantsev, Eric Moulines, Maxim Panov +2Post-Hoc Calibration Conformal Prediction
Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, United Arab Emirates · École pour l’informatique et les techniques avancées (EPITA), Paris, France

May 18, 2026J/K move · Enter open · S save

Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibration

Fanyi Wu, Lihua Niu, Samuel Kaski, Michele Caprio

Department of Computer Science, University of Manchester, Manchester, UK · UKRI AI Centre for Doctoral Training in Decision Making for Complex Systems · Department of Computer Science, Aalto University, Espoo, Finland+1

Conformal Prediction Regression Prediction Intervals

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Bayesian conformal optimisation methods often use the same held-out data both to search for efficient prediction sets and to certify coverage or risk. This coupling is natural for high-probability risk-control guarantees, but it is not necessary when the target is standard finite-sample marginal conformal coverage. We propose Decoupled Conformal Optimisation (DCO), a train-tune-calibrate design principle that uses an independent tuning split for efficiency-oriented structural selection and a fresh calibration split for the final conformal quantile. Conditional on the tuned structure, standard split-conformal exchangeability yields finite-sample marginal coverage for any candidate class, without a confidence parameter or multiple-testing correction. DCO therefore targets a different finite-sample guarantee from PAC-style methods: marginal conformal coverage rather than high-probability risk control. Under consistency assumptions on the coupled risk bound, the two approaches nevertheless converge to the same population threshold. Across classification and regression benchmarks, including ImageNet-A, CIFAR-100, Diabetes, California Housing, and Concrete, DCO tracks the nominal coverage level closely while often reducing average prediction-set size or interval width relative to PAC-style calibration. On ImageNet-A, for example, the average set size decreases from

26.52

25.26

and the 95th-percentile set size from

58.95

53.73

; on Diabetes, the average interval width decreases from

2.098

1.914

Abstract

Conformal Prediction

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