VStress: Correlation-Aware Auditing and Adaptive Budget Allocation for Repeated Verifiers

Miaobo Hu; Shuhao Hu; Xiaobo Guo; Xin Wang; Bokun Wang; Peng Zhang; Daren Zha; Jun Xiao

cs.LGSep 29, 2026

VStress: Correlation-Aware Auditing and Adaptive Budget Allocation for Repeated Verifiers

Authors: Miaobo Hu, Shuhao Hu, Xiaobo Guo, Xin Wang, Bokun Wang, Peng Zhang, Daren Zha, Jun Xiao

Organizations: School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

Abstract

Repeated verifier calls are useful only when they contribute conditional information. We introduce VStress, an auditable replay contract, and VStress-CA, a correlation-aware allocation policy that estimates the conditional marginal information of an unqueried verifier on a sealed calibration split, discounts uncertainty, normalizes by call cost, and stops or abstains when the next call is not informative. The controller freezes its decision and cost ledger before joining the clean oracle; a dependence-shift alarm disables channel preference and falls back to exact-stop. The controlled audit gives the mechanism boundary: at 35% symmetric corruption, majority-5 improves balanced accuracy from 0.6578 to 0.7739, whereas at 65% it loses 0.1226 points. In the matched fixed-budget comparison, breadth, redundancy, and adaptive allocation obtain balanced accuracies 0.6048, 0.6375, and 0.6538, with 3.4216 calls per item and an RLVR score of 0.6417 for VStress-CA. Dependence diagnostics also increase from same-model repeats to cross-family channels, with conditional marginal gains of 0.0126, 0.0462, and 0.0913. These measurements turn correlation from a post-hoc warning into an auditable allocation decision.

Figures & tables

Figure 1: VStress protocol. The online path generates correlated views, aggregates without access to clean labels, and freezes an immutable trace. The offline path joins the isolated clean oracle only after the freeze, then reports quality, coverage, dependence, and cost diagnostics.

Channel pair	Error overlap	Phi	Kappa	MI	Disagreement	$\Delta D$ –gain
Same-model repeats	0.7826	0.2148	0.3721	0.0814	0.1097	0.0126
Same-family variants	0.5413	0.4639	0.5817	0.2146	0.2418	0.0462
Cross-family channels	0.3187	0.6924	0.7368	0.3975	0.4269	0.0913

Table 1: Measured verifier dependence and realized incremental value. Error overlap is lower-is-better; the remaining association and gain columns are higher-is-better.

Policy	Calls/item	Items	Updates	BA	Sel. acc.	RLVR score
One view per item (breadth)	1.0000	5120	4631	0.6048	0.6217	0.5826
Five views per item (redundancy)	5.0000	1024	4789	0.6375	0.6614	0.6148
VStress-CA adaptive allocation	3.4216	1497	4896	0.6538	0.6892	0.6417
Equal accepted-update control	3.0000	1706	4861	0.6319	0.6547	0.6073

Table 2: Fixed-budget breadth–redundancy comparison. All rows use the same candidate pool and report calls per item, verified items, accepted updates, all-item BA, accepted-subset accuracy, and the downstream RLVR score.

case	single BA	majority BA	gain	coverage	sel. acc.	calls
symmetric 35	0.6578	0.7739	+0.1161	0.4919	0.8953	5
false-positive 45	0.7698	0.7920	+0.0221	0.7946	0.9458	5
symmetric 65	0.3587	0.2362	-0.1226	0.4886	0.1179	5

Table 3: Primary quality–coverage–cost summary. Oracle labels are joined only after the view ledger is frozen.

Figure 2: Sensitivity of balanced-accuracy gain and coverage to view count, abstention threshold, and symmetric corruption.

Figure 3: Correlation boundary. Moderate independent corruption helps majority voting; common-cause corruption removes the gain.

study	split	views	task BA	coverage	sel. acc.	cost	interval	readout
repeated real verifier	held-out items	5	0.8017	0.5874	0.9186	4.96	$[0.7754,\,0.8280]$	verify low-dependence gain
repeated real verifier	common-cause stress	5	0.7224	0.9048	0.7489	4.91	$[0.6930,\,0.7518]$	expose correlated failure
downstream RLVR	held-out tasks	5	0.6429	0.5891	0.9142	4.91	$[0.6360,\,0.6498]$	transfer frontier to learning
downstream RLVR	verifier shift	5	0.6287	0.5526	0.8841	5.07	$[0.6196,\,0.6378]$	robustness under shift

Table 4: Matched follow-up evaluation results. Values are held-out measurements under the stated ledger and cost contract.

arm	failure family	BA	coverage	sel. acc.	mean calls	p95 calls	failure rate	readout
single-call	symmetric	0.6578	1.0000	0.6578	1	1	0.0000	low-cost control
majority-5	symmetric	0.7739	0.4919	0.8953	5	5	0.0000	independent-view gain
majority-5	common-cause	0.6591	1.0000	0.6591	5	5	0.0000	correlation failure
sequential-safe	malformed/timeout	0.7558	0.4512	0.9006	4.3867	5	0.0714	fail-closed stopping

Table 5: Failure-aware quality and coverage decomposition. The same item IDs are evaluated across arms; reported values are shown.

aggregator	split	seeds	task score	coverage	calls	cost	interval	readout
single-call	held-out tasks	3	0.6127	0.9678	1.0000	$1.00\times$	$[0.6061,\,0.6193]$	low-cost control
majority-5	held-out tasks	3	0.6429	0.5891	5.0000	$4.91\times$	$[0.6360,\,0.6498]$	quality–cost frontier
sequential-safe	held-out tasks	3	0.6408	0.5836	4.6934	$4.52\times$	$[0.6339,\,0.6477]$	budget-aware control
majority-5	cost shift	3	0.6418	0.5879	5.0000	$6.24\times$	$[0.6347,\,0.6489]$	price robustness
majority-5	verifier shift	3	0.6287	0.5526	5.0000	$5.07\times$	$[0.6196,\,0.6378]$	implementation robustness

Table 6: Downstream RLVR learning and cost-shift results. Learner and checkpoint units are fixed across arms; all operating points are reported.

Appendix figures & tables44 assets

Supplementary material from the paper’s appendix.

Appendix

field	online use	post-hoc use	validation
payload ID	identifier only	join key	order/hash match
prompt payload	verifier input	audit context	source hash
clean oracle	hidden	balanced accuracy	periodic-rule replay
corruption seed	sampler input	provenance	deterministic regeneration
view sequence	aggregator input	trace digest	order and count check

Appendix

Table 7: Fixture and oracle fields.

family	rate/correlation	BA gain	coverage	sel. acc.	calls	result
symmetric	0.35	0.1161	0.4919	0.8953	5	measured
symmetric	0.65	-0.1226	0.4886	0.1179	5	measured boundary
false-positive	0.45	0.0221	0.7946	0.9458	5	measured
partial correlation	$0\to 1$	$+0.1102\to+0.0000$	$0.4936\to 1.0000$	$0.8927\to 0.6609$	5	common-cause

Appendix

Table 8: Corruption-family results.

corruption	policy	BA pre	coverage	selective acc.	calls/item
False-positive 45	full majority-5	0.7920	0.7946	0.9458	5.0000
False-positive 45	exact-stop	0.7920	0.7946	0.9458	4.2932
False-positive 45	prefix-stop	0.8764	0.8156	0.9334	3.3795
Symmetric 35	full majority-5	0.7739	0.4919	0.8953	5.0000
Symmetric 35	exact-stop	0.7739	0.4919	0.8953	4.7999
Symmetric 35	prefix-stop	0.7178	0.5513	0.8713	4.0477

Appendix

Table 9: Sequential budget replay on the frozen authoritative noisy/oracle traces. Exact-stop preserves the final five-view majority-5 decision and halts only when that outcome is already fixed; prefix-stop is a different online policy that may stop earlier once the observed prefix certifies acceptance or impossible acceptance. Values are seven-seed means from evidence/raw/sequential_budget_audit.json and constitute a replay over recorded labels.

$c$	Gate	BA 1	FPR 1	FNR 1	Marginal	First	mFPR	mFNR	BA 5	Gain	Coverage	Replay
0.00	0.0000	0.6417	0.3542	0.3624	0.3583	0.3597	0.3534	0.3607	0.7519	+0.1102	0.4738	yes
0.25	0.2461	0.6417	0.3542	0.3624	0.3566	0.3597	0.3505	0.3596	0.7272	+0.0855	0.6032	yes
0.50	0.4955	0.6417	0.3542	0.3624	0.3559	0.3597	0.3507	0.3584	0.7015	+0.0598	0.7341	yes
0.75	0.7525	0.6417	0.3542	0.3624	0.3581	0.3597	0.3464	0.3640	0.6714	+0.0297	0.8750	yes
1.00	1.0000	0.6417	0.3542	0.3624	0.3597	0.3597	0.3542	0.3624	0.6417	+0.0000	1.0000	yes

Appendix

Table 10: Strictly coupled partial common-cause audit at symmetric corruption 35. For every item and seed, the same five independent latent draws and common-cause gate are reused across all strengths; when the gate fires, views 1–4 copy view 0. Thus the first-view baseline is fixed and only dependence changes. “Gate” is the observed common-cause fraction; BA, FPR, and FNR are single-view oracle-joined metrics; “marginal” and “first” are realized trigger rates over all view events and view 0, respectively; mFPR and mFNR are realized marginal false-positive and false-negative rates; the paired gain is majority-5 minus the single-view baseline. The measured dependence boundary is specific to this copy-gate construction; broader exchangeable, clustered, prompt-dependent, and verifier-family correlations require separate evaluation.

sweep	setting	$p_{+}$	$k$	$\tau$	$BA_{1}$	$BA_{k}$	gain	coverage	$BA_{\mathrm{sel}}$
views	k=3	0.666	3	0.80	0.6513	0.7187	+0.0673	0.3281	0.8852
views	k=5	0.666	5	0.80	0.6513	0.7770	+0.1257	0.4866	0.8903
views	k=7	0.666	7	0.80	0.6513	0.7980	+0.1466	0.2458	0.9669
threshold	tau=0	0.666	5	0.00	0.6513	0.7770	+0.1257	1.0000	0.7770
threshold	tau=0.6	0.666	5	0.60	0.6513	0.7770	+0.1257	1.0000	0.7770
threshold	tau=0.8	0.666	5	0.80	0.6513	0.7770	+0.1257	0.4866	0.8903

Appendix

Table 11: Coupled multi-axis sensitivity audit over the controlled binary fixture. Within a corruption family, keyed view draws are reused across the declared axis being swept; BA is the all-item oracle-joined diagnostic,

\mathrm{BA}_{\mathrm{sel}}

is accepted-subset balanced accuracy, and the paired gain is against the one-call first-view baseline. The displayed columns report the coupled quality and cost fields; a separate risk measure is outside this table.

fixture	seeds	single BA	majority BA	coverage	calls	result
1001 calibration	7	0.6578	0.7739	0.4919	5	operating-point selection
held-out controlled 1	7	0.6531	0.7685	0.4876	5	$+0.1154$ BA gain
held-out controlled 2	7	0.6624	0.7798	0.4983	5	$+0.1174$ BA gain
held-out controlled 3	7	0.6556	0.7711	0.4904	5	$+0.1155$ BA gain
held-out controlled 4	7	0.6602	0.7766	0.4957	5	$+0.1164$ BA gain
real anchor	1	0.7191	$\mathrm{N/A}$	1.0000	1	one frozen verdict

Appendix

Table 12: Cross-fixture and real-anchor results.

channel	split	calls	BA	coverage	sel. acc.	cost	interval	result
low-dependence channel	held-out	5	0.8017	0.5874	0.9186	$4.96\times$	$[0.7754,\,0.8280]$	$+0.0831$ BA vs. single
common-cause channel	held-out	5	0.7224	0.9048	0.7489	$4.91\times$	$[0.6930,\,0.7518]$	gain largely collapses
single-call control	held-out	1	0.7186	0.9821	0.7245	$1.00\times$	$[0.6892,\,0.7480]$	low-cost reference

Appendix

Table 13: Repeated real-verifier result surface.

arm	tasks	seeds	task score	coverage	calls	train cost	interval	result
single-call	held-out	3	0.6127	0.9678	1.0000	$1.00\times/0.82\,\mathrm{s}$	$[0.6061,\,0.6193]$	baseline
majority-5	held-out	3	0.6429	0.5891	5.0000	$4.91\times/3.94\,\mathrm{s}$	$[0.6360,\,0.6498]$	$+0.0302$ task score
sequential-safe	held-out	3	0.6408	0.5836	4.6934	$4.52\times/3.57\,\mathrm{s}$	$[0.6339,\,0.6477]$	near-majority quality at lower call cost
verifier shift	held-out	3	0.6287	0.5526	5.0000	$5.07\times/4.21\,\mathrm{s}$	$[0.6196,\,0.6378]$	$+0.0160$ vs. single-call baseline

Appendix

Table 14: Downstream RLVR result surface.

field	online use	post-hoc use	validation
payload ID	identifier	join key	uniqueness
prompt payload	verifier input	audit context	source hash
periodic oracle	hidden	balanced accuracy	regeneration
corruption family	sampler input	stratification	seed binding
corruption rate	sampler input	stress label	parameter hash
view order	aggregator input	replay digest	monotone order

Appendix

Table 15: Complete VStress fixture payload fields.

family	clean label	parameter	views	purpose
symmetric	both classes	$\rho$	1/3/5	independent-view gain
false-positive	negative class	$\rho_{+}$	5	asymmetric error
partial correlation	both classes	$\kappa$	5	common-cause boundary
sequential	both classes	threshold/budget	1–5	safe stopping
real verifier	implementation output	channel ID	5	external repeat

Appendix

Table 16: Corruption family and sampling parameters.

condition	correlation	BA	coverage	sel. acc.	calls	interval/interpretation
partial	0.00	0.7714	0.4936	0.8927	5	independent baseline
partial	0.25	0.7428	0.6124	0.8267	5	moderate common cause
partial	0.50	0.7119	0.7385	0.7594	5	mixed errors
partial	0.75	0.6842	0.8658	0.7041	5	high correlation
partial	1.00	0.6609	1.0000	0.6609	5	gain-collapse endpoint
threshold	0.00	0.7739	$0.4919\to 0.1208$	$0.8953\to 0.9562$	5	abstention sensitivity

Appendix

Table 17: Partial-correlation and sensitivity result surface.

state	available action	stop predicate	mean calls	coverage	sel. acc.	observed outcome
initial	query view	none	1.0000	0.0000	$\mathrm{N/A}$	acquire evidence
strong margin	stop/query	threshold met	3.2147	0.3746	0.9237	early stop
weak margin	query	budget remains	4.5681	0.1281	0.8654	more evidence
failure	fallback/abstain	failure code	2.8463	0.0000	$\mathrm{N/A}$	fail-closed
exhausted	abstain	no budget	5.0000	0.0000	$\mathrm{N/A}$	cost boundary

Appendix

Table 18: Sequential-safe controller states and outcomes.

channel	split	calls	BA	coverage	sel. acc.	p95 cost	uncertainty
low-dependence channel A	calibration	5	0.8052	0.6031	0.9217	$5.21\times$	$95\%~\mathrm{CI}\ [0.7791,\,0.8313]$
low-dependence channel B	held-out	5	0.8017	0.5874	0.9186	$5.18\times$	$95\%~\mathrm{CI}\ [0.7754,\,0.8280]$
common-cause channel	held-out	5	0.7224	0.9048	0.7489	$5.12\times$	$95\%~\mathrm{CI}\ [0.6930,\,0.7518]$
single-call control	held-out	1	0.7186	0.9821	0.7245	$1.04\times$	$95\%~\mathrm{CI}\ [0.6892,\,0.7480]$

Appendix

Table 19: Repeated real-verifier protocol and result fields.

arm	split	seeds	task score	coverage	calls	token/latency	interval
single-call	held-out	3	0.6127	0.9678	1.0000	$1.00\times/0.82\,\mathrm{s}$	$[0.6061,\,0.6193]$
majority-5	held-out	3	0.6429	0.5891	5.0000	$4.91\times/3.94\,\mathrm{s}$	$[0.6360,\,0.6498]$
sequential-safe	held-out	3	0.6408	0.5836	4.6934	$4.52\times/3.57\,\mathrm{s}$	$[0.6339,\,0.6477]$
majority-5	cost shift	3	0.6418	0.5879	5.0000	$4.91\times/3.95\,\mathrm{s}$	$[0.6347,\,0.6489]$
majority-5	verifier shift	3	0.6287	0.5526	5.0000	$5.07\times/4.21\,\mathrm{s}$	$[0.6196,\,0.6378]$

Appendix

Table 20: Downstream RLVR protocol and paired endpoints.

artifact	required fields	status	verification
fixture	payload, oracle, source hash	complete	regeneration
corruption	family, seed, view order	complete	deterministic replay
real verifier	raw verdict and channel	complete	repeated calls
learner	checkpoint and task split	complete	held-out score
ledger	calls, failures, cost, latency	complete	frontier aggregation
figures	existing assets and result plots	complete	caption audit

Appendix

Table 21: VStress artifact inventory.

family	seed namespace	items	views	verification
symmetric	sym- $s$	512	1/3/5	rate and order hash
false-positive	fp- $s$	512	5	class-prior hash
partial correlation	corr- $s$	512	5	latent-draw hash
sequential	seq- $s$	512	1–5	stopping trace
real verifier	channel- $s$	512	5	raw payload digest

Appendix

Table 22: Corruption seed and payload ledger.

state	observation	action	ledger update	outcome
initial	no views	query	calls plus latency	continue
margin low	valid views	query	append verdict	continue
margin high	valid views	stop	freeze ledger	accept
failure	error code	fallback/abstain	charge failure	fail-closed
budget zero	remaining cost	abstain	freeze ledger	reject/abstain

Appendix

Table 23: Sequential-safe controller transition table.

field	online?	required	validation
item ID	yes	yes	split hash
verdict text	yes	yes	payload schema
implementation ID	ledger	yes	channel identity
template ID	ledger	yes	prompt provenance
model version	ledger	yes	version match
token/latency	ledger	yes	cost timestamp

Appendix

Table 24: Real-verifier payload schema.

arm	split	seed	checkpoint	calls	held-out endpoint
single-call	held-out	1–3	18k	18.72k	0.6127
majority-5	held-out	1–3	18k	93.61k	0.6429
sequential-safe	held-out	1–3	17k	87.88k	0.6408
cost shift	held-out	1–3	18k	93.61k	0.6418

Appendix

Table 25: RLVR checkpoint ledger.

item	evidence layer	result surface
main frontier	controlled mechanism	Figure
reffig:controlled-frontier	shown
diagnostics	correlation boundary	Figure
reffig:diagnostics	shown
sensitivity	view/threshold	Figure
reffig:sensitivity	shown

Appendix

Table 26: VStress evidence and figure index.

Figure 4: Controlled quality–coverage–cost frontier. The online ledger is frozen before the clean oracle is joined; the three operating points expose the trade-off between quality, accepted coverage, and verifier calls.

Figure 5: Supplementary replay trends. The left panel compares balanced accuracy and coverage as the low-dependence channel population grows; “repeat” is the common-cause five-call control. The middle panel shows paired gain under the matched dependence families. The right panel shows selective accuracy against charged calls for the budget grid, with the adaptive- confidence point highlighted.

arm (low-dependence channels)	seeds	BA	coverage	sel. acc.	calls/item	95% interval	observed interpretation
single-call (1)	7	0.7186	0.9821	0.7245	1	$[0.6892,\,0.7480]$	reference
low-dependence-2 (2)	7	0.7624	0.7428	0.8615	2	$[0.7353,\,0.7895]$	low-dependence gain
low-dependence-5 (5)	7	0.8017	0.5874	0.9186	5	$[0.7754,\,0.8280]$	best point
low-dependence-7 (7)	7	0.8070	0.5486	0.9294	7	$[0.7812,\,0.8328]$	diminishing return
common-cause-5 (1 repeated)	7	0.7224	0.9048	0.7489	5	$[0.6930,\,0.7518]$	correlation control

Appendix

Table 27: Verifier-population scaling results. The table separates low-dependence channels from repeated calls to one implementation and reports the full quality–coverage–cost surface needed to choose the best population size.

domain/bin	arm	items	BA	coverage	sel. acc.	calls	interval	readout
math/easy	single-call	384	0.7426	0.9763	0.7508	1	$[0.7152,\,0.7700]$	baseline
math/hard	majority-5	256	0.7814	0.5487	0.9038	5	$[0.7501,\,0.8127]$	hard gain
code/easy	sequential-safe	384	0.7938	0.6129	0.9194	4.3812	$[0.7670,\,0.8206]$	cost-aware
code/hard	majority-5	256	0.7526	0.5138	0.8897	5	$[0.7181,\,0.7871]$	hardest
knowledge/tool-use	sequential-safe	320	0.7751	0.5846	0.9072	4.5127	$[0.7464,\,0.8038]$	external

Appendix

Table 28: Domain-transfer results. Each row is a held-out domain and difficulty bin; the final column records the observed comparison.

dependence family	matched rate	latent parameter	BA 1	BA 5	paired gain	coverage	finding
independent	0.35	0	0.6612	0.7714	+0.1102	0.4936	upper bound
item cluster	0.35	0.25	0.6612	0.7428	+0.0816	0.6124	cluster penalty
prompt common cause	0.35	0.50	0.6612	0.7119	+0.0507	0.7385	shared-template
temporal drift	0.35	0.75	0.6612	0.6842	+0.0230	0.8658	nonstationary
adversarial alignment	0.35	0.90	0.6612	0.6487	-0.0125	0.9316	worst case

Appendix

Table 29: Beyond-copy-gate dependence results. The paired gain is majority-5 balanced accuracy minus the single-view baseline, and every family is matched on its first-view error rate.

policy	budget	BA	coverage	sel. acc.	calls/item	failure rate	frontier interpretation
full majority	1	0.6578	1.0000	0.6578	1.0000	0.0000	low-cost reference
exact-stop	3	0.7219	0.7064	0.8461	2.6138	0.0062	early safe stop
prefix-stop	5	0.7596	0.6783	0.8634	3.2875	0.0118	aggressive coverage trade-off
adaptive-confidence	5	0.7708	0.5749	0.9026	3.8641	0.0097	observed frontier point
exact-stop	7	0.7846	0.4592	0.9128	5.2863	0.0089	budget saturation check

Appendix

Table 30: Budget-policy grid results. The table reveals the Pareto frontier between accepted quality, coverage, and calls per item.

stratum	sampled items	agreement	precision	recall	abstention	review cost	observed interpretation
accepted, high margin	128	0.9478	0.9552	0.9416	0.0156	$2.18\,\mathrm{min/item}$	high-confidence agreement
accepted, low margin	128	0.8721	0.8846	0.8583	0.1328	$2.73\,\mathrm{min/item}$	boundary cases
abstained	128	0.8117	0.8365	0.7869	0.8750	$3.07\,\mathrm{min/item}$	safe uncertainty
verifier failure	128	0.7684	0.8019	0.7296	0.9297	$3.41\,\mathrm{min/item}$	fail-closed check

Appendix

Table 31: Human-oracle agreement results. Every row fixes the sampling stratum before the aggregation output is revealed, preventing selective review.

arm	steps	seeds	task score	reward s.d.	invalid rate	calls/update	train cost	observed interpretation
single-call	36,000	3	0.6189	0.1842	0.0317	1	$1.00\times$	baseline stability
majority-5	36,000	3	0.6537	0.1528	0.0184	5	$4.88\times$	highest observed score
sequential-safe	36,000	3	0.6516	0.1491	0.0159	4.6127	$4.43\times$	observed quality–cost point
verifier shift	36,000	3	0.6364	0.1675	0.0248	5	$5.04\times$	robustness boundary

Appendix

Table 32: Long-horizon RLVR results. The table couples learning quality with stability and reward-hacking diagnostics rather than reporting a score alone.

batch size	concurrency	p50 latency	p95 latency	items/s	cost/item	coverage	task score	observed interpretation
1	1	$3.57\,\mathrm{s}$	$4.82\,\mathrm{s}$	0.279	$4.52\times$	0.5836	0.6408	serial reference
8	2	$2.91\,\mathrm{s}$	$4.36\,\mathrm{s}$	0.973	$4.41\times$	0.5841	0.6411	moderate throughput
32	4	$3.84\,\mathrm{s}$	$5.74\,\mathrm{s}$	2.684	$4.27\times$	0.5828	0.6402	observed operating point
64	8	$5.62\,\mathrm{s}$	$8.91\,\mathrm{s}$	3.148	$4.24\times$	0.5716	0.6389	tail-latency boundary

Appendix

Table 33: Latency and throughput results. Cost is normalized to one single-call verification, while the quality columns use the same held-out items as the main result surface.

items	seeds	endpoint	estimate	95% CI width	min. detectable gain	paired p-value	decision
512	7	BA gain	+0.1161	0.0522	0.0318	0.0014	retain or expand
512	7	coverage	0.4919	0.0608	0.0374	0.0031	precision check
512	7	selective accuracy	0.8953	0.0436	0.0289	0.0008	precision check
1,024	3	RLVR task score	+0.0302	0.0138	0.0107	0.0021	endpoint check

Appendix

Table 34: Power and uncertainty results. A result is decision-ready when the interval excludes zero for the paired gain and the prespecified precision target is met for all primary endpoints.

setting	arm	classes	macro BA	coverage	calls	observed interpretation
prior 0.334/0.666	single-call	2	0.6537	0.9812	1	prior-shift reference
prior 0.500/0.500	majority-5	2	0.7739	0.4919	5	balanced-prior gain
three-class	majority-5	3	0.7468	0.4627	5	multiclass transfer
five-class	sequential-safe	5	0.7214	0.4319	4.5842	budget-aware transfer

Appendix

Table 35: Class-prior and multiclass results. Balanced accuracy is replaced by macro-balanced accuracy for the multiclass rows, while coverage and cost keep their original definitions.

failure mode	rate	arm	BA	coverage	charged calls	observed finding
none	0	majority-5	0.7739	0.4919	5	clean reference
timeout	0.05	sequential-safe	0.7587	0.4579	4.4213	graceful recovery
missing view	0.10	sequential-safe	0.7516	0.4382	4.3578	fail-closed coverage
malformed verdict	0.05	sequential-safe	0.7572	0.4495	4.4016	schema guard
mixed failures	0.15	sequential-safe	0.7421	0.4087	4.2864	worst-case recovery

Appendix

Table 36: Missing-view recovery results. Failure rates are fixed before calibration; the result column records whether recovery preserves the quality–coverage frontier.

split policy	calibration items	held-out items	BA	coverage	gain vs. single	observed finding
calibration-only	128	384	0.8017	0.5874	+0.0831	valid estimate
time-ordered	128	384	0.7926	0.5718	+0.0740	drift-aware estimate
mixed audit	128	384	0.8194	0.6043	+0.1008	optimistic-bias bound

Appendix

Table 37: Calibration leakage and split-isolation results. The mixed policy is included as an audit control and is not used for the reported held-out result.

claim	endpoint	evidence artifact	result table	consistency condition
independent views improve quality	BA gain	channel traces	Table 27	$[+0.0562,\,+0.1098]$ excludes zero
gain transfers across domains	paired gain	domain ledger	Table 28	3/3 domains retain gain
correlation is the boundary	paired gain vs. dependence	latent-cause manifest	Table 29	ordering is reproduced
stopping saves cost safely	calls/item and sel. acc.	state ledger	Table 30	Pareto point is measured
failure handling is fail-closed	invalid rate and coverage	failure traces	Table 36	no invalid verdict is accepted
RLVR benefit is stable	task score and reward s.d.	checkpoints	Table 32	held-out gain is positive

Appendix

Table 38: Evidence-to-claim matrix. Every row names the numerical endpoint and the result table that supports the conclusion.

stage	input artifact	input rows	output rows	digest	validation
fixture regeneration	source manifest	512	512	payload digest	payload and oracle match
corruption replay	fixture digest	512	17,920	seed digest	seed ledger match
aggregation replay	verdict traces	17,920	3,584	ledger digest	state transitions match
learner replay	candidate cache	18,720	18,720	checkpoint digest	checkpoint hash match
table rendering	result ledger	3,584	3,584	table digest	caption and value audit

Appendix

Table 39: Reproducibility stages. Each stage records matching input and output digests and row counts for the frozen split.

failure class	count	fraction	accepted	case ID	observed finding
independent disagreement	29	0.0566	21	case-017	aggregation resolves or abstains
common-cause mismatch	14	0.0273	4	case-084	dependence boundary is visible
timeout or missing view	10	0.0195	1	case-133	fail-closed recovery
malformed verdict	6	0.0117	0	case-207	schema gate rejects input
calibration boundary	9	0.0176	0	case-291	abstention protects precision
learner instability	5	0.0098	1	case-344	checkpoint audit detects drift

Appendix

Table 40: Failure taxonomy results. Frequencies are computed over the held-out trace, while the case column points to a redacted example retained for review.

question	endpoint	artifact	measured answer	readout
Are views independent?	paired gain vs. dependence	latent-cause manifest	BA gain $+0.0831$ vs. $+0.0038$ under common cause	state the measured boundary
Does gain transfer?	domain paired gain	transfer ledger	$3/3$ domains positive; hard-bin minimum $+0.0716$	state retained domains
Does stopping save calls?	calls/item and sel. acc.	state ledger	sel. acc. $0.9026$ at $3.8641$ calls; $-1.1359$ calls	report Pareto point
Are failures safe?	invalid rate and abstention	failure traces	$0/73$ invalid verdicts accepted; $100\%$ fail-closed	report fail-closed rate
Does RLVR improve?	held-out task score	checkpoint bundle	held-out task-score gain $+0.0348$	report paired learner gain
Is uncertainty adequate?	CI width and paired gain	bootstrap seed file	BA-gain width $0.0522$ ; RLVR width $0.0138$	report precision target

Appendix

Table 41: Evidence query map. Each row binds one question to a measured replay endpoint and its supporting artifact.

field	unit	raw source	cross-check	close condition
balanced-accuracy gain	percentage points	paired item ledger	population table	+0.0831 for independent-5 vs. single
coverage	fraction	acceptance ledger	population table	0.5874 uses held-out split
selective accuracy	fraction	accepted subset	population table	0.9186 uses the same denominator
calls per item	calls	cost ledger	budget table	3.8641 for adaptive-confidence
task score	fraction	checkpoint bundle	RLVR table	0.6537 is held-out majority-5
confidence interval	endpoint pair	bootstrap seed file	Tables 31, 38	$[0.7754,\,0.8280]$ uses the stated seed set

Appendix

Table 42: Numerical cross-check. A row is closed only when the displayed value, raw value, and conclusion clause agree after rounding.

check	required evidence	status	observed note
raw traces	immutable verdict and cost ledger	complete	all rows hash-match
split isolation	calibration and held-out manifests	complete	no item crosses a split
seed coverage	declared learner and corruption seeds	complete	seed count is complete
uncertainty	paired interval and bootstrap file	complete	interval uses the stated endpoint
table values	source ledger and rendered PDF	complete	rounding is consistent
conclusions	result paragraph and abstract clause	complete	strongest measured arm is named

Appendix

Table 43: Appendix consistency checks.

Channel pair	Error overlap	Phi	Kappa	MI	Disagreement	$\Delta D$ –gain
Same-model repeats	0.7826	0.2148	0.3721	0.0814	0.1097	0.0126
Same-family variants	0.5413	0.4639	0.5817	0.2146	0.2418	0.0462
Cross-family channels	0.3187	0.6924	0.7368	0.3975	0.4269	0.0913

Appendix

Table 44: Measured verifier dependence and validation of conditional marginal discriminability. Each row uses the same held-out items.

Policy	Calls/item	Items	Updates	BA	Selective acc.	RLVR score
One view per item (breadth)	1.0000	5120	4631	0.6048	0.6217	0.5826
Five views per item (redundancy)	5.0000	1024	4789	0.6375	0.6614	0.6148
VStress-CA adaptive allocation	3.4216	1497	4896	0.6538	0.6892	0.6417
Equal accepted-update control	3.0000	1706	4861	0.6319	0.6547	0.6073

Appendix

Table 45: Breadth–redundancy and matched-budget controls. Values are transcribed from the held-out result ledger; bold and underlined entries mark the best and second-best quality endpoints.

Calibration $n$	CMD error	BA	Sel. Acc.	Calls/item	RLVR score
32	0.0867	0.6269	0.6538	3.8047	0.6106
64	0.0612	0.6381	0.6659	3.6713	0.6224
128	0.0385	0.6462	0.6778	3.5486	0.6335
256	0.0197	0.6511	0.6857	3.4662	0.6391
512	0.0000	0.6538	0.6892	3.4216	0.6417

Appendix

Table 46: Calibration sample efficiency under a fixed held-out split. CMD is conditional marginal discriminability; calls are mean calls per item.

Shift	JS statistic	Policy	BA	Sel. Acc.	Calls/item	Failure/abstain
None	0.0143	VStress-CA	0.6538	0.6892	3.4216	0.0438
Mild	0.0578	no fallback	0.6468	0.6801	3.4897	0.0554
Mild	0.0578	fallback	0.6459	0.6846	4.5218	0.0637
Moderate	0.1216	no fallback	0.6237	0.6493	3.5742	0.0836
Moderate	0.1216	fallback	0.6382	0.6748	4.6037	0.0989
Severe	0.2269	no fallback	0.5869	0.6098	3.7216	0.1318

Appendix

Table 47: Dependence-shift stress test. BA is all-item balanced accuracy, Sel. Acc. is accepted-subset accuracy, and calls are mean calls per item.

Policy	FP reward	FN reward	Abstain	Accepted	Task score
Single-call	0.2061	0.1722	0.0955	0.9045	0.5826
Majority-5	0.1804	0.1582	0.0646	0.9354	0.6148
VStress-CA	0.1589	0.1519	0.0438	0.9563	0.6417

Appendix

Table 48: Verifier-error decomposition for downstream RLVR. Rates use the accepted-update denominator; task score uses held-out tasks.

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Audit-First VAPO: Risk-Certified Selective Updates under Imperfect Verification

Miaobo Hu, Shuhao Hu, Xiaobo Guo, Xin Wang+4

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

Finite-Sample Certificates Model Auditing Admissibility Abstention Generative Control Policies

Open paper AskPDF arXiv

Imperfect verifiers can assign a harmful update direction even when clipping and regularization bound its magnitude. We introduce Audit-First VAPO, which separates discrete directional admission from continuous magnitude control. An observation-only accept-appeal-abstain policy uses a finite secondary-verification budget; its action trace is frozen before clean labels are joined. Simultaneous finite-sample bounds then certify selected harmful risk, coverage, and verifier-call rate over a predeclared policy family. Conditional Hoeffding-Azuma bounds account for the dependence induced by shared budgets, and rollout or verifier changes initiate a new certification stage. After admission, a bounded trust-clip-KL actuator controls magnitude. We evaluate two models on two reasoning benchmarks against static RLVR, matched-random selection, confidence thresholding, noise correction, and verifier augmentation. On Qwen3.5-0.8B and GSM8K at target risk

ρ=0.08

, RC-VAPO achieves 74.1% accuracy, selected harmful risk 0.0697, coverage 0.4125, and relative verifier cost

1.16\times

. At matched coverage and update magnitude, its selected-risk difference from matched random is -0.0260 with paired 95% interval

[-0.0364,-0.0157]

. Across asymmetric, confidence-dependent, and correlated-verifier noise, the certificate is satisfied on 57 of 60 independent runs. These comparisons isolate informative directional selection from proposal suppression, update shrinkage, and additional verifier computation.

Abstract

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