Evaluating Persistent Calibration under Evolving Model Knowledge

Victor Wang; Thomas Hofweber; Mohit Bansal; Elias Stengel-Eskin

cs.LGSep 30, 2026

Evaluating Persistent Calibration under Evolving Model Knowledge

Authors: Victor Wang, Thomas Hofweber, Mohit Bansal, Elias Stengel-Eskin

Organizations: University of Texas at Austin · University of North Carolina at Chapel Hill

Abstract

As AI systems move from static repositories to agents that are capable of continual adaptation and learning, maintaining their trustworthiness means equipping the models backing them with the ability to produce confidence estimates that dynamically reflect their changing skills and knowledge. We introduce the problem of persistent calibration, which requires a confidence estimator to faithfully reflect the knowledge contained in a model as that knowledge changes, without recurring supervision. We operationalize this by examining persistent calibration across checkpoints of open models, asking whether confidence estimators trained on earlier checkpoints can generalize to later ones. Specifically, we aim to shed light on whether confidence is dependent on knowledge, a question with implications for the reliability of confidence estimates. To measure this relationship, we define and evaluate calibration on knowledge contrast sets: subsets containing questions that one checkpoint answers correctly and another checkpoint answers incorrectly, reflecting a change in knowledge. We show that both inference-time and fine-tuning methods fall short on contrast-set calibration compared to oracle methods trained on future checkpoints, even for methods that are well-calibrated on the full dataset. We provide evidence for the hypothesis that persistent calibration is challenging because there is a vast space of possible confidence functions that are well-calibrated on a given checkpoint, out of which only some rely on meta-knowledge features that would generalize to other checkpoints. Towards improving contrast-set calibration, we show that multi-checkpoint training helps, suggesting an avenue for identifying confidence features that remain robust across changing knowledge.

Figures & tables

Figure 1: (Left) Our setup for evaluating persistent calibration. During training, the model encounters the training data instance “Paris is the capital of France” , causing a change in knowledge between checkpoints

{\color[rgb]{0.8477,0.1055,0.375}\text{C}_{\text{2}}}

and

{\color[rgb]{0.1172,0.5352,0.8984}\text{C}_{\text{3}}}

. A confidence estimator that is faithful to the model’s evolving knowledge (Hypothesis 2) should produce a higher confidence on the checkpoint

{\color[rgb]{0.1172,0.5352,0.8984}\text{C}_{\text{3}}}

with increased knowledge; however, an estimator could instead capture Hypothesis 1, which performs equally well on the training distribution

{\color[rgb]{0.8477,0.1055,0.375}\text{C}_{\text{2}}}

but fails to generalize to

{\color[rgb]{0.1172,0.5352,0.8984}\text{C}_{\text{3}}}

. (Right) To measure the dependence of confidence on knowledge, we evaluate calibration on a contrast set consisting of questions that one checkpoint answers correctly and another checkpoint answers incorrectly, testing whether a change in knowledge is accompanied by a change in confidence.

	Olmo 3 7B			Marin 8B			Olmo 3 32B
	Contrast		Full	Contrast		Full	Contrast		Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$
	TriviaQA
End-correct baseline	0.000	0.627	0.530	0.000	0.783	0.547	0.000	0.712	0.548
Self-consistency	0.297	0.733	0.884	0.263	0.823	0.897	0.362	0.808	0.903
Non-oracle training	0.333	0.748	0.880	0.227	0.806	0.834	0.285	0.688	0.860

Table 1: SC and non-oracle training consistently fall short on contrast-set calibration compared to oracle training, even when full-set calibration is saturated. Results in Section 3 are averaged over 3 seeds. In each column, we bold the best result and underline results not significantly worse under a paired test (

\alpha=0.05

; see Section A.8 for tests); tables in Section 3 share this text styling. See Section B.2 for all evaluation metrics and Jeopardy results.

	Olmo 3 7B			Marin 8B			Olmo 3 32B
	Contrast		Full	Contrast		Full	Contrast		Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$
Self-consistency	0.297	0.733	0.884	0.263	0.823	0.897	0.362	0.808	0.903
$\llcorner$ Surrogate	0.211	0.637	0.859	0.277	0.695	0.871	0.288	0.688	0.883
$\llcorner$ Copy	0.000	0.500	0.832	0.000	0.500	0.829	0.000	0.500	0.846
Non-oracle training	0.333	0.748	0.880	0.227	0.806	0.834	0.285	0.688	0.860

Table 2: Comparing SC and non-oracle training with ablations controlling for knowledge already present in an earlier checkpoint. Beating these ablations is necessary for a nontrivial demonstration of persistent calibration. SC generally beats its ablations, while non-oracle training has mixed results. Results on TriviaQA; see Section B.2 for all metrics and Jeopardy results.

	Olmo 3 7B			Marin 8B			Olmo 3 32B
	Contrast		Full	Contrast		Full	Contrast		Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$
Non-oracle
Multi-ckpt	0.333	0.748	0.880	0.227	0.806	0.834	0.285	0.688	0.860
Single-ckpt	0.332	0.750	0.876	0.221	0.642	0.783	0.251	0.673	0.849
Oracle

Table 3: Multi-checkpoint training improves contrast-set and full-set calibration. Results on TriviaQA; see Section B.3 for Jeopardy.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
Multi-ckpt	0.379	0.424	0.255	0.285	0.795	0.185	0.061	0.890	0.131	0.032
$\llcorner$ Single-ckpt data	0.373	0.368	0.252	0.258	0.768	0.197	0.096	0.887	0.134	0.044
Resp-ckpt	0.351	0.396	0.241	0.274	0.778	0.193	0.070	0.884	0.133	0.030
$\llcorner$ Pooled data	0.360	0.357	0.248	0.251	0.757	0.203	0.104	0.887	0.132	0.035

Table 4: Ablating factors contributing to the gains of multi-checkpoint training (oracle).

\rm Single\text{-}checkpoint\ data

uses only one checkpoint’s answers for multi-checkpoint training.

\rm Pooled\ data

trains each checkpoint’s adapter on the same data as (unablated) multi-checkpoint training. Multi-checkpoint training beats both, meaning that both the training data and multiple checkpoint views contribute. Results on TriviaQA, Olmo 3 7B; see Section B.3 for Jeopardy.

Figure 2: GCM’s headroom on contrast-set AUC grows for larger models where the GCM backbone (Qwen3-8B) knows the answer less often. Thus, a static external verifier does not adapt to a model’s capability, motivating meta-knowledge for persistent calibration.

Figure 3: (Left) Transfer between pairs of training and eval checkpoints (Olmo 3 7B, TriviaQA; Jeopardy in Section B.6 ). Forward transfer (top right) is strong, while backward transfer (bottom left) is weak. (Right) Transfer of multi-checkpoint training, where the second checkpoint gets random labels. The second-checkpoint AUC generally plummets, at no penalty to the first checkpoint.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

19th Century America	3-Letter Words	4-Letter Words
American History	American Literature	Americana
Animals	Annual Events	Architecture
Around The World	Art	Art & Artists
Astronomy	Authors	Awards
Ballet	Biology	Bodies Of Water
Books & Authors	Business & Industry	Classical Music

Appendix

Table 5: Jeopardy categories included in our evaluation.

Type	Question	Reference answer(s)
Factoid	What is the main use of ETD fragmentation?	Analysis of intact proteins
Factoid	Which disease can be treated with Delamanid?	tuberculosis
List	List approved radioprotective compounds. Just output one of the answers.	[[‘amifostine’], [‘palifermin’]]
List	List the 5 different human immunoglobulin heavy chains. Just output one of the answers.	[[‘alpha’], [‘delta’], [‘epsilon’], [‘gamma’], [‘mu’]]

Appendix

Table 6: BioASQ example questions. For list questions, an answer matching any of the reference answers is accepted.

Olmo 3 7B
			Accuracy (%)
Short name	Checkpoint ID	Training data (trillions of tokens)	TriviaQA	Jeopardy	BioASQ
10%	stage1-step141000	0.59	51.9	64.8	40.2
20%	stage1-step283000	1.19	55.5	68.5	41.7
30%	stage1-step424000	1.78	57.8	70.7	44.0
40%	stage1-step566000	2.37	59.5	72.1	44.5

Appendix

Table 7: Cumulative training data and performance for the checkpoints used in our experiments.

Olmo 3 7B
	40%	50%	90%	100%
40%	–	642 (354)	771 (516)	753 (527)
50%	642 (288)	–	715 (455)	697 (466)
90%	771 (255)	715 (260)	–	538 (289)
100%	753 (226)	697 (231)	538 (249)	–

Appendix

Table 8: TriviaQA contrast-set sizes for each pair of evaluation checkpoints. The full-set size is 4960. In a cell, the first number is the total size of the contrast set, and the second number is the number of questions that the row checkpoint gets incorrect and the column checkpoint gets correct. Contrast-set sizes that are grayed out are too small (fewer than 500 questions) and are not used ( Section A.3 ).

Olmo 3 7B
	40%	50%	90%	100%
40%	–	738 (406)	767 (526)	796 (559)
50%	738 (332)	–	695 (453)	720 (484)
90%	767 (241)	695 (242)	–	517 (277)
100%	796 (237)	720 (236)	517 (240)	–

Appendix

Table 9: Jeopardy contrast-set sizes for each pair of evaluation checkpoints. The full-set size is 4998. In a cell, the first number is the total size of the contrast set, and the second number is the number of questions that the row checkpoint gets incorrect and the column checkpoint gets correct. Contrast-set sizes that are grayed out are too small (fewer than 500 questions) and are not used ( Section A.3 ).

Olmo 3 7B
	40%	50%	90%	100%
40%	–	457 (273)	490 (312)	475 (328)
50%	457 (184)	–	483 (264)	466 (279)
90%	490 (178)	483 (219)	–	389 (218)
100%	475 (147)	466 (187)	389 (171)	–

Appendix

Table 10: BioASQ contrast-set sizes for each pair of evaluation checkpoints. The full-set size is 2719. In a cell, the first number is the total size of the contrast set, and the second number is the number of questions that the row checkpoint gets incorrect and the column checkpoint gets correct. Contrast-set sizes that are grayed out are too small (fewer than 300 questions) and are not used ( Section A.3 ).

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
	Olmo 3 7B, TriviaQA
End-correct baseline	0.000	0.254	0.000	0.236	0.627	0.355	0.340	0.530	0.370	0.308
Self-consistency	0.297	0.329	0.190	0.212	0.733	0.212	0.084	0.884	0.140	0.069
$\llcorner$ Post-hoc	0.298	0.330	0.210	0.234	0.734	0.215	0.097	0.884	0.133	0.019
Non-oracle training	0.333	0.324	0.236	0.239	0.748	0.206	0.104	0.880	0.136	0.032

Appendix

Table 11: Expanding on Table 1 , we consistently find that SC and non-oracle training fall short on contrast-set calibration compared to oracle training, even when full-set calibration is saturated. Notably, even after applying post-hoc calibration to SC (isotonic regression via the pool adjacent violators algorithm fitted on the train set of the non-oracle checkpoints, applied with linear interpolation), full-set ECE becomes negligible and yet contrast-set AUC does not improve.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
	Olmo 3 7B, TriviaQA
End-correct baseline	0.000	0.254	0.000	0.080	0.627	0.230	0.000	0.530	0.370	0.308
Self-consistency	0.297	0.329	0.161	0.180	0.739	0.205	0.080	0.884	0.140	0.069
$\llcorner$ Post-hoc	0.298	0.330	0.163	0.181	0.740	0.205	0.080	0.884	0.133	0.019
Non-oracle training	0.333	0.324	0.211	0.219	0.759	0.196	0.092	0.880	0.136	0.032

Appendix

Table 12: Analogous setup to Table 11 , but using a fitted normalization function ( Section B.1 ) instead of Eq. 1 . The two tables share the finding that SC and non-oracle training underperform oracle training on contrast-set calibration, even when full-set calibration is saturated.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
	Olmo 3 7B, TriviaQA
Self-consistency	0.297	0.329	0.190	0.212	0.733	0.212	0.084	0.884	0.140	0.069
$\llcorner$ Surrogate	0.211	0.191	0.204	0.184	0.637	0.304	0.208	0.859	0.163	0.094
$\llcorner$ Copy	0.000	0.000	0.000	0.000	0.500	0.250	0.127	0.832	0.161	0.033
Non-oracle training	0.333	0.324	0.236	0.239	0.748	0.206	0.104	0.880	0.136	0.032

Appendix

Table 13: Expanded version of Table 2 , for both TriviaQA and Jeopardy. A confidence estimator must outperform its ablations for a nontrivial demonstration of persistent calibration. Based on contrast-set AUC, SC outperforms its ablations in 5/6 cases, while non-oracle training outperforms its ablations in only 3/6 cases.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
Non-oracle	Olmo 3 7B
Multi-ckpt, $\text{n}_{\text{cand}}$ =2	0.333	0.324	0.236	0.239	0.748	0.206	0.104	0.880	0.136	0.032
Multi-ckpt, $\text{n}_{\text{cand}}$ =1	0.332	0.335	0.223	0.233	0.749	0.204	0.094	0.877	0.137	0.032
Single-ckpt, $\text{n}_{\text{cand}}$ =2	0.332	0.340	0.216	0.227	0.750	0.203	0.093	0.876	0.140	0.048
Single-ckpt, $\text{n}_{\text{cand}}$ =1	0.314	0.339	0.208	0.225	0.746	0.206	0.086	0.870	0.146	0.063

Appendix

Table 14: Multi-checkpoint and multi-answer training often yields substantial gains. TriviaQA results; see Table 15 for Jeopardy.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
Non-oracle	Olmo 3 7B
Multi-ckpt, $\text{n}_{\text{cand}}$ =2	0.476	0.476	0.360	0.365	0.821	0.177	0.094	0.871	0.119	0.038
Multi-ckpt, $\text{n}_{\text{cand}}$ =1	0.438	0.438	0.327	0.328	0.802	0.186	0.103	0.863	0.124	0.042
Single-ckpt, $\text{n}_{\text{cand}}$ =2	0.447	0.457	0.318	0.327	0.808	0.181	0.094	0.860	0.124	0.039
Single-ckpt, $\text{n}_{\text{cand}}$ =1	0.418	0.441	0.278	0.294	0.796	0.185	0.090	0.851	0.130	0.050

Appendix

Table 15: Multi-checkpoint and multi-answer training often yields substantial gains. Jeopardy results; see Table 14 for TriviaQA.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
Multi-ckpt	0.506	0.536	0.379	0.402	0.855	0.156	0.057	0.888	0.111	0.020
$\llcorner$ Single-ckpt data	0.517	0.517	0.382	0.383	0.841	0.164	0.087	0.885	0.115	0.041
Resp-ckpt	0.471	0.485	0.352	0.364	0.826	0.172	0.079	0.877	0.116	0.028
$\llcorner$ Pooled data	0.506	0.499	0.380	0.376	0.833	0.169	0.094	0.884	0.113	0.027

Appendix

Table 16: Counterpart to Table 4 (TriviaQA) for Jeopardy. Multi-checkpoint training continues to outperform its two ablations, although the single-checkpoint data ablation is able to match the unablated multi-checkpoint training on the class-balanced contrast-set metrics

\Delta^{b}_{0},\Delta^{b}

, suggesting that access to multiple checkpoints’ weights accounts for most of the performance gain of multi-checkpoint training.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
	Olmo 3 7B, TriviaQA
GCM	0.446	0.448	0.331	0.335	0.808	0.182	0.088	0.869	0.191	0.181
$\llcorner$ Post-hoc	0.446	0.448	0.333	0.337	0.812	0.179	0.085	0.869	0.142	0.035
Oracle training	0.379	0.424	0.255	0.285	0.795	0.185	0.061	0.890	0.131	0.032
	Olmo 3 7B, Jeopardy

Appendix

Table 17: GCMs underperform oracle training, especially for larger models, highlighting that a static external verifier does not adapt to a model’s capability, motivating meta-knowledge for persistent calibration. This holds even with post-hoc calibration on GCM; see Table 11 for a description.

	Contrast							Full
Method	$\Delta_{0}^{b}$ $\scriptstyle\uparrow$	$\Delta_{0}$ $\scriptstyle\uparrow$	$\Delta^{b}$ $\scriptstyle\uparrow$	$\Delta$ $\scriptstyle\uparrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$	AUC $\scriptstyle\uparrow$	BS $\scriptstyle\downarrow$	ECE $\scriptstyle\downarrow$
	Olmo 3 7B, TriviaQA $\to$ BioASQ
Self-consistency	0.122	0.137	0.075	0.083	0.602	0.260	0.121	0.738	0.216	0.087
Non-oracle training	0.223	0.239	0.149	0.163	0.680	0.234	0.106	0.805	0.189	0.090
Oracle training	0.211	0.256	0.131	0.155	0.691	0.223	0.072	0.805	0.184	0.054
	Olmo 3 7B, Jeopardy $\to$ BioASQ

Appendix

Table 18: Transfer from TriviaQA or Jeopardy to BioASQ. The advantage of oracle training over other methods does not hold under domain transfer, consistent with prior work on the domain-specificity of correctness signals ( Sky et al., 2024 ) .

Layer	Mean $\rho$	Median $\rho$
1	0.920	0.929
2	0.914	0.929
3	0.631	0.750
4	0.507	0.536
5	0.533	0.714
6	0.535	0.750

Appendix

Table 19: Variance analysis ( Section B.7 ). Spearman correlations between checkpoint index and adapter variance for Olmo 3 7B on TriviaQA. For each question and layer, we compute the total variance (i.e. trace of the covariance matrix) of the model’s hidden states across 10 confidence adapter training seeds, and we compute the correlation between this total variance and checkpoint index. We find that the mean/median correlation across questions is positive for all layers, suggesting that later checkpoints tend to have a larger space of viable confidence features that confidence adapters can pick up on.

Figure 4: (Left) Transfer between pairs of training and eval checkpoints (Olmo 3 7B, Jeopardy, see Fig. 3 for TriviaQA). Forward transfer (top right) is strong, while backward transfer (bottom left) is weak. (Right) Transfer of multi-checkpoint training, where the second checkpoint gets random labels. The second-checkpoint AUC generally plummets, at no penalty to the first checkpoint.

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