Adaptive Conformal Guidance for Learning under Uncertainty
Authors: Rui Liu
Peng Gao
Yu Shen
Ming Lin
Pratap Tokekar
Venue: ICLR 2026 Poster (2026)
Keywords: Conformal Prediction
Learning under Uncertainty
Learning with Guidance
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: A broadly applicable approach that dynamically modulates guidance signals based on associated uncertainty, providing a simple yet effective solution for incorporating uncertainty-aware guidance.

Abstract: Learning with guidance has proven effective across a wide range of machine learning systems. Guidance may, for example, come from annotated datasets in supervised learning, pseudo-labels in semi-supervised learning, and expert demonstration policies in reinforcement learning. However, guidance signals can be noisy due to domain shifts and limited data availability and may not generalize well. Blindly trusting such signals when they are noisy, incomplete, or misaligned with the target domain can lead to degraded performance. To address these challenges, we propose Adaptive Conformal Guidance (AdaConG), a simple yet effective approach that dynamically modulates the influence of guidance signals based on their associated uncertainty, quantified via split conformal prediction (CP). By adaptively adjusting to guidance uncertainty, AdaConG enables models to reduce reliance on potentially misleading signals and enhance learning performance. We validate AdaConG across diverse tasks, including knowledge distillation, semi-supervised image classification, gridworld navigation, and autonomous driving. Experimental results demonstrate that AdaConG improves performance and robustness under imperfect guidance, e.g., in gridworld navigation, it accelerates convergence and achieves over $\times 6$ higher rewards than the best-performing baseline. These results highlight AdaConG as a broadly applicable solution for learning under uncertainty.

Published as a conference paper at ICLR 2026
ADAPTIVE CONFORMAL GUIDANCE FOR LEARNING UNDER UNCERTAINTY
Rui Liu', Peng Gao?, Yu Shen?, Ming Lin', Pratap Tokekar'
l University of Maryland, College Park
North Carolina Satate University
3 Adobe Research
ABSTRACT
Learning with guidance has proven effective across wide range of machine learn- ing systems. Guidance may, for example, come from annotated datasets in super- vised learning, pseudo-labels in semi-supervised learning, and expert demonstra- tion policies in reinforcement learning. However, guidance signals can be noisy due to domain shifts and limited data availability and may not generalize well. Blindly trusting such signals when they are noisy, incomplete, or misaligned with the target domain can lead to degraded performance. To address these challenges. we propose Adaptive Conformal Guidance (AdaConG). simple yet effective approach that dynamically modulates the influence of guidance signals based on their associated uncertainty, quantified via split conformal prediction (CP). By adaptively adjusting to guidance uncertainty, AdaConG enables models to reduce reliance potentially misleading signals and enhance learning performance. We validate AdaConG across diverse tasks, including knowledge distillation, semi- supervised image classification, gridworld navigation, and autonomous driving. Experimental results demonstrate that AdaConG improves performance and ro- bustness under imperfect guidance, e.g., in gridworld navigation, it accelerates convergence and achieves over 6x higher rewards than the best- pessfperrfoming base- line. These results highlight AdaConG broadly applicable solution for learn- ing under uncertainty.
INTRODUCTION
Machine learning systems often rely some form of guidance during training to enhance perfor- mance (Hinton) 2015) Romero et al.] 20144 Zagoruyko and Komodakis [2016] Passalis and Tefas] 2018), bootstrap learning in data-scarce scenarios (Sohn et al. [2020] Zhang et al. 2021), and im- prove sample efficiency (Hu et al. 2023 Bhaskar et al.) 2024b). While such guidance has proven valuable, critical challenge arises when this guidance is noisy. In supervised learning, richly notated datasets provide guidance to enhance model performance, and leveraging pretrained models (Hinton 2015) Romero et al. 2014 Zagoruyko ko and Komodakis 2016; Passalis and Tefas 2018 Kim
et al. 2018) Wang et al. 2023 Xue et 2022 Huo et al.) [224 Cuu et 2 Jin et al. 2023 has
become an effective strategy boost performance and enable deployment in resource-constrained
environments, with wiggtt models that either use reduced modalities or smaller architectures
during inference (Shen et al., 2023, Gu et al. 2023; Liu al. c)25b]c). These teacher-student frameworks allow the student to benefit from the teacher's 's superior predictions. However, this setup critically assumes that the teacher's outputs remain reliable when applied to the student's 's target domain. In practice, domain shifts can render the teacher's guidance noisy or misleading.
Similarly, semi-supervised learning (SSL. expands the effective training set through pseudo-labeling to bootstrap learning in data-scarce scenarios (Sohn et al., 2020 Zhang et al.) (201)) However, the quality of these pseudo-labels may not be high due to the inherent uncertainty. This uncertainty stems from several factors (Scherer et al.) 2022 Xia et al. 2023; Kage et al. 2024): the small labeled set may not fully represent the data distribution, the model's 's early mistakes can propagate through self- training, and the confidence thresholds for pseudo-labeling may not perfectly filter out incorrect labels. As a result, noisy pseudo-labels can misguide the learning process, potentially reinforcing errors and degrading model performance.

---

Published as a conference paper at ICLR 2026
I-e
Ri-a
Calibration
Pretrained
Adaptive Weighting w
Uncertainty
Model
Pseudo Labels
Guidance
Guidance Loss Lg
Expert Policy
w Lg
Labeled Cat
Supervised
Learning
Unlabeled
Training Data
Semi Supi--Supervised
Task Loss 4p
Learning
Reinforcement
Lr + W
Lg
Observation
Learning
Updates
Figure 1: Overview of the AdaConG approach. AdaConG leverages split CP with calibration to quantify the uncertainty of guidance signals and adaptively modulate their influence. The estimated uncertainty u. converted into an adaptive weight w, which reweights the guidance loss. This weighted guidance loss is then combined with the task loss to update the model, enabling effective learning under uncertain guidance.
In reinforcement learning, agents employ imitation-leanen policies for guidance (Hu et al. 2023 Bhaskar et al.] 2024b) to reduce exploration demands and improve sample efficiency, yet critical challenge emerges when the target environment differs from the ones used for the expert demon- strations. While imitation learning provides valuable behavioral priors, these policies often struggle to generalize beyond their training distribution. When the RI. agent encounters states or observa- tions outside the expert's is demonstration space, the imitation policy's guidance becomes increasingly noisy, potentially leading to suboptimal exploration.
In all these scenarios, blindly relying on noisy guidance can propagate errors and lead subopti- mal model performance, as the learning system overfits to potentially misleading information, yet discarding potentially valuable guidance wastes computational resources and domain knowledge. Despite its fundamental importance, the challenge of effectively leveraging noisy guidance while maintaining robust learning capabilities remains largely unaddressed across machine learning sys- tems. The central question becomes: How can we effectively leverage potentially valuable guidance while appropriately accounting for its uncertainty to ensure robust model learning?
While prior works have explored uncertainty-avve
learning (Angelopoulos et al.] 2020 Mossinal Zhao et al., 2024
al.
2024
Lu et al., 2022 Karimi and Samavi 2023
al. 2025 Zhang
et al.
2024 Edupuganti et al.) 2020 Kwon et al. 2020 Wang et al. 2020 Gao and Zhang 2021
Gao et al. 2023) Liu et al. 2023] 2024b] 2025e 2026), they typically focus on heuristic uncertainty estimates, domain-specific solutions,
post-hoe calibration. Monte Carlo dropout (Zhao et al. 2024), entropy-based reweighting (Su et al. 2025) Liu et al.] (025d)), or perturbation of the distil- lation loss Zhang et (2024), tackle uncertainty by modulating loss terms via heuristics or series approximations. However, these approaches remain confined to supervised classification, and the effectiveness may degrade under distribution shifts. Other methods address uncertainty only within
narrow domains, e.g., medical imaging (Edupuganti et al. 2020 Kwon et al. 2020; Wang et al., 2020) or human-robot interaction Gao and Zhang (2021); ;; Gao et al. al. (2023). Techniques such as
conformal prediction (CP) have been used primarily to calibrate model outputs after training (An-
gelopoulos al. 2020 Mossina et al. 2024
Lu al. 2022 Karimi and Samavi 2023).
In contrast, propose the first framework AdaConG that embeds split CP directly into the training loop to adaptively weight guidance across supervised, semi-supervised, and reinforcement learning settings. Simple yet effective, our method serves broadly applicable solution for incorporat- ing uncertainty-
guidance, as illustrated in Fig. I While CP has primarily been applied for post-hoc calibration, its potential to inform real-time training dynamics remains underexplored. CP provides a distribution-fi
aagnos-gnootic approach to constructing prediction sets (Shafer and Vovk 2008 Angelopoulos and Bates 2021), making it suited across diverse learning systems. Un-
2

---

Published as a conference paper at ICLR 2026
like heuristic uncertainty estimates such as entropy (Namdari and Li 2019) maximum softmax probability (MSP) PPaaree et al., 2021) which rely on the softmax outputs that are often overcon- fident and poorly calibrated, CP provides more ngorous uncertainty estimates (Shafer and Vovk
2008 Angelopoulos and Bates 2021), even when the underlying distribution changes (Zhou et al,
2025
Gibbs and Candès 2021).
We validate our approach through extensive experiments across multiple tasks, including knowledge distillation, semi-supervised image classification, gridworld navigation, and autonomous driving, demonstrating improvements in performance and robustness compared to conventional methods. Our results underscore the critical importance of adaptive uncertainty weighting scenarios where guidance signals may be imperfect, providing solution toward more reliable machine learning systems. Overall, the key contributions of our work are as follows:
We propose AdaConG, an approach that adaptively modulates the influence of guidance signals based on their uncertainty, ensuring effective learning without over-relying on unreliable guidance. AdaConG is broadly applicable across diverse learning systems including supervised, semi- supervised, and imitation-guidees reinforcement learning.
AdaConG can extract useful insights even when guidance underperforms, unlike conventional methods that assume guidance is always trustworthy. In gridworld navigation, it enables faster convergence and achieves over 6x higher rewards than the strongest baseline.
2 RELATED WORK
Learning with Guidance. Learning with guidance has been common and effective strategy across various machine learning systems. supervised learning, annotated datasets provide explicit guidance for model training, and many works leverage pretrained models to further boost perfor- mance. For instance, |inton (2015); Jiin et al. (2023): [un et al. (2024) focused on transferring soft probabilities from teacher models" logits to guide student models, while Romero et al. (2014);
Zagoruyko and Komodakis (2016); Passalis and Tefas (2018); Kim et al. (2018) emphasized trans- ferring intermediate features. Cross-modal guidance has also been explored: [Wang et al. (2023) proposed a prototype-base based distillation method for medical image segmentation, where a multi- modal teacher guides single-modal student: [hhnn al. (202)) introduced the Auxiliary Modality Learning (AML) framework, enabling a teacher model with access to multiple modalities to transfer knowledge student operating with fewer modalities test time; and Liu et al. (2025b) extended this idea to multi-agent settings. In semi-supervised learning (Sohn et al., 2020) Zhang et al. [02TT) pseudo-labels generated from unlabeled data provide implicit guidance to bootstrap learning with limited labeled data. In reinforcement learning, pretrained imitation learning (IL) (Bhaskar et al., 2024a Liu et al. 2024a 2025a) policies derived from expert demonstrations have been used to guide RL agents and improve sample efficiency (Hu et al., 2023 Bhaskar et al. (024b)).
However, key limitation of most existing methods is their reliance on static guidance, which as- sumes that guidance signals are always reliable. This assumption often breaks down when guid- ance contains uncertainty, due to domain shifts in supervised learning, limited labeled data in semi-supervised learning, or generalization constraints of IL policies in reinforcement learning. In contrast, AdaConG introduces a principled approach that dynamically modulates the influence of guidance signals based on their associated uncertainty, offering simple yet effective, and broadly applicable solution for incorporating uncertainty-awan guidance.
Conformal Prediction. Conformal prediction (CP) (Angelopoulos al. 2020 Angelopoulos and Mossina et al. 2024 Karimi and Samavi 20233 Tibshirani et al. 2019] [Shafer and Vovk et al. 2020) is parametric, distribution-free and model -agnostcc framework designed to provide reliable prediction sets. In machine learning systems, CP has primarily been utilized for post-hoe uncertainty calibration. For instance, (Angelopoulos et al. (2020) introduced an algorithm that adapts any image classifier to output predictive sets containing the true label with user-specing specified probability. [Mossina et al. (2024) proposed a computationally lightweight approach to quantify predictive uncertainty in semantic image segmentation using CP. Similarly, Lu et al. (2022) applied CP to deep learning models for grading the severity of spinal stenosis in lumbar spine MRI, while Karimi and Samavi (0023) leveraged CP to measure uncertainty in deep learning models.
Bates
2021
Vovk 2008
Despite recent advancements, the application of CP to inform real-time training dynamics remains underexplored. In this work, extend split CP to learning with guidance under uncertainty, using it
3

---

Published as a conference paper at ICLR 2026
module for adaptive weighting. By modulating the uncertainty of the guidance signal, enable the model to reduce dependence on potentially misleading guidance and encourages the model to discover patterns that may be overlooked when strictly following uncertain guidance.
APPROACH
Preliminaries. In our framework, we leverage split conformal prediction (CP) to conformalize a guidance signal and quantify its uncertainty. CP is distribution-free method that provides predic- tion sets with guaranteed coverage levels, regardless of the underlying model or data distribution Angelopoulos and Bates 2021 Shafer and
Split CP uses a nonconformity score s' to measure how unusual a prediction for a new test in- put, based on a calibration set Deat, a held-out dataset used to compute the empirical distribution of nonconformity scores. The score 8' can defined in various ways. For instance, in regres- sion, it is often the absolute residual s' = gg ((z)l, where is the ground truth and ((z) is the model's prediction for an input ō E Daal- In classification, a common choice is the confidence score s' 1 Py(F), where Pz(#) is the model's estimated probability for the true class ÿ. Additional examples can be found in (Angelopoulos and Bates) [022] I Shafer and Vovk 2008). Given a cali- bration set, we compute the quantile a of the nonconformity scores with a as an allowable error rate. The quantile is denoted as 91-a = Quantile ($1 . , S ). representing a threshold below which 1 of the data falls. This threshold is then used to construct prediction sets. For test input T the prediction set is constructed as C(rree) = {y- s' dFriest: y) S (1-a)- Under the assumption of exchangeability, the coverage guarantee holds that the probability of the true label yhest falling within C ((Test) satisfies P(tes E ((tes)) 2 1 - a (Angelopoulos and Bates 2021).
Adaptive Conformal Guidance. AdaConG is a general framework, as illustrated in Fig. D We show how use it in supervised, semi-supervised, and amitation-guicee reinforcement learning settings. The core idea is to learn adaptive weights based on the uncertainty of the guidance signal, enabling dynamic modulation of its influence during training.
SUPERVISED LEARNING. We consider supervised learning problem in which a pretrained model guides the training of a target model under potential domain shift. Formally, let the source domain dataset be denoted as D., and the (shifted) target domain dataset as D.. We represent the pretrained model on D. as fp X + y, and the target model under training the input space and Y is the output space. Our goal is to leverage fp to bootstrap the learning of fi that it outperforms both supervised training from scratch and standard knowledge distillation under domain shift. To do so, we introduce an adaptive weighting mechanism based on split CP to modulate the guidance of the pretrained model. This is particularly important when Dj differs from D., making (2) uncertain for input & E 'D.
ft X + V. where X' is
Given the target domain dataset D,, we split it into three subsets: the training set Di used train the target model f;; the calibration set Deal, used to transform any heuristic measure of uncertainty from the pretrained model fp into rigorous one; and the testing set Diest for validate the target model performance. This setup ensures that the calibration set is representative of the inputs on which the guidance will be applied. We conformalize the pretrained model fp following the approach as described in S To quantify the guidance uncertainty, we leverage the size of the prediction set C(x)) for an input æ. Specifically, we define the guidance uncertainty as
u(x)= = ((((())))
n-1 for a K-class problem). The where g is mapping ensuring u(x) E [0. 1] (e.g., g(n) = K-I adaptive weight is computed as
w(x) = h())=((u(x))) h((x)))
where h is monotonically decreasing function (e.g., exponential decay h(u) (ss((Ku) with temperature & > 0) such that high uncertainty results in a lower weight. Then we define the loss function of training the target model as C An + w(x) Aguidee_g where L. is the task loss (e.g., cross entropy loss), Eg is the guidance loss (e.g., KL divergence between target model and pretrained model logits), Aunk and Aguide are the coefficients. Essentially, the adaptive weighting mechanism of AdaConG allows the model to balance between relying on the pretrained guidance and self-exploration.
4

---

Published as a conference paper at ICLR 2026
LEARNING. In semi-supervised learning (SSL), our goal is to leverage lim- ited set of labeled data D) {(T,, ) along with a large set of unlabeled data D., { J For each unlabeled sample x E Du. the model f produces a prediction 1 = ( using a weakly augmented view Tweak- The pseudo-label ÿ is obtained by thresholding the model's output on this weakly augmented input. The same model is then trained to predict ÿ from a strongly augmented version Tstrong of the same input.
Along with obtaining pseudo-labels, we introduce an adaptive weighting mechanism grounded in split CP to modulate the influence of each pseudo-label during training. We construct a calibration set Deal by taking the labeled data and applying the same weak augmentation used for the unlabeled data. The CP procedure for generating a prediction set C(x) for an unlabeled sample r follows the
approach detailed in Section 3 The adaptive weight wx(z) is defined similarly as in Eq. 2 Then
the unsupervised loss is defined as Lu = P.. ExED, w(x) ([(rro)) ū), where ((-:)) denotes
the cross-entropy loss commonly used in SSL,, which enforces consistency regularization between the strongly augmented prediction and the pseudo-label. This loss adaptively weighted by the
confidence of the pseudo-label w(x)). The supervised loss over the labeled set is given by another cross-entropy loss L. = [D]] Σ (x.))ED, {(f(z), v)- The final objective function, which balances the contributions from both supervised and unsupervised components, is defined as L L, + XuCus with X, controlling the relative weight of the unsupervised loss.
IITATION-GUIDER REINFORCEMENT LEARNING. Consider a Markov Decision Process de- fined by the tuple A, R),,, where S is the state space, AA is the action space, P is the transition dynamics, R is the reward function, and y is the discount factor. We focus on off-policy RL methods due their higher sample efficiency. We focus on cases where there is an imitation policy learned from expert demonstrations to guide the reinforcement learning.
To quantify uncertainties of the II and RL policy, log π [a]s). For the static imitation policy TI we pre-collect a calibration set Deal. {(s a. ) by rolling out गj in the target environment. Then we compute a constant quantile Φ for the IL pol-
use the nonconformity score s(8, a)
/i=1
icy. For the RL policy TR
(!) we leverage adaptive CP (Zhou et al. 2025 Gibbs and Candès 2021)
maintaining dynamic calibration set (()) via sliding window of size N, which we initialize as ((0) D 1- At each subsequent training step i, we add new batch of m state-action pairs (t) from rollouts of `R and discard the oldest. Then we update the RL quantile af( using expo-
nential moving average (EMA): (()) + (1 -p) (t-(t-1)
+ pāk where fft) is computed from the current window's 's scores and p smoothing factor. We warm-start the RL quantile by initializing
it with the quantile of the imitation policy, i.e., (0) = â- Finally, the II. and RI. policy uncer- tainties are defined (s) (s)) and (s(s) (s(CR(s))), using the static quantile & for my and the adaptive quantile OR. for TR where y is a mapping, e.g., the identity function. The loss for training the RL. policy defined
((4)
L L, w(s)) f.g. where L, is the task loss (e.g., E log (a(ss) A(s, a)] with A(s, a) as the advantage function), which corresponds to the RL objective. Eg E ( Il TT (-(s)) is the KL divergence between the RL policy and the IL policy, serving as the guidance loss. The weight is defined as: w(s) = h(m1(s), us())), e.g., w(s) exp(- (xpp( "n]")) In RL. the CP set measures policy's self-consistenny,, not action correctness, and we use ws)) as an uncertainty-drivt drrven guidance weight. This reduces reliance on imitation guidance when the IL policy's uncertainty is high. The same adaptive weight w(s) is also
exp(= ((())
used during data collection: at each state, the agent selects at with probability w(s) and on with probability 1 1- wss). This sampling mechanism is the practical realization of the adaptive guidance and complements the KL-based regularization in the objective.
4 EXPERIMENTS
To validate our approach, we conduct experiments across diverse range of tasks, including knowl- edge distillation, semi- supervised image classification, gridworld navigation, and autonomous driv- ing steer prediction.
Knowledge Distillation. We first evaluate framework's 's effectiveness in improving classifica- tion performance over traditional supervised learning by leveraging knowledge distillation from a pretrained teacher to a student model. This evaluation is conducted under domain shift and noise,
5

---

Published as a conference paper at ICLR 2026
where the teacher may underperform. Specifically, we aim to address the following question: When the teacher model is underperformance, can it still provide useful "dark knowledge" to enhance the performance of the student model beyond what is achievable by training from scratch?
EXPERIMENTAL SETUP. We conduct our experiments on the CIFAR-100 dataset (Krizhevsky) et al. 2009) and report the mean and standard deviation over four repeated runs. We introduce do- main shifts to the datasets by adding Gaussian noise of zero mean and standard deviation of 0.05, which may lead to underperformance of the teacher model. We evaluate two settings: (1) Homoge- neous Structure, where the teacher and student share the same architecture type (c.g., ResNet-32x4 and ResNect-844) and (2) Heterogeneous Structure, where the teacher and student use different ar- chitectures (e.g., ResNet-32x4 and ShuffleNet- V1). For further details the models evaluated and the dataset, please refer Appendix [A.2] To quantify the prediction uncertainty of the pretrained teacher model fp. we utilize the RAPS algorithm (Angelopoulos et al. 2020). Given an input image J, we obtain the prediction set C(x) with
0.1 and define the uncertainty as u(x)
[C(x)]-1 -1
(Vovk al. 2016), where K 100 is the total number of classes. The adaptive weight is computed
as w = exp(->a) with r = 10.0, as described in Section 3
Please see Appendix [A.2.3 for an
detailed analysis of the design choices for the hyperparameters.
We follow the same experimental
settings as in previous work (Tian et al. 2019 Sun et al. 2024 for the coefficients Auak and Aguide.
as well as other training details.
BASELINES. We measure Top-1 classification accuracy for range of baselines, including classic distillation methods, KD (Hinton 2015). FitNet (Romero al. 2014), PKT (Passalis and Tefas 2018), FT (Kim et al. 2018), and LS-KD (Sun et 2024), evaluating each both with and without approach AdaConG, alongside uncertainty-awarc adaptations such EA-KD (Su et al. 2025) and PTLLss (Zhang et al, 2024), as well as KD leveraging heuristic confidence estimators including maximum sofumax probability (MSP) (Pearce et al.] 202T Monte Carlo (MC) dropout (Gal and
Ghahramani 2016), and output entropy (Namdari and Li 2019).
Table 1: Top-1 1 accuracy (%) of various knowledge distillation methods on CIFAR-100 under homo- geneous structure where teacher models underperform due to domain shift. A indicates performance gain over the base method. Following the protocol in (Sun et al., 2024), we highlight in orange A greater than 0.15, indicating non-trivial enhancement. We observe up to + +10.89% higher accuracy.
Teacher model
ResNet1 10
ResNec56
ResNer32xx4
VGG13
WRN-40-2
WRN-40-2
Teacher accuracy
58.78
56.23
62.61
61.47
58.76
58.76
Student model
ResNet20
ResNet20
ResNet8
VGG8
WRN-40
WRN- 16-2
Student accuracy (from scratch)
66.5110014
66.51110.14
69.14
67.1810.18
69.03:10.21
70,341:.20
KD (Hinton 2015
57.23110.24
56.27110117
58.9010.31
61.00 61.00:0.25
58.4410.16
59,40:10.33
KD + Adacoon
66.53
66.98:10.25
68.45
67.53
69.31
70.29
9.30
10.71
6.53
10.87
10.89
Fileet Romero al. 2014
60.35
64.98.10.16
69.21
67.1910.39
68.7410024
70.4910.27
FitNet Adacort
67.06-+0.13
66.9140.14
69.49-+018
67,58-40.0
69.114-0.18
71.004-0.3
2.41
1.93
0.28
0.39
0.37
0.51
PKT Passalis and Telas 2018
66.67:10.17
66.54110.26
69.69:10.34
67.00 67.06:10.09
69.12.10.22
70.55:10.26
PKT Adatton
60.55
67.42.0.51
0..27:10.39
68.50
10.03
71.22.0.47
0.88
0.88
0.58
1.44
0.91
0.67
FT Kim et 2018 FT Fadacort A
66.47-40.09
66.05+-0.40
69.55
67,28+00 17
68.05++0.42
69.86-+-0.4
66.58++0.12
66.55+00.9 33
69.85++0.33
67.54+0.19 19
69.03-+0.3
70.9140.30
0.11
0.50
0.30
0.26
0.98
1.05
LS KD (Sun et al. 2024
63.38 1.0.29
62.66.10.220
63.49 10.06
66.66 1..10.0..10
1..10
66.58.10.17
L.S-KD Adacons A
67.174-0.00
67.28-40.18
70.33-+0.14
68.99-0022
69.80-+0.18
71.48-4028
3.79
4.62
6.84
2.33
4,08
4,90
Entropy Namdari
2019
60.24110.23
60.29:10.19
62.3740.23
64.37:0.29
62.47:10.21
63.1740..3
MC dropout (Gal and Ghaliamam 2016
63.59.10.13
63.42:10.27
67.9410.05
67.90
69.64.1.11
70.23-10.24
EA-KD
Su al 2025
66.30:10.20 20
66,5240.30 30
69.041:0115
67.05=0.07
69.374:023
70.3340.20
MSP (Parce el 2021
60.71
60.62:10.16
62.77110.36
64.56:10.23
62.80-10.22
63.70.10.10
PTL Zhang al 2024
15.96-1-0.18
66.28-10.16
6..27-40.02
66.524-019
6..59100.21
6..35-10.1
EXPERIMENTAL RESULTS. We present the results in Table Following the protocol outlined in
Sun et al.) 2024), we highlight in orange the improvements greater than 0.15, indicating non-trivial enhancements. Traditional knowledge distillation methods typically assume that the teacher model is reliable and superior to the student. However, shown in Table T when the teacher performs worse than the student under domain shift, following the teacher will result in students that perform worse than those trained from scratch. In contrast, integrating AdaConG not only improves model

---

Published as a conference paper at ICLR 2026
performance by up to 10.89% but also enables the student surpass that from scratch. These find- ings highlight AdaConG's effectiveness in enhancing supervised learning, leveraging a pretrained model as guidance, even when the guidance is unreliable. By selectively leveraging useful "dark knowledge" while avoiding misleading supervision, AdaConG ensures robust model learning.
We also compare against other uncertainty-awaat KD methods (Su et al. 2025 Zhang al. 2024
Pearce et al., 2021: Namdari and Li] 2019| Gal and Ghahramani, 2016). Results show that KD combined with AdaConG outperforms these baselines. This is because existing methods primarily rely on heuristic uncertainty estimates, which can be overconfident and poorly calibrated, particu- larly under domain shifts. In contrast, AdaConG can provide more adaptive and reliable guidance. Moreover, methods such as MC dropout require multiple forward passes, which is computationally expensive. Please refer to Appendix AA.2.1 AdaConG and MC dropout.
(opendix(AA...10 for comparison of the computation overhead between
ABLATION STUDIES. We evaluate the performance of heterogeneous teacher-student framework and present the results in Table 5 in Appendix [A.222] The results show that, for all knowledge distillation methods, performance improves when combined with AdaConG, further validating the effectiveness of our approach across different teacher-student structures.
We also explore another hard version of the weighting function: w = 1 if = 0. w = 0 > Vook et al., 2016), which is similarly effective, please see the results in Appendix A.2.4 The rationale for the hard weighting function follows (Vovk et al.) 2016). which aims to ensure that prediction sets are as close as possible to single-clement sets, making them more informative.
Semi-Supervised Image Classification. We evaluate the effectiveness of our framework in im- proving the performance of semi sumi-supervised learning methods, regarding classification tasks.
EXPERIMENTAL SETUP. We conduct experiments on several SSL image classification bench- marks, including CIFAR-10/10 (Krizhevsky et al. 2009) and STL-10 (Coates al.] 201T). For all experiments, we report the mean and standard deviation over four repeated runs We measure the Top-1 accuracy for range of baselines, including UDA (Xie et al. 2020p, Fix (Sohn) iet al. (2000) and FlexMatch (Zhang et al.) 2021). evaluating each both with and without AdaConG. For an unlabeled image x, we construct the prediction set C(x) for pseudo-labeling using confi- dence score as described in Section 3 with a 0.05. The associated uncertainty is defined as [(()] (Vovk et al. 2016). where K is the total number of classes. The adaptive weight is given by exp(-ru) with y 8.0. Please refer to Appendix A.3.2 for a sensitivity analysis of the hyperparameter choices and Appendix A.3.I for the training details.
u(xx K
Table 2: Top-1 accuracy (%) of various baselines with and without AdaConG several semi- supervised image classification benchmarks, using cross-entropy as the guidance loss. A shows mean performance gain w.r.t. conventional methods without AdaConG, upto +5.98 % in accuracy.
Appeoadi
CIFAR-10
4000 Bools
CIFAR-100
labels
1000016b26
STL-10
2301abals
UDD Nieetal 2000
57,711858
918610.75
15.95
37.510.1
66.9110..66
53.810088
759110000
5.33
ULM Aalebon
61.28466.35
92 69
98.1720.10
28.0-00.54
38.54+1130
67.5020.35
54.70=01511
77.454012
36.3120.10
A
3.58
3.25
1.31
3007
0.9
0.56
0.82
0.54
11.72
PiaMacc Sohn et 2020
66.1814.57
89:9111004
91.910055
40.3610883
61,441000
67.0110.5
58.011 28
758910.06
58.4110.0
MisMach- moscens
70.16.13344
92.23.10.22
93.9710.11
41,98.0.55
63.4111466
70.0010099
62 62.70.0844
808510039
89:35_00.10
4
5.98
2.26
2.66
1.62
2.27
2.43
4.67
1.94
11.11
Maesaaich Zhang al 2221
13
90:22:0.49
92.11:0.47
51 11.25:1.33
63.59
71 31:6300488
62.55::222
62.33 20
89
09.94:0.200
FexManch
76.881045
81.8910100
94.2820.10
35.03.1.20
09.2210.52
12.7110028
15.9511355
839611015 1.31
92.27-00100
3.74
2.27
4.38
5.63
3.43
2.33
As shown, integrating AdaConG consistently improves performance across all baselines. This highlights the effective- ness of AdaConG in supi-supe learning. By adaptively reweighting the influence of pseudo- labels, AdaConG reduces reliance on noisy supervision, mitigating error propagation and leading to improved overall performance.
EXPERIMENTAL RESULTS. We present the results in Table 2
As ablation studies, in addition to the commonly used cross-entropy loss for guidance in SSL, we investigate the mean-squared error (MSE) loss as an alternative. Specifically, we apply the MSE loss between the logits of a strongly augmented input Zstonng and its weakly augmented counterpart Tweak As shown in Table 3 our method remains effective under this alternative formulation and continues to yield performance improvements.
7

---

Published as a conference paper at ICLR 2026
Gridworld Navigation. We investigate the use of reinforeement learning for solving grid- world navigation tasks, leveraging pretrained imitation policy as prior guidance. We demon- strate how AdaConG improves policy learn- ing efficiency and robustness in challenging and unseen environments when the imitation policy is limited due to generalization constraints.
Table 3: Top-1 accuracy (%) on CIFAR-100
for semi-supervised image classification. We compare multiple baselines with and without AdaConG using MSE as the guidance loss. A indicates the average improvement over each cor- responding baseline.
Approsch
400 labels
2500 labels
10000 labele
UDA Xie at. 2020
6.36 1: 0.47
$1.88 0:058
57.50 1: 0.31
32,00 0.22
69.79 0.11
EXPERIMENTAL SETUP. We evaluate AdaConG across three gridworld environment Boisseet et al. 2024) scenarios, as illustrated in Fig. 2 For the environment details, please refer to Appendix [A.4 We collect expert demonstration for the Lava and Door environments to train IL policies via behavior cloning. After training the IL policy Ti, we utilize it to guide the training of the RL policy TR- The Lava 2 environment represents a shifted variant of Lava 1, featuring modified environmental configurations. Importantly, we do not collect expert demonstration for Lava 2, and no IL policy is trained on this environment. For a given state 8, the guidance weight is defined as: w((s)
1,40
Mashhtch mal
8:56
+
60.05 0.41
35.35 1.00
01.74 0.20
1.26
2:22
FloxMatch (Zang al. 2011
10.04
36.10
0.95
61.36
0.07
11.07
0.55
38.87
1. 0.82
62.80 1. 0.21
1.03
2:77
1.44
where "1 and uR are the prediction uncertainties of the IL and RL policies described in Section 3 And sample the action a E {01, [0I, } to take according to the distribution induced by this guidance weight. Furthermore, we explore another hard variant of AdaConG, instead of defining w(s) probability distribution informed by the relative uncertainties of the IL and RL policies, we take argmax to compare IL and RL prediction uncertainties: w(s) when (s(s) us(s), otherwise w(s) = O. Based on ws)), we dynamically decide which action to take: a = at if w(s) = 1, otherwise a ag.
expl exp(- my(s)
BASELINES. We compare AdaConG and Hard AdaConG against several baselines, including (1)
Soft Actor Critic (SAC) (Haarnoja et al. 2018). a purely RL approach, (2) IBRL (Hu et al. 2023).
which leverages pretrained imitation learning (IL. model to bootstrap RL. During the training process, IBRL queries the target Q-network and selects actions by comparing the Q-values of two candidate actions and taking the action with the higher Q-value, and (3) Soft IBRL (Hu al.) 2023). a probabilistic variant of IBRL. Instead of selecting the action via a hard argmax, Soft IBRL samples the action according distribution proportional the Q-values.
EXPERIMENTAL RESULTS. We run all experiments across ten random seeds and present the re- sults in Fig. 2 First, we compare the learning curves of AdaConG and Hard AdaConG against other baselines across three environments: Lava 1, Lava 2, and Door. Both AdaConG and Hard AdaConG demonstrate similar performance, converging faster and achieving higher rewards than all other baselines. Before the agent reaches the goal, the reward function is defined as the negative Manhattan distance between the agent's 's current location and the goal, normalized by the maximum step limit of 100. Consequently, the accumulated episode rewards initially decrease as the agent explores the environment and accrues negative rewards but increase as it learns. The rewards of AdaConG and Hard AdaConG are consistently higher than those of other baselines while con- verging faster. This can be attributed to the efficiency of AdaConG, as it compares the prediction uncertainties of teacher and student models instead of relying on Q-values. Methods like IBRL and Soft IBRL, which depend on Q-values to decide between IL or RL actions, may make suboptimal decisions initially due to poorly trained Q-networks. For instance, even if an IL action is superior, its Qavalue might be lower than that of an RL action.
In the shifted environment Lava 2, the overall rewards of the IL policy are lower due to gener- alization constraints. IBRL and Soft IBRL rewards eventually converge close to the IL policy's s performance, as these methods are not uncertainty-aware. Blindly relying on a IL policy underper- forming due to environment shifts can lead to suboptimal performance. In contrast, AdaConG and Hard AdaConG consider the IL policy's prediction uncertainty. enabling faster convergence and achieving rewards over 6x higher than the best- pest-performing baselines after convergence. When the IL policy's 's predictions are confident, the RL agent relies more on them; otherwise, the RL agent explores independently. Even though the II. policy's 's overall reward is not high, it still provides use-
8

---

Published as a conference paper at ICLR 2026
-10
-15
-20
Staps
-20g
UX
-16
486
-10
286
156
2.5
(a) Lava
(b) I Lava
(c) Door
(d) Prediction Uncertainty
Figure 2: (a-c) Learning Curves. We compare AdaConG and Hard AdaConG with other baselines,
including SAC, IBRL, and Soft IBRL, and present their learning curves across three environments:
(a) Lava 1, (b) Lava 2, and (c) Door. AdaConG and Hard AdaConG perform similarly, converg- ing faster and achieving higher rewards than other baselines in all environments. (d) Prediction Uncertainty. We show the average prediction uncertainties of AdaConG and other baselines, tak- ing the Lava environment as the example. Over time, the uncertainty of AdaConG shrinks and approach that of the IL policy, demonstrating the development of a well-learned RL policy. In ad- dition, ConG maintains lower prediction uncertainty than other baselines, indicating stronger robustness to uncertainty.
ful knowledge. This allows the RL agent to learn from the IL policy and eventually achieve higher rewards than the II. policy.
We also show the average policy prediction uncertainties of AdaConG and Hard AdaConG, for Lava environment, in Fig. 2d Over time, their prediction uncertainties decrease and approach that of the IL policy, demonstrating the progression toward a well-learned RL policy.
Autonomous Driving. This task involves learning stecring prediction policy in autonomous driv- ing for an RGB-only input model, guided by a pretrained multi-modal teacher to transfer knowledge to the student model. We evaluate the effectiveness of different knowledge distillation methods un- der domain shifts and sensor noise, comparing performance with and without the use of AdaConG.
EXPERIMENTAL SETUP. We adopt mean ac- curacy (mAce) as the evaluation metric for the task of steer prediction, following prior works (Shen et al.) 2021] 2023 2024). We use the real-world driving dataset SullyChen (Chen) 2018) for evaluation, which includes diverse driving scenarios with various road types and conditions. We use Nvidia PilotNet (Bojarski 2016) as the backbone for both the teacher and student models. The teacher model is multi- modal network that takes RGB images, depth, and edge maps as input, while the student model is unimodal, relying solely on RGB images. For more details of the setup, please see Appendix 1 We first train the teacher model f, offline. Then we use it to guide the student model fa learning, while the RGB images for Sn training have domain shifts by Gaussian noise corruption compared to the ones used for fp training. Detailed information about domain shifts and model training can be found in Appendices A.5.2 and A.5.4. respectively. We evaluate multiple knowledge distillation methods as baselines, comparing their performance with and without the integration of AdaConG, including KD (Hinton 2015), FitNet (Romero et al. 2014), PKT (Passalis and Tefas 2018), and FT (im et al. 2018).
Table 4: Mean accuracy (%) of steer prediction of different knowledge transfer methods with and without AdaConG under domain shifts.
Approuch
Mean Accuracy (%)
Willhout
ndacon
KD FilNer PKT
76.
72.4
76.2
72.8
73.9
3.1
FT
73.1
76.4
3.3
Texcher DeCD--Deph-Dlgo Acc.
75.5
Studemt (RGBB) Ace. from scratch
71.8
EXPERIMENTAL RESULTS. We report the mean accuracy of steer prediction for various KD methods under domain shifts with and without AdaConG Table 4 As observed, incorporating AdaConG consistently enhances the accuracy. This demonstrates the effectiveness of AdaConG in improving model performance, as its adaptive guidance mechanism strategically prevents over- reliance on uncertain teacher predictions, facilitating more reliable and robust target model learning.
5 CONCLUSIONS
We propose AdaConG, an approach for learning with guidance under uncertainty. AdaConG inte- grates split conformal prediction to adaptively modulate the influence of guidance signals based on their associated uncertainty. By selectively leveraging reliable signals and filtering out misleading supervision, AdaConG enables effective learning even in the presence of noise. Unlike conven-

---

Published as a conference paper at ICLR 2026
tional methods that assumee guidance is always trustworthy, AdaConG still extract useful "dark knowledge" under uncertainty. The framework simple yet effective, and broadly applicable to a wide range of tasks. We validate AdaConG across diverse settings and tasks including knowledge distillation, semi-supervised image classification, gridworld navigation, and autonomous driving, demonstrating improved performance and robustness. For discussion future work, please Appendix A.6
6
REPRODUCIBILITY STATEMENT
To ensure reproducibility, we provide detailed descriptions of all training setups in the experiment
Section 4 with additional specifications in Appendix AA.2 Appendix A.3.T Appendix A.4 and
Appendix A.5.1
All datasets used are publicly available.
ACKNOWLEDGEMENTS
This work is supported in part by Dr. Barry Mersky and Capital One E-Nnovte Endowed Professor- ships, University Maryland Distinguished University Professorship, and ARL-UMD ArtIAMAS Cooperative Agreement.
REFERENCES
Rishabh Agarwal, Max Schwarzer, Pablo Samuel Castro, Aaron C Courville, and Mare Bellemare. Reincarnating reinforcement learning: Reusing prior computation to accelerate progress. Ad- vances in neural information processing systems, 01128955-28971, 2022.
Anastasios Angelopoulos, Stephen Bates, Jitendra Malik, and Michael Jordan. Uncertainty sets for image classifiers using conformal prediction. arXiv preprint arXiv:2009.1411 14193, 2020.
Anastasios N Angelopoulos and Stephen Bates. A gentle introduction conformal prediction and distribution-free uncertainty quantification. arXiv preprint arXiv:2 20221
Amisha Bhaskar, Rui Liu, Vishnu D Sharma, Guangyao Shi, and Pratap Tokekar. Lava: Long- horizon visual action based food acquisition. In 2024 JEEE/RSJ International Conference Intelligent Robots and Systems (IROS), pages 8929-8935. IEEE, 2024a.
Amisha Bhaskar, Zahiruddin Mahammad, Sachin R Jadhav, and Pratap Tokekar. Planrl: A motion planning and imitation learning framework to bootstrap reinforcement learning. arXiv preprint arXiv:2408. 04054, 2024b.
Mariusz Bojarski. End end learning for self-driving cars. arXiv preprint 1rXiv:1604.07316. 2016.
Michele Caprio, Souradeep Dutta, Kuk Jin Jang, Vivian Lin, Radoslav Ivanov, Oleg Sokolsky, and Insup Lee, Credal bayesian deep learning. Transactions on Machine Learning Research, 2024.
ISSN 2835-8856. URL http::tt:///// httptppss///ppeeeveeeeee net forum 4NHF 9AC5ui
Michele Caprio, David Stutz, Shuo Li, and Arnaud Doucet. Conformalized credal regions for classi- fication with ambiguous ground truth. Transactions Machine Learning Research, 2025. ISSN 2835-8856. URL
Sully Chen. A collection of labeled car driving datasets. Collection of labeled car driving datasets, 2018.
Maxime Chevalier-Boisverr Bolun Dai, Mark Towers, Rodrigo Perez- Vicente, Lucas Willems, Salem Lahlou, Suman Pal. Pablo Samuel Castro, and Jordan Terry. Minigrid & miniworld: Mod- ular & customizable reinforcement learning environments for goal-oriented tasks. Advances in Neural Information Processing Systems, 36, 2024.
Adam Coates, Andrew Ng, and Honglak Lee. An analysis of single-layer networks in unsupervised feature learning. In Proceedings of the fourteenth international conference on artificial intelli- gence and statistics, pages 215-223. JMLR Workshop and Conference Proceedings, 2011.
10

---

Published as a conference paper at ICLR 2026
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszko- reit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale, 2020.
Souradeep Dutta, Michele Caprio, Vivian Lin, Matthew Cleaveland, Kuk Jin Jang, Ivan Ruchkin, Oleg Sokolsky, and Insup Lee. Distributionally robust statistical verification with imprecise neural networks, 2025. URL https:t:
org/ abs/ 2308. 14815
Vineet Edupuganti, Morteza Mardani, Shreyas Vasanawala, and John Pauly. Uncertainty quantifica- tion in deep mri reconstruction. IEEE Transactions on Medical Imaging, 40(1):239-22) 250, 2020.
Yarin Gal and Zoubin Ghahramani. Dropout as bayesian approximation: Representing model uncertainty in deep learning. In international conference on machine learning, pages 1050-1059. PMLR, 2016.
Peng Gao and Hao Zhang. Bayesian deep graph matching for correspondence identification in collaborative perception. In Robotics Science and Systems (RSS), 2021.
Peng Gao, Qingzhao Zhu, and Hao Zhang. Uncertainty-aware correspondence identification for collaborative perception. Autonomous Robots, 47(5):635-645 2023.
Isaac Gibbs and Emmanuel Candès. Adaptive conformal inference under distribution shift, 2021.
URL httts:t//axxiii org/ abss/106 00170
Yuxian Gu, Li Dong. Furu Wei, and Minlie Huang. Knowledge distillation of large language models.
arXiv preprint arXiv:2306. 23000433330.. 2023.
Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with stochastic actor. In International confer- ence on machine learming, pages 1861-1870. PMLR, 2018.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016.
Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common ruptions and perturbations. Proceedings of the International Conference on Learning Represen- tations, 2019.
Geoffrey Hinton. Distilling the knowledge in neural network. arXiv preprint WrXiv:1503.0255 2015.
Hengyuan Hu, Suvir Mirchandani, and Dorsa Sadigh. Imitation bootstrapped reinforcement learn- ing. arXiv preprint arXIv:2311.02298, 2023.
Jie Hu, Li Shen, and Gang Sun. Squeeze-and-exciaatio networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018.
Fushuo Huo, Wenchao Xu, Jingcai Guo, Haozhao Wang. and Song Guo. C2kd: Bridging the modal- ity gap for cross cross-modal knowledge distillation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages (6006-16015, 2024.
Ying Jin, Jiaqi Wang, and Dahua Lin. Multi-level logit distillation. In Proceedings of the IEEE/CVF 2023.
Conference Computer Vision and Pattern Recognition, pages
Patrick Kage, Jay Rothenberger, Pavlos Andreadis, and Dimitrios Diochnos. A review of pseudo- labeling for computer vision. arXiv preprint vrXiv:2408.072211 2024.
Hamed Karimi and Reza Samavi. Quantifying deep learning model uncertainty in conformal pre- diction. In Proceedings of the AAAI Symposium Series, volume 1, pages 142-148, 2023.
Jangho Kim, ScongUk Park, and Nojun Kwak. Paraphrasing complex network: Network compres- sion via factor transfer. Advances in neural information processing systems, 31, 2018.

---

Published as a conference paper at ICLR 2026
Diederik P Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6988. 2014.
Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
Yongchan Kwon, Joong-Ho Won, Beom Joon Kim, and Myunghee Cho Paik. Uncertainty quan- tification using bayesian neural networks in classification: Application to biomedical image seg- mentation. Computational Statistics & Data Analysis, 142:1068 16, 2020.
Yann Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7,7):3, 2015.
Rui Liu, Guangyao Shi, and Pratap Tokekar. Data-driven distributionally robust optimal control with state-dependent noise. In 2023 JEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 9986-9991. IEEE, 2023.
Rui Liu, Amisha Bhaskar, and Pratap Tokekar. Adaptive visual imitation learning for robotic assisted feeding across varied bowl configurations and food types. arXiv preprint arXiv:2403. 12891, 2024a.
Rui Liu, Anish Gupta, Erfaun Noorani, and Pratap Tokekar. Towards efficient risk-sensitive policy gradient: An iteration complexity analysis. arXiv preprint wrXXi:2403.08955, 2024b.
Rui Liu, Zahiruddin Mahammad, Amisha Bhaskar, and Pratap Tokekar. Imrl: Integrating visual, physical, temporal, and geometric representations for enhanced food acquisition. In 2025 IEEE International Conference Robotics and Automation (ICRA), pages 741-747. IEEE, 2025a.
Rui Liu, Yu Shen, Peng Gao, Pratap Tokekar, and Ming Lin. Caml: Collaborative auxiliary modality learning for multi-agent systems. arXiv preprint 2xX.:2250.1/822 2025b.
Rui Liu, Zikang Wang, Peng Gao, Yu Shen, Pratap Tokekar, and Ming Lin. Mmed: Multi-modal col- laborative decision-making for connected autonomy with knowledge distillation. arXiv preprint arXiv:2509. 18198, 2025c.
Rui Liu, Dian Yu, Lei Ke, Haolin Liu, Yujun Zhou, Zhenwen Liang. Haitao Mi, Pratap Tokekar, and Dong Yu. Stable and efficient single-rollout rl for multimodal reasoning. arXiv preprint arXiv:2512.1822 18215, 2025d.
Rui Liu, Dian Yu, Tong Zheng, Runpeng Dai, Zongxia Li, Wenhao Yu, Zhenwen Liang, Linfeng Song, Haitao Mi, Pratap Tokekar, et al. Vogue: Guiding exploration with visual uncertainty improves multimodal reasoning. arXiv preprint arXiv:2510.01444 2025e.
Rui Liu, Pratap Tokekar, and Ming Lin. Active asymmetric multi-agent multimodal learning under uncertainty, arXiv preprint arXiv:2602.04766 2026.
Charles Lu, Anastasios N Angelopoulos, and Stuart Pomerantz. Improving trustworthiness of ai disease severity rating in medical imaging with ordinal conformal prediction sets. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 545-554. Springer, 2022.
Pengyuan Lu, Michele Caprio, Eric Eaton, and Insup Lee. lbel: Zero-shot model generation under stability-plasticee trade-offs, 2024. URL https: /ttp:::://rxiiii http:///xxvvv//o/e abs http:///r/rbb//.....33.. 22.5
Ningning Ma, Xiangyu Zhang, Hai-Tar Zheng, and Jian Sun. Shufflenet v2: Practical guidelines for efficient enn architecture design. Proceedings of the European conference on computer vision (ECCV), pages 1 116-131, 2018.
Luca Mossina, Joseba Dalmau, and Léo Andéol. Conformal semantic image segmentation: Post- hoc guantification of predictive uncertainty. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3574-3584, 2024.
Alireza Namdari and Zhaojun Li. A review entropy measures for uncertainty quantification of stochastic processes. Advances in Mechanical Engineering, 11(6):168781 4019857350, 2019.
12

---

Published as a conference paper at ICLR 2026
Nikolaos Passalis and Anastasios Tefas. Learning deep representations with probabilistic knowledge transfer. In Proceedings of the European Conference on Computer Vision (ECCV), pages 268- 284, 2018.
Tim Pearce, Alexandra Brintrup, and Jun Zhu. Understanding softmax confidence and uncertainty. arXiv preprint #rXiv:210600497: 2021.
René Ranftl, Alexey Bochkovskiy, and Vladlen Koltun. Vision transformers for dense prediction. In Proceedings of the IEEE/CVF international conference on computer vision, pages 12179-12188, 2021.
Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio. Fitnets: Hints for thin deep nets. arXiv preprint arXiv:1412.6550, 2014.
Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh Chen. Mo- bilenetv2: Inverted residuals and linear bottlenecks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4510-4520, 2018.
Sebastian Scherer. Robin Schön, and Rainer Lienhart. Pseudo-label noise suppression techniques for semi-supervised semantic segmentation. arXiv preprint arXiv:2210.10426. 2022.
Glenn Shafer and Vladimir Vovk. tutorial on conformal prediction. Journal of Machine Learning Research, 9(3), 2008.
Yu Shen, Laura Zheng, Manli Shu, Weizi Li, Tom Goldstein, and Ming Lin. Gradient-free adversar- ial training against image corruption for learning- based steering. Advances in Neural Information Processing Systems, 02222250-222660 2021.
Yu Shen, Xijun Wang. Peng Gao, and Ming Lin. Auxiliary modality learning with generalized curriculum distillation. In International Conference on Machine Learning, pages 31057-31076. PMLR, 2023.
Yu Shen, Laura Zheng, Tianyi Zhou, and C Lin. Task-driven domain-agnostic learning with infor- mation bottleneck for autonomous steering. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 6858-6865. IEEE, 2024.
Karen Simonyan. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556. 2014.
Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raffel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying semi-supervised learning with consistency and confidence. Advances in neural information processing systems, 33:596-608, 2020.
Xavier Soria, Angel Sappa, Patricio Humanante, and Arash Akbarinia. Dense extreme inception network for edge detection. Pattern Recognition, 139:109461, 2023.
Chi-Ping Su, Ching-Hsun Tseng, Bin Pu, Lei Zhao, Zhuangzhuang Chen, and Shin-Jye Lee. Ea- kd: Entropy-based adaptive knowledge distillation, 2025. URL https://arxii.. www./vorg/aaa.. abs/
2311. 13621
Shangquan Sun, Wenqi Ren, Jingzhi Li, Rui Wang, and Xiaochun Cao. Logit standardization in knowledge distillation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15731-15740, 2024.
Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initial- ization and momentum in deep learning. In International conference on machine learning, pages 1139 147. PMLR, 2013.
Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive representation distillation. arXiv preprint arXiv:1900. 10699, 2019.
Ryan Tibshirani, Rina Foygel Barber, Emmanuel Candes, and Aaditya Ramdas. Conformal pre- diction under covariate shift. Advances in neural information processing systems, 32, 2019.
13

---

Published as a conference paper at ICLR 2026
Faraz Torabi, Garrett Warnell, and Peter Stone. Behavioral cloning from observation. arXiv preprint arXiv:180S.01954. 2018.
Vladimir Vovk, Valentina Fedorova, Ilia Nouretdinov, and Alexander Gammerman. Criteria of efficiency for conformal prediction. In Conformal and Probabilistic Prediction with Applications: 5th International Symposium, COPA 2016, Madrid, Spain, April 20-22, 2016, Proceedings 5, pages 23-39. Springer. 2016.
Vladimir Vovk, Ivan Petej. Paolo Toccaceli, Alexander Gammerman, Ernst Ahlberg, and Lars Carls- son. Conformal calibrators. In conformal and probabilistic prediction and applications, pages 84-99, PMLR, 2020.
Shuai Wang, Zipei Yan, Daoan Zhang, Haining Wei, Zhongsen Li, and Rui Li. Prototype knowledge distillation for medical segmentation with missing modality. In ICASSP 2023-2023 IEEE Inter- national Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5, IEEE, 2023.
Yixin Wang. Yao Zhang, Jiang Tian, Cheng Zhong, Zhongchao Shi, Yang Zhang, and Zhiqiang He. Double-unce uncertaitcy weighted method for remi-superviseer learning. In Medical Image Computing and Computer Assisted Intervention-MICCAl 2020: 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Pari / 23, pages 542-551. Springer, 2020.
Kun Xia, Le Wang, Sanping Zhou, Gang Hua, and Wei Tang. Learning from noisy pseudo labels for sumi-supe temporal action localization. Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10160-10169, 2023.
Qizhe Xie, Zihang Dai, Eduard Hovy, Thang Luong, and Quoc Le. Unsupervised data augmentation for consistency training. Advances in neural information processing systems, 1186256-62666 2020.
Zihui Xue, Zhengqi Gao, Sucheng Ren, and Hang Zhao. The modality focusing hypothesis: Towards understanding crossmodal knowledge distillation. arXiv preprint arXiv:2206.0661 000487,2022 2022.
Peihong Yu, Manav Mishra, Alec Koppel, Carl Busart, Priya Narayan, Dinesh Manocha, Amrit Bedi, and Pratap Tokekar. Beyond joint demonstrations: Personalized expert guidance for efficient multi-agent reinforcement learning. arXiv preprint arXiv:2403.089336 2024.
Sergey Zagoruyko. Wide residual networks. arXiv preprint arXiv:1605.07146 2016.
Sergey Zagoruyko and Nikos Komodakis. Paying more attention to attention: Improving the perfor- mance of convolutional neural networks via attention transfer. arXiv preprint arXiv: wrXiv:6612.03928 2016.
Bowen Zhang, Yidong Wang, Wenxin Hou, Hao Wu, Jindong Wang. Manabu Okumura, and Takahiro Shinozaki. Flexmatch: Boosting semi-supervised learning with curriculum pseudo la- beling, Advances in neural information processing systems, 34:18408-18419, 2021.
Rongzhi Zhang, Jiaming Shen, Tianqi Liu, Jialu Liu, Michael Bendersky. Mare Najork, and Chao Zhang. Knowledge distillation with perturbed loss: From vanilla teacher to proxy teacher. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3278-4881 2024.
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. In Proceedings of the IEEE conference computer vision and pattern recognition, pages 6848-6856, 2018.
Rui Zhao, Kui Wang, Yang Xiao, Fei Gao, and Zhenhai Gao. Leveraging monte carlo dropout for uncertainty quantification in real-time object detection of autonomous vehicles. IEEE Access, 2024.
Hao Zhou, Yanze Zhang, and Wenhao Luo. Computationally and sample efficient safe reinforce- ment learning using adaptive conformal prediction, 2025. URL https::/ //tp///avvv/////////a//eaa/aaaa. org/ abs/ 2503 17678
14

---

Published as a conference paper at ICLR 2026
A APPENDIX
A.1 THE USE OF LLMS
We use LLMs to polish writing and refine grammar of the manuscript.
A.2 KNOWLEDGE DISTILLATION
We evaluate two settings: (1) Homogeneous Structure, where both the teacher and student models share the same type of architecture (e.g.. ResNet-32x4 and ResNet-8x4), and (2) Heterogeneous Structure, where the teacher and student models are of different architectures (e.g.. ResNet-32x4 and ShuffleNet-VI
We evaluate a wide range neural network architectures, including ResNet (He et al. 2016), WRN (Zagoruyko 2016). VGG (Simonyan, 2014). ShuffleNet-VI (Zhang et al. V0187V2 Ma et al. 2018), and MobileNet-V2 (Sandler et al. 2018).
A.2.1 DATASET DETAILS
We conduct our experiments on the CIFAR-100 dataset Krizhevsky et al. (2009), ) which consists of 60K images, 50K for training and 10K for testing, across 100 distinct categories. We introduce domain shifts to the dataset for training the target model. We add Gaussian noise with a standard deviation of 0.05 to 40% of the training data of 50K images, where the noisy samples are selected uniformly random across the entire dataset ensure consistent noise distribution. Then we shuffle the dataset and randomly split it into a 90% training set Di and a 10% calibration set Deat, ensuring that both sets drawn from the same underlying distribution. Additionally, the same Gaussian noise is added to 40% of the testing data of 10K images, to form the noisy test set Diest which allows evaluate the performance of the target model.
and
A.2.2 HETEROGENBOUS
STRUCTURE
Table 5: Top-1 accuracy (%) of various knowledge distillation methods with and without AdaConG on CIFAR-100 under heterogeneous structure. We use A to show mean performance gain relative to conventional knowledge distillation methods without AdaConG. We highlight in orange deltas greater than 0.15, indicating non-trivial enhancement following the protocol in Sun
al. (2024).
ResNet50
VGG13
WRN-40-2
Teacher
62.79
61.47
58.76
Student
ShuffleNet-VI
MobileNet-V2
ShufticNet-V2
64.52++0.2
56.47+00.03
66.35++0.12
KD Hinton 2015
58.3011.24
53.0810.57
50.61
KD AcaConG
60.71
57.69:0.52
67.57=1.22
7.41
4.41
7.96
FitNet Romero et al. 2014
63.97-10.25
54.77:10.40
06.03340.48
FitNet AdaCone
64.49=20.15
55.75-0037
67.69=10.11
0.52
0.98
1.66
PKT Passalis and Tefas 2018
66.26 66.2611.266
56.5311.113
66.38110.18
PKT AdaconG
66.65=0.116
57.01
67.8810.42
0.39
0,48
1,50
FT Kim et al 2018
63.8510.34
$6.36:10.49
66.3410.21
AdaCons
63.13-20.3
57.40=1.200
67.29:1011
1.28
1.04
0.95
As part of ablation studies, evaluate the performance of heterogeneous teacher-student framework and present the results in the following Table The table shows that, for all knowl- edge transfer methods, performance improves when combined with AdaConG, further validating the effectiveness of our approach across different teacher-studes structures.
A.2.3 HYPERPARAMETER SENSITIVITY ANALYSIS
We conduct sensitivity analysis for the design choices of the key hyperparameters, including the emror rate a for split CP and the temperature y of the adaptive weighting w = exp(-ru). We use ResNet- 1 10 as the pretrained teacher and ResNet-20 the student model to train.
15

---

Published as a conference paper at ICLR 2026
64.05
64.26
64.24
64.53
65.12
65.23
65.15
66.15
66.55
66.35
60
57.23
Accuracy (%)
40
20
Standard
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
V value
Figure 3:
Top-1 accuracy of KD using AdaConG with varying temperature y values for adaptive weighting.
66.79
66.81
66.54
60
57.23
Accuracy (%)
40
Standard
0.01
0.05
0.10
0.15
a value
Figure 4: Top-1 accuracy of KD using AdaConG with varying a values. The results demonstrate that our approach is robust the choice of and consistently outperforms standard KD.
We first analyze the sensitivity of the temperature parameter y in the adaptive weighting function. The results are presented in Fig. 3 showing how y affects the student's Top-1 accuracy with a = 0.1. Across all tested values, combining KD with AdaCont consistently outperforms standard KD. We observe that accuracy generally increases as increases. This trend intuitive, when ? is too small, the exponential decay used for reweighting may sufficiently suppress the influence of noisy teacher predictions. We select 10.0 as our default setting, since performance tends to not increase for 7 10.0.
We then analyze the sensitivity of a. We present the results in Fig. 4 showing how a influences the student's Top-1 accuracy with y 10.0. The results demonstrate that our approach robust to the choice of a and consistently outperforms standard KD. We choose a = 0.1 which yields slightly better results. The underlying insight as follows: when a is small, the prediction set becomes large, indicating lower teacher confidence. As a result, the teacher's guidance becomes less informative, and the student relies more on its own learning, reducing the benefit of distillation, even when the teacher is accurate. Conversely, when is large, the prediction set shrinks, making the teacher appear overly confident. In this case, the student may rely too heavily on potentially noisy teacher predictions, leading to suboptimal knowledge transfer. We further support this interpretation by presenting the average size the prediction set for the teacher model in Fig. S which aligns with our observations.
16

---

Published as a conference paper at ICLR 2026
10.34
Average size
4
2.01
0.01
0.05
0.10
0.15
value
Figure Average size the prediction set for the teacher model.
A.2.4 HARD WEIGHTING FUNCTION
We explore another hard version weighting function: w if 0, 0 0 (Vovk et al. 2016). We use ResNet-110 10 as the pretrained teacher and ResNet-20 as the student model to train. The rationale for the hard weighting function follows (Vovk et al. (016)), which aims to ensure that prediction sets are as close possible to single-element sets, making them more informative. This scheme is simple and effective, allowing the student to learn from high-confidence teacher predictions while filtering out potentially misleading guidance. Experimental results in Table 6 show that combining this hard weighting scheme with AdaConG outperforms standard knowledge distillation methods.
Table Top-1 accuracy (%) of various knowledge distillation methods without and with AdaConG using the hard weighting function. We use A to show performance gain relative con- ventional knowledge distillation methods and highlight in orange deltas greater than 15, indicating non-trivial enhancement following the protocol in (Sun et al. 2024).
Approach
Accuracy (%)
KD (Hinton 2015)
57.21
KD AdaConG
66.52
9.31
FitNet Romero al. 2014
64.65
FitNet AdaConG
66.88
2.23
PKT Passalis and Tefas 2018
66.50
PKT + AdaConG
66.83
A
0.33
FT Kim et al.
2018
66.47
FT
AdaConc
66.69
A
0.22
LS-KD (Sun et al. 2024)
63.40
LSSKD AdaConG
67.11
3.71
A.2.5 DIRECT USE OF NONCONFORMITY SCORES
We conduct additional experiments to compare the performance of directly using nonconformity scores versus applying AdaConG with quantile computation, as ablation studies, across different teacher/student setups with KD (Hinton 2015). The results are shown in Table 7 reporting the mean and standard deviation over four repeated runs. As shown, AdaConG outperforms the direct of nonconformity scores. This indicates that computing the quantile of the nonconformity scores helpful, it is necessary to construct the prediction set for split CP. therefore transferring non conformalized uncertainty measures into rigorous
17

---

Published as a conference paper at ICLR 2026
Table Top-1 accuracy (%) on CIFAR-I00 for the KD approach, comparing direct use of noncon- formity scores versus AdaConG using quantile computation. AdaConG outperforms the direct use of nonconformity scores.
Approsuch
ResNet 10/
ResNet56/ResNe120
RewNec32xAAResNetkk
VGG13/VGGB
WRN-40-2/WBN.
Nonconformity score
64.17 + 0.41 66.33 0.55
64.90 + 0.28
06.89 0.15
65.19 1108=0.33 0.34
68 18.06-2 0.13
AdaConG
66.98
68.45
67.53
A.2.6 EXPERIMENTS CIFAR-100-C DATASET
We conduct additional experiments on the more challenging CIFAR-100- benchmark (Hendrycks) and Dietterich, 2019). We evaluate under the Gaussian noise corruption with five levels of severity, larger severity corresponds to stronger noise and greater distribution shift. More details can be found in (Hendrycks and Dietterich, 2019). We use two pretrained teacher models, ResNet-1 10 and ResNet-56, both trained on the clean CIFAR- 100 dataset, and perform knowledge distillation under different methods, including KD (Hinton 2013) and LS-KD (Sun et al. 2024). with both homogeneous and heterogeneous teacher-student structures.
The results in Tsow that incorporating AdaConG consistently improves student performance across all settings. These gains further demonstrate that our method effectively modulates imperfect teacher signals under distribution shift and enhances learning performance.
Table 8: Top-1 accuracy (%) of different knowledge distillation methods CIFAR-100-C. A indi- cates performance gain over the base method. We observe up to + +18.62% higher accuracy improve- ment.
Teacher model
ResNetl 10
ResNet56
ResNetl 10
ResNet56
Teacher accuracy
24.84
20.61
24.84
20.61
Student model
ResNer20
ResNet20
ShuffleNet-Vi
ShuffleNet-V2
Student accuracy (from scratch)
41.24:10.55
41.24:10.55
35.43110.68
35.56 #0.61
KD Hinton 2015
24.32-10.36
20.54:10.53
24.60:10.17
20.58110.27
KD AdaConG
02.16-t0.36
0..16+0.43
35.57=
37.22:+0.49
A
17.84
18.62
10.97
16.64
LS-KD (Sun et 2024
41.02++0.52
38.58+00.8
33.93++0.70
3..94-1092
LS KD + AdaCont
44.4411.38
43.33::.21
37.76110.3
40.3411063
3.42
4.75
3.83
5.40
A.2.7 EXPERIMENTS ON LARGER DATASET AND LARGER BACKBONE
We also conduct additional experiments on larger dataset and larger backbone to further validate our approach. Specifically, we use a larger dataset Tiny ImageNet (Le and Yang 2015), which contains 100K training images and 10K testing images across 200 classes. For the teacher model, we adopt a larger backbone ViT-B (Dosovitskiy et al., (020)) and train it on the clean Tiny ImageNet dataset for 50 epochs. During knowledge distillation to different student models, we introduce noise into the Tiny ImageNet dataset following the procedure described in Appendix [ This places the pretrained teacher model under distribution shift, making its prediction noisy and unreliable. this setting, leverage AdaConG to dynamically modulate the guidance from the imperfect teacher. The results in Table[]shov show that incorporating AdaConG consistently improves student performance across both backbone scales, demonstrating that our approach remains effective with larger dataset and larger backbone.
A.2.8 QUALITATIVE ANALYSIS
In this section, we present a qualitative analysis demonstrating how AdaConG assigns higher or lower uncertainty to different inputs, providing deeper insight into its behavior. We sample multi- ple clean images from the CIFAR-100 dataset and generate corresponding noisy images by adding Gaussian noise with zero mean and standard deviation 0.05. For both clean and noisy images, apply a pretrained ResNet-1 10 model with conformal prediction to obtain the prediction set for each image. We then convert the size of each prediction set into uncertainty score using Eq. then
18

---

Published as a conference paper at ICLR 2026
Table 9: Top-1 accuracy (%) of different knowledge distillation methods on Tiny ImageNet. A indicates performance gain over the base method. We observe up to +19.02% higher accuracy.
Teacher model
ViT-B
ViT-B
ViT-B
Teacher accuracy
33.06
33.06
33.06
Student model
ResNet20
ShuffleNet-Vi
ShufflcNet-V V2
Student accuracy (from scratch)
43.50=0015
50.08=0.21
51.79+t0.11
KD Hinton 2015
31.21
32.87=0.33
33.00
KD AdaConG
43.42++0.32
51.20=0.21
52.02:+0.25
A
12.21
18.33
19.02
LS-KD (Sun 2024
42. 02.1
48.59=0.16
49.76=0.17
LS-KD + AdaConG
45.50=0.28 3.34
52.65=0.41
54,69:0.28
A
4.06
4,93
Clean 5:2, W:0.90
Clean S:2, W:0.90
Clean S:1, W:1.00
Clean S:1, W:1.00
Noisy S:6, W:0.60
Noisy S:6, W:0.60
Noisy 5:4, W:0.74
Noisy S:3. W:0.82
Figure 6: Qualitative analysis of adaptive weights. The first row shows original clean images from CIFAR-106 100, and the second row shows their noisy counterparts. Each image annotated with the prediction set size (S) and the corresponding adaptive weight (W). Clean images produce smaller prediction sets, indicating lower uncertainty and thus higher weights, while noisy images yield larger prediction sets, reflecting higher uncertainty and consequently lower weights.
adaptive weight using Eq. 2 clean images, while the second row shows their noisy counterparts. For each image, annotate the prediction set size (S) and the obtained adaptive weight (W). As shown, clean images yield smaller prediction sets and thus higher adaptive weights, whereas noisy images produce larger prediction sets, indicating higher uncertainty and consequently lower adaptive weights for the guidance signal.
We present the results in Figure 6 the first row contains the original
A.2.9 TRAINING DETAILS
For the experiments, we use the stochastic gradient descents (SGD) (Sutskever et al. 2013) as the optimizer with momentum 0.9 and weight decay 5e - The epoch number 240 and the batch size 128. The initial learning rate is set to 0.01 for MobileNet (Sandler et al. 2018 2018/Shufflel al. 2018) architectures and 0.05 for other architectures. The model is trained on Nvidia RTX 3090 GPU with AMD Ryzen 9 5900 CPU and 32 GB RAM.
(Zhang
A. COMPUTATION OVERHEAD
We compare the training cost of our approach AdaConG against standard knowledge distillation (KD) and KD with MC dropout on an RTX 3090 GPU. For MC dropout, we perform ten forward passes and average the outputs. Compared to MC dropout, the training cost using AdaConG is much lower. Compared to standard KD, the training cost of AdaConG is close, since using split CP is just a single pass, as shown in Table I0 From the results Table I0 using AdaConG just adds around 0.003 ms overhead per sample during training.
19

---

Published as a conference paper at ICLR 2026
Table 10: Comparison of computational overhead between standard KD, KD with AdaConG, and KD with MC dropout.
Approach
Time/Epoch (s)
KD
6.87
KD AdaConG
7.04
KD MC dropout
44.90
62.69
63.51
64.5/
64.57
64.85
65.85
66.95
62.27
60.14
60
62.00
Accuracy (%)
40
20
Without AdaConG
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Y value
Figure 7: Prediction accuracy of FixMatch using AdaConG with varying temperature values for adaptive weighting.
A.3 SEMI-SUPERVISED IMAGE CLASSIFICATION
A.3.1 TRAINING DETAILS
Following the setup Sohn al. (2020; Zhang et al. (2021). we use the WRN-28-8 architecture Zagoruyko (2016) for the CIFAR- 10 and CIFAR- 100 datasets Krizhevsky et al. (2009), and WRN- 37-2 Zagoruyko (2016) for the STL-10 dataset Coates al. (2011). We adopt stochastic gradient descent (SGD) Sutskever et al. (2013) the optimizer with a momentum of 0.9. The weight decay set to 10 for CIFAR 10 and STL-10, and X 10-3 for CIFAR-100. Models are trained for 51,200 iterations with batch size of 64 and initial learning rate of 0.03. Experiments
conducted on an Nvidia RTX 3090 GPU with AMD Ryzen 9 5900 CPU and 32 GB RAM.
A.3.2 HYPERPARAMETER SENSITIVITY ANALYSIS
We conduct sensitivity analysis for the design choices of the key hyperparameters, including for split CP and the temperature for the adaptive weighting w = exp(-yu). We conduct experiments using the approach FixMatch (Sohn et 2020) combined with AdaConG on the CIFAR- 10 dataset with 40 labels.
We first analyze the sensitivity of the temperature parameter y in the adaptive weighting function. The results are presented in Fig. 3 showing how y affects the prediction accuracy with = 0.1. Across all tested values, accuracy generally increases as y increases, which expected, when y too small, the exponential decay used for reweighting may not sufficiently suppress the influence of noisy laeudo-labels. We select 7 = 8.0, as performance begins to slightly decline when 7 > 8.0.
We then analyze the sensitivity of a. The results, shown in Fig g illustrate how affects prediction accuracy with > = 8.0. FixMatch combined with AdaConG outperforms the standard approach across all values. The accuracy first increases and then decreases performance achieved at a 0.05. Therefore, we select a 0.05. The underlying insights are similar those observed in the knowledge distillation experiments.
increases, with the highest
20

---

Published as a conference paper at ICLR 2026
72.96
68.77
66.67 66.67
63.97
62.00
Accuracy (%)
Without AdaConG
0.01
0.05
0.10
0.15
value
Figure Prediction accuracy FixMatch using AdaConG with varying a values.
A.3.3 COMPUTATION OVERHEAD
We compare the training cost of the key SSL baseline FlexMatch with and without our method AdaConGon the CIFAR-I00 dataset. As shown in Table incorporating AdaConG introduces only minimal additional computational overhead.
Table 11: Comparison of computational overhead between FlexMatch and FlexMatch AdaConG. Incorporating AdaConG adds only minimal computation.
Approach
Time/Epoch (s)
FlexMatch
91.52
FlexMatch AdaConG
97.63
A.4 IMITATION-GUIDER REINFORCEMENT LEARNING
We explore reinforcement learning for grid-world navigation, leveraging pretrained imitation pol- icy to provide prior guidance. The environment scenarios shown in Fig. 9 are adapted from Yuu al.] (024) and developed using the Minigrid framework (Chevalier-Boisvert et al., (024). They are fully observable with discrete state and action spaces. In each environment, the agent' ' state cor- responds to {x, }) coordinates on the map, and the action space comprises five discrete actions: left, right, up, down, and stay. Fach episode is capped at maximum of 100 steps. In the Lava and Lava 2 environments, the reward function is computed as the negative Manhattan distance between the agent's current position and the goal, normalized by the maximum step limit of 100. Upon reaching the goal, the agent receives a terminal reward of 10 the lava results in reward of -1, and the episode terminates immediately. Similarly, in the Door environment, the reward structure follows the same formulation but without lava, encouraging the agent to minimize its distance to the goal, with the same terminal reward applied upon successful completion.
x step count. Stepping into max step
We collect expert demonstration data comprising state-action pairs for the Lava I and Door envi- ronments to train imitation learning (IL) models via behavior cloning (Torabi al.) 2018). The demonstration data are inherently uncertain, as multiple valid actions may exist for the same state, as illustrated in Yu al. 2024). introducing ambiguity in the model's predictions.
We calibrate both the II policy and the RI. policy wR. and estimate their prediction uncertainties Uy and ug with g as the identity mapping. a = 0.1, N 1000 and m 128, as described in Section 3 For a given state 8, the guidance weight is defined as: w(s)
And we {az, ag) } to take according the distribution induced by this guidance weight. To encourage exploration by the RL policy, we define a probability = min(0.5 Sme + 0.5 Eing 1),
exp( exp(=
+ex)
sample the action
where t is the current training step, e is the current episode, Sweal and E are the total training steps and episodes, respectively. At each step, if random probability p the agent takes
21

---

Published as a conference paper at ICLR 2026
action from the RL policy, otherwise it takes action based AdaConG. As increases time, the agent progressively shifts to learned RL policy, while initially relies more on the IL policy through AdaConG to facilitate learning.
A.4.1 ENVIRONMENT DETAILS
3
(c) Door
(a) Lava
(b) Lava
Figure 9: Gridworld Environment Scenarios. (a) Lava 1: An autonomous agent (red dot) must navigate to a target position (diagonal square) while avoiding lava regions. (b) Lava 2: domain- shifted variant of Lava with altered environment dynamics and layout. (c) Door: The agent must traverse a structured environment with doors and walls to reach the designated target position.
A.4.2 TRAINING DETAILS
For the inntattionguidedl reinforcement learning experiments, we employ a batch size 512 and the Adam optimizer (Kingma 2014) with initial learning rate of 3e-4. For each method and environment scenario, we train for 1000 episodes across 10 different random seeds. The model is trained on Nvidia RTX 3090 GPU with AMD Ryzen 9 5900 CPU and 32 GB RAM.
A.4.3 EXPERIMENTS WITH ADDITIONAL RL BASELINE
We conduct additional experiments with the RL baseline QDagger (Agarwal et al. 2002) on the Lava environment, which unseen for the pretrained IL policy. QDagger leverages a teacher policy as soft imitation regularizer. This mechanism works best when the teacher provides useful corrective guidance on the target environment. However, in our setup, the imitation policy is trained on different environment and then directly deployed to poorly. As result, the teacher provides unreliable guidance on the new environment, and QDagger's distillation term ends up regularizing the student toward suboptimal erroneous actions. QDagger thus underperforms in this setting, whereas AdaConG effectively adapts to the imperfect teacher signals and achieves higher rewards, shown in Figure 10
unseen environment, where it generalizes
A.4.4 COMPUTATION OVERHEAD
We compare the training cost of our approach AdaConGagainst key RL baselines, including the pure RL method SAC and IBRL. As shown in Table 12 incorporating AdaConG introduces only minimal additional computational overhead.
Table 12: Comparison of computational overhead across key RL baselines.
Approach Time/Epoch (s)
SAC
1.87
IBRL
2.34
AdaConG
3.08
A.5 AUTONOMOUS DRIVING
A.5.1 EXPERIMENTAL. SETTINGS
We first define the accuracy with respect to a specific degree threshold 7 as acc, = count( < n), following prior works (Shen et al. 2021 2023 2024), where is the number of test cases;
22

---

Published as a conference paper at ICLR 2026
10
5
0
Rewards
-5
-10
Iaard AdaConG
-15
Onagger
SAC
-20 10K
20K
30K
40K
Steps
Figure 10: Additional experiments comparing with the QDagger RL baseline. QDagger under- performs in this setting whereas AdaConG effectively adapts the imperfect teacher signals and achieves higher rewards.
and represent the ground truth and the predicted steer angle, respectively, for T E T (1.5, 3.0, 7.5, 15.0). Then compute the mean accuracy (mAcc) by averaging acc, across dif- ferent thresholds.
The SullyChen (Chen 2018) dataset contains approximately 63,000 images, each with a resolution of 455 x 256, paired with corresponding steer angle annotation. We show some sample images in Fig. II To generate edge maps from RGB images, we employ DexiNed (Soria et al. 2023). To generate depth maps, we utilize DPT (Ranftl et al. (201)). Following (Shen et al. 2023). we use channel-level attention to represent the importance each modality. For the teacher model fp- we combine the data from different modalities (RGB, depth, and edge) at the channel level and pass them through an Squeeze-and-Exctee Excitatiin (SE) block (Hu et al.) 2018), followed by a 1x convolution layer to make the channel number to be the same as the main modality RGB. We first train the teacher model offline. Then we use it to guide the target student model ft training through knowledge distillation, while the RGB images for fi training has domain shifts compared to the ones used for fp training. For the details of domain shift, please refer to Appendix A.3.2
We compute nonconformity score the residuals between the predicted and true steer angles from
the calibration set to get the quantile value Qi-a with = 0.1. A sensitivity analysis for different a it to construct the prediction set C(x) for given input
values presented in Fig. 12 Then
RGB image æ. We define the teacher's uncertainty as the size of the prediction set: u(x) = [C())]
The dynamic weight assigned as w(x) 1 if uxx) 7. otherwise w(x) O, for E T. We
set the coefficients Ausk and Aguide in Eq. for all knowledge distillation methods following (Shen
al. 2023).
A.5.2 DATA PROCESSING
After generating depth and edge maps, we split the dataset into 80% training and 20% testing. Then we train the multi-modal teacher model on the training data offline. After training the teacher model. we introduce domain shift to the training data compared to the teacher's pretraining data. Specifically, we add Gaussian noise with zero mean and standard deviation of 0.1 to 30% of the RGB images, where the noisy samples are selected uniformly at random across the entire training set to ensure consistent noise distribution. We do not add Gaussian noise to the generated depth and edge maps, as they are not used for the student model. Then we shuffle the training data and randomly split it into a 90% training set Di and a 10% calibration set Deal. ensuring that both sets drawn from the same underlying distribution. Additionally, the same Gaussian noise is added to 30% the testing data of RGB images, to form the noisy test set D prss, which allows us to evaluate the performance of the models under noise conditions.
23

---

Published as a conference paper at ICLR 2026
Figure 11: Sample images of the real-world SullyChen dataset. SullyChen (Chen) 2018 is real-world driving dataset which includes diverse driving scenarios with various road types and conditions.
80
74.40
76.80
73.50
Mean Accuracy (%)
60
20
Without AdaConG
0.01
0.05
0.10
0.15
a value
Figure 12: Mean accuracy KD for steer prediction using AdaConG with varying a values.
A.5.3 HYPERPARAMETER SENSITIVITY ANALYSIS
We conduct sensitivity analysis for a and present the results in Fig. 12 illustrating how different values of a affect the student model's mean accuracy (mAcc) on the steer prediction task using KD Hinton 2015). We select 0.10 that yields slightly better performance.
A.5.4 TRAINING DETAILS
For the experiments, initial learning rate of 1e-3, and a weight decay of le - 5. The model is trained on an Nvidia RTX 3090 GPU with AMD Ryzen 5900 CPU and 32 GB RAM for 240 epochs.
employ batch size of 32 and the Adam optimizer (Kingma 2014) with an
A.5.5 COMPUTATION OVERHEAD
We compare the training cost of the key baseline KD and KD with approach AdaConG. As shown in Table leveraging AdaConG only introduces minimal computation overhead.
Table 13:
Comparison computational overhead between standard KD and KD with AdaConG in autonomous driving steer prediction.
Approach
Time/Epocc (s)
KD
11.34
KD AdaConG
13.68
24

---

Published as a conference paper at ICLR 2026
A.6 DISCUSSIONS AND FUTURE WORK
AdaConG dynamically modulates the influence of guidance signals, allowing models to reduce reliance potentially misleading information and thereby enhance learning performance. It also suggests promising directions for future work. Currently, AdaConG relies on well-defined ground truth; however, its foundation in conformal prediction allows for natural extension to settings with ambiguous or imprecise labels (Caprio et al. (025). By designing nonconformity scores that capture label ambiguity, prediction sets can constructed to reflect varying degrees uncertainty. This flexibility enables adaptive weighting even under uncertain supervision. Furthermore, integrating concepts from Imprecise Probabilistic Machine Learning, such as credal sets (Caprio et al., (2024) and imprecise probabilities (Dutta et al. 2025), along with strategies from Active Learning and Continual Learning (Lu et al. 2024). could further enhance AdaConG's capacity to manage complex uncertainty.
25


Reviews:
[{"review_id": "AJxOc2AoFF", "reviewer": "Reviewer_rRGf", "summary": "The paper proposes Adaptive Conformal Guidance. This is a simple, plug‑in mechanism that uses split conformal prediction (CP) to quantify the uncertainty of guidance signals (teacher logits in KD, pseudo‑labels in SSL, imitation policies in RL) and adaptively modulate how strongly the learner follows them. Concretely, it builds a prediction set (or interval), maps its size/measure to an uncertainty score u, transforms it to a weight and uses it to attenuate a guidance loss (KD/SSL) or to arbitrate between policies (RL). Experiments on CIFAR‑100 KD, SSL (CIFAR‑10/100, STL‑10), MiniGrid navigation, and autonomous driving steer prediction show consistent gains, including large improvements when the teacher underperforms under shift. The paper's appeal in my opinion is breadth and simplicity of the work (of course, it also helps that it is well written and articulated).", "questions": "Please see the Weaknesses section.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "(1) The idea is elegant, simple and scales well across SSL, KD and imitation RL.\n\n(2) Experiments are rigorous and covers a strong empirical breadth. \n\n(3) It seems to be very lightweight and model agnostic compared to MC-dropout-style approaches. \n\n(4) The paper is well written and articulated.", "weaknesses": "Weaknesses and questions:\n\n(1) From my understanding, w(s) weighs a KL guidance loss; in Experiments, however, looks like w(s) chooses actions (stochastic arbitration) and a hard argmax variant. These are different algorithms! Please explicitly state it (if it was not a mistake).\n\n(2) \\gamma is being overloaded ((i) RL discount, (ii) temperature in h(u), EMA smoothing factor all use \\gamma). \n\n(3) Similarly s is being used for score and state. \n\n(4) Coverage guarantees require exchangeability, several passages imply robustness and in RL the CP set measures self‑consistency of a policy, not correctness. I would rephrase those sentences and state conditions.\n\n(5) In the SAC baseline, generally SAC is meant to be continuous, but how is it using discrete actions? \n\n(6) f_s is undefined (should it instead be \\pi_R)? \n\n(7) Typos I was able to catch (there might be more): \"Disucssions\" (A.6), \"mdoel\" (Page 9), \"is is\" (Page 5). \n\n(8) Does the claimed 0.08 ms/sample latency not contradict the epoch timings (\\Delta ~= 0.17 s/epoch = ~0.003 ms/sample for 50k samples)?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Qkn8NoGRc1", "reviewer": "Reviewer_a8X8", "summary": "The paper proposes Adaptive Conformal Guidance (AdaConG), to consider the uncertainty against noisy guidance signals for different tasks. Simply, the method dynamically modulates the influence of guidance signals based on the uncertainty quantified by split conformal prediction (CP), which enabling the models to reduce reliance on potentially misleading signals. The proposed method is evaluated on different tasks, including knowledge distillation, semi-supervised image classification, gridworld navigation, and autonomous driving. The experiments demonstrate the effectiveness of the proposed method", "questions": "1. The proposed method requires an amount of available target data for calibration during training. However, the target data may not available or hard to collect in some real applications, so the available target data is limited. How could the proposed method handle these cases? How many target data does the method required for calibration and training for different tasks?\n\n2. I'm also curious about whether the proposed method can be extended to self-supervised learning.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper is well written and easy to follow.\n\n2. The idea of the paper is straightforward.\n\n3. The experiments on diverse tasks demonstrate the effectiveness of the proposed method.", "weaknesses": "1. As discussed in the abstract and introduction, the learning-with-guidance methods are easy to be influenced by noisy guidance lead by domain shifts or limited data, where considering the uncertainty is important. However, in the experiments, the datasets and cases are used for evaluation seems more simple, without considering distribution shifts or limited data. I suggest to add some experiments on these difficult cases, such as datasets like CIFAR-C, ImageNet-C.\n\n2. The method is also evaluated on small datasets and backbones. It is not clear how it works on larger backbones like ViT/B, ViT/L, and larger datasets like ImageNet.\n\n3. Lack of comparisons with CP alternatives in the experiments\n\n4. I assume the proposed method would lead to more computational costs for training and calibrating, which are not discussed in the main paper.\n\n\nlarger backbones\n\nlarger datasets", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iix2qiewCn", "reviewer": "Reviewer_YaJZ", "summary": "The authors address the problem of noisy and unreliable guidance signals in machine learning. To mitigate this issue, they propose AdaConG, a strategy that reduces the model's reliance on guidance when misleading signals are present and adaptively adjusts the influence of guidance signals. They conduct comprehensive experiments across four popular ML tasks, demonstrating that AdaConG is more robust to guidance uncertainty than baseline methods and generalizes well across diverse tasks and scenarios.", "questions": "1. What is the baseline for the last section of Table 1? It appears that EA-KD (line 314) outperforms the proposed method (line 301) in half of the cases. Could you clarify this comparison and discuss why EA-KD shows superior performance in these instances?\n\n2. In Fig. 2(d), could you provide the prediction uncertainty curves for other baseline methods? This would help better contextualize the advantages of AdaConG in uncertainty calibration.\n\n3. In Table 4 (last row), under what setting is the result for \"Student (RGB)\" obtained? Specifically, is this model trained from scratch, or does it use some form of pre-training/initialization?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The experimental design is comprehensive and rigorous, effectively validating the proposed method's robustness to misleading signals.\n\n2. All experimental results report mean and standard deviation over multiple runs, demonstrating scientific rigor and reproducibility.\n\n3. The core idea of improving learning quality by modulating the uncertainty of guidance signals is inspiring, with valuable practical implications across a wide range of tasks.\n\n4. Incorporating conformal prediction to inform training dynamics is novel and represents an underexplored direction that could benefit the community.", "weaknesses": "1. I found some of the tables challenging to parse at a first glance (e.g., Table 1 and 4). Reformatting them to be more self-explanatory would enhance the paper's readability.\n\n2. I only found efficiency analysis for KD task. I would recommend the authors also include (training time, computation overhead) comparison in other tasks with key baselines.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iSrGGva8rM", "reviewer": "Reviewer_sHk1", "summary": "This paper proposes AdaConG, that dynamically modulates guidance signals (e.g., from teacher models, pseudo-labels) based on their uncertainty. This uncertainty is quantified using split conformal prediction (CP), which is embedded into the training loop to re-weight the guidance loss. The method is simple, broadly applicable, and validated across diverse tasks (including knowledge distillation, SSL, and imitation-guided RL), showing improved robustness and performance under imperfect guidance.", "questions": "None", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- extensive and diverse experimental setups (also good results)\n- simple, easy to re-implement\n- minimal computational overhead compared to MC-dropout", "weaknesses": "- lack qualitative analysis. For instance, providing visualizations of why AdaConG assigns high or low uncertainty to specific inputs (e.g., showing example images or states and their corresponding CP-derived weights) would offer deeper insight into the method's behavior.\n- In RL exps, the comparison is limited to SAC (a standard RL baseline) and IBRL/Soft IBRL (which rely on Q-values). The paper would be strengthened by comparing against other methods that are also designed to handle suboptimal or noisy expert guidance, beyond just Q-value comparison (maybe some baselines in [1]).\n- In SSLs, the labeled dataset is used both to construct the calibration set and to compute the training loss. This appears to violate the standard split conformal inprediction assumption. Does it affect the statistical guarantees of CPs? \n\n\n[1]  Agarwal et al. , Beyond Tabula Rasa: Reincarnating Reinforcement Learning. NeurIPS, 2022.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)