Conformalized Hierarchical Calibration for Uncertainty-Aware Adaptive Hashing
Authors: Junyu Luo
Jinsheng Huang
Yang Xu
Lutong Zou
Xiao Luo
Bohan Wu
Yifan Wang
Wei Ju
Ming Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Adptive Hashing Retrieval
Hashing Retrieval
Unsupervised Domain Adaptation
Primary area: transfer learning, meta learning, and lifelong learning

Abstract: Unsupervised domain adaptive hashing transfers knowledge from labeled source domains to unlabeled target domains, addressing domain shift challenges in real-world retrieval tasks. Existing methods face two critical limitations: target domain noise severely misleads model training, and indiscriminate domain alignment strategies treat all target samples equally, potentially distorting essential feature structures. We propose an uncertainty-aware adaptive hashing approach that addresses these challenges through a hierarchical conformal calibration framework. At the semantic level, we employ conformal inference to generate confidence prediction sets, replacing single pseudo-labels with set-based predictions whose sizes directly quantify sample reliability for weighted pseudo-label learning and domain alignment. This enables the model to focus on reliable samples while suppressing noise. At the representation level, we predict the stability of individual hash bits, where bit-level confidence guides a robust weighted quantization loss and enables dynamic weighted Hamming distance during retrieval, fundamentally enhancing hash code quality and retrieval robustness. Through this hierarchical calibration mechanism, our method achieves more adaptive and robust cross-domain knowledge transfer. Extensive experiments on multiple benchmark datasets demonstrate significant improvements over existing approaches, validating the effectiveness and superiority of our method.

Published as a conference paper at ICLR 2026
CONFORMALIZED HIERARCHICAL CALIBRATION FOR IITERTAINTT-AAAA ADAPTIVE HASHING
Junyu Luo',, .Jinsheng Huang', Yang Xu², Lutong Zou', Xiao
Luo Xiao
Bohan Wu',
Yifan Wang', Wei Ju Ming Zhang"
1 State Key Laboratory for Multimedia Information Processing.
School Computer Science, PKU-Anker LLM Lab, Peking University
School of Mathematical Sciences, Peking University
3 Department of Statistics, University of Wisconsin-Maate Madison
4 University of International Business and Economics
luo. junyusout com, hjs@stu. pkusstu.puu.... edu. en, xuyang1014@pku, en, bbf@stu. porfsstu.pu.eee eku edu. en, slaowuuowiscc. edu, wxtpkulpku. edu. cn, yi yifanwang@uibe. www.:uiieeeeeeee.........e....e. edu. en, juwe eiweippku.o edu. en, wazhang_ss@pkie edu. cn
ABSTRACT
Unsupervised domain adaptive hashing transfers knowledge from labeled source domains to unlabeled target domains, addressing domain shift challenges in real- world retrieval tasks. Existing methods face two critical limitations: target domain noise severely misleads model training, and indiscriminate domain alignment strategies treat all target samples equally, potentially distorting essential feature structures. We propose an uncertainty-aware adaptive hashing approach that ad- dresses these challenges through hierarchical conformal calibration framework. At the semantic level, we employ conformal inference to generate confidence pre- diction sets, replacing single needo-llbells with set-based predictions whose sizes directly quantify sample reliability for weighted pseudo-label learning and domain alignment. This enables the model to focus reliable samples while suppressing noise. At the representation level, we predict the stability individual hash bits, where bit-level confidence guides robust weighted quantization loss and enables dynamic weighted Hamming distance during retrieval, fundamentally enhancing hash code quality and retrieval robustness. Through this hierarchical calibration mechanism, our method achieves more adaptive and robust cross-domain knowl- edge transfer. Extensive experiments multiple benchmark datasets demonstrate sigmificant improvements over existing approaches, validating the effectiveness and superiority of our method.
INTRODUCTION
Efficient approximate nearest neighbor (ANN) similarity retrieval plays critical role in recom- mender systems (Tan et al., 2020), visual search (Pu et al., 2025), and retrieval- augmented genera- tion (RAG) (Zhao al., 2024). Deep hashing, which replaces moating-point distance computations with bitwise operations, offers significant advantages in both retrieval latency and storage costs, making it key technology for large-scale retrieval systems (Wang et al., 2017; Luo al., 2023b; Cui et al., 2024). The capability of deep lcarning models generate semantically discriminative hash codes has substantially advanced applications.
However, real-world deployment inevitably encounters domain shift: variations in imaging devices, capture styles, and background distributions cause trained hashing models exhibit semantic con- fusion and overconfidence in target domains. To bridge this gap, unsupervised domain adaptive hashing (UDAH) has attracted considerable attention (Wang et al., 2023c; Venkateswara et al., 2017; Wang et al., 2023a; Long al., 201 8a; Huang al., 2021; Wang et al., 2023b; Huang et al., 2020; He et al., 2019). The objective is to transfer labeled source domain knowledge to unlaheled tar-
'Coreeponding authors.

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Published as a conference paper at ICLR 2026
get domains. Existing domain adaptive hashing methods typically advance along two pathways: pseudo-labeling, where models generate supervisory signals for target data based on their own predictions (Lee et al., 2013; Xia et al., 2021b), and @ domain alignment, which aims to minimize distributional discrepancies between source and target features or adversarial training (Lee et al., 2019h; Ganin et al., 2016; Zhang et al., 2019; Lu al., 2023a).
While these methods have achieved commendable progress, their performance is often constrained by fundamental limitation: unreliable and heuristic handling of model uncertainty. Existing approaches suffer from three key issues. O They rely on simple heuristics, such as softmax-base confidence thresholding, to filter high-quality pseudo-labels and guide alignment (Sohn et al., 2020). This approach is inherently risky, as softmax scores are not reliable indicators of correctness, as neu- ral networks are prone to overconfident yet erroneous predictions, especially for quitt--distriuution samples (Saito & Saenko, 2021; Li et al., 2021), as shown in Figure 1. @ They lack verifiable char- acterization of model uncertainty, with heuristic methods providing no theoretical guarantees and exhibiting extreme sensitivity to manually-tuned thresholds (Chen et al., 2022). s They treat differ- ent aspects of uncertainty as a monolithic concept, conflating semantic-level judgment uncertainty with level representation stability uncertainty without employing targeted strategies.
In this work, we argue that unlock- ing the next generation of power- ful UDAH requires moving beyond fragile heuristics toward a princi- pled, multi-level uncertainty quan- tification framework. We introduce Conformal Hierarchical Calibration Adaptive Hashing (COLA), a novel paradigm that quantifies and lever- ages uncertainty from semantic to bit levels. The core innovation of COLA lies in its hicrarchical conformal calibration framework that provides rigorous statistical guarantees for uncertainty quantification at both semantic and representation levels.
Existing: Overconfident & Misguided
COLA: Conformalized Callbration
Conformal Caturation
Chair
Chair Bed Desk
Error
Covibration
Robust
Retrieval
Retrieval
COLA (right) employs hierarchical calibration to replace the single pscudo-labels of existing methods (left) with conformal prediction sets, and weights hash codes with bit-wise confidence to achieve robust retrieval.
Figure 1:
COLA operates through a synergistic two-tier calibration process, as shown in Figure At the semantic level, replace risky point predictions with coverage-controllee prediction sets, whose sizes serve as natural and rigorous measures of semantic uncertainty, enabling more robust pseudo- label learning and domain alignment. At the representation level, introduce novel bit-level calibration mechanism specifically designed for hashing. We model the reliability of each individ- ual bit in generated hash codes through bit stability prediction, yielding fine-grained hash confi- dence scores. The score could guide weighted quantization losses during training and, crucially, enable novel uncertainty-aware weighted Hamming distance during retrieval. Finally, we design a self-regulating mechanism that aggregates semantic and bit confidences into endogenous control domain alignment, and quantization intensity while significantly reducing hyperparameter sensitivity.
signals, dynamically balancing
Our main contributions can be summarized as follows: We design a shift from heuristic confidence-based methods to uncertainty quantification frameworks with rigorous statistical guar- antees. We propose COLA that dissects and addresses uncertainty at both semantic and rep- resentation levels, yielding more reliable pseudo-supervision and more robust hash codes. @ We introduce an elegant self-regulating mechanism that uses quantified uncertainty to dynamically bal- ance multi-objective optimization, achieving truly adaptive learning and enhanced training stability. @ Extensive experiments on challenging benchmark datasets demonstrate that COLA significantly outperforms existing state-of-the-art methods.
2 RELATED WORK
Deep Hashing generating compact binary hash codes to preserve the semantic relationships of data in the Hamming space (Doan et al., 2022; Chen et al., 2024; Tu et al., 2021). This approach signif- icantly reduces storage and computational requirements, making it critical for large-scale retrieval systems (Luo et al., 2023a). Current methods can be fall into two types: supervised (Zhan et al., 2020; Xu et al., 2023; Lu et al., 2023b) and unsupervised (Jin al., 2020; Wang et al., 2022; Song
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Augmented
Code Generation
Representotion-Leen Calibration
T.
guunnd
Layer
Stubilty Lobel 1/z
Training Set
Der
ft
Bit Head
Ctil_
Source Domain
Confidence Vector up
Feoture Extraction airaaciion
Conformal Prediction
Self-Regulating
ka EMA
Semontic Confidence 2013
COLA
Ararge
Botcn
Callbracion Set Deal
Conformay Score
Adoptation
ply
Conformat C(as)
Average Confidence
Origin
Semantic-Level Calibration
Classifier
Auagge
Laarget
Poy Pl3)
Aslau
Target Set
Calian
Taract
Stop
Torget Domain
Domain Discrepancy
Contormal
Figure 2: Overview of COLA, hierarchical conformal calibration framework that addresses un-
certainty in domain adaptive hashing through: (1) Semantic- Calibration for handling pseudo- label noise (3.2), (2) Representation-Levee Calibration for enhancing hash code robustness (3.3), and (3) a Relf-Regul module for dynamically balancing learning objectives (3.4).
et al., 2023; Li et al., 2022; Zhao et al., 2022; Xiao et al., 2023). Unsupervised methods, circumvent the reliance labels by exploiting the intrinsic structure of the data. However, exitsing methods' retrieval accuracy in practical applications is often affected by potential domain shifts.
Unsupervised Domain Adaptive Hashing (UDAH) has emerged an important research area (Ju et al., 2024; Tang et al., 2024) to address the challenge of domain shift. UDAH targets at transferring knowledge from label-rich domain to label-scarse target domain (Long al., 201 8b; He al., 2022: Lee et al., 2019a). Existing methods typically follow two main strategies: self-learning and domain alignment. Self-learning methods generate supervision for target data based on the model's own prediction (Lee et al., 2013). Domain alignment methods reduce the discrepancy between do- mains through adversarial training or distribution matching (Huang et al., 2021; Xia al., 2021a). Despite these advances, existing methods exhibit fundamental limitations in handling model uncer- tainty, as their strategies are heuristic-driven and inherently unreliable.
Uncertainty in Retrieval. Recent works have explored uncertainty modeling in retrieval. (Warburg et al., 2021; 2023) proposed Bayesian metric learning to model alcatoric and epistemic uncertainty via stochastic embeddings. (Tang al., 2025) utilized probabilistic embeddings for composed image retrieval. In hashing, (Wang & Zhou, 2023; Wang et al., 2025) introduced generative ap- proaches to estimate hash code uncertainty. Unlike these model-based methods, COLA employs a distribution- conformal prediction framework. It provides rigorous coverage guarantees un- der domain shift and hierarchically calibrates uncertainty at both semantic and representation levels without expensive sampling.
METHODOLOGY
3.1 PRELIMINARIES AND OVERVIEW
Problem Definition. This work addresses unsupervised domain adaptive hashing (UDAH). Given labeled source domain D. = {xx; y ) and an unlabeled target domain D; = { the same label space but differ in data distribution, input image æ to an L-bit binary hash code {-1, 1 The learned function should ensure that semantically similar images have closer distances in Hamming space and enable efficient retrieval.
17 )- that share aim learn a hash function that maps any
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Conformal Prediction Basics. Conformal prediction is distribution- framework that con- structs prediction sets with rigorous statistical guarantees. Given a calibration set and a user-defined error rate a, it produces a set C(x) for any new such that the ground truth y is contained in C(x)) with probability at least - a. This coverage guarantee relies on the exchangeability of data, which address in the domain adaptation setting via weighted conformal prediction.
Method Overview. The core framework of COLA is a hierarchical conformal calibration mecha- nism that constitutes our primary contribution. COLA consists of two progressive calibration levels:
Semantic-level calibration addresses noisy pseudo-labels in the target domain by replacing risky point predictions with theoretically-grounded conformal prediction sets. The size of these sets rig- orously quantifies model uncertainty and is directly converted to weights that adaptively suppress the harmful effects of high-uncertainty samples in pscudo-label learning and domain alignment. @ Representation-llvel calibration deepens uncertainty analysis to bit-level. We predict the sta- bility of each bit in its generated hash codes. This bit-level confidence guides weighted quantization loss during training and also during retrieval, fundamentally enhancing hash code robustness.
Beyond these core calibration components, we establish self-regulating mechanism as an auxil- iary component. This mechanism uses the real-time uncertainty quantified by both calibration levels as intrinsic control signals to adjust the learning focus.
3.2 SEMANTIC-LEVEL CONFORMAL CALIBRATION: FROM POINT TO SET
In UDAH, pseudo-label quality fundamentally determines model success. Traditional ap- proaches (Lee et al., 2013; Sohn et al., 2020; Hu et al., 2025) exhibit extreme sensitivity to threshold settings and often fail to ensure pseudo-label reliability under complex domain shifts. To address this fundamental limitation, we introduce conformal prediction theory to establish a semantically uncertain quantification and utilization mechanism with rigorous statistical guarantees. Our core insight abandons high-risk point predictions in favor of constructing prediction sets that theoreti- cally cover the true label with probability 1 (Liang et al., 2025). The size of this prediction set naturally and rigorously quantifies the predictive uncertainty (encompassing both aleatoric and epistemic uncertainty) for each sample.
3.2. CONFORMALIZATION VIA CALIBRATION SET
To ensure the calibration set is effective for the target domain, especially under significant domain shifts, we construct it using a targeted selection strategy. First, we extract features for samples in both the source domain D., and the target domain D,, We then compute the feature centroid of the target domain by averaging all of its feature vectors. Subsequently, for each source sample, calculate the Euclidean distance between its feature vector and this target centroid. The reat% source samples exhibiting the smallest distances are selected to form the calibration set Deal- Teal 20% according to Section 4.2. The remaining source samples constitute the training set Der- The targeted selection strategy ensures that our calibration is performed on source data that closely mirrors the characteristics of the target domain, thereby producing more reliable uncertainty estimates for the adaptation task.
We define a conformity score s(z, y) ppy x) to measure the compatibility between sample x and its true label y, where p(y x)) represents the model's predicted softmax probability. Lower scores indicate stronger model confidence the prediction.
Subsequently, we compute conformity scores for all samples in Deal yielding score collection Seal. Traditional conformal prediction methods (Vovk et al., 2005; Papadopoulos et al., 2002; Lei al., 2018) employ a fixed, user-predefined error rate to calculate quantile threshold However, fixed a fails to adapt to model capability changes throughout the lengthy training process. During early training, overly strict may sult in empty prediction sets, while during later stages, overly lenient a cannot effectively identify uncertainty.
0.15
0.14
0.13
0.12
0.11
5
10
15
20
Epoch
Figure 3: Dynamic a during train-
To overcome this limitation, we design a dynamic a adjust- ment mechanism based validation accuracy the source
ing on Office- Ar - Re task.
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domain, linearly transforming from static hyperparameter into dynamic variable ay that evolves with the model's performance. To prevent a₁ from fluctuating dramatically due to single evaluation variations, introduce exponential moving average (EMA) for smooth updates, ensuring adjust- ment process stability. The dynamic a schedule on Office-Home illustrated in Figure 3.
According conformal prediction theory, for new 2a sampled from the same distribution the calibration set, the probability that its true label y/ falls within the following prediction set C(²,) is least 1 -0+;
C(x²) {y )' s( 3) S "
where qW g (Seat, (te) denotes the weighted quantile threshold. We all conformity scores {s(z,, y4) Jest in ascending order and select the [Neat + 1)(1 ax) 1eth value as q"
3.2.2 THEORETICAL ANALYSIS
A critical theoretical question arises when applying conformal prediction in UDAH: standard con- formal prediction theory requires the calibration data and new test data to be exchangeable, an assumption that breaks down when distribution shifts exist between source and target domains. Therefore, we must address the fundamental question: do the theoretical coverage guarantees of constructed prediction sets C(x)) remain valid on the target domain?
To answer this question, building on prior analyses of conformal prediction under covariate or dis- tribution shift (e.g. Barber et al. (2023)), provide theoretical analysis demonstrating that our framework remains robust under this limitation. As stated in Theorem 3.1, the coverage guarantee does not completely fail but degrades in quantifiable and graceful manner.
Theorem 3.1 (Coverage Guarantee under Domain Shift). Let drv denote the total variation dis- tance. Suppose (Xirain, Yuaiu) and (Xtest, Ylest) are random samples from the source and target distributions, respectively. Let qw be derived from equation Then, the following coverage guar- antee holds for the target domain:
P (s(Xrest: Yrest) S ) 21 aa drv (s(Xerains Yurin): s( (reests Yrest)).
(2)
If we further assume that the conformal score has continuous distribution in both domains, then we also have the upper bound:
P (s Yiess) S $1 a1 n + drv (s(Xerain: Yuriuu,, s(teest Yees)).
(3)
The proof and related discussion are provided in Appendix E. This theorem serves as the theoret- ical foundation of our methodology, revealing the intrinsic logic of synergistic cooperation among various modules in our framework. It implies that our subsequent domain alignment work (detailed in Section 3.2) serves not merely as heuristic feature distance reduction. By minimizing the latent distribution differences between source and target domains, we are implicitly minimizing the total variation distance between their conformity score distributions.
Our theoretical analysis demonstrates that conformal prediction coverage guaran- tees remain bounded under domain shift. The essential role of domain alignment is to actively reduce the error term in this theoretical bound, making our uncertainty quantification for target domain samples more precise and reliable.
Take Away:
3.2.3 UNCERTAINTY-DRIVVE ADAPTIVE LEARNING
With this theoretically-grounee and aaamiically-adjustaal prediction set C(x)), we transform into effective signals that guide model adaptive learning.
The semantic confidence weight theoretically grounded in conformal prediction. By Theorem 3.1, smaller prediction sets indicate higher model certainty with statistical coverage guarantees. [C(x;)] serves as natural and rigorous uncertainty measure. We define its reciprocal as the semantic confidence weight, which modulates each target sample's contribution:
p(c x1)) Ifc E C(x))
Te(c)
(4)
[((,,]]
ESec(e)) p( x,)
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This soft label more faithfully reflects the model's judgment within its confidence range compared to hard labels, avoiding overly absolute supervision on uncertain samples.
Combining these two mechanisms, pseudo-superrisson loss. This loss function achieves dual protection: inter-sample, through wi to suppress the overall influence of high-uncertainty samples; intra-sample, through provide smoother and more reliable supervision distribution:
construct the semantically-weighee target domain
Ltrrget =
Σ B.
"e CF p(- [x)))
(5)
B&
3.2.4 CONFIDENCE-GUIDEL DOMAIN ALIGNMENT
Beyond constructing more robust single-sample supervision for the target domain, we further apply semantic confidence to guide the macroscopic domain alignment process, correcting the blindness of traditional alignment methods.
Traditional domain alignment approaches uniformly minimize distributional differences between source and target domains. However, when the target domain contains numerous semantically am- biguous boundary samples, forced alignment of these samples may actually distort the semantic structure of the shared feature space. To address this issue, we first compute the average semantic confidence within a target batch and use it weight for the alignment loss:
sem B,
B.
Σ E.
wi
Lalign = W Bi
sem
B.
Σ ((G()) ZEB
- B
Σ (G(x))) (6) BEB.
where G(-) denotes the feature extractor and Φ(+) represents the MMD kernel mapping. This batch- level macroscopic weighting mechanism operates under the following logic: when target batch exhibits low overall confidence, we correspondingly reduce domain alignment intensity to prevent the model from being misled by these problematic samples. Conversely, we strengthen alignment when confidence high. This enables the model to preferentially align core data manifolds with clear semantics in both domains, achieving more stable and meaningful feature distribution align- ment that establishes a solid semantic foundation for subsequent high-quality hash code learning.
3.3 REPRESENTATION--LVVELL CALIBRATION: BIT-WISE RELIABILITY MODELING
While semantic-level calibration addresses the reliability of what to learn, representation--eve cali- bration focuses on the intrinsic stability of how to learn hash codes effectively. A high-quality hash code must not only maintain semantic discriminability but also ensure that each individual bit is bust and exhibits low redundancy. The flipping of single unreliable bit can cause dramatic changes in Hamming distance, severely affecting retrieval precision. Therefore, extend uncertainty anal- ysis from the macroscopic semantic level to the microscopic bit level.
Proxy Task for Bit Stability. To quantify the reliability of each bit, we design self-supervised proxy task. The core assumption is that a robust bit should maintain sign stability when facing minor perturbations in input data.
Specifically, for each sample x; in the source domain, we obtain its feature vector ft. An augmented version f is created by applying Gaussian noise to ft. After passing f. and f through the hash layer, they yield continuous pre-hash vectors h, and h/. Based on these, we generate stability label Wi.k for each bit of h4:
Us = I(sign(he..) = (hgn())
(7)
where II(-) denotes the indicator function. Then, we introduce a lightweight bit confidence prediction head Gbie.)) that operates in parallel with the backbone network. It receives image features and predicts an L-dimensional confidence vector bit E [0. 1]. This head is trained through binary cross-entropy loss predict Uz which naturally drives the predicted confidence polarize toward binary values {0, 1} without requiring explicit thresholds. We employ a separate prediction head rather than on-the-fly perturbation during inference ensure retrieval efficiency. Direct perturbation would require multiple forward passes per query, significantly increasing latency. Our lightweight head predicts stability in single pass (O(1)), maintaining the speed advantage of hashing.

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3.3.1 CONFIDENCE- HASH LEARNING AND RETRIEVAL
The learned bit confidence bit plays a crucial role in both training and testing phases, enabling end-to-end uncertainty awareness.
Weighted Quantization Loss. Traditional quantization loss ||A sign(h)]l uniformly penalizes all bits that deviate from =1. We leverage bit confidence to weight this loss, making the model focus more on bits predicted to be stable and reliable during training, while providing greater tolerance for unstable bits and allowing them more thorough exploration in continuous space. We reweight the quantization term using bit confidence, apply-
ing stronger constraints only on trustworthy bits while reduc-
1.00
ing backward noise from unstable bits:
0.75
Lquant
stop_ gop_grad("21) bit - max (0, 1 1- 1-
0.50
LBLL
0.25
DEB k=1
(8) where biop_grad prevents the model from circumventing quantization by manipulating whit, The dynamics of bis are illustrated in Figure 4, where bit is the average of bith in mini-batch.
0.00
5
Epoch
Figure 4: Bit-level calibration hit on Office-Home Ar task.
Uncertainty- Weighted Hamming Distance. During retrieval, we leverage the learned bit confidence to dynamically weight Hamming distance, sup- pressing contributions from unreliable bits. We use the bit confidence whit of query sample Tig as dynamic weights to construct a novel distance metric. This ensures that when computing distances between query and database samples, bit positions where the query sample itself exhibits uncertainty receive lower weights, naturally reducing the noise impact from unreliable bit flips and significantly enhancing retrieval robustness:
dUWHD (1ig Fa)
Σ Wggk -1--ba bl.bba) k=1
where Wg.b [0, 1] represents the bit-level weight derived from query confidence w Note that Eq. utilizes continuous weights primarily for differentiable optimization during training. For effi- cient large-scale retrieval, the metric to a masked Hamming distance, enabling UWHD to be computed via efficient bitwise operations. This series of designs enables our model to not only learn hash code generation but also develop quality assessment capabilities for its own generated hash codes, integrating this assessment ability throughout the entire lifecycle from learning to application.
binarize the query weights Wg.A {0, 1} via rounding. This reduces
3.4 BELU-REGGLA CALIBRATED ADAPTATION: CLOSEED-LOOP LEARNING SYSTEM
We further construct a self-regulating mechanism that transforms these tools from passive active compo- nents. This mechanism addresses the classic challenge of manually balancing loss weights multi-objective optimization by using the model's real-time uncertainty as intrinsic control signals to dynamically adjust learn- ing focus, forming intelligent closed loop system.
Retrieval-time Re-Calibration
1
Query Code b,
query-side weights only
Database Codes
Specifically, we compute the average semantic confi- dence Wp. and average bit confidence whit for each batch B,- These aggregated indicators reflect the model's overall grasp of the current batch data at the adaptive weights X(-) to dynamically modulate the intensity of various loss terms:
Figure 5: Illustration of biv-l uncer- tainty calibration mechanism.
present stage. We them as inputs to
(10) where f()) represents linear scaling functions, and the stop_graa _raddgr operation ensures these weights do not directly participate in gradient computation, guaranteeing training stability.
Atarget (B,) = fsem _epp_grddaap
Aquant (B₂) fquaut sstop_grad(ubi))
The intuitive logic follows a natural learning progression. During early training, with low them re- sulting in small Atarget and Aatign the model treats pseudo-labels and domain alignment cautiously,
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Table 1: Performance of cross-domain retrieval (mAP%) on Effice-Home and Office-31.
OFFICE-HOME
OFFICE31
Methods
Pr-Re
CI- QI-RR
Re-AAr
Re -Pr Re-CI
Ar-Re
Am DD-
Am
We
We-Ds
Dm->Am
We-+Am
Ds->We
Avg.
ITQ
26.81
14.83
25.37
28.19
14.92
25.88
29.55
28.53
58.00
26.83
25. 25.09
$8.89
30.24
OCH
18.65
10.27
17.54
20.15
10.05
18,09
24.86
22.49
51,03
22.45
20.79
53.64
24.17
DSH
5.47
9.67
8.26
5.28
13.58
SGH
24.51
13.62
22.53
25.73
13.51
22.93
24.98
22.47
53.94
22.17
20.52
56.36
26.94
GraphBit
18.91
24.48
21.34
GTH-gg
20.00
10.99
18.28
21.95
11.68
19.05
23,08
21.20
49.38
19.52
17.41
50.14
23.56
PWCF
39.78
35.12
35.01
72.91
DHI ing
48.47
30.81
38.68
45.24
25.15
43,30
41.96
45. 10
75.23
42.89
41.74
79.91
46.54
DAPH
27.20
15.29
27.35
19
15.29
26.37
32.80
28.66
60.71
28.
27.59
64.11
31.85
PEACE
53.04
38.72
42.68
54.39
28.36
45.97
46,69
48.89
78.82
46.91
46.95
83,18
51.22
DANCE
53.73
39.03
43.54
55.14
28.87
44.53
44.78
47.66
78.39
46.68
48.61
84.75
51.31
IDEA
59.18
45.71
49.64
61.84
32.77
51.19
48.70
54.43
84.97
53.53
53.71
88.69
57.03
COUPLE
63.94
49.24
54.35
64.29
41.39
54.14
50.27
59.32
85.26
56.04
56.35
88.90
60.29
COLA
67.04
52.65
57.23
67.88
41.71
57.35
52.51
62,08
87.28
58.09
57.60
89.65
62.59
Table 2: Performance of cross-domaies retrieval (mAP%) on MNIST and USPS.
MNIST USPS
USPS
MNIST
Methods
16
48
96
32
64
128
Avg.
ITQ
13.05
15.57
18.54
20.12
23.12
23.89
13.69
17.51
20.40
20.30
22.79
24.59
OCH
13.73
17.22
19.59
20.18
20.66
23.34
15.51
17.75
18.97
21.50
21.27
23.68
19.45
DSH
20.60
22.21
23.68
24.28
25.73
26.50
19.54
21.22
22.89
23.79
25.91
26.46
23.57
SGH
14.24
16.69
18.72
19.70
21.00
21.95
13.26
17.71
18.22
19.01
21.69
22.09
18.69
GraphBit
13.92
17.86
20.17
20.82
21.32
23.19
15.16
16.82
17.87
19.85
20.10
22.54
19.13
GTH-g
20.45
17.64
16,60
17.25
17.26
17.06
15.17
14.07
15.02
15.01
14.80
17.34
16.47
PWCF
47.47
51.99
51.44
51.75
50.89
59.35
47.14
50.86
$2.06
$2.18
57.14
58.96
52.60
DHLing
49.24
54.90
56,30
58.28
58.80
59.14
50.14
51.35
53.67
58.65
58.42
59.17
55.67
DAPH
25.13
27.10
26.10
28.51
30.53
30.70
26.60
26.43
27.27
27.99
30.19
31.40
28.16
PEACE
52.87
59.72
60.69
62.84
65.13
68.16
53.97
54.82
58.69
60.91
62,65
65.70
60.51
DANCE
53.18
57.98
61.23
63.15
65.92
68.87
54.31
55.64
$7.26
61.49
63.43
66.23
60.72
IDEA
58.89
64.48
65.72
67.48
70.24
74.34
60.99
61.47
65.45
67.97
69.72
72.31
COUPLE
60.56
66.05
66.23
67.98
73.02
75.12
63.28
64.94
67.44
70.19
72.87
74.62
68.53
COLA
62.21
67.72
67.35
68.91
75.09
77.67
65.11
67.27
69.83
72.94
74.33
76.33
70.40
avoiding aggressive adaptation before sufficiently understanding the target domain. This mecha- nism naturally acts as warm-up strategy: early in training, high uncertainty leads to low Atarget. preventing the model from overfitting to noisy pseudo-labels. As the model learns from the source domain, uncertainty decreases, and the target adaptation gradually engages.
Finally, our total training objective integrates all modules through dynamic balancing via the self- regulating mechanism:
Liotal Lsource + Lhit_bead + Atarget Crarget + Aalign + Aquant
(11)
This design paradigm enables the entire adaptation process to be governed by the model's own cognitive state, achieving truly adaptive, robust, and efficient end-to-end learning.
Computational Complexity. The calibration phase requires only one-time sorting and weighted quantile estimation with complexity O log Real), where nicl is the size of the calibration set. This can be approximately reduced to linear time using quantile sketching algorithms.
4 EXPERIMENT
4.1 EXPERIMENTAL SETTINGS
Datasets. We compare our COLA with extensive baselines on three popular cross-domain bench- marks: Office-Home (Venkateswara et al., 2017), Office-31 (Saenko et al., 2010), and Dig- its(MNIST (LeCun et al., 1998) and USPS (Hull, 1994).). We follow the transfer tasks as previous research (Wang al., 2023b; Luo et al., 2025) for fair comparison.
Baselines. We compare our COLA with state-of-the-art hashing methods, including five unsuper- vised methods (ITQ (Gong et al., 2012), OCH (Liu et al., 2018), DSH (Jin et al., 2013), SGH (Jiang & Li, 2015), GraphBit (Wang et al., 2022)) and eight domain domain-adaptive methods (GTH-g (Zhang et al., 2019), PWCF (Huang et al., 2020), DHLing (Xia al., 2021a), DAPH (Huang et al., 2021), PEACE (Wang et al., 2023a), DANCE (Wang et al., 2023b). IDEA (Wang et al., 2023d), COU- PLE (Luo et al., 2025)) baselines. More details can be found in Appendix C.
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Table Comparison of model variants on the Office-Home with 64 bit hash code.
Variants
SC
RC
SR
Pr-Re
CI-+Re
Re-+Ar
Re-+Pr
Re-+CI
Ar-Re
Avg.
COLA (None)
59.65
46.47
49.66
59.56
31.92
47.56
49.14
COLA-SC
59.92
47.08
49.89
59.81
32.07
47.82
COLA-RC
/
60.83
48.64
51.33
61.22
35.84
52.70
51.76
COLA-SR
61.41
47.77
52.24
61.69
35.11
51.06
51.55
COLA w/o SC
/
65.13
48.89
54.12
65.97
40.01
53.04
54.53
COLA w/o RC
V
65.95
49.39
56.16
66.87
39.68
53.18
55.21
COLA w/o SR
V
/
65.25
49.30
53.29
65.62
39.95
55.03
54.74
COLA (Full Model)
V
/
/
67.04
52.65
57.23
67.88
41.71
57.35
57.31
Re
Re
Ar
60
Bi:
88
128 Bil
Bit
mAP (%)
58
128 BIL
3X
ma MAP (%)
58
125 BiL
Bi:
mAP
86
56
56
64
54
10
20
30
25
15
25
Calibration set ratio Fear (%)
Calibration set ratio Fool (%)
Calibration set ratio (%)
Figure 6: Sensitivity analysis calibration set ratio Teal-
Implementation Details. To guarantee fair comparison, our model configuration is set in (Wang et al., 2023d; Luo et al., 2025). All experiments are implemented in PyTorch and conducted on single NVIDIA Hopper GPU. The hash layer consists of a two-layer MLP, and the same structure is used for bit head prediction. We use the Adam optimizer and the initial learning rate is set to 0.001. The batch size is set to 32. The training epoch set to 35, And we set the proportion of the calibration set to 0.2, the mapping range for to [0.05, 0.2], and EMA smoothing coefficient to 0.7 as common practice.
We use several standard metrics to assess our COLA: : mean Average Precision (mAP), Top-N accuracy curve, Top-N recall curve, and precision-recat curve. The mAP widely adopted to measure the overall retrieved list. Top-N accuracy and recall curves can demonstrate the performance given varying retrieval quantities. The precision-recall curve is also widely popular due to the trade-off between the precison and recall.
Evaluation Metrics.
4.2 EMPIRICAL RESULTS
Performance Comparison. To begin with, we compare the retrieval performance of all approaches on three benchmark datasets, as shown Tables and 2. Table reports the cross-domain retrieval results Office-Homm and Office-31 31 with fixed 64-bit hash code length. Furthermore, tigated the cross cross-domain performance of each method under varying hash code lengths on the USPS and MNIST datasets, and the results are presented in Table 2. From the results reported in Tables and 2, we observe that COLA consistently and significantly outperforms existing state-of-the-art approaches, achieving an average improvement of around 3.3% retrieval performance. Earlier methods, such as DAPH (Huang et al., 2021), PEACE (Wang et al., 2023a) generally suffer from in- ferior performance due relatively simplistic domain adaptation strategies. The performance gain of our COLA over advanced baselines can be largely attributed to its unique hierarchical uncertainty calibration framework. To better understand our COLA. we also conduct qualitative analysis exper- iments. In particular, precision-recall curves, Top-N precision curves, and Top-N recall curves are compared. The more detailed qualitative analysis of these results is provided in the Appendix D.
inves-
Ablation Study. Table 3 reports the retrieval performance of ablation variants on the Office- dataset. We can conclude that COLA is best performance, demonstrating the importance of each component. The variant COLA (None) in Table 3 represents the baseline with all three compo- nents (SC, RC, SR) removed, which serves as a standard UDAH baseline. Disabling semantic- calibration leads to significant performance drop from 57.31% % to 54.53% in average mAP. This underscores the critical role of conformal prediction in quantifying semantic uncertainty to generate reliable soft pseudo- labels and guide domain alignment. Excluding representation-level calibration

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IDEA
COUPLE
Ours
IDEA
COUPLE
Ours
Figure 7: The t-SNE visualization of three methods Office-Homi Home; The correlation heatmaps of 16-bit binary codes on Office-Home (Ar -> Re).
degrades the mAP to 55.21%, %, which demonstrates the importance of modeling bit-wise reliabil- ity. These substantial performance degradations empirically validate the necessity of our weighting mechanisms, with each component contributing meaningfully to the final performance. Also, re- moving the self-regulating results in a notable performance decrease to 54.74%. This confirms the benefit of dynamically balancing the learning objectives based on the model's real-time uncertainty. We also compared with other variants that contain single component. Note that the centroid- based calibration set essential for the SC module to compute semantic distances, and dynamic is inherent to the SR mechanism. Thus, ablation design properly isolates the contribution of each component within the coherent framework. More details of the ablation study are in the Appendix D.2.
Uncertainty Analysis. We analysed the bit-level confidence of larget domain across different hash lengths (32, 64, and 128 bits) on Office-Home dataset. From the results shown in figure
1.0
can draw the following conclusions. Firstly. the bit-level confidence starts near 0.5, reflecting the model's s random initial state, then sharply drops near-zero as the model begins learning and calibrating its uncertainty. Fi- nally, as the model converges and learns a stable feature rep- resentation, the confidence rises high and stable value. Secondly, shorter codes (32-bit) achieve higher final con- fidence, as each bit must be more informative. Conversely, longer codes (128-bit) require more time to stabilize, result- ing in slower confidence recovery during training.
0.6
0.4
Wraee
0.2
Weace
0.0
10
20
30
Epoch
Figure 8: Bit-level confidence evolu- tion during training across different hash code lengths (32, 64, and 128 bits) on Office-Home dataset. (Art Real World task.)
Sensitivity Analysis. We conduct the sensitivity analysis to access the robustness of the proposed COLA with respect to the hyperparameter calibration set ratio Teat- The analysis is performed onOffice-Home with different hash code lengths. As Figure 6 shows, the retrieval performance of COLA remains stable across a wide range of calibration set ratios. We observe a better performance when Teal is set to 20%. More details are in Appendix D.3.
Visualization. To further understand the semantic structure of the learned representations, we adopt t-SNE visualization demonstrate the discriminative binary codes on Office-Home The results are shown in Figure? 7. From the results, we can observe that our proposed COLA can generate more discriminative binary codes compared the other two baseline methods.
CONCLUSION
To address the unreliable uncertainty handling in existing unsupervised domain adaptive hashing methods, this paper introduces COLA based on hierarchical conformal calibration. Our approach abandons traditional heuristic strategies favor of principled mechanism with rigorous statistical guarantees that quantifies uncertainty at both semantic and representation levels, thereby generat- ing more reliable supervision signals for the target domain and modeling the stability each hash bit. Extensive experiments multiple benchmark datasets validate the superiority of our method, demonstrating consistent and significant improvements over state-of-the-an approaches. sum- mary, COLA provides more reliable and adaptive solution for cross-Be doms-d retrieval tasks through systematic utilization of uncertainty, establishing a new paradigm that transforms uncertainty from an obstacle into valuable resource for robust domain adaptive hashing.
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ETHICS STATEMENT
Our research adheres to the ICLR Code of Ethics. The code and related materials will be appropri- ately released to ensure transparency and reproducibility of our work. All datasets used in this study are publicly available.
ACKNOWLEDGMENT
Ming Zhang, Jinsheng Huang and Junyu Luo are supported by grants from the National Key Re- search and Development Program of China with Grant No. 2023YFC334122 and the National Natural Science Foundation China (NSFC Grant Number 62276002).
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A ACKNOWLEDGMENTS OF LLM USAGE
We utilized large language model to aid our writing process. specifically for correcting gram- mar, improving sentence structure, and fetching related papers. The scientific contributions remain entirely our own.
B DATASET DETAILS
We evaluate our method on three widely-used cross-domain benchmarks for unsupervised domain adaptation tasks.
Office-Home (Venkateswara et al., 2017): This dataset contains four distinct domains: Artistic (Ar), Clip Art (CI), Product (Pr), and Real- World (Re). To ensure fair comparison with previous work, we follow the standard protocol and establish six cross-domain image retrieval tasks among these domains, including: Pr-+Re, CI-+Re, Re-AAr Re-PPr, Re-CII Ar-
Offiiee31 (Saenko et al., 2010): This dataset contains 31 categories from three domains: Amazon (Am), Webcam (We), and DSLR (Ds), with total over 4000 images. similarly set up image retrieval transfer tasks on this dataset: Am-DDs, Am->ee We-+Ds, Ds Am,, We-+Am, We.
Digits: For handwritten digit recognition, we utilize the classic datasets, MNIST (LeCun et al., 1998) and USPS (Hull, 1994). By alternating them as the source and target domains, we constructed transfer tasks: MUIST~UUSPS and USPS-*MISS
C BASELINE DETAILS
To comprehensively evaluate COLA, selected series of state-of-the-art hashing algorithms as comparative baselines, covering both unsupervised and adaptive hashing cat- egories. To ensure fairness in comparison, the experimental results of all baseline methods were reproduced to match the reported results in their original publications. The core ideas the base- line methods are briefly summarized follows.
ITQ (Gong et al., 2012): A simple yet efficient alternating minimization algorithm with both supervised and unsupervised learning paradigms.
OCH (Liu al., 2018): Approximates ordinal relations by a tensor ordinal graph, and employs ordinal constraint projection with a small set of centroids.
DSH (Jin et al., 2013): A variant of locality-sensitic hashing (LSH), which employs random projections to generate multi-view representations for metric learning.
SGH (Jiang Li, 2015): Designed to transform high- high-dimensional features into binary codes, well-suited for large-scale semantic similarity mining tasks.
GraphBit ( (Wang et al., 2022): Explores bit-level interactions among features in continuous space, substantially alleviating the expensive search costs arising from training convergence difficulties in reinforcement learning.
GTH-g (Zhang et al., 2019); Finds the optimal hashing mapping functions for the target domain based on source-domain samples.
PWCF (Huang et al., 2020): Leveraging a Bayesian model for learning discriminative hash codes and infers the similarity structure through histogram features.
DHLing (Xia et al., 202 Ia): Optimizes hash codes through learnable clustering, and introduces memory-bank mechanism to mitigate the effects domain shift.
DAPH (Huang al., 2021): Learning domain-invariant feature projections, which effectively reducing distribution discrepancies.
PEACE (Wang el al., 2023aj: Applies pseudo-labeling techniques learn target semanties, and subsequently minimizes domain transfer through implicit and explicit strategies.
DANCE (Wang et al., 2023b): dual-level hashing learning framework that optimizes cross- domain high-level feature prototypes via contrastive learning.
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Pr + Re
Re + Ar
Re + C1
OurS COUPLE
0.8
Qurs
0.5
Ours
0.8
COUPLE
COUPLE
IDEA
IDEA
IDEA
0.6
Precision
0.6
Precision
Precision
044
0.4
0.3
0.4
0.2
0.2
0.2
0.0
0.0
0.0
0.8
Recall
Recall
Recall
Cl + Re
Re Pr
Ar Re
0.8
Ours
Chora
0.9
Oura
0.7
COUPLE
0.7
COUPLE
COUPLE
IDEA
IDEA
IDEA
Precision
0.6
0.5
Precision
0.6
0.5
Precision
0.8
0.4
0.4
0.4
0.3
0.2
0.2
0.1
0.0
0.2
0.4
0.8
1.0
0.4
0.6
0.8
1.0
0.2
0.4
0.6 Recall
0.8
1.0
Recall
Recall
Figure 9: The comparison of precision-reee recall curves with 64-bit hash code on the Office-Home dataset.
IDEA (Wang et al., 2023d): Decomposes visual representations into causal features which carry curical semantics and non-causal features, and produces binary codes from the causal components.
COUPLE (Luo al., 2025): Simulates the dynamic process via graph flow diffusion, and employs hierarchical mixup to achieve progressive cross-domain alignment.
D MORE EXPERIMENT RESULTS
D.1 PERFORMANCE COMPARISON
To gain deeper insights of our COLA, we also conduct qualitative analysis experiments. We com- pared various approaches via precision-recall curves, Top-N precision curves, and Top-N recall curves. The results shown in Figure 9, 10, and 11.
From the precision-recall curves in Figure 9, our COLA consistently outperforms all baseline meth- ods across different dross-domain tasks the Office- Hffee-Home dataset. The curves demonstrate that COLA maintains higher precision values at all recall levels, indicating superior retrieval quality. Notably, the area under the PR curves for our method is significantly larger than that of competing approaches, suggesting more robust performance across varying similarity thresholds. The Top-N precision analysis Figure 10 reveals that COLA achieves the highest precision scores across dif- ferent values of N. This improvement is particularly pronounced when N is small, which is crucial for practical retrieval applications where users typically focus on top-ranked results. The consistent performance advantage across all six cross-domain tasks demonstrates the generalizability of our uncertainty calibration mechanism. Similarly, the Top-N recall curves Figure 11 show that our method achieves superior recall rates compared to baseline approaches. The faster convergence of recall curves indicates that COLA can retrieve more relevant items within smaller candidate sets, which is essential for efficient large-scale retrieval systems. The substantial improvement margins across different domain adaptation scenarios validate the effectiveness of our conformal prediction- based calibration strategy in handling domain shift challenges.
17

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Published as a conference paper at ICLR 2026
Pr Re
Re Ar
Re C1
0.93
0.84
0.65
Ours COUPLE IDEA
Ours COUPLE
Ours COUPLE
0.75
0.67
0.52
IDEA
Precision
0.66
Precision
0.58
Precision
0.46
0.57
0.49
0.39
0.48
0.41
0.33
0.29
0.24
0.20
0.11
0.06
0.08
Top-N
Top-N
Top-N
C1 + Re
Re - Pr
Ar - Re
0.81
0.87
Ours
Ours
Curs
0.73
COUPLE
0.76
COUPLE
0.79
COUPLE
0.66
IDEA
0.68
IDEA
0.70
IDEA
Precision
Precision
Precision
0.62
0.50
0.52
0.54
0.34
0.36
0.37
0.26
0.29
0.19
0.20
0.20
0.11
0.12
0.12
10
20
30
40
50
10
20
30
40
10
20
30
40
50
Top-N
Top-N
Top-N
Figure 10: The comparison of Top-N precision curves with 64-bit hash code Office-Home.
Table 4: The comparison of model variants on the Office-Home with 64-bit hash code.
Variants
SC
RC
SR
Pr-+Re
CI-+Re Re-+Ar
Re
Re-+CI
Ar-
Avg.
COLA (Nonc)
59.65
46.47
49.66
59.56
31.92
47.56
49.14
COLA-SC
59.92
47.08
49.89
59.81
32.07
47.82
49.43
COLA-RC
60.83
48.64
51.33
61.22
35.84
$2.70
51.76
COLA-SR
61.41
47.77
52.24
61.69
35.11
51.06
51.55
COLA w/o SC
65.13
48.89
54.12
65.97
40.01
53.04
54.53
COLA w/o RC
65.95
49.39
56.16
66.87
39.68
53.18
55.21
COLA w/o SR
65.25
49.30
53.29
65.62
39.95
55.03
54.74
COLA (Full Model)
67.04
52.65
57.23
67.88
41.71
57.35
57.31
D.2 ABLATION STUDY
To investigate the effectiveness of the core components in COLA, we conduct comprehensive ab- lation studies by systematically removing or modifying key components from the full model. We define several ablation variants to analyze different aspects of our approach:
COlA(Full Model): The complete COLA with all proposed components including semantic- level calibration, representation--evell calibration, and self-regulating mechanism.
COLA w/o SC: Removes the conformal prediction-baute semantic uncertainty quantification module, using standard pseudo-labeling without uncertainty estimation.
COLA w/o RC: Excludes the bit-wise reliability modeling component, treating hash bits equally without considering their individual confidence levels.
COLA w/o SR: Disables the dynamic objective balancing mechanism, using fixed weights for different loss components throughout training.
COLA-SC: Retains only the semantic-level calibration component while removing other mod- ules.
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Published as a conference paper at ICLR 2026
Re
Re Ar
Re
0.77
0.75
0.49
Ours COUPLE
Ours COUPLE
Ours
COUPLE
0.63
IDEA
0.63
IDEA
0.40
IDEA
0.56
0.57
0.36
Recall
0.49
Recall
0.51
0.31
0.42
0.45
0.27
0:23
0.28
0.33
0.18
0.14
0.21
0.10
Top-N
Top-N
Top-N
Pr
Ar + Re
Ours
Ours
Outs
0.62
COUPLE
0.70
COUPLE
0.89
COUPLE
IDEA
IDEA
IDEA
0.49
0.36
0.55
Recall
Recall
0.49
0.48
0.36
0.41
0.40
0.30
0.34
0.33
0.27
0.26
0.17
0.20
0.19
6
10
8
10
10
Top-N
Top-N
Top-N
Figure 11: The comparison Top-N recall curves with 64-bit hash code on Office-Home Dataset.
Keeps only the representation-leel calibration while excluding semantic and self- regulating components.
COLA-RC:
Maintains only the dynamic balancing mechanism without uncertainty calibration modules.
COLA-SR:
COLA(None):: Removes all three core components, which reduces standard deep unsuper- vised domain adaptive hashing baseline that relies solely on basic source supervision, a standard quantization loss, and unweighted domain alignment loss.
Table reports the comprehensive retrieval performance comparison of these ablation variants on the Home dataset across all six cross-domain tasks. The experimental results provide several important insights:
Impact of Semantic-Level Calibration: Removing the conformal prediction-based semantic cal- ibration leads to the most significant performance degradation, with average mAP dropping from 57.31% 54.53%. This substantial decrease demonstrates the critical importance of uncertainty quantification in generating reliable soft pseudo-labels. Without proper semantic uncertainty esti- mation, the model struggles to distinguish between confident and uncertain predictions, leading to noisy supervision signals that harm domain alignment effectiveness.
Importance of Representation-Leww Calibration: Excluding the bit-wise reliability modeling results in notable performance decline 55.21% average mAP. This confirms that not all hash bits contribute equally the final representation quality, and modeling individual bit confidence essential for robust cross-domain hashing. The representation-leve calibration enables the model to focus on reliable bits while suppressing unreliable ones during the learning process.
Effectiveness of Self- Regulating Mechanism: Disabling the dynamic objective balancing leads to a performance drop to 54.74 44.74% average mAP. This validates the importance of adaptively adjusting the learning objectives based real-time uncertainty estimates. The self-regulating mechanism prevents the model from over-fitting to uncertain predictions and ensures stable training dynamics across different domain adaptation scenarios.
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Pr Re
Re - Ar
Re - Cl
60
32 BIL
32. Bn
68
128 Bit
65 Ritt
MAP (%)
188
64 TU
128 Bit
mAP (%6
68 BR
123
66
56
64
54
Calibration Fear (%)
Calibration ratio Foo (%6
Calibration Fox (%)
Cl + Re
Re - Pr
Ar Re
70
22 Bit
32.80 BR
M1 I!I
66 nn
125 Di
60
128.81
MAP (%)
128 Bit
mAp
52
mAp
66
50
Calibration Feat (%)
Calibration ratio Fowl (%)
Calibration Foal (%6
Figure 12: Sensitivity analysis on calibration ratio real on Office-Home with different hash code
lenghts.
Table 5: Retrieval time cost (ms) varies with code length.
16 Bit
32 Bit
48 Bit
64 Bit
96 Bit
128 Bit
Dense Vector
440.3
493.0
547.0
605.3
659.7
700.3
Vanilla Hash Code
15.38
17.94
20.32
18.97
21.83
22.37
UWHD
15.94
18.55
21.00
19.63
22.59
23.20
Speed Up
27.62
26.58
26.05
30.83x
29.20x
30.19x
Individual Component Analysis: The variants with only single components (Only Semantic: 53.89%, Only Representation: 53.12%, Only Self-Regulating: 52.95%) all perform significantly worse than the full model, indicating that the synergistic combination of all components is crucial for optimal performance. Each component addresses different aspects of the cross-domain hashing challenge, and their integration creates more robust and effective framework.
These ablation results conclusively demonstrate that each proposed component contributes meaning- fully to the overall performance, and their combination in COLA achieves the best balance between uncertainty calibration and cross-domain adaptation effectiveness.
D.3 SENSITIVITY ANALYSIS
We conduct the sensitivity analysis on the hyperparameter calibration set ratio Teat- The analysis performed on the Office-Home dataset with different hash code lengths. Figure experimental results of sensitivity analysis.
shows all
D.4
CASE STUDY
We perform hash-based retrieval and present the top-5 results in Figure 13. COLA achieves higher retrieval accuracy than advanced baselines, validating the effectiveness of our proposed COLA and benefiting downstream retrieval-base tasks.
D.5
SPEED TEST
In this part, we conducted speed evaluation COLA and dense vector retrieval. Following previous works (Luo et al., 2025), we use a database of 80 items. Each method was run 10a times. We report the average retrieval time (ms) in Table 5. The results indicate that COLA could achieve substantially faster retrieval than dense vectors, and the inference- calibration will not affect the efficiency, underscoring COLA'S efficiency in large-scale retrievals. Since the inference-time
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Ours @5
CUOUPLE @5
DELL
IDEA @5
Ours @5
CUOUPLE @5
IDEA @5
Figure 13: Case study COLA, COUPLE and IDEA. Query the top 5 images the Office-31 with 64 bits hash code.
metric binarized into masked Hamming distance, it remains compatible with standard hardware- accelerated bitwise operations and existing ANN indexing structures.
D.6 CALIBRATION STRATEGY ANALYSIS
To validate calibration construction, we compared target centroid-based strategy with random, per-class, and density-aware sampling on Office-Home. As shown in Table 6, our method achieves the lowest MMD (0.0025) and highest mAP, indicating that our Deat best approximates the target distribution Dr-
Table 6: Comparison calibration set selection strategies on Office-Home (Ar-Ree..
Strategy
mAP (%)
MMD (Deat D₁)
Ours
56.34
0.0025
Random Sampling
55.21
0,0087
Per- Per-Class Sampling
55.67
0,0057
Density- Aware (K-Means)
55.85
0.0032
D.7 DYNAMIC ALPHA ABLATION
We compared our dynamic a mechanism with a fixed a baseline. Table shows that dynamic a consistently outperforms fixed across all datasets, achieving higher mAP and better empirical coverage (closer to a)) The EMA parameter 0.7 was chosen to balance stability and adaptability.
We further investigated the impact of the EMA smoothing parameter Osmm As shown in Table 8, asm = 0.7 yields the best performance, providing an optimal balance between stability and adaptiv- ity.
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Conformal Coverage Analysis: Strategy Comparison
ideal 1-43
Centroid Strategy
6.9
Rendom Sempling Stretejy
Target Domain Coverage Rate
6.7-
Better Coverage
6.6
6.4
0.1
02
0.3
Target Error Rate (cc)
Figure 14: Conformal coverage analysis comparing our Target Centroid Strategy with Random Sam- pling. Our method (blue) closely follows the ideal coverage line (y 1 1-a), while random sampling (red) exhibits significant deviation.
Table Ablation study of Fixed vs. Dynamic a.
mAP (%)
Coverage
Dataset
Fixed a Dynamic a
Fixed a
Dynamic
Office-Home
55.22
57.31
0.87
0.91
Office-31
66.43
67.11
0.88
0.93
Digits
69.57
70.41
0.91
0.94
D.8 STANDARD HAMMING DISTANCE COMPARISON
To verify that our performance gain is not solely due to the weighted distance metric, we evalu- ated variant COLA (w/ Standard Hamming) which uses the full model but retrieves with standard Hamming distance. As shown in Table 9, it still outperforms the best baseline COUPLE.
D.9 THEORETICAL DISCUSSION
Theorem 3.1 indicates that the coverage guarantee depends on minimizing the TV distance hetween conformity score distributions. While directly computing this TV distance intractable, our Rep- resentation Calibration (RC) serves as an effective empirical proxy. By enforcing bit stability, RC implicitly aligns the feature distributions of the source and target domains. As shown our abla- tion study, the inclusion of RC significantly improves mAP (+2.62%) suggesting that it effectively reduces the distributional discrepancy and thus tightens theoretical bound.
E PROOF
Here we provide the detailed proof for Theorem 3.1. This theoretical guarantee of conformal predic- tion relies on the assumption that minimizing the feature distribution discrepancy (e.g., via MMD) effectively reduces the total variation distance between the conformity score distributions. This as- sumption holds approximately when the conditional distribution of conformal scores can be well approximated by a broad class of distribution families (Gretton al., 2012). In such cases, the duction feature discrepancy implies the closeness of distributions. Conformal Prediction under covariate shift distribution shift has been explored in prior work (Tibshirani et al., 2019; Bar- ber et al., 2023; Guan, 2023). For comprehensive introduction to conformal prediction, we refer readers Angelopoulos & Bates (2021).
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Table 8: Impact of EMA smoothing parameter Osm on mAP (%).
Dataset
Osm 0.5
Osm
0.6
O'mm
0.7
O'm
0.8
Osm 0.9
Offece-Home
57.22
57.28
57.31
56.97
56.93
Office-31
66.83
67.03
67.11
66.71
66.56
Digits
69.98
70.34
70.41
70.33
70.13
Coverage Rate Comparison Digits
0.975
Food (1-4)
Empiicall Rrad
ideal Dyna mic (1-0)
Emptiical Dynamic
Coverage Rate
0.900
0.875
15
30
45
60
75
90
Epochs
Coverage rate comparison on Digits dataset. Fixed a (red dashed) leads under- coverage in early training, while our Dynamic (blue solid) adaptively adjusts to maintain stable coverage around the ideal level.
Figure 15:
Theorem E.1 (Coverage Guarantee for Conformal Prediction under Domain Shift). Let dry denote the total variation distance. Suppose (Xtrains Ytraia) and (Xtests Ytest) are random samples from the source and larget distributions, respectively. Let qW be derived from equation 1. Then, the following coverage guarantee holds for the targel domain:
IP (s(Ntests Ytest) S 21 drv (s(Xtrains Ytrasn), s ((Srests Ytest))
(12)
If we further assume that the conformal score has continuous distribution in both domains, then we also have the upper bound:
I (s(Ntest, Ylest) S ) s1-a+ n x+1
+ drv (s(Xtrain Yerain), S s(Xtest, Ytest)). (13)
Proof. By the coverage guarantee of conformal prediction the source domain (Theorem 2.1 of Lei al. (2018)), we have:
P ([((train: Ytraán) S ( > -
(14)
Recall that for any two random variables U and V, the total variation distance is defined as
dTv(U, sup IP(U A) P(V e A)).
(15)
AEF
Here F is the o-algebra of measurable events. Now, consider the event A = {s < G... Applying the definition of total variation, immediately obtain:
IP (s(Xrests Ylest) S (W)
=P (s (X(trai Ytrain) S q (P (s(Xtrains Ytrain) S sQ")- -P
-P(ss (s((Xtest, Vrest) S ()))
21 drv (s(Xirains Ytrain), s ((Xrest- Ytest))
(16)
we further assume that the conformal score has a continuous distribution in both domains, then by the upper bound for conformal prediction on the source domain (Lei et al., 2018) 8), we have:
1
(s(Xtrain Yerain) S 5 a
(17)
+1
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Table 9: Standard Hamming Distance Comparison on Office-Home (64 bits).
Method
Avg mAP
COUPLE
54.56
COLA (w/ Standard Hamming)
56.23
COLA (Full w/ UWHD)
57.31
Following the same logic as the proof of the lower bound, obtain the corresponding upper bound:
IP (s(X Ytest) S (W))
=P (s (x(Xrrasss Ytrain) S q)) (P (s(Niests Yiest) S qq)) P (s (Xrrran Virai)) I q²))
< + drv (x(trann Yerain), a s(Xtest Yrast)).
(18)
This completes the proof.
24


Reviews:
[{"review_id": "ZZrBaapD3a", "reviewer": "Reviewer_bmwE", "summary": "This paper addresses the problem of uncertainty estimation in unsupervised domain adaptive hashing (UDAH). It introduces COLA, a hierarchical framework that unifies semantic-level conformal calibration and representation-level (bit-wise) reliability modeling under a self-regulating training scheme. At the semantic level, COLA employs conformal prediction to generate multi-label prediction sets instead of single pseudo-labels, ensuring controlled coverage even under domain shift. At the representation level, COLA estimates per-bit reliability by measuring feature stability under perturbations. These bit confidences reweight quantization loss and are also applied during retrieval as a query-weighted Hamming distance, enabling uncertainty-aware retrieval. Extensive experiments on Office-Home, Office-31, and MNIST-USPS datasets show consistent improvements in mAP and robustness, supported by ablations for each module.", "questions": "1. The current ablation toggles semantic calibration (SC), representation calibration (RC), and self-regulation (SR), and concludes that each helps. However, this does not isolate which part of the proposed conformalization is responsible for the final mAP improvements, because all components are evaluated under the same centroid-based D_{\\text{cal}} and dynamic \\alpha_t. To make the causal story convincing, please provide an ablation that (i) fixes D_{\\text{cal}} to a random subset and (ii) fixes \\alpha, and then measures the marginal gain from adding SC and RC separately. This will show whether the benefit truly comes from conformal calibration, rather than from generic confidence weighting.\n\n2. All reported experiments are on Office-Home, Office-31, and MNIST↔USPS, which are small-to-moderate in size. Yet the method introduces a retrieval rule that is more expensive than standard binary hashing. Please clarify the intended scope of the claim: is COLA meant only for moderate-scale UDAH (as in the current experiments), or is it intended to be a scalable, uncertainty-aware hashing method? If the latter, additional experiments on larger-scale benchmarks (DomainNet, VisDA-2017, or NUS-WIDE/MS-COCO for retrieval timing) are needed to support that scope.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- A clear strength of this paper is its two-level uncertainty design, which handles noise both in pseudo-label assignment and binary code learning. The semantic-level conformal predictor generates calibrated prediction sets to control pseudo-label confidence, while the representation-level reliability estimator measures bit-level stability and integrates these confidences into the learning process. This combination enables consistent management of uncertainty from prediction to representation.\n\n- The paper provides an explicit theoretical framing via Theorem 3.1, which establishes a coverage bound of 1 - \\alpha_t - \\text{TV}(P_s, P_t) under domain shift. The theorem connects conformal calibration with target-domain generalisation, grounding the semantic calibration step in probabilistic coverage terms. Although the reduction of the TV term has not been empirically proven, the presence of an analytical coverage expression distinguishes the paper from heuristic uncertainty-weighting works.\n\n- The inclusion of a self-regulating mechanism that reweights alignment and quantisation losses according to aggregated confidence metrics represents another notable design feature. By dynamically adjusting these weights, the framework avoids the need for manual tuning of trade-off hyperparameters and adapts its learning emphasis based on reliability feedback.", "weaknesses": "1) **Retrieval efficiency and scalability untested.** The proposed uncertainty-weighted Hamming distance (Eq. 9) replaces the standard bitwise XOR + popcount kernel that underpins hashing’s speed with a per-bit weighted sum. While accuracy gains are clearly demonstrated on Office-Home, Office-31, and Digits benchmarks, these datasets are only moderate in size and do not represent million-scale retrieval scenarios. The paper does not report retrieval latency, throughput, or index compatibility for this weighted metric, and its complexity analysis covers only calibration (sorting O(n_{\\text{cal}}\\log n_{\\text{cal}})). Thus, the impact on large-scale system efficiency remains unquantified.\n\nThis is because the proposed distance fundamentally changes the computation model from binary bit-operations to floating-point per-bit weighting. Therefore, it alters the very assumption that gives hashing its appeal: sub-millisecond similarity search using bitwise logic. Demonstrating that the new retrieval kernel still scales efficiently is therefore not an auxiliary test but a technical validation step. It confirms that COLA preserves hashing’s defining property of efficiency while adding uncertainty awareness. Without such timing and scalability evidence, the proposed method’s theoretical soundness is intact, yet its practical completeness is uncertain. At least, it is unclear to me whether the algorithm remains a true hashing framework or behaves more like a compact continuous embedding model.\n\nAdding runtime and scalability experiments on standard large-scale retrieval corpora such as NUS-WIDE, MS-COCO etc, along with a UDA-at-scale check on VisDA-2017 or DomainNet would directly verify that the uncertainty-weighted Hamming distance maintains the computational advantages of hashing.\n\n\n2. **Calibration-set construction is heuristic.**\nThe paper defines D_{\\text{cal}} as the top r_{\\text{cal}} of source samples nearest to the target centroid (default 20%). While this is a reasonable heuristic and sensitivity to r_{\\text{cal}} is analyzed, there is no comparison with alternative calibration-set selection rules (e.g., per-class, random, or density-aware sampling). Since Theorem 3.1’s coverage guarantee assumes that the calibration distribution approximates the target-domain score distribution, could the authors clarify how representative the chosen D_{\\text{cal}} is of the target domain in practice? Have the authors tested whether alternative calibration-set constructions produce similar coverage and retrieval performance, or could provide evidence (e.g., distributional similarity or coverage plots) to verify that the conformal bound remains valid under this heuristic?\n\n3. The adaptive \\alpha_t is an elegant idea, but its contribution is not explicitly ablated against a fixed-\\alpha baseline. That is, the paper introduces an EMA-based dynamic \\alpha_t, but there is no analysis of why a time-varying \\alpha_t yields better or more stable coverage than a fixed \\alpha, nor is there an ablation comparing the two. Since \\alpha_t directly controls prediction-set size and, through it, the confidence-weighted alignment, please provide: (i) a fixed-\\alpha baseline on all three datasets; (ii) a plot of empirical coverage vs. time for both fixed and dynamic \\alpha; and (iii) an explanation of how the EMA parameters were chosen. Without this, the dynamic schedule appears ad hoc rather than necessary.\n\n4. The theoretical result (Theorem 3.1) depends on a reduction of the TV distance between source and target conformity-score distributions through alignment. However, the paper does not empirically estimate or proxy this TV term, so the connection between the alignment loss and actual coverage improvement remains unverified experimentally. Please (i) justify why this bound is meaningful under the non-exchangeable source/target feature distributions in these datasets, and (ii) provide an empirical proxy (e.g., pre-/post-alignment MMD on the conformity scores) to support the claim that alignment makes the conformal coverage guarantee non-vacuous.", "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": "NuDapgfrAU", "reviewer": "Reviewer_uPy1", "summary": "This paper proposes a conformalized hierarchical calibration method called COLA for unsupervised domain adaptive hashing that integrates uncertainty quantification at both semantic and representation levels. The method leverages conformal prediction to produce confidence-calibrated pseudo-labels and introduces bit-level reliability modeling for hash code robustness. Additionally, a self-regulating mechanism dynamically balances learning objectives based on real-time uncertainty. Experiments on some benchmarks demonstrate improvement over state-of-the-art baselines.", "questions": "see weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe use of conformal prediction for uncertainty estimation in domain adaptive hashing is innovative and grounded in theory, supported by formal coverage guarantees under domain shift.\n\n2.\tThe hierarchical semantic and bit-level calibration is well-structured and addresses both label noise and representation robustness.\n\n3.\tExtensive experiments and clear performance gains across diverse benchmarks demonstrate effectiveness and robustness.", "weaknesses": "1.\tThe method includes introduces multiple components inducing semantic-level conformal calibration, dynamic threshold, bit-level reliability modeling, and a self-regulating optimization mechanism. While each is well-motivated, it would be beneficial if the authors could more explicitly clarify which part constitutes the core contribution and novelty of the method.\n\n2.\tThe model contains many weighting mechanisms such as semantic-level sample weights, batch-level confidence weights, bit-level stability weights, and dynamically regulated loss coefficients. While each seems intuitively reasonable, the true necessity and effectiveness of these weights remain unclear. Although the conformal calibration module is theoretically grounded, the other weighting mechanisms also appear heuristic.\n\n3.\tSome notations and equations need further explanations. For example, how to compute $\\hat{q}^W$ in Eq. 1 is unclear.", "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": "Z1ULT89F8H", "reviewer": "Reviewer_eXJx", "summary": "This paper proposes an uncertainty-aware deep hashing method for cross-domain retrieval, addressing the problem of domain shift through conformal prediction. The conformal prediction strategy transforms the predicted classes with the highest softmax probabilities into a pseudo-label set, which serves as a surrogate for potentially noisy ground-truth labels. The resulting confidence estimates of the hash codes are then used to guide domain alignment, hash learning, and retrieval. Experimental results demonstrate consistent improvements over existing baselines.", "questions": "1. Line 144-146: \"The size of these sets rigorously quantifies model uncertainty and is directly converted to weights that adaptively suppress the harmful effects of high-uncertainty samples in pseudo-label learning and domain alignment. \" The authors should clarify why this uncertainty is categorized as model uncertainty rather than data uncertainty. Since the uncertainty appears to arise from the variability or ambiguity in the data samples (e.g., ambiguous labels or overlapping class features), it might be more appropriately described as data uncertainty. A brief justification or theoretical reasoning distinguishing the two types of uncertainty in this context would strengthen the conceptual rigor of the paper.\n\n2. The paper employs a conformal prediction strategy to transform high-confidence softmax predictions into pseudo-label sets that replace the original noisy labels. However, at the early stages of training — when the model is randomly initialized — the softmax probabilities are effectively random. This implies that the generated pseudo-label sets could be even noisier than the original labels, potentially leading to unstable or misleading supervision.\nCould the authors provide a discussion or empirical justification addressing this issue? For example, is there any mechanism (e.g., warm-up phase, confidence thresholding, or delayed pseudo-labeling) to mitigate the effect of unreliable predictions during early training?\n\n3. Section 3.3: Proxy Task for Bit Stability. It appears that the stability measure $v_{i,k}$ could be obtained directly by adding perturbations (e.g., Gaussian noise) to the feature representation and simulating the corresponding bit responses. If that is the case, could the authors clarify why a separate confidence prediction head, $G_{bit}$, is necessary?\n\n4. Experimental Setup and Fairness of Comparison\nIt is unclear whether the proposed model and the baseline models are evaluated using the proposed Uncertainty-Aware Weighted Hamming Distance (UWHD) or the standard Hamming distance. If the proposed method uses UWHD while the baselines rely on the original Hamming distance, this may introduce a fairness issue in performance comparison.\nThe authors may need to clarify this point and provide additional experiments where: (1) Baseline models are also evaluated using the proposed UWHD to ensure a fair comparison under consistent retrieval metrics. (2) An ablation study isolates the contribution of UWHD itself to quantify its effect on retrieval accuracy and runtime.\nThis clarification is important because the proposed UWHD may both increase retrieval cost and contribute independently to performance improvements.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Presentation. \nThe paper is well-structured and clearly written, with a logical flow and well-defined sections. The mathematical notation is consistent and easy to follow, making the technical content accessible to readers familiar with the field.\n\n2. Empirical Evaluation. \nThe experimental evaluation on benchmark datasets is comprehensive and convincing. The inclusion of detailed plots and visualizations effectively illustrates the results and provides clear insights into model behavior. The figures are well-designed and aesthetically appealing.\n\n3. Originality and Significance. \nWhile several prior studies have explored uncertainty-aware hashing strategies, the application of conformal prediction to deep hashing remains relatively underexplored. This work thus presents a novel and interesting direction that could inspire further research in uncertainty modeling for retrieval under domain shift.", "weaknesses": "1. Need for a Brief Introduction to Conformal Prediction. \nThe paper would benefit from a short subsection introducing the basic concepts and principles of conformal prediction. This would make the paper more self-contained and accessible to readers who may not be familiar with this framework.\n\n2. Missing Discussion of Related Work\nThe literature review omits several recent works that have explored uncertainty-aware deep hashing or uncertainty modeling in retrieval, which are directly relevant to this study. In particular, the following papers should be cited and discussed for a more comprehensive positioning of the proposed approach:\n\n- Warburg, Frederik, et al. \"Bayesian triplet loss: Uncertainty quantification in image retrieval.\" Proceedings of the IEEE/CVF International conference on Computer Vision. 2021.\n\n- Warburg, Frederik, et al. \"Bayesian metric learning for uncertainty quantification in image retrieval.\" Advances in Neural Information Processing Systems 36 (2023): 69178-69190.\n\n- Wang, Yucheng, and Mingyuan Zhou. \"Uncertainty-aware unsupervised video hashing.\" The 26th International Conference on Artificial Intelligence and Statistics. PMLR, 2023.\n\n- Wang, Yucheng, Mingyuan Zhou, and Xiaoning Qian. \"Hashing with Uncertainty Quantification via Sampling-based Hypothesis Testing.\" Transactions on Machine Learning Research.\n\n- Tang, Haomiao, et al. \"Modeling uncertainty in composed image retrieval via probabilistic embeddings.\" Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.\n\n3. Some design choices lack sufficient motivation. Please refer to Question 3 for details.\n\n4. Missing Complexity Analysis: Section 3.3.1: Uncertainty-aware Weighted Hamming Distance.\nWhile the introduction of a weighted Hamming distance adds modeling flexibility, the paper does not provide a computational complexity analysis. This omission is problematic because the weighting mechanism changes the operational nature of the distance metric — from bitwise operations to floating-point vector arithmetic — which may significantly impact runtime performance and scalability in large-scale data retrieval. A formal complexity discussion, or at least empirical runtime analysis, is necessary to demonstrate the method’s feasibility in real-world retrieval settings.\n\n5. Could the authors provide an ablation experiment in which all three components (SC, RC, and SR) are removed? This would help clarify the individual contribution and overall effect of each module.", "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": "PznEh8Igco", "reviewer": "Reviewer_TTx6", "summary": "This paper introduces Conformal Hierarchical Calibration Adaptive Hashing, a framework for Unsupervised Domain Adaptive Hashing. The core problem it addresses is that existing UDAH methods suffer from noisy pseudo-labels and heuristic uncertainty handling, e.g., softmax thresholding, when adapting from a labeled source domain to an unlabeled target domain. At the semantic level, it uses conformal prediction set sizes to weight pseudo-label and alignment losses. At the representation level, it predicts individual hash bit stability to guide a weighted quantization loss and a novel weighted Hamming distance during retrieval. Experiments show COLA outperforms state-of-the-art methods on benchmark datasets.", "questions": "1. How does the domain shift severity influence the best threshold $r_{cal}$? This seems also heuristic.\n2. Hashing retrieval are also designed for multi-label scenarios. Does the proposed method apply to them?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "The framework extends uncertainty quantification to the representation level by modeling the stability of individual hash bits. The proposed self-regulating mechanism intelligently uses quantified uncertainty signals to balance the multi-objective loss. The method achieves state-of-the-art performance, outperforming recent strong baselines on multiple benchmarks.", "weaknesses": "1. The paper's main solution adopts current theoretical results and methods in the literature of conformal prediction under domain shift, limiting its novelty.\n2. The paper uses CP-based set size $1/|\\mathcal{C}(x_t)|$ as its uncertainty measure. However, the paper does not compare it against a baseline that uses simpler heuristics (e.g., SoftMax threshold) within the COLA framework.\n3. The retrieval efficiency could be low. Despite a comparison to dense vector in D.5, the current hash code weighted by floating points can show substantial time consumption compared to common binary hashing methods, violating the basic goal of hashing retrieval.\n4. Formatting issues and typos:\n - Figure 5 obscures some text above it.\n - Typo around Line 231: \"learnin\"", "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)