Title: SEGA: Shaping Semantic Geometry for Robust Hashing under Noisy Supervision
Venue: NeurIPS 2025
Accepted: yes
Keywords: Robust Hashing

Semantic Geometry

Noisy Supervision
Abstract: This paper studies the problem of learning hash codes from noisy supervision, which is a practical yet challenging task. This problem is important in extensive real-world applications such as image retrieval and cross-modal retrieval. However, most of the existing methods focus on label denoising to address this problem, but ignore the geometric structure of the hash space, which is critical for learning stable hash codes. Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. Specifically, we first learn dynamic class prototypes as semantic anchors and cluster hash embeddings around these prototypes to keep structural stability. We then leverage both the energy of predicted distributions and structure-based divergence to estimate the uncertainty of instances and calibrate the supervision in a soft manner. Moreover, we introduce structure-aware interpolation to improve the class boundaries. To verify the effectiveness of our design, we give the theoretical analysis for the proposed framework. Experiments on a range of widely-used retrieval datasets justify the superiority of our SEGA over extensive strong baselines under noisy supervision.

SEGA: Shaping Semantic Geometry for Robust Hashing under Noisy Supervision

Abstract

This paper studies the problem of learning hash codes from noisy supervision, which is a practical yet challenging task. This problem is important in extensive real-world applications such as image retrieval and cross-modal retrieval. However, most of the existing methods focus on label denoising to address this problem, but ignore the geometric structure of the hash space, which is critical for learning stable hash codes. Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. Specifically, we first learn dynamic class prototypes as semantic anchors and cluster hash embeddings around these prototypes to keep structural stability. We then leverage both the energy of predicted distributions and structure-based divergence to estimate the uncertainty of instances and calibrate the supervision in a soft manner. Moreover, we introduce structure-aware interpolation to improve the class boundaries. To verify the effectiveness of our design, we give the theoretical analysis for the proposed framework. Experiments on a range of widely-used retrieval datasets justify the superiority of our SEGA over extensive strong baselines under noisy supervision.

1 Introduction

Deep hashing methods are significant for large-scale and efficient information retrieval. The goal of these approaches is to generate compact binary codes retaining good semantic similarity [56]. In the past few years, supervised deep hashing has performed well in various retrieval tasks, such as image retrieval and multi-modal retrieval [34, 4, 35, 69, 32]. However, label noise is still an outstanding challenge when it comes to practical applications [50, 20, 31]. In real-world datasets, labels are often incomplete, ambiguous, or incorrect [68, 60, 18]. These problems may stem from inconsistent human annotations, noisy web collection, loose category definitions, and intrinsic semantic ambiguity [23, 65]. The discrete property of hash codes makes this problem worse. Hashing models are sensitive to noisy supervision, where small label errors can cause large output shifts. This leads to fragmented representations and unstable similarity preservation [47]. When supervision

is unreliable, models that fit labels directly tend to overfit noise [64, 14] instead of learning real class structure [1, 38]. The main challenge in noisy multi-label hashing is not only to maintain class separability under weak signals but also to build an embedding space that is semantically consistent, geometrically smooth, and robust to supervision noise.

In order to alleviate this problem, previous studies mainly focused on denoising labels or regularizing predictions. These include approaches that reweight or clear training samples [39, 7], estimate noise transition matrices [43], apply auxiliary consistency constraints [68], or perform confidence-based sample selection [20, 31]. These strategies have been proven to be effective in reducing the impact of noisy supervision, mainly by improving the quality of labels or learning stability. However, they basically follow a label-centric paradigm, assuming the label, whether observed or corrected, remains the main source of supervision. In contrast, we propose a complementary perspective that focuses on modeling and reinforcing the semantic geometry of the representation space. The goal of deep hashing is to encode the inputs into discrete codes that reflect semantic similarity. The learned hash codes may be suboptimal when hash embeddings fail to align with the underlying semantic manifolds. In contrast, the semantical and topological consistency of the hash space can make the hash codes more robust against label noise. It raises two key challenge to build such a geometry-aware framework for robust hash learning: (1) How can we evaluate the uncertainty of supervision accurately in the presence of label noise? It is difficult to determine the uncertainty of supervised signals from traditional confidence measures under heavy label noise. However, we can capture additional cues of uncertainty from the geometric structure of representations. (2) How to capture the underlying semantic structure of data effectively under noisy multi-label supervision? It is promising to shape the semantic geometry of hash space to align the semantic relationship among the instances.

Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. It integrates three mutually promoting components into a closed-loop training system. First, Prototype-Guided Semantic Anchoring aligns instance embeddings with dynamic class prototypes that evolve during training, which serve as structural anchors. Second, Uncertainty-Guided Supervision Calibration calculates a unified uncertainty score by combining energy-based prediction confidence and structure-based divergence, allowing soft weighting of noisy labels. Third, Structure-Aware Mixup interpolates between samples with different uncertainties but similar semantics to refine ambiguous regions, so as to promote continuity and improve decision boundaries. These modules enable representations, supervision, and uncertainty to coevolve in a tightly coupled geometric loop. We have verified SEGA from both theoretical and empirical aspects, and the results show that it can approximately evaluate the reliability of labels to achieve supervised weighting, and maintain semantic consistency in the interpolation process, thus reducing structural fragmentation and regularizing decision boundaries under noise. Experiments on noisy multi-label hashing benchmarks show that SEGA achieves state-of-the-art robustness, particularly under extreme label corruption. In addition to numerical improvement, the visualization results also confirm that SEGA can construct discriminative and semantically coherent representations under noisy supervision. These findings suggest that shaping semantic geometry, rather than merely correcting supervision, is crucial for resilient hash algorithms.

Our main contributions are as follows. (1) New Perspective . We present a geometric view of learning under noisy supervision. The multi-label hashing problem is reformulated as semantic structure alignment rather than simple label recovery. (2) Novel Methodology. We propose SEGA, a closedloop framework that unifies prototype anchoring, uncertainty-guided soft labeling, and structure-aware interpolation into a geometry-aware semantic learning process. (3) Extensive Experiments. We evaluate SEGA on four benchmark datasets. It consistently achieves state-of-the-art performance and shows strong robustness across diverse noisy multi-label settings.

2 Related Work

Deep Hashing Methods. Deep hashing has become a core approach for scalable similarity retrieval. It learns compact binary codes that preserve semantic relations in Hamming space. Supervised methods usually build pointwise, pairwise, or triplewise objectives based on label-derived similarity [34, 69, 4, 32]. For instance, GreedyHash [51] utilizes the greedy strategy to address the gradient-vanishing problem in discrete hashing optimization. CSQ [63] proposes a global central similarity metric to improve hash learning efficiency. Unsupervised hashing methods usually leverage the intrinsic relationships in data to avoid label dependence. For example, WCH [62] introduces

Training

Images

Deep

Hashing

Model

Hash

Embedding

𝒉

Prototype-Guided

Semantic Anchoring

Class

manifolds

Cosine

Similarity

Noisy

Clean

set

Noisy

set

ℒ

!"#$%

ℒ

!&%'

Uncertainty-Guided

Supervision Calibration

Energy

Geometric Isolation

Soft Label:

𝒚

!

" (1 - 𝑈

!

)

Structure-Aware

Interpolation

Uncertain

Sample

Interpolation

ℒ

!$"()

ℒ

*(+

-1 +1 +1 +1

-1

-1

-1 -1 +1

+1

+1

+1

Binary

Hash

Code

weighted contrastive learning and mutual attention mechanism to enhance data similarity mining. These methods perform poorly when the provided supervision contains noise, as they are unable to effectively utilize the useful signals within the noisy supervision or reduce the interference caused by the noise. Recent efforts toward noise-robust hashing include DIOR [55] and STAR [41]. DIOR utilizes a dual-partition strategy to relieve the impact of noisy labels. STAR leverages a hybrid sample selection mechanism and selective centroid learning to help capture similarity structure. however, they mainly focus on label denoising and local noise reduction, but overlook the structural fragility of the global hash space. Towards this end, we propose a novel framework that explicitly refines the semantic geometry of hash space to alleviate the influence of label noise.

Learning with Label Noise. Label noise is common in real-world datasets and has motivated extensive researches on robust learning against noise [50, 26, 17]. The existing methods can be mainly divided into three categories. The first category of methods refines losses by modeling noise transformation [43, 15, 45]. The second one leverages sample selection to identify clean data [20, 31, 68]. The third one utilizes regularization to alleviate memorization of noisy labels [66, 21, 57]. Co-teaching [20] introduced a dual-network design that filters noisy samples through crossselection of small-loss instances. Mixup [66] provides implicit regularization by linearly interpolating samples and labels, reducing overfitting to corrupted data. Recent advances combine contrastive learning [9, 27] with noise-robust representations [13, 61] and apply curriculum learning to control memorization dynamics [1]. Early learning regularization [38] limits overfitting by focusing on clean patterns in early training. Despite this progress in image classification, robust learning for structured outputs such as hashing remains less explored, especially under ambiguous multi-label supervision.

3 Methodology

3.1 Problem Definition

Let D = { ( x i , y i ) } N i =1 be a training set of N examples, where x i ∈ R d is an input instance and y i ∈ { 0 , 1 } C is a one-hot or multi-hot label vector over C semantic categories. In practical settings, these labels are often noisy due to annotation errors, class ambiguity, or missing tags. The goal is to learn a hash function H : x ↦→ b ∈ {-1 , +1 } L that encodes each sample into an L -bit binary code, such that semantically similar inputs are mapped to nearby codes in the Hamming space.

3.2 Framework Overview

SEGA addresses this goal by shaping a robust semantic geometry in the embedding space, even under noisy multi-label supervision. We adopt a deep hashing model f : x ↦→ h ∈ R L to produce continuous hash embeddings, which are binarized as b = sign ( h ) . However, directly training on corrupted labels y i often induces semantic misalignment, especially when representations are influenced by unreliable or ambiguous supervision. To address this problem, SEGA shapes the semantic geometry of the representation space with three key parts. First, prototype-guided semantic

anchoring aligns embeddings with class prototypes to keep the geometry stable. Second, uncertaintyguided supervision calibration reduces the weight of unreliable labels using energy and structural divergence. Third, structure-aware interpolation mixes only semantically similar samples with different uncertainty levels to create smooth transitions near class boundaries. The components form a closed loop. Supervision, uncertainty, and geometry co-evolve and reinforce each other through training. The overview of the proposed framework SEGA is illustrated in Figure 1.

3.3 Prototype-Guided Semantic Anchoring

SEGA builds a semantic scaffold in the hash space using a set of learnable class prototypes { p c } C c =1 . Each prototype p c ∈ R L is randomly initialized and updated together with the model. These prototypes act as anchors that guide instance embeddings toward meaningful semantic directions. For each input x i , we obtain its continuous hash representation h i = f ( x i ) and normalize it as ˆ h i = h i / ∥ h i ∥ . Similarly, we normalize all prototypes to get unit-length semantic anchors: ˆ p c = p c / ∥ p c ∥ . The logit vector for classification is then computed as:

which yields cosine similarities between the embedding and each class prototype. To assess the semantic reliability of supervision, we define a soft-alignment score that evaluates the agreement between model prediction and the observed (possibly noisy) label vector y i :

where σ ( · ) denotes the softmax function. This score measures how well the model's predicted distribution aligns with the noisy label in the prototype-induced space. Based on the q r -th percentile of the alignment scores { S ( i ) r } N i =1 , we compute a dynamic threshold τ r to partition the dataset into a clean set D c , containing semantically reliable samples, and a complementary noisy set D n :

Clean samples in D c are supervised using a softmax-based prototype alignment loss [55] that treats the noisy label vector as a probabilistic guide:

To regularize noisy samples in D n and prevent semantic drift, we adopt a contrastive loss [46, 27, 54]. It pulls embeddings of related samples closer and pushes unrelated ones apart by a margin m . For two samples x i , x j ∈ D n with noisy labels y i and y j , we define:

where I [ i ∼ j ] = 1 if y ⊤ i y j > 0 (i.e., positive pair), and I [ i ̸∼ j ] = 1 otherwise (i.e., negative pair). Prototype-guided alignment provides reliable supervision. Contrastive regularization stabilizes learning in noisy regions. Together, they help build a structured representation space that preserves semantic geometry under label noise.

3.4 Uncertainty-Guided Supervision Calibration

The previous module divides the dataset into clean and noisy parts using prototype alignment. This hard split ignores the reliability differences within each part. Some clean samples lie near decision boundaries or show structural ambiguity. Some noisy samples still contain useful semantic information. To handle this, we introduce a novel metric to evaluate uncertainty [44, 11] of samples and then calibrate the supervision in a soft manner. Specifically, we combine energy-based prediction confidence and structure-based neighborhood divergence to estimate an uncertainty score. We then leverage this score to reduce the weight of supervision for ambiguous samples and filter out unreliable gradients. It also guides later sample selection in structure-aware interpolation.

Energy-based prediction confidence. We measure the confidence of the model using the energy [40, 67] of its logit distribution:

A high energy value means that the distribution is flat and the prediction is less certain. We normalize the energy in each mini-batch as ˜ E i = E i -min j E j max j E j -min j E j , so that all values stay on a comparable scale.

Structure-based divergence. Confidence alone cannot reflect spatial consistency in the embedding space. We therefore define a divergence score. It measures how far a sample spreads from its K nearest neighbors in geometry:

Here, N i is the set of topK nearest neighbors for sample x i . A larger δ i means the sample is more isolated in geometry. Such samples often lie near class boundaries or in under-represented semantic zones.

Unified uncertainty. The total uncertainty is defined as:

This design captures two kinds of cues: vertical cue from prediction confidence and lateral cue from structural smoothness. It gives a unified measure of semantic reliability. Instead of discarding uncertain samples, we calibrate their gradient impact by softly reweighting the label signal [42, 29]:

where σ ( · ) is the softmax function. This calibration reduces the effect of samples that are semantically or structurally uncertain. It improves the shape of semantic manifolds and strengthens alignment inside coherent regions. The resulting gradients mainly update well-supported semantic areas and smooth the uncertain ones without forcing hard boundaries.

Theoretical Analysis. We now give a theoretical explanation for our uncertainty-guided supervision calibration. The uncertainty score U i combines semantic confidence and structural consistency. It approximates the posterior probability that the observed label is correct. With a mild conditional independence assumption, 1 -U i can be used as a proper weight in the supervision loss.

Theorem 3.1 (Uncertainty-Weighted Confidence Approximates Label Correctness) . Let x i be a training sample with observed label ˜ y i and true (latent) label y ∗ i . Define the energy-based prediction confidence as E i = -log ∑ C c =1 exp( l ic ) , and ˜ E i = E i -min j E j max j E j -min j E j , the structure-base divergence as δ i = 1 -1 K ∑ j ∈N i cos( ˆ h i , ˆ h j ) . If we assume the probability that the label is correct depends solely on the semantic and structural reliability of the sample, and these two sources are conditionally independent given x i , then:

This result provides a probabilistic interpretation of 1 -U i as an estimate of label correctness. By treating semantic confidence and structural consistency as two independent indicators of supervision quality, 1 -U i serves as a soft surrogate for the reliability of the observed label. Therefore, using 1 -U i to weight the label signal helps the model reduce gradients from noisy or ambiguous samples. It keeps stronger supervision for reliable regions. This process aligns the learning dynamics with semantically meaningful structures.

3.5 Structure-Aware Interpolation for Boundary Regularization

Uncertainty-guided calibration reduces noisy gradients but does not handle semantic ambiguity near decision boundaries. Samples in these areas are often uncertain and structurally isolated. To solve this, we draw inspiration from Mixup [53, 59, 37], which smooths class transitions and

makes representations more generalizable by mixing samples. Based on this idea, we design a structure-aware interpolation mechanism for refining boundaries in noisy multi-label hashing.

Traditional Mixup mixes any two samples without restriction. In our method, we mix only pairs that are semantically similar but have different uncertainty levels. We split the clean set D c into two parts: a confident subset D con and an uncertain subset D un. The split is based on the mean uncertainty ¯ U :

For each uncertain sample x i ∈ D un, we find its most similar confident sample x ∗ j ∈ D con. The two samples must share at least one common label, that is, y ⊤ i y j > 0 . We measure similarity by cosine distance in the normalized embedding space:

This rule keeps interpolation between samples that share some labels. It preserves semantic consistency and uses confident samples as anchors to guide uncertain ones. We then generate interpolated virtual samples and soft labels as:

Here, ˜ y i and ˜ y ∗ j are the uncertainty-calibrated soft labels described in Section 3.4. The coefficient λ comes from a symmetric Beta distribution to provide diverse mixing strengths. We define the mixup loss as follows:

where f ( · ) is the hash encoder and σ ( · ) denotes the softmax function. This structure-aware interpolation transmits semantics and supervision signals from confident samples to uncertain samples, which introduces additional regularity near the decision boundaries.

Theoretical Analysis. We provide a theoretical analysis to justify the effectiveness of structure-aware interpolation. It demonstrates that the interpolation keeps the consistency of the semantic structure in the hash space.

Theorem 3.2 (Structure-Preserving Interpolation Bound) . Let x i and x j be two clean samples belonging to class c , i.e., y ic = y jc = 1 . ˆ h i and ˆ h j represent the normalized hash embeddings of these two samples. Let p c be the unit-norm prototype vector of class c . For any λ ∈ [0 , 1] , the interpolated embedding is defined as follows:

The cosine similarity between ˜ h and p c has the following lower bound:

This result indicates that structure-aware interpolation preserves the proximity to the class prototype along the interpolation path. It enhances the consistency of the semantic structure in uncertain regions and improves the class boundaries.

3.6 Unified Training Objective

We integrate all modules into a unified training objective. It includes four complementary loss terms that jointly learn semantic anchors, maintain structural stability, calibrate noisy supervision, and improve class boundaries against label noise.

Each loss term contributes to shaping the semantic geometry of the hash space differently: (1) L clean clusters clean samples around their corresponding prototypes, which ensures stable class semantics; (2) L cont enhances the structural consistency for noisy instances; (3) L calib alleviates the impact of unreliable supervision using both the energy of predicted distributions and structure-based divergence; (4) L mix facilitates the consistency of the semantic structure in uncertain regions and regularizes the class boundaries. It makes the learned hash codes more robust and generalizable to optimize the total loss objective. The overall training algorithm of our proposed SEGA is provided in Algorithm 1.

4 Experiments

4.1 Setup

Datasets. We evaluate SEGA on four widely-used image retrieval benchmarks: CIFAR-10 [28], Flickr25k [24], NUS-WIDE [10], and MS COCO [36]. CIFAR-10 is a balanced single-label dataset with 10 classes of images. Flickr25k and NUS-WIDE are multi-label web datasets with 38 and 81 categories, respectively; we follow prior work [55] by selecting the top 10 classes in NUS-WIDE. MS COCO provides multi-object annotations over 80 classes with dense labels per image. All datasets come with clean annotations. To simulate realistic training noise, we inject synthetic corruption into a portion of training labels using two schemes: symmetric and pairwise noise. Noise rates are varied from 20% to 80% in steps of 20%. Symmetric noise randomly replaces each label with any other class, while pairwise noise flips labels only to semantically related categories [2].

Baselines and metrics. We compare SEGA with a diverse set of baselines grouped into three categories: (1) Standard Deep Hashing Methods , including DPSH [33], HashNet [5], SPQ [25], DCH [6], FSDH [19], GreedyHash [51], JMLH [48], DPN [12], WGLHH [52], CSQ [63], and OrH [22]; (2) General Label Noise-Robust Methods , including REL [57] and Jo-SRC [61]; and (3) Noise-Resilient Hashing Methods , including DIOR [55] and STAR [41]. We evaluate all methods at four code lengths: 16, 32, 64, and 128 bits. Performance is measured using the standard retrieval metric, i.e., mean average precision (MAP).

Implementation Details. All experiments are finished using PyTorch on a NVIDIA A40 GPU. We utilize stochastic gradient descent (SGD) with a momentum of 0.9 and a batch size of 24. The learning rate is initialized at 0.001, with weight decay set to 0.0004 and dropout rate to 0.5. The backbone network is initialized from a pretrained VGG-16 [49] model, consistent with all baseline

Method

CIFAR-10

NUS-WIDE

MS COCO

Bits

16

32

64

128

16

32

64

128

16

32

64

128

16

32

64

128

45.36

47.35

48.27

49.06

56.67

57.09

57.86

58.24

44.03

44.82

45.60

45.97

30.29

31.21

31.87

32.46

HashNet

42.54

43.24

44.47

45.29

53.47

54.69

56.03

56.87

43.21

44.37

45.12

46.05

27.17

27.69

28.54

28.89

DCH

45.29

47.75

48.19

49.24

57.02

58.20

58.44

59.12

44.36

44.21

44.98

45.88

31.55

32.39

32.99

33.41

GreedyHash

42.73

45.96

47.51

49.81

56.89

57.21

58.01

58.95

43.17

43.82

44.45

45.00

30.70

31.24

31.97

32.63

46.58

48.15

48.74

48.89

57.53

58.55

59.13

60.94

44.47

45.56

45.92

46.02

31.38

32.64

33.19

33.77

DPN

44.57

47.08

48.09

48.56

56.82

57.43

58.26

59.83

44.87

45.72

46.11

46.19

31.11

31.65

31.59

32.13

WGLHH

47.92

49.83

50.19

52.35

57.17

57.99

58.46

59.23

45.11

45.91

46.68

47.32

32.21

33.13

33.74

34.11

CSQ

50.08

51.75

54.21

55.39

57.38

58.15

58.88

59.12

46.01

46.55

47.08

47.65

31.97

32.45

33.71

34.60

OrH

49.87

50.65

51.98

53.26

57.16

58.73

59.12

60.04

46.58

47.13

47.86

49.24

31.76

32.74

33.06

33.89

REL

50.39

51.21

52.64

53.97

58.68

59.02

59.46

60.35

47.05

47.67

48.18

48.86

32.47

33.27

34.29

35.01

50.82

51.42

51.96

53.62

58.12

58.91

59.89

60.87

47.79

48.14

48.97

49.34

32.59

33.19

34.61

35.11

DIOR

58.76

59.30

59.82

60.99

63.83

64.05

64.97

65.40

52.26

52.78

53.61

54.06

35.13

36.33

37.01

38.22

STAR

64.85

65.03

65.52

66.76

69.57

70.11

70.84

71.53

57.24

57.83

58.64

59.89

40.80

41.22

41.87

42.79

SEGA (Ours)

65.34

65.87

67.11

69.01

70.23

71.50

72.66

75.04

59.06

60.72

63.91

64.12

43.31

45.01

46.50

47.31

0.2

0.3

0.4

0.5

0.6

0.7

0.8

40

50

60

70

80

Mean Average Precision

Ours

STAR

DIOR

CSQ

DPN

(a) Flickr25K (pair)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

40

50

60

70

80

Mean Average Precision

Ours

STAR

DIOR

CSQ

DPN

(b) Flickr25K (sym)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30

40

50

60

70

Mean Average Precision

Ours

STAR

DIOR

CSQ

DPN

(c) NUS-WIDE (pair)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30

40

50

60

70

Mean Average Precision

Ours

STAR

DIOR

CSQ

DPN

(d) NUS-WIDE (sym)

methods to ensure a fair comparison. Specifically, the first seven convolutional layers are fine-tuned, while the final fully connected hashing layer is trained from scratch. More details about the datasets and implementation can be found in the Appendix.

4.2 Empirical Results

Performance Comparison. We report the retrieval performance of all methods on four benchmark datasets under two types of label noise in Tables 1 and 2. Noise rates of both types are 60%. The results are measured by mean average precision (MAP) across different code lengths (16, 32, 64, and 128 bits). Table 1 shows the MAP scores under pairwise label noise. Table 2 reports the results under symmetric noise. Several clear observations can be made from the results. (1) Overall, SEGA achieves the highest MAP scores across all datasets and noise types, showing strong robustness to both structured and unstructured label corruption. SEGA clearly outperforms both conventional deep hashing models and recent noise-robust approaches. Specifically, SEGA achieves 64.61 MAP on NUS-WIDE with pairflip noise at 128 bits, more than 10% above DIOR and STAR. These findings confirm that SEGA can preserve semantic similarity under supervision noise. (2) Our SEGA consistently outperforms all the baselines, and as the dimension of the hash codes increases, the performance gap widens generally. This shows the strong scalability and robustness of our method in terms of the hash encoding dimension. (3) On MS COCO, which has dense and noisy multi-label annotations, our SEGA delivers particularly solid performance. This demonstrates its adaptability for real web data where the quality of annotations is poor.

Effects of Different Noisy Rates. Figure 2 shows the robustness of SEGA under different noise levels with 64-bit hash codes. Both pairwise and symmetric noise types are evaluated. As the noise rate increases from 0.2 to 0.8, most baseline methods drop sharply in performance. CSQ, Jo-SRC, and DPN degrade quickly beyond 0.4 noise rate, showing poor tolerance to heavy label corruption. In contrast, SEGA keeps consistently high MAP scores across all noise levels. The drop is smooth even when the noise rate reaches 0.8. For example, under pairflip noise on NUS-WIDE (Figure 2(c)), SEGA maintains a MAP above 60. It outperforms STAR and DIOR by large margins as noise increases. The advantage becomes most obvious at high noise levels, where other methods collapse but our structure-aware model stays stable. These results show that learning semantic geometry and calibrating supervision jointly gives better robustness than label correction alone.

Ablation Study. We evaluate the contribution of each module in SEGA through ablation experiments, where one loss term is removed at a time. Table 3 reports the MAP scores under symmetric and pairflip noise on four datasets. Removing L clean results in a clear drop across all datasets, showing that prototype-guided supervision is essential for stable learning. When L cont is excluded, performance

Method

CIFAR-10

Flickr25K

NUS-WIDE

MS COCO

sym.32

pair.32

sym.64

pair.64

sym.32

pair.32

sym.64

pair.64

sym.32

pair.32

sym.64

pair.64

sym.32

pair.32

sym.64

pair.64

SEGA w/o

L

clean

60.61

68.63

61.62

72.03

62.04

70.02

62.18

67.81

51.52

54.75

51.88

58.70

41.37

41.41

41.55

40.22

SEGA w/o

L

cont

64.14

69.86

64.59

71.20

70.25

71.24

70.40

74.26

60.03

56.31

61.28

58.05

43.12

44.36

45.11

47.06

SEGA w/o

L

calib

62.95

70.45

66.33

71.87

68.47

70.10

68.37

73.35

59.09

58.05

62.70

59.34

44.89

44.85

42.23

43.74

SEGA w/o

L

mix

60.48

70.12

63.05

71.39

68.26

69.94

68.46

73.38

58.72

57.34

61.65

60.70

44.20

45.23

44.84

46.90

SEGA (Ours)

65.87

70.59

67.11

72.34

71.50

72.14

72.66

74.49

60.72

59.52

63.91

61.86

45.01

46.08

46.50

47.21

0.1

0.3

0.5

0.7

0.9

Percentile

qr

60

65

70

75

80

Mean Average Precision

pairflip

symmetric

(a) Flickr25K

0.1

0.3

0.5

0.7

0.9

Percentile

qr

50

55

60

65

70

Mean Average Precision

pairflip

symmetric

(b) NUS-WIDE

-40

-20

0

20

40

t-SNE Dimension 1

-20

-10

0

10

20

30

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(c) Baseline

-60

-40

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-30

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(d) Ours

Figure 3: (a)(b) Sensitivity analysis of percentile threshold q r with 64-bit hash codes. (c)(d) t-SNE visualization of 128-bit hash codes on CIFAR-10 under symmetric noise. The baseline for comparison is STAR, the strongest competing method.

decreases, especially under pairflip noise, indicating its necessity to maintain structural consistency on noisy areas. Excluding L calib compromises robustness to both settings of noise and confirms that soft supervision limits the impact of annotation errors. Removing L mix also causes consistent performance loss, particularly on MS COCO, demonstrating the advantage of boundary regularization. Collectively, these results demonstrate the necessity of the elements of SEGA and their effectiveness in complementing each other. The Appendix contains additional ablation results.

Sensitivity analysis. We evaluate the sensitivity of SEGA to hyperparameter q r under pairflip and symmetric noise with 64-bit hash codes. The best performance appears when the q r value is set to 0.3 or 0.5, from Figure 3(a) and 3(b). Performance drops when q r is too high, as excessive filtering removes many clean samples. Denoising becomes weak when q r is too low, since noisy samples remain unfiltered. These observations imply a moderate threshold to achieve the best compromise between over-filtering and under-filtering.

Visualization. To analyze the learned semantic structure, we visualize the hash embeddings using t-SNE on the CIFAR-10 dataset. The experiment is performed under symmetric noise with 128-bit hash codes. Specifically, SEGA generates clusters that are far more separated than STAR, as shown in Figure3(c) and 3(d). Our SEGA presents a clearer boundary for each category, which indicates our framework learns more discriminative hash embeddings. Conversely, STAR shows evident overlaps between classes, demonstrating lower robustness to label noise. These results show SEGA learns hash codes that are semantically consistent and robust against noisy supervision.

5 Conclusion

In this paper, we present a unified framework named SEGA for robust multi-label hashing under noisy supervision. The method models semantic geometry to improve the reliability of learned hash representations. We first use prototype-guided semantic anchoring to align embeddings with class semantics and maintain structural stability. Next, we design an uncertainty-guided calibration module to adjust the effect of unreliable labels. We also apply a structure-aware interpolation strategy to smooth decision boundaries and enhance local consistency in noisy regions. In theory, SEGA reduces semantic misalignment and improves class boundaries. Experiments on several noisy hashing benchmarks show clear robustness gains. Although built for multi-label hashing, the core ideas of SEGA can be extended to other structure-sensitive learning tasks, such as multi-modal retrieval and multi-label classification under weak or noisy supervision.

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A More Experiment Results

We conduct ablation studies on 16-bit and 128-bit hash codes. As shown in Table 4, removing any loss term leads to a clear drop in performance across all the datasets. This demonstrates that each module plays a necessary role in learning robust hash codes against label noise. For instance, removing L calib causes clear drops in performance across all the datasets, especially with 16-bit hash codes. This justifies the benefit of uncertainty-guided supervision calibration in noisy environments. Turning off L mix also reduces MAP, particularly on Flickr25K, showing its effect in regularizing category boundaries. These results confirm that all modules in our framework are complementary and necessary under different code lengths.

B Proofs of Theorems

Theorem 3.1 (Uncertainty-Weighted Confidence Approximates Label Correctness) . Let x i be a training sample with observed label ˜ y i and true (latent) label y ∗ i . Define the energy-based prediction confidence as E i = -log ∑ C c =1 exp( l ic ) , and ˜ E i = E i -min j E j max j E j -min j E j , the structure-base divergence as δ i = 1 -1 K ∑ j ∈N i cos( ˆ h i , ˆ h j ) . If we assume the probability that the label is correct depends solely on the semantic and structural reliability of the sample, and these two sources are conditionally independent given x i , then:

Proof. The probability that a sample is confidently predicted is proportional to the negative energy in energy-based learning [40]: Pr[ semantic correctness | x i ] ∝ exp( -E i ) .

After batch normalization, ˜ E i ∈ [0 , 1] maintains a monotonic relationship with E i and thus Pr[ semantic correctness | x i ] ∝ 1 -˜ E i .

The structural divergence score δ i reflects how well a sample aligns with its local neighborhood. Samples in high-density regions with consistent semantic structure are more likely to have correct labels under the widely adopted cluster assumption. In contrast, geometrically isolated samples, those with low average similarity to neighbors, are often located near semantic boundaries or in underrepresented regions of the data manifold and are thus more prone to label noise.

This assumption is supported by several foundational approaches. In graph-based semi-supervised learning [70, 3], Laplacian regularization encourages neighboring nodes to share similar outputs. Label propagation methods [8] assume that labels should remain consistent within locally coherent regions. Moreover, the low-density separation principle [16] suggests that well-formed clusters of correctly labeled data tend to lie in structurally connected, high-confidence zones. Therefore, a smaller divergence score (i.e., a larger 1 -δ i ) indicates stronger neighborhood support and a higher likelihood of label correctness. We thus approximate structural confidence as being proportional to the complement of divergence:

According to the assumption, we can obtain

On the other hand,

when ˜ E i and δ i are relatively small (i.e., low uncertainty), the second term is small, and

Under the assumption that label correctness depends only on semantic and structural confidence, modeled respectively by energy-based and neighborhood-based signals, the complement of the joint uncertainty score 1 -U i provides a proportional estimate of the posterior label correctness probability.

Theorem 3.2 (Structure-Preserving Interpolation Bound) . Let x i and x j be two clean samples belonging to class c , i.e., y ic = y jc = 1 . ˆ h i and ˆ h j represent the normalized hash embeddings of these two samples. Let p c be the unit-norm prototype vector of class c . For any λ ∈ [0 , 1] , the interpolated embedding is defined as follows:

The cosine similarity between ˜ h and p c has the following lower bound:

Proof. Since both ˆ h i and ˆ h j are normalized to unit norm (i.e., ∥ ˆ h i ∥ = ∥ ˆ h j ∥ = 1 ), and p y is also a unit-norm vector (i.e., ∥ p y ∥ = 1 ), we begin by expanding the cosine similarity between ˜ h and p y :

Applying linearity of inner product:

Thus,

Since ∥ ˜ h ∥ ≤ 1 by convexity of Euclidean norm (specifically, Minkowski inequality), we conclude:

cos( ˜

as desired.

C Dataset Details

We evaluate our method on four widely used image retrieval benchmarks. All datasets are standard in deep hashing and image retrieval literature, with consistent splits across prior work [55].

CIFAR-10 [28, 30]. This is a single-label dataset containing 60,000 natural images evenly divided into 10 categories. Each image is 32 × 32 in resolution with three color channels. We sample 1,000 examples per class as queries. The remaining examples are utilized as the retrieval database, from which 500 images per class are further sampled for training. The low resolution and compact structure make this dataset a challenging testbed for semantic feature extraction.

Flickr25K [24]. The Flickr25K dataset collects 25,000 multi-label images from the Flickr platform. Each image in the dataset is tagged with one or more labels from 38 semantic concepts. We utilize the 24 most frequent concepts as the label set following [55]. We use 2,000 images as queries, and sample 10,000 images for training from the remaining retrieval set. The annotations are sparse in this dataset, where each image is assigned 4.7 labels on average.

NUS-WIDE [10]. The NUS-WIDE dataset includes 269,648 web images with 81 semantic tags. We utilize the 10 most frequent tags as the target categories following [55]. We employ 5,000 images as queries, and sample 5,000 images from the remaining retrieval set for training.

MS COCO [36, 58]. The MS COCO dataset contains more than 120,000 images, where each image is tagged by some of 80 categories. We adopt the 2014 release and use 5,000 images as queries. From the remaining retrieval set, 10,000 are sampled for training. Its complex scenes and dense annotations make it a challenging dataset for fine-grained image retrieval.

h

,

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,

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.

D Implementation Details

All experiments are implemented in PyTorch and run on a single NVIDIA A40 GPU in a standard Linux environment. Two types of label noise are introduced. In symmetric noise, each label is randomly replaced by another class with equal probability. In pairwise flip noise, labels are switched to semantically related categories according to predefined mappings [55]. The noise rate ranges from 20% to 80% in increments of 20%. During mixup training, interpolation coefficients are sampled from a symmetric Beta distribution with α = 0 . 4 as in [66]. The percentile threshold q r for selecting clean samples is set to 0.3 by default. The code can be found at https://github.com/dllab001/SEGA .

E Broader Impacts and Limitations

This paper deals with a problem of robust image retrieval under noisy supervision and proposes a generic framework called SEGA to do so. With this process our approach is scalable and reliable in real-world settings where label quality is imperfect: e.g. web-based image indexing and large-scale multimedia systems. As well, although our framework is instantiated in multi-label hashing, its essential principles are not domain-specific and can be readily adapted to more general tasks, e.g. multi-modal retrieval, multi-label classification and other structure-sensitive learning tasks under weak or noisy supervision. However, one limitation of our current solution is that we use a static retrieval database, which does not have the ability to cope with the change in the data distribution in dynamic environments. Future work could adapt SEGA to continual learning or online retrieval situations.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nTo learning from noisy multi-label supervision in hashing, this paper introduces a geometric perspective, formulating multi-label hashing as a semantic structure alignment problem rather than a conventional label recovery task. Moreover, this paper proposes a closed-loop framework termed SEGA that integrates prototype anchoring, uncertainty-calibrated soft labels, and structure-aware interpolation into a unified and geometry-aware semantic learning process. The experiments in the paper are very abundant and perfectly validate the innovations of the paper.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n1) This paper introduces a geometric perspective for learning from noisy multi-label supervision in hashing.\n\n2) The SEGA framework has a certain degree of innovativeness and has effectively solved the current problems. \n\n3) The experiments in the article are very abundant and perfectly validate the innovations of the paper.\n\n4) The writing of the article is highly logical, and the charts and graphs are also very clear.\n\nWeaknesses\n\n1) In section 3.3, the accuracy of the prototype will directly determine the quality of the division between clean and noisy samples, if its accuracy is ensured.\n\n2) It is suggested that the relationship between Energy-Based Prediction Confidence and samples could be demonstrated with figure, for example, blue represents correct samples and red represents noisy samples.\n\n3) Please explain intuitively why label soft reweighting in Eq. (9) can be beneficial for noisy learning. How would the performance be if we use Energy-based prediction confidence or Structure-based divergence alone, without employing Unified uncertainty?\n\nQUESTIONS:\nIn addition to the Weaknesses, I also have the following concerns:\nMore textual explanation is needed on why the contrastive learning loss is robust on noisy datasets. The origin of this contrastive learning should be correctly cited. Please confirm whether using the contrastive learning loss on the clean dataset would further enhance the performance.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nSEGA is a deep hashing method for noisy multi-label data that focuses on shaping the geometry of the representation space. Instead of just cleaning or reweighting labels, it trains the model to form smooth, class-consistent manifolds even under label noise.\n\nIt introduces three components:\n\n1. Prototype-Guided Anchoring: Learnable class prototypes pull clean sample embeddings toward class centers, promoting semantic alignment.\n2. Uncertainty-Guided Calibration: Each label is weighted based on a sample-specific uncertainty score, which combines prediction confidence and local feature consistency. Noisy labels are downweighted accordingly.\n3. Structure-Aware MixUp: Interpolation is done between similar samples with differing uncertainty, smoothing boundaries without mixing unrelated classes.\n\nFinally, SEGA brings a geometric perspective to noisy-label learning and shows strong retrieval performance under heavy noise.\n\nSTRENGTHS AND WEAKNESSES:\nQuality:\n\n1. The paper is technically solid and thorough. The method is well-motivated, leveraging ideas from metric learning and robust training. Each SEGA module is justified both intuitively and theoretically.\n2. The inclusion of formal guarantees (Theorems 3.1 and 3.2) is a strength -- Theorem 3.1 links the uncertainty score to true label correctness, supporting label reweighting; Theorem 3.2 ensures interpolating with prototype-aligned neighbors preserves class consistency.\n3. Experiments are strong: SEGA outperforms prior work across four datasets and two noise types, especially under heavy noise (e.g., 80% on NUS-WIDE, where others drop below 50% mAP while SEGA stays above 60%).\n4. Ablations (Table 4) show that removing any component leads to performance drops, confirming each part is useful.\n5. Weakness 1: The added complexity. SEGA introduces several hyperparameters (e.g., \n$q_r$, $\\alpha$, $K$) and requires prototype updates and k-NN per epoch. While some sensitivity is analyzed, runtime/memory overhead is not discussed. The method is rigorous and effective, with minor concerns around scalability and reproducibility.\n\nClarity:\n\n1. The writing is clear and well-organized.\n2. Motivation is strong, and experiments are extensive and easy to follow.\n\nSignificance:\n\n1. Robust multi-label hashing under noise is practically important.\n2. SEGA brings a new perspective: shaping semantic geometry instead of just filtering labels. The gains in high-noise settings are substantial.\n3. The approach could extend beyond hashing (e.g., to classification or structured outputs), opening doors for future work.\n4. Weakness 2: the method is evaluated only in the multi-label retrieval setting, which is narrower but still highly relevant (e.g., web images, tag-based search).\n5. Overall, this is a meaningful contribution both scientifically and practically.\n\nOriginality:\n\n1. The shift from “fixing labels” to “shaping geometry” is a novel framing for noisy-label learning in hashing.\n2. Weakness 3: SEGA combines known tools (prototypes, uncertainty weighting, MixUp), but the way they're fused is original and purposeful.\n3. Using neighborhood consistency with energy-based confidence to form $U_i$ , and guiding MixUp and contrastive learning with that, are novel in this context.\n4. Contrastive learning applied only to noisy samples is a nice detail that helps regularize without reinforcing noise.\n5. One possible critique is that the method combines many known techniques -- but the integration is guided by a clear principle and leads to strong results. It’s an original contribution, even if composed of familiar pieces.\n\nQUESTIONS:\n1. Computational Overhead and Scalability: SEGA requires maintaining class prototypes and computing $K$-nearest neighbors per sample to estimate structural divergence $\\delta_i$. For datasets with tens of thousands of images, was this handled efficiently (e.g., batch-wise approximations, FAISS)? How does SEGA's training time compare to standard hashing baselines? If scaled to millions of samples or hundreds of classes, would these operations become a bottleneck? It would be helpful to know if any optimizations (e.g., periodic prototype updates or mini-batch $K$-NN) were used. Also the retrieval done within the training set? Would it be overfitted easily?\n2. Multi-Label Handling: SEGA normalizes multi-hot labels into a probability distribution for prototype alignment, similar to OrthoHash. Did you consider using standard multi-label losses like independent sigmoid cross-entropy? If so, how did they compare in practice?\n3. Behavior in Noise-Free or Low-Noise Settings: While SEGA targets noisy labels, how does it perform when supervision is clean? Could the added structure (e.g., prototype anchoring or guided MixUp) limit performance in noise-free scenarios? Any results or insights on 0% noise would clarify if robustness comes at a cost in clean settings.\n\nLIMITATIONS:\n1.  Most limitations are acknowledged in the appendix, but a dedicated section in the main paper would improve transparency. A key assumption is the presence of known class structure -- SEGA relies on predefined prototypes and assumes each sample has at least one true label. It may struggle with open-set noise or entirely unlabelled data.\n2. SEGA depends on tuning the clean sample threshold $q_r$, which may be difficult under very high noise or skewed alignment distributions. Early-stage prototype alignment might be unreliable when noise exceeds 90%, though the paper mitigates this via dynamic updates. In biased or asymmetric noise (e.g., label flips between visually similar classes like dog vs. wolf), prototype drift or collapse could occur. More discussion on how SEGA handles non-uniform noise or partial label missingness would be valuable.\n3. The method's complexity is also a practical limitation -- it introduces more moving parts and hyper-parameters than some simpler baselines. This might make reproduction or deployment harder, though the release of code helps alleviate that. Finally, while the authors showed robustness on synthetic noise, applying SEGA to real-world noisy datasets (with unknown noise type) would be the next step to fully validate it.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes SEGA (Semantic Geometry Shaping) for robust hashing under noisy multi-label supervision, integrating prototype-guided anchoring, uncertainty-calibrated soft labels, and structure-aware interpolation. While experiments on CIFAR-10, Flickr25K, NUS-WIDE, and MS COCO show state-of-the-art mAP gains, critical limitations in theoretical innovation and practical validation hinder its novelty.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n1.Empirical Validation: SEGA outperforms baselines (STAR, DIOR) across noise types, with notable robustness under high noise rates.\n\n2.Closed-Loop Design: The framework jointly optimizes supervision, uncertainty, and geometry, shown via ablation studie .\n\n3.Theoretical Formulation: Theorems 3.1 and 3.2 provide probabilistic grounding for uncertainty weighting, though assumptions (conditional independence) are strong .\n\nWeaknesses\n\n1.Incremental Innovation: Prototype learning and uncertainty-based weighting replicate prior work (e.g., CSQ [50], DivideMix [23]), lacking novel architectural breakthroughs .\n\n2.Computational Overhead: Multi-component design (prototype updates, structure-aware MixUp) increases training complexity, but the paper omits inference time/memory comparisons .\n\n3.Noise Type Bias: Performance gains are more significant under structured noise (pairflip) than symmetric noise, indicating limited generalizability .\n\n4.Small-Dataset Gap: SEGA is untested on small-scale/noisy datasets (e.g., CUB-200), critical for real-world applicability .\n\nQUESTIONS:\n1.Novelty vs. Recent Baselines: Why exclude comparisons with DCMIP [2024] and PCL [2023]? Provide cross-method mAP on NUS-WIDE .\n\n2.Computational Efficiency: What is the training time/memory cost of SEGA vs. STAR on MS COCO? .\n\n3.Theoretical Assumptions: Validate Theorem 3.1’s conditional independence with real-world noise datasets .\n\n4.Small-Dataset Performance: Report results on CUB-200 with 50% symmetric noise .\n\nLIMITATIONS:\nSEGA relies on pre-trained VGG-16 features, limiting generalizability to feature-agnostic scenarios. The framework’s sensitivity to hyperparameters (e.g., K in structure-based divergence) and lack of real-world deployment cases further restrict its impact .", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces SEGA (Semantic Geometry Shaping), a novel framework for robust multi-label hashing, specifically addressing the challenging problem of learning under noisy supervision. The core idea revolves around explicitly sculpting the semantic geometry of the representation space rather than solely focusing on label correction. The proposed method integrates three synergistic components: prototype-guided semantic anchoring, uncertainty-guided supervision calibration, and structure-aware interpolation. The paper provides theoretical justifications and extensive empirical evaluations, demonstrating state-of-the-art performance on various benchmarks under different noise regimes.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n- The paper introduces a fresh and compelling perspective by shifting the focus from mere label correction to actively shaping the semantic geometry of the representation space. This is a significant conceptual contribution to robust learning under noise, especially for structured outputs like hash codes.\n\n- SEGA's three core components (prototype anchoring, uncertainty calibration, and structure-aware interpolation) are not standalone heuristics but are thoughtfully designed.\n\n- The inclusion of theoretical analyses (Theorem 3.1 and 3.2) providing probabilistic interpretations for uncertainty weighting and demonstrating structure-preserving interpolation adds significant rigor to the paper.\n\n- The paper is well-written, clear, and easy to follow. The figures (especially Figure 1) effectively illustrate the framework.\n\nWeakness:\n\n- While sensitivity analysis for q_T (percentile threshold for clean/noisy set partition) is provided, the framework still introduces several hyperparameters (e.g., m for contrastive loss, K for nearest neighbors, alpha for Beta distribution in MixUp). The robustness to these other hyperparameters is not fully explored, and their optimal selection might be dataset-dependent.\n\n- The proposed method involves maintaining dynamic prototypes, calculating neighbor-based divergence, and performing selective MixUp. While the paper mentions using a single NVIDIA A40 GPU, a more explicit discussion or comparison of the computational cost (training time, memory usage) against baselines would be beneficial.\n\nQUESTIONS:\n- The prototypes are randomly initialized. How sensitive is the final performance to this initialization, particularly when dealing with datasets that have highly imbalanced classes or very noisy initial labels?\n\n- The paper mentions that multi-label scenarios can have intrinsic semantic ambiguity. How does SEGA differentiate between true semantic ambiguity (where multiple labels are genuinely appropriate) and label noise (where a label is simply incorrect)? And how does its uncertainty estimation handle this distinction?\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a novel framework, named SEGA, for robust multi-label image hashing under noisy supervision. The main contributions include:\n- The paper presents a geometric perspective for learning under noisy supervision.\n- The proposed method considers three components during learning: (1) prototype anchoring, (2) uncertainty-calibrated soft labels, and (3) structure-aware interpolation\n- The experimental results show promising improvements compared with prior works on 4 popular benchmark.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Idea: The proposed semantic geometry shaping (SEGA) considers the semantic geometry for optimization. The three proposed modules enable representations, supervision, and uncertainty to co-evolve in a close-loop. The idea of closing the loop is interesting.\n- Design of SEGA moduel: The idea of prototype anchoring could reduce the requirement of clean labels. The structure-aware MixUp is also a good design.\n- Strong Results: The paper presents experiments on CIFAR-10, Flickr25K, NUS-WIDE, MS COCO. The proposed method achieves comparable or better performance than the previous works in terms of MAP.\n- Comprehensive analysis: The paper presents ablation studies to examine the importance of each component. Sensitivity analysis is also provided. The paper also presents the robustness of SEGA under different noise levels. Overall, the experiments are compelling.\n\nWeakness:\n- Scalability: The experiments are conducted to small or medium size of datasets. There is no large-scale dataset considered, which is the real scenario for hashing. \n- Generalizability: It might be supplemented to include discussions on possible extensions to other tasks, such as zero-shot retrieval (or other tasks that also require semantic geometry)\n- Readability: The paper is not easy to follow, especially theoretical analysis.\n\nQUESTIONS:\nsee weakness\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}