Dual-Res Tandem Mamba-3D: Bilateral Breast Lesion Detection and Classification on Non-contrast Chest CT
Authors: Jiaheng Zhou
Wei Fang
Luyuan Xie
Yanfeng Zhou
Lianyan Xu
Minfeng Xu
Ge Yang
Yuxing Tang
Venue: NeurIPS 2025 poster ()
Keywords: Opportunistic Bilateral Breast Cancer Analysis
Non-contrast Chest CT
Joint Detection and Classification
State Space Models
Primary area: applications

Abstract: Breast cancer remains a leading cause of death among women, with early detection significantly improving prognosis. Non-contrast computed tomography (NCCT) scans of the chest, routinely acquired for thoracic assessments, often capture the breast region incidentally, presenting an underexplored opportunity for opportunistic breast lesion detection without additional imaging cost or radiation. However, the subtle appearance of lesions in NCCT and the difficulty of jointly modeling lesion detection and malignancy classification pose unique challenges.
In this work, we propose Dual-Res Tandem Mamba-3D (DRT-M3D), a novel multitask framework for opportunistic breast cancer analysis on NCCT scans. DRT-M3D introduces a dual-resolution architecture, which captures fine-grained spatial details for segmentation-based lesion detection and global contextual features for breast-level cancer classification. It further incorporates a tandem input mechanism that models bilateral breast regions jointly through Mamba-3D blocks, enabling cross-breast feature interaction by leveraging subtle asymmetries between the two sides. 
Our approach achieves state-of-the-art performance in both tasks across multi-institutional NCCT datasets spanning four medical centers. Extensive experiments and ablation studies validate the effectiveness of each key component.

Dual-Res Tandem Mamba-3D: Bilateral Breast Lesion Detection and Classification on Non-contrast Chest CT
Jiaheng Zhou *..5.
Wei Fang .
Luyuan Xie
Yanfeng Zhou'
Lianyan Xu"
Minfeng Xu"
Ge Yang
Yuxing Tang
Institute of Automation, Chinese Academy Sciences
School of Artificial Intelligence, University of Chinese Academy of Sciences
DAMO Academy, Alibaba Group HHpan Laboratory, Hangzhou, China V Zhejiang University
Peking University
a Shenzhen University
"ZhongShan Hospital, Fudan University
Wook done during an internship at the Medical AI Lab, DAMO Academy, Alibaba Group.
Eqqual contribution. (lucas fw, yuxing. t) 20allbbbb-iinn
"Corresponding authors.
(zhoujiaheng2022, wwa.yannnn..a.....m ac.
Abstract
Breast cancer remains leading cause of death among women, with early de- tection significantly improving prognosis. Non-contrast computed tomography (NCCT) scans of the chest, routinely acquired for thoracic assessments, often capture the breast region incidentally, presenting an underexplored opportunity for opportunistic breast lesion detection without additional imaging cost or radiation. However, the subtle appearance of lesions in NCCT and the difficulty of jointly modeling lesion detection and malignancy classification pose unique challenges. In this work, we propose Dual-Res Tandem Mamba-3D (DRT-M3D), novel multitask framework for opportunistic breast cancer analysis on NCCT scans. DRT-M3D introduces a dual-resolution architecture, which captures fine fne-grained spatial details for segmentation based lesion detection and global contextual fea- tures for breast-level cancer classification. It further incorporates a tandem input mechanism that models bilateral breast regions jointly through Mamba-3D blocks, enabling cross-breast feature interaction by leveraging subtle asymmetries between the two sides. Our approach achieves state-of-the-ar performance in both tasks across multi-institutional NCCT datasets spanning four medical centers. Extensive experiments and ablation studies validate the effectiveness each key component.
Introduction
Breast cancer remains of the most prevalent and deadly diseases among women worldwide (8].
Early detection is critical for improving survival out- comes [74). While screening techniques such as mammography, ultrasound, and magnetic resonance imaging (MRI) are well established, they require dedicated protocols and are not routinely performed during thoracic exams for unrelated conditions [13]. However, non-con contrastt chest computed tomography (chest NCCT) is widely available and frequently con- ducted for pulmonary evaluation, which naturally in- cludes the breast region [61]. As illustrated in Fig. [] this creates valuable opportunity for breast cancer assessment without additional imaging cost radia- tion exposure.
Mammagaahhy
Brcaal Himsound
Brassl MR!
sugosding mur::
advanced examinations
Lassel Le reliannt
& Barzel IL bone
Preliminary warning for
Nen-omtma Cheet CT
Non-contrast chest CTs enable oppor- tunistic breast cancer analysis without additional Leveraging bilateral information leads more reliable detection and classification.
Figure 1:
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Despite this potential, breast cancer analysis on chest NCCT poses several technical challenges. First, the absence of contrast enhancement in NCCT hampers lesion conspicuity against surrounding tissue. Second, lesion detection and malignancy classification serve complementary clinical purposes: the former focuses on localization, the latter supports diagnosis. Yet they are often treated as separate tasks, limiting the opportunity to share relevant features. Third, most existing approaches process each breast separately, overlooking the bilateral context that radiologists routinely use to detect asymmetries and subtle lesions. These limitations underscore the need for unified framework that jointly models both tasks and captures long-range interactions between bilateral breast regions.
However, building such unified framework remains challenging [60]. Segmentation architectures like UNet (5T) and its variants rely on convolutional backbones with limited capacity for global context [2], while vision transformers (ViTs) [44 enable long-range modeling but suffer from high computational cost or low spatial resolution 21J, compromising fine-grained lesion localization/sgmmenttiion A promising direction lies in selective state space models (SSMs), such as Mamba [TO 17]. which offer linear computational complexity with respect to sequence length, making it possible to use smaller patch sizes while preserving the ability to model long-range dependencies.
In this work, we propose Dual-Res Tandem Mamba-3D (DRT-M3D), multitask framework that jointly performs segmentation-basee lesion detection and breast-level malignancy classification. Based on Mamba (S6) [7]. selective state space model with linear complexity, DRT-M3D effi- ciently captures long-range dependencies across 3D volumes while preserving fine spatial granularity, which is crucial for detecting subtle lesions.
DRT-M3D introduces a qusl-tesolution architecture that separates voxel-level segmentation and breast-level classification into high-resolution and low-resolution paths, respectively. Mutual fusion modules align information across these two paths improve representation quality without task interference. To model inter-breast context, we introduce tandem input mechanism that processes bilateral breast volumes jointly, enabling cross-side interaction and the learning of asymmetry-awaan representations, which are critical for detecting subtle signs of malignancy.
Experiments on three internal datasets and one external dataset demonstrate that DRT-M3D enables effective breast cancer analysis on chest NCCT scans, achieving state-of-the-art performance in both breast lesion segmentation and cancer classification tasks. Extensive ablation studies verify the effectiveness of each design choice, and we demonstrate that the tandem input strategy can also benefit vision transformer models when extended appropriately.
We summarize our contributions as follows:
We propose unified multi-task framework, DRT-M3D, for segmentation- -based lesion detection and breast-level classification, enabling opportunistic breast cancer analysis on non-contrast chest CT scans.
We design a dual-resolution architecture with mutual fusion to balance fine-grained spatial detail and global semantic context.
We introduce a tandem input mechanism for bilateral modeling, enabling the network to leverage cross-side context as a structural prior.
Evaluation on nultiiinnsituutional datasets shows that our model surpasses competitive baselines on both internal and external cohorts, demonstrating strong potential for clinical application.
2
Related Works
2.1 Breast Lesion Analysis in Medical Imaging
Breast lesion analysis has been widely studied across dedicated imaging modalities such as mammog- raphy 53154,)54) ultrasound [7 (5 65 66). MRI [T6 and modal scenarios [15 28 50). with deep learning models addressing tasks including lesion detection, segmentation, and malig- nancy classification. In contrast, research on breast cancer using non-contrast chest CT (NCCT)
scans remains relatively underexplored (2 33 56 U-Net variants dominate segmentation tasks
'Throughout this paper, detection refers to segmentation baaeddd lesion detection, i.e., identifying lesions through oxxe-wwise segmentation maps. We use segmentation and detection interchangeably in this context.

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across modalities 3 68 while classification is typically performed via feature aggregation from segmentation backbones [39 72 or using standalone CNN/ViT- classifiers [76
Bilateral comparison is a routine practice in clinical mammography, and learning- methods have explored dial-view fusion and symmetry-aware modeling [49 67 A few methods incorporate handcrafted symmetry features or pairwise comparisons [5 12]. However, most approaches operate on 2D images and lack end-to-end bilateral modeling. In NCCT, where lesion visibility is often subtle due to low contrast, bilateral context is especially valuable yet remains underutilized, forming one of the key motivations of this study.
2.2 State Space Models for 3D Visual Data
State space models (SSM), such as structured state space sequence models (S4) [8 20], have emerged as linear-complexity alternatives to Transformers (59], alleviating the quadratic cost of attention for and has proven effective in capturing long-range dependencies in visual data, making it compelling alternative to Vision Transformers (14), especially in 3D tasks. VideoMamba (36) extends bi-
processing. Mamba (S6) [7 extends S4 with selective mechanism,
directional Mamba layers from 2D [73] to 3D (video) data. VMamba (44) introduces tailored
SSM scanning strategy for 2D images, while Mamba-ND (38) generalizes into Mamba-3D blocks,
simplifying volumetric modeling without complicating the internal SSMs. E-ViM (70] further
demonstrates that pre-training Mamba-3D
masked autoencoder (MAE) 22 58
63
boosts
downstream task performance, echoing MAE's success VITs [14).
In medical image analysis, U-Mamba (46) integrates Mamba into UNet [51] backbone, though
demonstrates no clear benefits over conventional segmentation models [31] SegMamba 64
introduces tri-orientated Mamba modules to better capture 3D context. Swin-UMamba (42 43
leverages VMamba [44] backbones pre-trained on ImageNet-1K (IT) to improve performance on medical images, but remains limited to 2D analysis. EM-Net (6] combines Mamba with frequency- domain learning for multi-scale 3D features. More recently, Tri-Plane Mamba (62) incorporates SSMs into the Segment Anything Model (SAM)
332 for efficient interactive 3D segmentation.
Despite recent progress, existing methods are typically single-task, focusing solely on segmentation, without classification or bilateral context. In contrast, we integrate multi-task learning and bilateral- aware modeling into Mamba-3D, yielding unified framework for breast cancer analysis on NCCT.
Methods
3.1 Overall Pipeline
Our pipeline for opportunistic breast cancer analysis on non-contrast chest CT (NCCT) scans is illustrated in Fig. 2 takes the full NCCT 3D volume as input and produces both voxel-wise breast lesion segmentation and breast-level malignancy classification. The oggmentation-basee detection result highlights both benign and malignant lesions, guiding clinicians to focus on relevant areas. The classification result automatically identifies potentially malignant regions.
To focus the breast regions within the entire chest CT, introduce Pre-Stage using a pre-trained segmentation network to perform coarse localization and cropping of each breast. The Main-Stage performs core analysis on the cropped breast regions, with all methods using consistent pre-processing and post-processing for fair evaluation. Implementation details are provided in Sec.
3.2 Dual-Res Mamba-3D
We first introduce the Dual-Res Mamba-3D (DR-M3D) network, which addresses the two interrelated yet distinct tasks: segmentation-bant detection of breast lesions and malignancy classification on NCCT scans. DR-M3D operates independently on each breast region and also serves as a baseline for our study, in contrast to our full Dual-Res Tandem Mamba-3D (DRT-M3D) model.
3D data embedding Given 3D CT image X R LXDXHXW (with for one channel in grayscale CT, and D, H, W for depth, height, and width), we apply a 3D embedding layer to transforms X into the embedded feature map Y gl xCD,,xH,,*x Each token in Y with embedding dimension C
3

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Nomai (aae-azec)
Classification (R)
Low- (R)
Low Res
Non-contraat
Crupped right breast (R)
-iax
Segmentation (R)
UNetalite Segmenttttinn Network
Nomsal e Bargr
Pazch Enchedlligg
Makanani
Dual-Res Tandem!
Classification (L)
Mamba-3D
Crupped breast (l.)
Ron (1)
High-Rau
Segmentation (I.)
Pre-Stage: breast localization (cropping)
Main-Stage: breast lesion segmentation + cancer classification using Dual-Res Tandem Mamba-311
I: left side R: right side
Figure 2: The overall pipeline of the opportunistic breast cancer analysis approach. The Pre-Stage employs pre-trained segmentation network to perform coarse-grained localization and cropping of each breast region. The Main-Stage consists of the proposed Dual-Res Tandem Mamba-3D (DRT-M3D) network, which jointly performs segmentation-bast based detection breast lesions and malignancy classification by leveraging dual- resolution features (intuitively represented by orange arrows) and facilitates cross-breat feature interaction between bilateral breast regions (green arrows). Please refer to Sec. 3.2 Sec. 3.3
and Fig. for more details.
corresponds to a Pa Ph Xw patch in the original image, where Pa
H. and Pw w. Ph H Dr
D
w
We independently apply implitude-learnable sinusoidal embeddings along each dimension and add them to equally split segments of the embedding space to help preserve spatial structure.
Dual-resolution design with mutual fusion breast-level malignancy classification, DR-M3D adopts a dual-resolution architecture. Specifically, the embedded feature map Y E R xH, is further downsampled via 3D MaxPooling to generate lower-resolution feature map Z E IR c''D', x',,, Here, C' denotes the increased embedding dimension for a more powerful representation for the low-resolution path, and the He
To support both fine- theeggraned lesion segmentation and
downsampling factors are defined as Dp D, H.
We and P = w Thus, Y and Z are used as the initial inputs the high-resolution (HR) and oewresolution (LR) paths, respectively, denoted as y and z in the following text.
As the DRT-M3D block shown in Fig. 3 (a), each DR-M3D block also contains an HR and an LR Mamba-3D sub-block, forming (uul--ptthe structure. From black-box view, the i-th DR-M3D block defines the mapping (yit1 z DR-M3D' (Y zz' while preserving the spatial resolutions of both paths. The HR path retains spatial details for voxel-level segmentation, whereas the LR path, operating on shorter sequences, captures long-range dependencies crucial for classification.
To facilitate cross-path information exchange, each DR-M3D block integrates a mutual fusion
mechanism. Specifically, after the HR Mamba-3I sub-block processes Y', the output F is downsampled and projected to match the LR resolution and channel dimension, allowing residual fusion with the LR path. Conversely, the LR output Zi+l is upsampled and projected to match the HR shape before being added the input of the next HR block.
Formally, the internal update process within the i-th DR-M3D block can be expressed as:
Y y ritl_ giit1
Z Z fdown (
(Zt1))
Z 7
where
i+l = Mamba-3D (
(2)
Z i+
Mamba-3D(22 3D

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4
2
Lan
2
"SMA""
El
Mareha- 10
4
Black
rid Flaticaing in the Bitsteral Pscodo-3D Space
FA
F
Vi
Vi
High-Ro
Isankon
Mansha Lighr
Blick
Freds.
P
Diabiitt Tandem
Marnba-3D Black
Bereanpphng
Tanden Mamiua-3 Black
Ayponr ancess Bifinoer Flateoing Moder Binu 4
Coocalanaion
(a) Dual-Res Tandem Mamba-3D Block with Mutual Fusion
(b) Tandem Input of Mamba-3D Blocks
Figure 3: Dual-Res Tandem Mamba-3D block. (a) The high-resolution (HR) path captures fine-graines local features, while the low-resolution (LR) path focuses global context. The upsampled LR output is fused back the HR path, facilitating joint feature alignment. (b) The Tandem Mamba-3D block flattens both 3D inputs ID with specific dimension-priorts flattening modes and concatenates them to form Tandem Input. This prevents mixing of bilateral information while enabling cross-side feature interaction during selective scanning.
and the downsampling and upsampling transformations are defined as:
Sdowa (Yit))
Sup (Z)
(Z ")
Our dual-resolution architecture assigns tasks to different paths, while residual coupling via mutual fusion encourages joint feature alignment. This setup can be seen a form of soft parameter sharing [9] under a multi-task optimization framework, also emulating how radiologists integrate local and global cues in clinical reading.
3.3 Tandem Input for Mamba-3D Blocks
Building the DR-M3D structure introduced in Sec. 3.2 we further seek exploit the inherent correlation between bilateral breasts, aiming to mitigate the limited feature richness of NCCT images. To achieve this, propose the tandem input mechanism illustrated in Fig. (b), which transforms each sub-block into a Tandem Mamba-3D block, forming the complete DRT-M3D architecture.
Specifically, we organize the tokens from the left and right breasts into bilateral pseudo-3D space. The right breast occupies the coordinate range from (1, 1, 1) to (Dn, HR. WR), while the left is positioned from (DR + 1, HR + 1, WR + 1) to (DR + Dr., HR + Hr, WR Wr.). For anatomical alignment, the left breast is pre-flipped along the X-axis, so both regions share the same orientation and are juxtaposed within the extended space, without assuming direct connectivity along any particular axis. By flattening the pseudo-3D volume while skipping unoccupied regions, we obtain the tandem input sequence shown in Fig. (b), which is equivalent to flattening the left and right breast regions separately with the same mode and then concatenate them end-to-end. The internal
different 3D flattening modes and scanning processes follow the Mamba-3D strategy [38 70 as
detailed in Sec. A and illustrated in Fig. 7
The tandem input design not only ensures that Mamba-3D scans all voxels from one breast before moving to the other, but also guarantees a roughly fixed distance between anatomically symmetric locations in the sequence, allowing the model to better capture cross- breast relationships. The LR path further enhances cross-side modeling by offering a shorter sequence and higher embedding dimensionality. Moreover, the prioritized scanning strategy across different axes aligns with the multi-orientation analysis and comprehensive assessment performed real clinical evaluation.
cross-breast
3.4 Training Procedure
Efficient self-supervised pre-training We adopt the efficient self-supervised pre-training strategy for Mamba-3D blocks proposed in [70], which improves downstream performance and accelerates convergence without extra data. We set the size of jointly masked regions in the HR path to match
the downsampling factors (pá. Ph. pw) from HR to LR, with masking ratio Pmask- This ensures
5

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that each LR token is computed only from unmasked HR tokens, avoiding information leakage and allowing for the removal of masked tokens during pre-training.
To construct the masked autoencoder 22 58 70]. we append M additional DRT-M3D blocks as the decoder following the backhone network. The pretext task is reconstruct the masked tokens from both the HR and LR outputs via token-to-patch linear projections. The pretraining objective is optimized using mean squared error (MSE) loss, formulated as:
IV aaaaloed
1
[Ixxmool, - [x],)' ([Xzpooo, -[x],
-[x],)
CRRE
(4)
V Waskeed
where V "masked denotes the set of masked voxels.
Joint segmentation and classification fine-tuning We fine-tune the network jointly for voxel-wise lesion segmentation and breast-level malignancy classification, while the network structure enforces partial task decoupling and soft feature interaction through the dual-resolution paths.
For the segmentation task, supervision is applied the HR path's output using hybrid loss composed of the Dice loss 48 and voxel-level cross-entropy (CE) loss:
M
LesG = Dice( M Mg)
+
Σ
CB CE( [Myxpool, - [Mg1l,
(5)
|V
where pred is the segmentation prediction obtained from the HR output Y N-1 via an MLP, Mg. the ground truth mask, and V denotes the of all voxels in the cropped 3D-image.
For the classification task, supervision is applied to the LR path's output using standard image-level cross-entropy loss:
LCtS CC( UZz-prdd Vg))
(6)
where y7e.pred is the predicted malignancy score obtained by applying global average pooling and an MLP to the LR output Z N-1 and Vg is the ground-truth breast-level malignancy label.
The overall fine-tuning loss the weighted of the task losses:
LFT
LSEG + AL
where A balances the relative importance of the two tasks. We empirically set À = 0.1, reflecting the relative simplicity and higher overfitting risk of the classification task.
4
Experiments
4.1
Experimental Setup
Following the medical image analysis paradigm, we use both internal and external datasets. The internal datasets include training and testing splits, while the external set is reserved for testing only, providing a distribution shift that enables a rigorous assessment of generalization.
Datasets
The internal data comprises three cohorts collected from separate institutions, referred to as Inst. 1-3, with training and testing splits contain (341/ /15, 239 / 921, 141 /113) and (82 / 78, 102 / 296, 34/ 28) cancerous non-cancerous breast cases, respectively. The external dataset contains 214 breast samples as ( [105/ 109) cancerous non-cuncerous.
For all datasets in the Main-Stage, bilateral breasts from the same patient are always assigned to the same split to avoid data leakage. Each sample consists of cropped NCCT image of the breast region, segmentation masks for the breast and lesions (if present), and binary cancer label. More details regarding the datasets and the Pre-Stage process can be found in Sec. B
Implementation Our model is implemented in PyTorch and trained on up to two NVIDIA A100 (80GB) GPUs. The training process consists of 500 epochs for self-supervised pre-training and 50 epochs for downstream fine-tuning, optimized using AdamW (5). The base learning rate is

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Table 1: Quantitative results of the internal evaluation across three datasets. The best and second-best results are bolded and underlined, respectively. (H..: Hit-Rate, Es.:: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Mathod
Test.
1 (Spec. -0.9115)
Inst. 2 (Spoc. -099955)
Inst.
(Spec.
-0.6433)
Dioe
H.r.
Fs.
Sene
AUC
Dice
H.r.
F4.
Sans
AUC
Dice
H.r.
F4.
Sens.
AUC
mUNe:
0.6174
0.9390
0,8358
0.8049
0.9558
0.5413
0.9099
0 1,8306
0,7647
0.9501
0.5080
0.8611
0.5764
0,7353
0.9170
nnNNet
0.9268
0,8760
0,9099
0.8694
0.8333
0.8194
mUNN--CC.
0.7927
0.9622
0,7549
0.9540
0,7353
0.9755
VNet
0,5623
0.9146
0,8553
0.7683
0.9500
0
0.8649
0.8198
0,7451
0.9418
0.5116
0.8056
0.7431
0,7553
0.8797
swinL NETR
0.5647
0.9146
0.9043
0.8171
0,9432
0,6009
0,9009
0.9423
0.7353
0.9423
0.5465
0.833
0.7764
0,7059
0.5981
nn Former
69
0.560]
0
0.9268
0.8150
0.6707
0.9595
0.6123
0 0.999
0. 0,5709
0,7549
0.9444
0.5298
0.8353
0.7709
0,7353
0.9377
3D UX Net
0,5669
0.9268
0.7811
0,7683
0.9361
0.6015
0.9279
0,8258
0,7353
0.9382
0.5213
0.8333
0.7327
0,7647
0.9391
MadNeXi
D.6175
0.9146
0.8719
0.7683
0.9500
0.6293
0.9369
0. 1.8919
0.6863
0.9510
0.5604
0.8333
0.7848
0.7647
0.0076
U-Mambba. Boc
46
0:6042
0.8659
0.8552
0.8049
0.9578
0.7858
0.7928
0.7451
0.95%6
0.5361
0.7500
0.7500
0.391
U Mamba Enc
36
0,5708
0.8171
0,8111
0.7805
0.9548
0,5671
0,7838
0.7928
0,7451
0.9561
0.4901
0.6944
0.6944
0,7059
0,8792
EM-Nett
0,5803
0.9268
0.8099
0,7439
0.9467
0.6203
0.9189
0.8587
0.7549
0.9540
0.5461
0.8056
0.7361
0.6705
0.9160
SegMamba 64
0.9146
0,8509
0.7805
0.9555
0.8919
0.8691
0,8039
0.9479
0.5109
0,7500
0.7152
0.7353
0.004
Sun al. 3025 56
0.6061
0 0.9268
( 0.8613
0.7561
0.9457
0.6317
0. 1.909
0. 0.9649
0.7647
0.9417
0.5859
0.8889
0.7778
0,7059
0.9144
DR-M3D (ours)
B.6553
20083
0.5330
2.0070
1:9045
0.770
0.9725
2000
0.6744
1:0075
0.9399
2.00
0,923
0,7549
6008
019986
3.0016
1:0078
0.000
0.870
20011
018264
0,7505
4.0245
0.9226
4.009/
DRT-M3D (ours)
0.6608
F.0018
0.9149
7,0070
0,9258
6.0063
0.9471
-00186
0,9909
+.0015
0.6730
+.0022
0.9279
00000
0.9212
1.0050
0.8366
0229
0,9743
+.0030
+.0148
0.6956
0.8796
+ +01661
0.8518
+.0080
0,8726
+0070
0.9471
+00044
set to 1e-3, with a linear warm-up phase followed by cosine annealing. Detailed experimental configurations and
provided in See. [
For baselines not compatible with MAE pre-training (mainly CNN-based models), we use supervised pre-training on segmentation followed by joint fine-tuning on segmentation and classification, which achieves better performance and enables a fairer comparison. For architectures that support MAE pre-training (i.e. Transformer or hamba-based models), we apply MAE pre-training (without extra data) and fine-tune with the same protocol as our method.
Evaluation metries For segmentation- based detection, we evaluate performance using the Dice Similarity Coefficient (Dice), Hit-Rate (H.r.), and FROC-Score (F.s.) (4I) derived from the Free- Response Receiver Operating Characteristic (FROC) curve (2). Among these, Dice measures voxel-level segmentation quality, while Hit-Rate and FROC-Score assess lesion-level sensitivity and the ability to control false positives. For classification, we report sensitivity (Sens.) at a fixed high specificity (Spec.) threshold for different methods and the Area Under the Receiver Operating Characteristic Curve (AUC). Further details on evaluation metries are available in Sec. D
4.2 Main Results
Quantitative comparisons on internal datasets Tab. [ presents quantitative results on three inter- nal datasets, comparing our method against strong baselines and tftte-- approaches. For UNet- based methods, we incorporate multi-scale feature fu- sion [40 72) for classification. To isolate the effect of task interaction, we include single-task nnUNet vari- ants: mnUNet-SEG (segmentation-onlly) and Unee CLS (classification-only Our method, DRT-M3D, achieves leading performance across most metrics on all three datasets. In particular, it consistently improves segmentation- based detection by reducing false positives (as reflected in the FROC-score), and boosts cancer classification performance in terms of Sensitivity and AUC. We also note that our baseline DR-M3D model performs competitively, further vali- dating the effectiveness of our dual-resolution design.
Table 2: Quantitative results of the external
evaluation. The best and second-bes results are bolded and underlined, respectively. (H.r: Hit- Rate, Fs.: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Estemal (Spec. = 009003)
Mechod
Dice
H.r.
Rs.
Sens.
ADC
anLiNer 30
0.5668
(13889
0.8173
0.0266
0.8899
0.8632
0.8173
0.7338
0.9156
VNei 48
0,5059
0.8120
0,7272
0.6571
0,8790
swint swintiNET
NETRR
0.5364
0.5803
0.7630
0.6476
0.8818
unformer 69
0.5270
0.3889
0.7508
0.6190
0.8866
3D UX Net
0,5217
0.8547
0,7589
0.6095
0,8777
MedNeXi
0,5787
0.8974
0.8120
0.6371
0.8945
U-Mamiu-
0,5615
0.7863
0,7799
0,8974
UtManio-Fac
0,5150
0.7436
0.7308
0.4055
0.8893
EM Net
6
0,3489
0.5547
0.7618
0.0000
0.8KIS
Sog Mamma
0.5388
0.5462
0.7639
0.6381
0.9083
Sun 2025
0.5624
0.3974
0,8246
0.6286
0,8827
DR-M3D
0,5909
10038
0.3974
0.8632
1.0066
0.7207
0,5082
1009
Quantitative comparisons on the external dataset The external dataset from a distinct institution (Inst. 4) poses a significant distribution shift, serving as a
0.5948
0.9117
0,8766
0.8762
0.9371
DRI-M3D (ours)
2.0077
4.0082
0.0057
1006
7

---

RAW
DRE-MD
FABENETE
UX--
U-Mario
IM
SegNaaka
(rakgwei ()
(8:99.)
(2.1814)
(1.119))
(M/2217)
(2:5540)
01.354))
(1.1648 (alen)
(8:1130)
(2.499)
thegge.
(6/042))
(9.9977)
(n (nlissTaaan
(8/2977)
(2.4150)
09.7000
(Pradde Falle)
(5 (3:4655 cul-))
(3 3770
(02117))
(3.7590)
(13071)
(2.2649)
(0.0945)
(B.1770
(8.1764)
121550
(eallgert)
(3:17%))
(37129)
Figure 4: Qualitative comparison of DRT-M3D with competing methods. Examples from internal external test sets are shown, including representative 2D slice and a 3D view for each case. Red, green, and blue masks represent breast regions, malignant, and benign lesions, respectively. White, yellow, and red arrows mark pronounced segmentation errors in the slice, missed lesions, and segmentation of non-existent lesions, respectively. Predicted malignancy scores are shown each case (higher malignant, lower benign). "Failed" denotes cases where none of the true lesions were localized (i.e., non-hit under the Hit-Rate metric).
Table 3: Ablation study on the designs of the proposed DRT-M3D network. DR, MP, and TT denote the use of Dual-Rusuuu ResoluReso Mutual Fusion, and Tandem Input, respectively. (Hr.: Hit-Rate, Rate, Fs.: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Variants
Internal (Spec.
0.9627)
External (Spec.
0.9083)
DR
MF 11
Dice
H.r.
Ess.
Sens.
AUC
Dice
H.r.
Fs.
Sens.
ALC
Vanilla M3D
0.6334
0.8908
0.8854
0.7936
0.9637
0.5788
0.8666
0,8359
0,7100
0,9053
0.6449
0.9170
0.8879
0,7982
0.9574
0.5848
0.8879
0.8509
0.6620
0.8940
DR-M3D
0.6564
0.9228
0.9027
0.8073
0.9690
0.5909
0.8974
0.8632
0.7207
0.9082
0.6388
0.8952
0.8876
0.8211
0.9625
0.5898
0.8880
0.8565
0.8522
0.9184
0.9719
0.5925
0.9022
0.9264
DRI-MD
0.6590
0.9229
0.9145
0.8578
0.9768
0.5948
0.9117
0.8766
0.8762
0.9371
strong generalization benchmark. As shown in Tab. 2 DRT-M3D maintains leading performance across all metrics, outperforming competing methods. The variant without tandem input (DR- M3D) also generalizes well, especially for segmentation, further supporting the robustness of the overall architecture.
For both DR-M3D and DRT-M3D, we report the mean and standard deviation of each metric over five runs with different random seeds, as reported in Tab. and Tab. 2
Visualization results for qualitative comparison Fig. Hig.Aish ssowws representative lesion detection and clas- sification outputs. DRT-M3D delivers accurate lo- calization and better differentiation between cancer- ous and non-cancerous cases. Competing methods more frequently miss lesions or misclassify malig- nant breasts.
0.66
0.95
0.90
0.85
0.62
Eoonel Doee
Ininol AUC
0.50
Deimal AUX
0.60
4.3 Ablation Studies
0.58
Ablation on architectural designs We evaluate the impact of key components in DRT-M3D through ablation studies on Rusolueeoo (DR, w/o means using the HR path for both tasks), Mutual Fusion (MF), and Tandem Input (TI). The results in Tab. demonstrate that the DR design enhances segmenta- tion, while TI improves breast-level cancer classifica-
12
0(ecratch)
200
Pre-training Eguchis
Figure 5; Ablation study on the training strategy. Error bars on the curves are obtained by repeating the experiments with five different random seeds.

---

Dice v.. FLOPss (inteenal)
Dice vs. FLOPs (external)
0.60
67
recuiiing GRAGD aur
Paundko (N)
6
15.4
BUIDa 1400-1
15.4
0.50
Te.1
47A
47.
0/62
FR
24062 grnse
0822200
0.60
prrths
0.38
vpp Supo
10/
10'
10/
10*
PLOP (G)
PLOP
ACC FLOPS (internal)
AUC FLOPs (external)
0.4
0.955
0.78
103400
47.4
4544
Machay
1400-144
628
34p5
0.0-
2000
Figure 6: Comparison of Dice and AUC vs. FLOPs on internal and external datasets. Each FLOPs value is computed per bilateral input (or two unilateral inputs). VIT: vanilla Vision Transformer, M3D: vanilla Mamba-3D, T--: tandem (bilateral) input form, -/p: patch size of (2, p. p).
tion. Additionally, the MF mechanism facilitates information sharing between the Dual-Res paths, boosting performance across all metrics. For Tandem Input specifically, we further compare several variants Sec. H
Ablation on the training strategy MAE pre-training has been shown to benefit Mamba-3D on high-level semantic tasks (70). Since our study also involves voxel-level segmentation, we further validate its effectiivnesss in this context. To fairly compare different pre-training durations, we adjust the fine-tuning epochs for full convergence. As shown in Fig. [5] the two-stage training strategy with adequate self-supervised pre-training also proves effective for the multi-task setting of segmentation and classification in this study.
Patch size tuning We further validate through experiments (see Fig. 6 that using relatively smaller patch size in height (Pt) and width (pw) of CT slices, such as (2, 4, 4) in our models, substantially improves performance. Due to the model's underlying linear computation design, this gain comes with minimal computational overhead. However, further reducing the patch size (e.g.. to (2, 2, 2)) leads to stagnation or even drop in performance, presumably due to increased token fragmentation and reduced contextual capacity. Conversely, variants with larger patch sizes can significantly reduce computational costs while still outperforming competing methods. Detailed configurations of each variant are provided Appendix Tab. and Tab. For experiments regarding the patch size in the depth dimension (pa). please refer to Sec.
Bilateral input on vision transformers To further evaluate the Mamba-31 -D (M3D) structure and tandem input concept, we integrate bilateral input into the commonly used VIT [14 for comparison. We adopt ViT-T and ViT-S as two different scales, and denote their bilateral variants as T-V In T-ViT, left-side and right-side encodings are added to the 3D positional encoding to distinguish patches. All VIT models follow the two-stage training pipeline as ours. As shown in Fig. 6 bilateral input improves cancer classification VIT models but still fall short compared to our M3D-based models, particularly for VIT/4 with the same patch size (2, 4, 4) as D3T. The performance gap
9

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is primarily due to the excessive number of tokens resulting from small patch sizes and bilateral input, which leads to peaked and less expressive attention distributions and thus hampers the learning of patch relationships [57]. For larger patch sizes, ViT"s performance remains clearly inferior, especially segmentation. Although larger patches reduce token count, they further decrease spatial resolution, and the lack of intrinsic local inductive bias in ViT prevents effective modeling of local structures.
5 Conclusion
In this paper, we propose DRT-M3D, a dual-resolution network for joint segmentation- based breast lesion detection and cancer classification non-contrast chest CT scans. By disentangling the two tasks into resolution-speccfic pathways, DRT-M3D enables complementary learning between segmentation and classification, while tandem bilateral inputs enhance contextual understanding of subtle features across bilateral breasts. Experiments on multi-institutional datasets demonstrate consistent improvements over strong baselines, underscoring the clinical potential of DRT-M3D for robust and generalizable opportunistic breast cancer analysis.
Limitations and future work This study only focuses breast cancer analysis using NCCT scans, but the idea of bilateral organs and the design of DRT-M3D may be applied to other organs such as lungs and kidneys. In addition, the data currently in all come from one country and have not been extended to a broader population. We have already started to collect more diverse data from a wider range of regions for future research.
10

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Acknowledgments and Disclosure of Funding
This work was supported in part by the National Natural Science Foundation of China (grant 92354307), the National Key Research and Development Program of China (grant 2024YTF0729202) and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDA0460305). This work was also supported by Alibaba Group through Alibaba Research In- tern Program.
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A Preliminaries on Mamba-3D Blocks
A.1 Selective State Space Models
Selective state space models (S6), which are represented by Mamba [17] are essentially derived from the vanilla state space models (SSM) based on continuous linear time-invariant (LTT) systems.
SSMs utilize N-dimensional latent state vector h(() R to model the transformation from one-dimensional continuous input signal to its corresponding output xztt) E R - s(t) E R:
h(( = Ah(() + Bx(()
v(t) Ch(() + Dx(()
where E IR N is the "state matrix", B E NxX the "input matrix", C IR 1x is the "output matrix", and TR 1g1x1, is the "feed-through matrix". These are system matrices governing the evolution and output of the system.
To make these models applicable in deep learning settings with discrete inputs, structured state space models (S4) [18-20) discretize these equations using numerical methods such as the zero-order hold (ZOH) 55 approach, yielding the following discretization:
A = exp(AA)
B (AA) [exp(AA) - 1] AB AB
where A denotes the discretization step size. The larger the step size A, the faster the hidden state h changes, and the greater the impact of the current token on the system.
In Mamba, A must be a diagonal matrix. Consequently, when entries A are sufficiently small, the approximation ( (AA) [exp( - -]] = holds true. This leads to the discrete-time S4 model for sequential input and output, as 2, E F Ye R:
h, Ah,1 + Br, exp(cA)) (AAA, ABr,
(10)
1/1 Ch, + Dar
For multi-channel inputs (i.e., x, E R) and the corresponding multi-channel outputs, the above operations are applied independently to each channel.
Building upon S4, the S6 structure enhances the model's expressiveness by making the parameters A, B. C dynamically input-dependent across all channels of x, E IR. which known as the selection mechanism:
B, = Linearc-N (xx)
C Linearg-N (x:)
(11)
A = softplus [Tinearc-c (x,)
With the discretization in Eq. 9 A, B, C are longer fixed parameters in the inference phase, allowing the model to adapt to varying input signals and provides greater modeling capabilities than the original SSMs. Overall, S6 can be expressed as:
h. exp( A)),, + A,B,T,
(12)
//1 C.h, + Dr,
The input-dependent nature of S6 (Mamba) makes it particularly suitable for processing patchified visual data, where different spatial regions may require distinct dynamic responses, similar to words in natural language processing. The exponential transition term captures long-range dependencies, while the learned A, modulates temporal sensitivity, making Mamba capable of adapting to both local and global features.
A.2 Mamba-3D Blocks
Unlike most visual Mamba works [36 44 73 that modify the internal structure of blocks to support multi-directional scanning, Mamba-3D 70 retains the original architecture of the Mamba block.
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Single Input
Tandem (bilateral) Input
LayerNorm
Ros Path
Moin Path
Gating Path
Linear
Linear
3D Patch Embedding
Wist ConviD
C.D.B,
C.P. H.D..H,.W
Vanilla Mamba block for "HWD"
2. UK,0)
56 with
A, A,
Vauilla Mamba block for reversed "HWD"
c.00,%%))
1666 0,95%)
Linear
Vanilla Mamba block
"DWH"
c. M,tD,
Vanilln Mamba block for reversed "DWHI"
(a) Vanilla Mamba Block
(D,H,%)
(0,H,, +,8,,%)
"HWD"
Vanilla Mamba
"DHW"
2 8pp
C, +D,
"DWH"
Vanilla Mamba block for reversed "DIIW"
"DHW"
C. 9
C.D. 2g
(b) Different Flattening Modes Mamba-3D
(c) Mamba-3D block with Single Input or Tandem (bilateral) Input
Figure 7: The internal structure of the proposed Tandem Mamba-3D block. (a) Vanilla Mamba block with selective state space module (S6). (b) Different sequence permutations used for the serial scanning processes in Mamba-3D. (c) Data flow inside one Mamba-3D block in the cases of Single Input and Tandem (bilateral) Input.
as depicted in Fig. (a). This design choice allows Mamba-3D to maintain the same computational cost while enabling deeper networks that better capture directional visual features, yielding improved performance on 3D visual tasks compared to methods that introduce complexity into the S6 internals.
Mamba-3D achieves effective processing of 3D data through specific transformations of the sequence order among different Mamba blocks, as illustrated in Fig. (b) and (c). Specifically, this involves separate forward and reverse Mamba operations across three permutations of the 3D axes: "HWD", "DWH", and "DHW", as three 3D-to-10 ID flattening modes. Each permutation ensures contiguity along the last axis after flattening, facilitating the modeling of local and non-local dependencies across spatial dimensions. Furthermore, the standard Single Input form and proposed Tandem (bilateral) Input are presented respectively in the left and right parts of Fig. (c).
B
Datasets
Further details on the datasets Our research utilizes three internal datasets from different insti- tutions for training and evaluation, as well as an external dataset for independent evaluation. The data distribution and characteristics of the external dataset are prominently different from those of the internal datasets, which makes more conducive to demonstrating the generalization capabilities of different methods. The number of samples in each dataset is shown in Tab. 4 The training and testing splits of internal datasets are designed to evenly distribute samples across different collection periods and varying lesion sizes.
The original data each dataset consists entirely non-contrast chest CT images with spatial resolution D x 512 x 512, where D denotes the number of slices per volume, typically ranging
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Table 4: Sample counts for the datasets used in this study.
Traning
Testing
Dataset
Cancerous
Non-cnccorus
Parients
Rreasts
Internal lnst.
541
315
80
Insernal Inst. 2
580
1160
239
921
199
398
102
296
Internal Test
254
113
31
Insc.
107
Total
1035
2070
721
1349
417
834
323
511
from several dozen to several hundred depending on acquisition settings. To ensure the reliability and accuracy of the annotations, experienced radiologists with years of expertise delineated the boundaries of breast lesions based on contrast-enhaneed CT images taken concurrently for each patient. These segmentation labels were then accurately registered to the non non-contrast CT (NCCT) volumes using DEEDS [25]. All malignant cases were confirmed via pathological reports, while benign or normal cases were validated either through pathological examinations or two-year clinical follow-ups.
In Fig. [8 we present the visualizations of representative data samples with lesions from each dataset, from left right including: (a) the representative NCCT 2D slice view with a window width of 300 and window level of 50, (b) the 2D view with segmentation labels for breast and lesion, (c) the registered CECT slices highlight the challenge of using non-contrast CT instead of contrast- enhanced CT, (d) the 3D rendered image, and (c) the 3D rendered image with segmentation labels for breast and lesion. Red annotations represents the breast, while green and blue annotations respectively represent malignant or benign lesions. The samples from the four institutions are presented consecutively from top to bottom, with two samples from each institution.
The study received approval from the Institutional Review Board (IRB) with Approval No.: B2025- 235R. All procedures adhered to established ethical standards and regulations. Confidentialitty of participant data was stringently maintained, with all identifying information anonymized during data collection and analysis. Regular audits were conducted to verify compliance with ethical guidelines, and any unforeseen ethical concerns that arose during the study were promptly addressed in consultation with institutional review boards.
we use pre-trained segmentation network to achieve coarse-gran coarse-grained cropping of each breast region in the Pre-Stage. Since this step does not require particularly precise segmentation results, we trained this coarse-grainn graiined segmentation model on a few hundred samples with breast masks using nnUNet [30], which achieved high Dice score of 0.9598, demonstrating its accuracy and reliability.
Pre-Stage:
breast region cropping As described in Sec. 3.1
To further minimize the risk of missing boundary lesions or subtle structures (e.g., in obese patients or cases with blurred borders), we adopted a conservative cropping strategy: the bounding box of the predicted breast mask is expanded by 2 voxels along the D-axis and 16 voxels along the H- and W-axes. This ensures that small lesions near the periphery are retained within the cropped region. In future deployment, extremely rare failure cases of the Pre-Stage can be flagged for manual review or fallback processing.
Following this, we obtained the training actually used in the Main-Stage, where each sample contained two partial NCCT images corresponding to the left and right breast regions, along with the voxel-level lesion masks and breast-level cancer classification labels. For methods that do not bilateral inputs, each side is treated as an independent sample. Additionally, we retained the breast region masks from this step third segmentation category, alongside the background and lesion masks, to guide effective learning in all networks, including ours and all competing methods.
C Implementation Details
This section elaborates on the implementation details of the Main Stanee in the overall pipeline (Fig. of this study, while the the Pre-Stage has been introduced in Sec. B
To ensure fair comparison, all methods in this study-including those used for benchmarking and ablation studies-shar identical pre-processing, post-processing. and data augmentation protocols. The only difference lies in the synchronization of randomness during data augmentation when bilateral inputs are used.
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Pre-processing Firstly, we unify the three- dinensiinnni spacings of CT images through resampling, with the target values being the median spacings of all samples in all training sets, which are (3 mm, 0.748 mm, 0.748 mm). Subsequently, we adopt the normalization scheme introduced by [30] to the Hounsfield Unit (HU) values of CT images. Let x denote the original Hounsfield Unit (HU) value of voxels in CT image. For all foreground voxels (že.. breast and lesion regions), we first compute the 0.5th and 99.5th percentiles of the HU distribution, denoted as 9o.5 and 499.5+ respectively. The voxel intensities are then clipped and standardized follows:
min( max((x, 9o.5), 999.5)
Xelipped
(13)
Xelipped
porm
where Xelipped is the HU value after quantile-based clipping; and a are the mean and standard deviation of the clipped HU values within the foreground: X is the final normalized HU value. This normalization procedure helps suppress noise and outliers, while ensuring a standardized input range for downstream processing.
Given that the cropped breast regions vary in size, we further crop each single breast in the Main-Stage nnUNet [30] did, so that it has uniform size as 56 x 160 x 192 when fed into our network and all the competitors, which is slightly smaller than the median size of all single-sided samples. In cases where the input no longer contains any lesion voxels after the uniformly sized cropping, modify the breast-level label to "non-cancerous" by verifying that no lesion voxels are present in the cropped region during training.
Data augmentations To leverage the symmetrie nature of breasts in alignment with our proposed Tandem Mamba-31) blocks, we flipped the left breast image along the X-axis (i.e. the W-axis in the network's inputs and outputs) prior applying data augmentations, thus treating it pseudo-right breast. During training, the cropped left and right breast images from the same patient undergo identical data augmentation procedures, which include random combination of scaling, rotation, Gaussian noise, Gaussian blur, brightness adjustment, contrast adjustment, inversion, gamma adjustment, and three-dimensional mirroring, as proposed and planned by (30]
Post- nost-prccessig for segmentation and classification As commonly used in medical image seg- mentation 4030 we apply a sliding window approach during inference to handle variations in sample sizes. For segmentation, the softmax values of each voxel are restored to the original cropped breast region's s size using Gaussian-weighted superposition and spacing resampling. For classification, the final score for malignancy (cancer) is taken as the highest score across all sliding windows.
In each window, mirroring is applied independently along all three dimensions, yielding eight different results. The averaged results are then used as the test-time augmentation. As mentioned carlier, the left breast is flipped to become a pseudo-right breast for bilateral inputs, and during the eight mirroring operations, the real-right and pseudo-right breasts are kept synchronized.
Detailed configurations and byper-parameters Leveraging the linear complexity of Mamba with respect to sequence length and its efficient implementation, we adopt a relatively small patch size to enhance segmentation performance. Unless otherwise specified, the default main hyper-parameter are set as follows: the patch size for the high-resolution (HR) path is (pa. Ph: Pw) = (2, 4, 4) with the embedding dimension of C 192; the downsampling factor from HR to low-resolution (LR) path
(pa. Ph: ) (2, 4, 4) with the LR embedding dimension of C' 384; the number of backbone blocks is N 6; the number of decoder blocks is M = 2; and the masking ratio for self-supervised pre-training is Piuask 0.8. Each Mamba layer follows the default configurations as the original Mamba 117
In Tab. 5 5nd Tab. we respectively summarize the training configurations and hyper-parameee used in self-supervised pre-training and downstream fine-tuning for the proposed DR-M DR-M3D and DRT-M3D networks, including their variants used in the ablation study of different patch sizes.
During inference, all methods-ood and the competing ones-produce the exact same output format in the Main-Stage, including the voxel-leval segmentation softmax scores for each D X H X W sliding window, and window-level classification scores after applying the test-time augmentation (i.e., mirroring and averaging as previously described).
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Table 5: Default configurations and hyper-paramectes of DRT-M3D and its variants of different patch sizes -elf-supe pre-training.
Configuation Hypa-Paramder
DR.MSD series
DRT-M3D series
DR MIDIJ
DR MEDVS
DR-M3D
DR: MR--M
DKT MILVI6
DRI DRE-MID DRT S
optimizer
A
with B1
0.0, .2
0.990, e 1e-15
weight decay
1e-1
learning cate schedule
cosine decay with linear warm
busic leaming rale
1e-3
leaming
1e-5
epuchs
5 opochs
total epachs
500 spochs
d/bttch size) 2(ranks) 4(accumolation)
2(bach size) 2(ranks) 4((ccummlation)
gradient
mixed precision
BFoodd66
function
Dual-Puth MSF
Fij
Input D))
[x X:6
192)
2x
X.56
100
Patch Size Ph. Pw)
(2, 16,16
(2,888)
(2,44))
(2
(2. 16, 16)
(2.8.8)
(2,4.4)
(2.
Low Res Pooling Size (Pa- Ph. Pw)
(2,1.)
(2,2.2)
(2,4,4)
(2,888)
1,
(2,2.2)
(2,4,4)
(2,8, 8)
High Res Embelding Dimension (C)
192
192
192
192
192
96
Low Embedeing Dimension (C')
Mutual Pision DownSanpting
MaxPoeling with (Pa- Pla Pur Linear C- C/
Mutual Pasion Upaamplin
3D Nearest Interpolation with size (Pa- Ph: Pw) Linens; C'
-
Buckbone Mamba: 3D Blocks (N)
Decder Mambu-3D
Masking Chain
1,
(2,2,
(2,4,4)
8,888
(2,
(2,4,4)
(2,8,8)
Masking Rario (przs))
0.8
Table 6: Default configurations and hyper-parameters of DRT-M3D and its variants of different patch sizes for downstream fine-tuning,
Configuraiion Hyper HyperrParamete Parameter
series
DR-M55N16
DR MEDIS
DR-M3D
DR DR-MADD2
DRT-MBEN16
DRT-MSDIS
DRT-M3D DRT-MBD-S
optimizer
AdamW
with
0.9,
0.999,
Ie-15
weight decay
1c-1
learning schodule
with wamm-up
basic leaming
1e-3
minimal kesming nite
1w-5
wa epochs
epoch
total epuchs
50 epochs
total batch size
32 = 4/batch size) x 2(ranks) x s(accomulation)
10 = 2(batc size) x 2(ranks) x 4(accummalttion)
max gradient norm
1.0
mixcal-rocision
loss fuaction
EsEO Acess Eq
with A= 0.1
Imput Size (1 x D)
1x x6
160 192)
2x 56
160 192)
(DG. Phe Pw)
(2, 16)
8.
(2,4.4)
(2
e2 16, 16)
82.8.8)
(2.4.4)
(,,
Pooling Sizee (Pa- Ph. Pw)
2.2.
(2.4.)
High-Res Emhhlding Dimension (C)
192
192
192
192
192
192
96
Low-Res Eimbedding Dimension (C')
184
Mutual Fusion DewnSumpling
3D MaxPoeling with size (74a Dja Pur) Linear
Fusion Upsampling
Interpolation size (Pa- Ph. Par)
C'
Rackhone Mamha- 3D Blocks (N)
Head for Segmentizion
Linear: C from High-Res Path - (3x Pa X Pi. ). "3" for (hackground, breast, lesion) AugPooling + MIP. C! Low-Res Path 512 Mullggant-- apit
for Clavifficaiion
For the sliding window strategy, we use a maximum stride of 50% of the window size along each dimension to determine the number of required steps. If the sizes of the left and right breast regions differ, we use the larger of the two to compute the step count. For generating Gaussian importance weights in each window, we set 0.125 when computing the weight tensor.
D Metrics
D.1 Lesion-Level (Segmentation-basee Detection) Metrics
Dice similarity coefficient (Dice) We directly evaluate the voxel-level accuracy of the segmented parts using the dice similarity coefficient:
[ 2 x |tipred
s
Dice =
(14)
S
(
26

---

where |s| denotes the total number of samples in the testing set; Si,pred is the foreground (lesion) voxel mask obtained by the model for the i-th sample; st.gt is the corresponding ground truth. The dice similarity coefficient is inherently normalized, making it suitable for targets of varying sizes or scales, particularly for breast lesion regions in this study. Moreover, the lesion boundaries breast CT images are often ambiguous. Consequently, employing the dice similarity coefficient that only considers the intersection and is more lenient towards minor deviations on the edges holds practical value.
Hit-rate (H.r.) We define breast-level prediction "hit" if the Dice score for that sample is greater than zero, otherwise as "non-hit". A "hit" indicates that the model has successfully segmented a lesion region that overlaps with the ground truth even if only partially, which can be sufficient to prompt further clinical attention. The Hit-rate is then defined as:
{ss E S Dice(s; (iedd si.g)) > 0}
H.r.
(15)
|s|
where the numerator (s, S Dice($t,pood $t.gt) ) 0} represents the number of samples where the dice similarity coefficient is greater than zero, indicating "hit"; the denominator |S| denotes the total number of test samples.
FROC-score (Fs..) For each connected region classified as the lesion class in the segmentation
results, we compute its lesion probability t as the mean of the softmax scores of all voxels in that region. Subsequenlly,
obtained the FROC curve (2 41] based on varying probability thresholds The x-axis of the FROC curve represents the false positive per breast (FPPB) indicating the average number of false positive lesion regions per breast. The y-axis the FROC curve represents the detection sensitivity indicating the proportion of true Lesion-containing breasts where at least one lesion is detected.
Unlike the standard ROC curve, the x-axis of the FROC curve spans [0, oo), making unsuitable for traditional AUC computation. Therefore, based the characteristics of the used datasets, we define the FROC-score as the average detection sensitivity at four predefined FPPBs (0.1, 0.2, 0.3, and 0.4):
Fs. Σ LesionSensitivity( RiaieenssiiiiiyyRRRe::ea Rg. |PPB,)
(16)
where each FPPB, is associated with a specific threshold used to determine Rpeed- the set of predicted lesion regions across all samples; Rg denotes the corresponding set of ground-truth lesion regions. Therefore, a higher FROC-score indicates better lesion detection performance with fewer false positive regions.
D.2 Breast-Level (Classification) Metrics
Sensitivity under fixed specificity (Sens.) For opportunistic breast cancer analysis, maintaining a relatively high specificity is crucial prevent excessive false positive alerts that could unnecessarily strain medical resources. Consequently, we selected a specificity value a (relatively high, while also avoiding excessively extreme classification score thresholds) for each dataset enable fair and effective comparisons of breast-level cancer classification across different methods:
TP
Sens.
(17)
TP FN Specificity=a
Under this setting, the sensitivity values may vary across methods, reflecting their ability to detect true positive cases at the same high specificity level. A higher sensitivity suggests more effective identification of true positives without increasing the false alarm rate.
Area Under the receiver operating characteristic Curve (AUC) Apart from the sensitivity under high specificity, we also evaluate the overall classification performance using the AUC metric, defined as:
AUC = S. Sensitivity(3)) dB
(18)
where 3 =11 -Specificity represents the false positive rate breast-level cancer classification ranging from 0 to which differs from the definition of FPPB used in lesion-level metrics.
27

---

E Additional Experiments
tuning In addition to the ablation studies in the main paper, we also conducted experiments on several other key hypee--arrmmetes, including the patch size in the D (slice of CT scans) dimension (pa). the embedding dimensions (C, C'), and the depth of the backbone (N).
More
As shown in Tab. 7 a smaller patch size in the D dimension, which better aligns with the larger spacing (3 mm vs. 0.748 mm in H and W dimensions), yields improved segmentation performance. However, this also leads to an increase in computational cost. To keep the computational cost (FLOPs) similar to the strong baseline (nnUNet (30), Pa 2 is used as the default. For the ablation study on patch size in the H and W dimensions, please refer to the main paper Sec.
As demonstrated in Tab. 8 increasing the High-Resolution Path's 's embedding dimension C' signifi- cantly improves the voxel-level metric (Dice), while increasing the Low-Resolution Path's 's embedding dimension C' can markedly enhance the breast-level metrics (Sens. and AUC). To balance parameter count and computational overhead, a moderate configuration (C 192 and C' 3844) adopted.
According to Tab. 9 Dice and FROC-score are relatively sensitive to the depth of the backbone (N), with significant improvements observed the network deepens. In contrast, the classification part reaches a near-optimal trade-off hetween complexity and performance when N = 6. At this setting, the model's parameter count (45.71M) and computational load (1162.65G FL.PP) are comparable to those of the strong baseline nnUNet 30). which has 31.00M parameters and 1185.24G FLOPs.
Comparison of other 1D sequence construction strategies with tandem input As described in the main text, the tandem input strategy first places the left and right 3D regions into the pseudo-3ID volume and then flattens them into a 1D token sequence. This approach is actually equivalent to independently flattening the tokens of the left and right breasts along the prioritized axis and then concatenating them to form the input sequence. To further validate the superiority of this strategy, we compare it with three alternative variants: 1. mast-axis-concat Concatenate along the last (prioritized) axis (i.e., D-, H-, W-axis for HWD, DWH, DHW scanning, respectively) before flattening. 2. W-axis- concat: Always concatenate along the W-axis before flattening. 3. interleaving: Interleave tokens from right and left breasts (i.e., R1, L1, R2, L2, ... ; Rx/Lx denotes the x-th token in the flattened right/left sequence). Results are shown in Tab. [T]
Notably, our tandem input design ensures that all tokens from one side are processed before those from the other within the Mamba layer, and also maintains an approximately constant distance between anatomically symmetric locations, regardless of scanning order. This facilitates effective learning and comparison of bilateral features. In contrast, all alternative variants introduce some degree of mixing between left and right tokens, which leads to information confusion-moo notably in the Interleaving variant, where the alternation of tokens from both sides results in the greatest disruption.
Bilateral input on CNN-based UNet In Sec. 4.3 of the main paper, we have attempted to apply the bilateral input concept to Vision Transformers [1]] and verified the effectiveness of this idea, yet DRT- M3D achieves substantially better results. Here, we further attempt to apply the bilateral input form to CNN-based UNet-like networks, as also shown in Tab. 10 The "UNet- W-xxis-concat" method concats bilateral breasts along the W axis as in the original NCCT images; the "UNet-channel--oncch method uses bilateral breast inputs two channels, with the left breast flipped as a pseudo-right breast; the "UNet-CI.s CLS--hed--mergee method processes unilateral breasts in the UNet, with features for classification concatenated, thereby mixing the bilateral information in the classification part.
CNNs are generally incapable of modeling long-range features, as their local receptive fields require stacking many convolutional layers to capture larger spatial extents, making them less effective than our proposed DRT-M3D. Thus, simply concatenating left and right views along the W-axis ("UNet- "UUNet---xii--on c-axis-concat") is not effective for explicit bilateral modeling. Although stacking these may seem like a reasonable alternative, breast symmetry
views as channels "UNNet-hhameel-onnss is not strictly voxel-to- toeeell--oxel--- coo-vooel-diee to natural anatomical differences, positional variation, and imaging variability-so this approach can mix features from non-corresponding regions and ultimately introduce negative effects, leading to the worst performance. Moreover, simply concatenating -"UNNe-CLSS-head--e ---hhed-meree""" does not allow the model to effectively exploit their spatial correspondence.
features from the two views at the network head ("UNet-CL.S
28

---

Comparison of model efficiency Tab. 12 provides the GPU memory usage, training time, and inference time for all major competing methods. The reported memory usage is measured per training sample, corresponding to one breast region. For bilateral methods, although each training sample contains two breast regions by design, we set the batch size to half that of their unilateral counterparts; this ensures that memory usage per breast region is fairly comparable across all methods. Training time reflects the sum of both pre-training and downstream fine-tuning phases (using two NVIDIA A100 80GB GPUs). Inference time is measured per patient (using single NVIDIA A100 80GB GPU).
In addition to comparing the performance and computational cost of each method using GLOPs in the main paper, we assess the practical deployment efficiency by replacing FLOPs with inference time for each patient. The results are shown in Fig.
Additional visualization results for qualitative comparison In Fig. 10 we present additional qualitative comparisons between the proposed DRT-M3D and competing methods, which serve as supplement to the results shown in Fig. 4f the main paper.
Delta visualization for the Tandem Input mechanism To better illustrate the advantages intro- duced by the Tandem (bilateral) Input mechanism in DRT-M3D, we visualize the Delta values (A, as described in Sec.A.T) of the Mamba-3D blocks in both DRT-M3D and DR-M3D. This allows a direct comparison of their responsiveness to different regions in the chest NCCT images, particularly along the low-resolution (LR) path. A larger step A, indicates faster change in the hidden state h2, implying a greater influence of the current token x, on the overall system dynamics. In this sense, A can be viewed as soft analog to attention weights in Transformers (5
I
To better observe responses across all layers, we use a simplified setup with N 1 for both models. meaning each high- (HR) and low-resolution (LR) path contains a single Mamba-3D block composed of six internal Mamba layers (as detailed in Sec. Be2. We generate the Delta visualization by averaging first over all channels and then across the six layers.
The resulting visualizations are presented in Fig. 11 The Delta responses on the HR path mainly reflect the model's focus on local textures and anatomical details, which aligns with its primary role for the segmentation task. Meanwhile, the LR path is designed to focus on capturing bilateral context with shorter sequence length when Tandem Input mechanism is used (i.e., in DRT-M3D), so the Delta visualization of the LR path shows clear cross-breast clues. This bilateral awareness enhances cancer classification reliability. Notably, the model's ability to focus on corresponding regions across both breasts is learned rather than derived from explicit coordinate symmetry, which is often lacking due to anatomical variation.
Results on contrast-enhanced CT data Here, we conduct additional experiments on contrast- enhanced CT (CECT) as the approximate upper bound of performance using NCCT data for this task. The data sources are as described in Sec. Since the corresponding CECT has been registered with NCCT, the segmentation labels used by both are exactly the same, with only the images being different. The intuitive differences between NCCT and CECT in breast lesions are shown Fig. The experimental results on internal and external datasets are presented in Tab. I1
F Discussion of Broader Impacts
As discussed in the main contributions of this paper, the proposed approach aims to enhance op- portunistic breast cancer analysis techniques while minimizing economic costs and radiation risks encountered by patients. This advancement holds the potential to provide earlier diagnosis and treatment options to a larger population of potential breast cancer patients, thereby significantly impacting their health outcomes.
Regarding potential negative impacts, it is important to note that this proposed method has not yet been deployed in practical healthcare systems. Nonetheless, it is foreseeable that unavoidable false positive cases may impose an additional burden on healthcare systems. Despite possible concerns, the anticipated benefits of carly detection, classification, further examination, and subsequent treatment expected to outweigh these drawbacks, resulting in an overall positive impact.
29

---

Table 7: Ablation study on the patch size in the D (slice of CT seans) dimension. All the experiments were conducted based on the default DRT-M3D model, with modifications applied to Pa- The gray row represents the default settings, (H.r:: HateRate, F.s.: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Variants
Complexity
Interal (Spec. 0.96277)
External (Spec.
0.9083)
Pa- Ph. Pw
Params (M)
FLOPs (G)
Dice
H..
Es.
Sens.
AUC
Dice
H.r.
Es.
Sens.
AUC
anLNeet [30]
31.00
1185.24
0.625y
0.9127
0,8548
0.7844
0,9536
0.5668
0,8889
0.8173
0.6286
0.8889
4.4.4
45.74
582.66
0.6517
0,9214
0,9065
0.8242
0.9737
0.5867
0.8975
0.8652
0,8309
0.9347
2,4.4
45.71
1162.65
0.6590
0.9229
0.9145
0.8578
0.9768
0.5948
0.9117
0.8766
0.8762
0.9371
1,4, 4
45.70
2322.66
0.6651
0.9243
0.9159
0.8654
0,9729
0.6143
0.9211
0.9142
0.9002
0,9439
Table 8: Ablation study on the embedding dimensions of two resolution paths. All the experiments were conducted based the default DRT-M3D model, with modifications applied to C for the Regh-lesooutton Path and C' for the Low-Resolution Path. The gray row represents the default settings. (H.r: Hit-Rate, Ess:: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Variants
Complexity
Internal (Spec. 0.9627)
External (Spec. = 00,0083)
C'
Params (M)
FLOPSs
Dice
H.r.
Es.
Sens.
AUC
Dice
H.r.
Ess.
Sens.
AUC
nnUNee [10]
31.00
1185.24
0,6259
0.9127
0.8548
0.7844
0,9536
0.5668
0.8889
0.8173
0.6286
0.8889
96
192
12.51
339.74
0.6404
0,9214
0.8767
0.8073
0.9674
0.5842
0.9093
0.8644
0.8202
0.9215
192
192
19.37
1075.07
0.6584
0.9083
0.9028
0,8073
0,9683
0.5920
0.9093
0.8653
0,8282
0,9319
192
384
45.71
1162.65
0.6590
0.9229
0.9145
0,8578
0,9768
0.5948
0.9117
0,8766
0,8762
0,9371
192
768
148.15
1498.35
0.6636
0.9258
0.9094
0.8624
0,9757
0.6015
0.9164
0,8795
0,8789
0,9414
384
768
175.76
4258.06
0.6716
0.9170
0.9127
0,8670
0,9771
0.6036
0.9235
0.8955
0,8762
0,9374
Table 9: Ablation study the number of backbone blocks. All the experiments conducted based on the default DRT-M3D model, with modifications applied to N. The gray row represents the default settings. (H.r.:
Hit-Rate, F.s.: FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Variants
Complexity
Intemal (Spec. = 0,9627)
External (Spec. = 0090083
N
Params (M)
FLOPs (C)
Dice
H.r.
Es.
Sens.
AUC
Dice
H.r.
F.s.
Sens.
AUC'
anNNeet (30
31.00
1185.24
0.6259
0.9127
0,8548
0,7844
0,9536
0.5668
0.8589
0.8173
0.6286
0,8889
8.47
196.28
0.6382
0,9214
0,8963
0.8165
0,9677
0.5769
0.9069
0,8674
0.8415
0,9252
23.37
582.83
0.6483
0,9214
0,8996
0,8318
0.9718
0.5925
0.9093
0,8760
0.8602
0.9331
45.71
1162.65
0.6590
0.9229
0,9145
0.8578
0.9768
0.5948
0.9117
0.8766
0.8762
0.9371
68.06
1742.48
0.6615
0.9228
0,9126
0.8486
0.9744
0.5960
0.9022
0,8809
0.8621
0.9357
12
90.40
2322.30
0.6659
0.9243
0.9120
0.8440
0.9738
0.5974
0.9046
0.8866
0.8629
0,9373
Table 10: Evaluation of several DRT-M3D variants for Tandem Input effectiveness, together with results of attempts using the bilateral input form on the CNN-based UNet. Representative unilateral (nnUNet, DR-M3D) models are also provided for comparison. (H.r.: Hit-Rate, F.s.; FROC-Score, Spec.: Specificity, Sens.: Sensitivity)
Internal (Spec. = 0,9627)
External (Spec. 0.9083)
Method
Dice
H.r.
Fss.
Sens.
AUC
Dice
H.r.
Fss.
Sens.
AUC
ont[Net
0.6259
0.9127
0.8548
0.7844
0.9536
0.5668
0.8889
0.8173
0.6286
0.8889
DR-M3D (ours)
0.6564
0.9228
0.9027
0.8073
0.9690
0.5909
0.8974
0.8632
0.7207
0.9082
0.6225
0.8940
0.8597
0.7431
0.9469
0.5696
0.8974
0.8120
0.6190
0.8936
UNet-channel-come
0.5888
0.8958
0,8400
0.7798
0,9498
0.5220
0.8461
0.7760
0,5143
0.8839
UNet CLS head merge
0.6208
0.9114
0.8575
0,8211
0,9559
0.5643
0.9059
0.8057
0.7333
0,9053
DRT last cxis-cuncal
0.6536
0.9127
0,9083
0,8440
0,9693
0.5808
0,9060
0.8729
0.8190
0,9206
DRT-M3D-X W -xixxs concal
0.6551
0.9039
0,9062
0,8532
0,9732
0.5923
0.9060
0.8708
0.8476
0,9258
DRT-MEDD-iterraaving
0.6414
0.9083
0.9018
0.8211
0.9650
0.5749
0.8974
0.8644
0,7810
0.9162
DRI-M3D (ours)
0.6590
0.9229
0.9145
0.8578
0.9768
0.5948
0.9117
0.8766
0.8762
0.9371
Table 11: Results on the corresponding contrast-enhanced CT (CECT) scans as the approximate upper bound of performance using NCCT scans for this task.. (H.r.: Hit-Rate, Es.: FROC-Score, Spec.: Specificity, Scns.: Sensitivity)
Internal (Spec. 0.9627)
Extemal (Spec. =0,9083)
Method
Dice
Sens.
AUC
Dice
Sens.
AUC
unU[Net 30
0.7078
0.9563
0.9323
0.8257
0.9724
0.6860
0.9487
0.9068
0.9238
0.9288
DR-M3D tours)
0.7252
0.9476
0.9436
0.9129
0.9736
0.6878
0.9345
0.9146
0.9302
0.9376
DRT-M3D (ours)
0.7263
0.9534
0.9479
0,9480
0.9795
0.7018
0.9544
0.9337
0,9365
0.9497
30

---

Table 12: Training memory usage, training time, and inference time for all major competing methods. Memory usage is measured per breast region. Training time sums pre-training and downstream fine-tuning (2xA100
GPUs), and inference time is per patient (1xA100 GPU).
Method
Training Memory (GB) Training Time (h)
Inference Time (S)
nnUNet 30
3,826
31.0
0.126
VNet [48]
3,489
28.9
0.112
swinUNETR 24
11.975
36.8
0.139
nnFormmr
699
2.063
10.9
0.029
UX-Net 34
8,754
67.0
0,251
MedNeXt
12.095
43.1
0.194
U-Mamba-Bat
46
6.105
44.4
0.196
U-Mamba Enc
46
11.810
77.9
0.291
EM-Net
6.218
34.9
0.116
SegMamba
64
9.580
66.2
0.318
VIT-S/8 14
4.611
22.1
0.034
T-ViT-S/8
4.629
26.9
0.047
DR-M3D/8 (ours)
2.565
0.049
DRT-M3D/8 (ours)
2,581
15.7
0.059
DR-M3D (ours)
9.187
30.4
0.143
DRT-M3D (ours)
9.202
34.2
0.171
31

---

L: malignant
R: normal
samples from Internal Institution
malignant malignant
L: benign
R: normal
samples from Institution
normal R: malignant
L: benign normal
samples from Internal Institation 3
La normal R: malignant
L: benign nomnal
samples
from
Extemnal Instination
L: malignant R: normal
(a) NCCT 2D sliees
(b) 2D with GT
(c) CECT 2D sliees
(d) NCCT 3D
(6) 3D with GT
Figure 8: Visualization of representative data samples from the four datasets used in this study. (a), (b) and (c) respectively show typical NCCT 2D slices, their corresponding segmentation ground truth, and the corresponding CECT slices that have already been registered NCCT. (d) and (e) present 3D renderings the NCCT images and their segmentation ground truth. Green and blue indicate malignant and benign lesions, respectively. The breast-leve classification labels are shown on the right side of each row, Note that the 2D slices viewed in the foot-to-head direction, meaning the left side of each image corresponds the right side of the human body.
32

---

Dice vs. Inference time (internal)
Dice vs. Inference time (external)
Pareetss (M)
Pacestes (M)
76.1
60
11.4
Bramas
381
114
60
Gibas
674
674
0/2
3050s
6.00
7100-314
paigen
pibtis
0,23
10
10
10
10"
Inference time
Inference time
AUC Inference time (internal)
AEC vL. Inference time (esturnal)
004
REANSS
DRTARO14
e74
600
Figure 9: Comparison of Dice and AUC Inference time for internal and external datasets. Each inference time is measured based on one bilateral (or two unilateral) input. VIT: vanilla Vision Transformer, M3D; vanilla Mamba-3D, T--; tandem (bilateral) input form, ~/p: patch size of (2, p. p).
(0.957)
(3.229)
(W-I3A)
(0-2055)
(33388)
(1.330))
(M-R3))
(B:304)
(3.2397)
(WUDSS)
(2.E772)
(UL2215)
(B.0135)
Figure 10: More visualizations supplement Fig. 4 iin the main paper. Red, green, and blue masks represent breast regions, malignant, and henign lesions, respectively. White, yellow, and red arrows mark pro- nounced segmentation errors in the slice, missed lesions, and segmentation of non-existent lesions, respectively. Predicted malignancy scores shown for each case (higher for malignant, lower for benign). "Failed" denotes where none of the true lesions were localized (i.e.. non-hit under the Hit-Rate metric).
33

---

Right
Left
Right
Left
Right
1.ef
Right
Left
RAW
GT
(malignant
(normal
(malignant
(nomal
Imalignane
(nomaal
(malignant
DRT-M3D HR Path
DRT-M3D Path
DRT-M3D
(0.99) (0.9984)
(0. (4133
(0.9262)
(0.0038)
(0.6304)
(0.2805)
(0.1331)
(0.8779)
DR-M3D Path
DR-M3D LR Path
DR-M3D
(0,5004)
Figure 11: Delta visualization of Mamba-3D blocks in DRT-M3D and DR-M3D. Each column shows test sample pair from three internal datasets and one external datasct; left and right images correspond to the right and left brcast, respectively. Rows display (1) raw CT. (2) ground truth (red: breast, green: lesion, below: classification label). (3-4) Delta heatmaps of DRT-M3D (HR and LR paths). (5) DRT-M3D predictions, (6-7) Delta heatmaps DR-M3D (HR and LR paths), and (8) DR-M3D predictions. The focus is LR heatmaps: DRT-M3D, with Tandem Input mechanism, highlights lesion areas and contralateral counterparts (red boxes), leading to superior classification results. In contrast, DR- MRD fundamentally lacks this ability to leverage contralateral information (light cyan boxes).
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Reviews:
[{"review_id": "Rm36zA0OlB", "reviewer": "Reviewer_oeU9", "summary": "This paper presents a dual-resolution 3D Mamba framework for breast lesion detection and classification from early breast CT images. The authors propose a multi-task learning framework that combines pixel-level lesion segmentation with image-level diagnosis tasks, effectively integrating both local details and global features. Experiments conducted on internal and external datasets demonstrate the state-of-the-art performance of the proposed method.", "questions": "1. The authors should compare their method with more recent state-of-the-art (SOTA) approaches for tumor classification based on segmentation methods, including those mentioned in the weaknesses section.\n\nFor example, A Data-Efficient Pan-Tumor Foundation Model for Oncology CT Interpretation, https://arxiv.org/abs/2502.06171\nFreeTumor: Large-Scale Generative Tumor Synthesis in Computed Tomography Images for Improving Tumor Recognition https://arxiv.org/abs/2502.18519\n\n2. The novelty of the proposed method should be further emphasized. What are the unique aspects and motivations behind this approach compared to other Mamba-based methods and related techniques?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. This paper presents a novel Mamba-based framework to address the important problem of early breast lesion detection. The design of the tandem input, which incorporates both left and right breast images, is particularly innovative and interesting.\n2. The authors conduct comprehensive experiments and present solid results across three datasets.\n3. The paper is well-organized, and the quality of the English writing is commendable.\n\nWeaknesses: \n\n1. Missing comparsion with SOTAs: The authors did not compare with recent SOTA such as [1]. \n\n[1] Sun J, Xi X, Wang M, et al. A deep learning model based on chest CT to predict benign and malignant breast masses and axillary lymph node metastasis[J]. Biomolecules and Biomedicine, 2025.\n\n2. Limited Novelty & Relations between task and architecture design: the author designed a framework specific for breast lesion detection and classification. The novelty of their framework seem only two fold: (1) using Mamba on breast lesion detection and classification (2) design a multi-task learning (classification and detection) strategy to obtain local & global features. However, regarding the first point, the author fails to thoroughly discuss the relation between mamba and this specific task, why should we use Mamba instead of other backbones? Is there any special characteristic of non-contrastive CT that mamba could excel at and outperform other backbones?\nRegarding the second point, I think there are plenty of previous works that has design such multi-task learning strategy [2,3], just on different modalities or different lesions, they also design their multi-task learning framework for the same purpose.\n\n[2] He Q, Yang Q, Su H, et al. Multi-task learning for segmentation and classification of breast tumors from ultrasound images[J]. Computers in Biology and Medicine, 2024, 173: 108319.\n[3] Xu, Mengjuan et al. “A Regional-Attentive Multi-Task Learning Framework for Breast Ultrasound Image Segmentation and Classification.” IEEE Access 11 (2023): 5377-5392.\n\n3. “Tandem input” is confusing: the definition of tandem input is a little confusing, is it just combine the feature sequence of left and right beast together as one unified sequence? I think the author should provide some references to give a better explanation of “tandem input”.\n\n4. Missing comparison with contrast CT: I believe including comparison with using contrast CT as upper-bound could better reveal the clinical value of the proposed method.\n\n5. Limited performance improvement: from Table.1, we can see that there is a very limited performance improvement comparing the proposed method and other very common baseline models, the author also didn’t compare methods that are specially designed for breast lesion classification.\n\n6. Unfair comparison: the author conduct a large-scale self-supervised pre-training for their proposed method before finetuning, however, for their counterparts which are majorly from computer vision field, they did not employ the pretraining, which resulted in unfair comparison.\n\n7. Unclear comparison in the visualization: In figure. 4, the authors present qualitative comparison results between their methods and other counterparts, however, the difference is too small and unclear. I think a zooming in and a highlight on the error part will do better.\n\n8. Model Efficacy: since the topic is early detection, I believe detection speed and efficacy are both important, the author should add training time/inference time, and memory consumption.", "was_revised": true, "final_justification": "I really appreciate the effort and explanation in the rebuttal, which helps a lot on addressing my concerns regarding the novelty, especially the motivation of the Mamba architecture design and MTL training strategy. After reviewing the authors’ rebuttal and other reviewers’ comments, my concerns about the novelty and necessity of the work have been addressed. I will raise my score to weak accept. I recommend the authors include the following in the final version:\n\n1) I recommend adding a discussion section to explore how the image modality relates to Mamba, including comparisons with different model backbones. \n2) Since this is the first work to use non-contrast CT for breast lesion detection, I think it is necessary to include a figure comparing contrast and non-contrast CT. This will help highlight the added challenges of using non-contrast CT instead of contrast CT.", "rebuttal": "**W1 & Q1**: comparison with more recent SOTAs\n\n**A**:  We appreciate the reviewer’s suggestion on conducting more comparisons with recent SOTA. We have added the results of 5 recent methods mentioned by the reviewer, using the same metrics and datasets as Table 3 in the main paper.\n\n|Method|Internal|Dice|H.r.|F.s.|Sens.|AUC|External|Dice|H.r.|F.s.|Sens.|AUC|\n|-|:-:|-|-|-|-|-|:-:|-|-|-|-|-|\n|Sun et al. 2025|\\||0.6153|0.9127|0.8548|0.7706|0.9444|\\||0.5624|0.8974|0.8246|0.6286|0.8827|\n|He et al. 2024|\\||0.5845|0.9039|0.7620|0.6789|0.9280|\\||0.5176|0.8462|0.6271|0.6381|0.8540|\n|Xu et al. 2023|\\||0.6069|0.9039|0.8526|0.7798|0.9566|\\||0.5672|0.8974|0.8160|0.6952|0.9023|\n|Lei et al. 2025|\\||0.6088|0.8996|0.8221|0.7890|0.9411|\\||0.5658|0.8803|0.7967|0.7048|0.8931|\n|Wu et al. 2025|\\||0.6140|0.9127|0.8384|0.7339|0.9512|\\||0.5636|0.8547|0.8358|0.6952|0.9014|\n|nnUNet|\\||0.6259|0.9127|0.8548|0.7844|0.9536|\\||0.5668|0.8889|0.8173|0.6286|0.8889|\n|**DR-M3D (ours)**|\\||0.6564|0.9228|0.9027|0.8073|0.9690|\\||0.5909|0.8974|0.8632|0.7207|0.9082|\n|**DRT-M3D (ours)**|\\||0.6590|0.9229|0.9145|0.8578|0.9768|\\||0.5948|0.9117|0.8766|0.8762|0.9371|\n\nIt should be noted that while some methods above are not designed for 3D data or CT modality, we have made every effort to adapt them to our 3D non-contrast CT setting (e.g., using Conv3D instead of the original Conv2D modules) for a fair comparison. The results show that our method has clear advantage over other methods. The strong performance of our method can be attributed to its Dual-Resolution and Tandem Input design, together with Mamba-3D's ability on local and global modeling, which is particularly beneficial for breast lesion detection and classification on NCCT. These merits are further explained in the answer to ***W2 & Q2***.\n\n**W2 & Q2**: concerns regarding task-architecture rationale and novelty\n\n**A**:  Thank you for the constructive feedback. We address these concerns from three aspects:\n\n1. Why Mamba (Mamba-3D) is well suited to this task:\n\n   * NCCT images pose unique challenges—lesions often appear subtle, and bilateral asymmetries serve as key diagnostic cues. This calls for a model that can capture long-range context without sacrificing local detail.\n   * Mamba fits this need well. Unlike CNNs, which are less effective at capturing global context, and ViTs, which trade local detail for manageable sequence length with large patches, Mamba supports small patch decomposition and long-range modeling. This enables retention of fine spatial resolution (important for segmentation) while also capturing global or even cross-breast patterns (critical for classification).\n\n   * As for Mamba-3D, the cyclically prioritized scanning strategy further enhances local spatial modeling for 3D data. Unlike ViT, which often struggles to capture neighborhood relationships as sequence length increases, Mamba-3D enables more efficient learning and faster convergence on volumetric medical images.\n2. Novelty of our multi-task design compared to existing methods:\n   * In previous studies, the classification branch was derived from the segmentation branch. This resulted in excessive feature sharing between these two tasks. Even though the tasks were related, it could still cause interference between features, leading to suboptimal performance.\n   * Our Dual-Resolution design explicitly balances dense (segmentation) and global (classification) tasks. By decoupling feature spaces while enabling interaction through Mutual Fusion, we reduce task interference and promote complementary learning, overcoming limitations seen in previous multi-task frameworks.\n   * The comparison results of the mentioned multi-task papers are provided in the table in ***W1***.\n3. Additional novelty:\n   * Our “Tandem Input” strategy within the Mamba-3D framework enables effective cross-breast contextual reasoning. This is important in clinical diagnosis but has been rarely explored in 3D settings. This strategy has demonstrated improved classification AUC for NCCT-based breast cancer analysis.\n   * To our knowledge, this is the first framework to jointly perform breast cancer detection and classification on non-contrast chest CT scans, demonstrating the clinical potential of NCCT for breast cancer opportunistic screening.\n\nIn summary, our work introduces targeted architectural and algorithmic innovations tailored to the unique challenges of breast cancer detection on non-contrast 3D CT. By combining effective sequence modeling for small 3D patches, decoupled multi-task design, and bilateral contextual reasoning, we achieve superior performance in both segmentation and classification.\n\n**W3**: a better explanation of “Tandem Input”\n\n**A**:  Thank you for pointing out the potential confusion around “Tandem Input”. “Tandem” is a term used to describe two or more things arranged one after another or working together in sequence. *For example, tandem bicycle refers to a bicycle with two seats and two sets of pedals, arranged one behind the other.*\n\nIn the context of our work, “Tandem Input” refers to the concatenation of left and right breast token sequences into a unified input while *maintaining anatomical alignment*. This not only ensures that Mamba-3D scans all voxels from one breast before moving to the other, but also guarantees a roughly fixed distance between anatomically symmetric locations in the sequence (just like the corresponding words in an antithetical couplet or rhyming lines), allowing the model to better capture cross-breast relationships.\n\nPlease refer to ***Reviewer y5XU’s W2*** for additional results of other mechanisms for constructing bilateral input sequences.\n\n**W4**: comparison with contrast CT\n\n**A**:  Thank you for highlighting the importance of comparison with contrast CT. To address this, we have supplemented our study with results based on contrast CT images which are used for initial tumor boundry delineation as mentioned in the Appendix B.\n\nThe table below summarizes the performance of our method on corresponding contrast CT data, using the same metrics as Table 3 in the main paper.\n\n|Method|Internal|Dice|H.r.|F.s.|Sens.|AUC|External|Dice|H.r.|F.s.|Sens.|AUC|\n|-|:-:|-|-|-|-|-|:-:|-|-|-|-|-|\n|nnUNet|\\||0.7078|0.9563|0.9323|0.8257|0.9724|\\||0.6860|0.9487|0.9068|0.9238|0.9288|\n|**DR-M3D (ours)**|\\||0.7252|0.9476|0.9436|0.9129|0.9736|\\||0.6878|0.9345|0.9146|0.9302|0.9376|\n|**DRT-M3D (ours)**|\\||0.7263|0.9534|0.9479|0.9480|0.9795|\\||0.7018|0.9544|0.9337|0.9365|0.9497|\n\nAs expected, contrast CT achieves higher performance, serving as a practical upper-bound for this task. Notably, our method on NCCT reaches performance (the last 3 lines of the Table in W1) that is close to that of contrast CT, demonstrating its effectiveness and potential clinical value—especially for large-scale screening workflows where contrast CT may not be feasible.\n\n**W5**: limited performance improvement and comparison with specially designed breast lesion classification methods\n\n**A**:  \n\n1. On performance improvements:\n\nWe respectfully disagree that the improvement is limited. As shown in Table 1 and Table 2 of the main paper, our method achieves notable gains over competing methods on key metrics—even though all baselines were thoroughly optimized under identical protocols (same training set, data augmentation, preprocessing, and postprocessing). The table below provides a summary for Dice and AUC. It is notable that even modest improvements are valuable in clinically challenging tasks where metrics such as AUC are already near the ceiling.\n\n|Datasets\\||Competing Methods' Dice\\||Ours Dice\\||Competing Methods' AUC\\||Ours AUC|\n|-|-|-|-|-|\n|Inst. 1|0.5601 ~ 0.6231|0.6608|0.9361 ~ 0.9622|0.9909|\n|Inst. 2|0.5671 ~ 0.6548|0.6750|0.9382 ~ 0.9596|0.9743|\n|Inst. 3|0.4901 ~ 0.5980|0.6056|0.8792 ~ 0.9391|0.9471|\n|Inst. 4|0.5059 ~ 0.5776|0.5948|0.8777 ~ 0.9156|0.9371|\t\n\n2. On comparison with specially designed breast lesion classification methods:\n\nWe have included results for all representative methods mentioned by the reviewer, as detailed in our response to ***W1***. Notably, most “specially designed” breast lesion classification methods are variants of nnUNet or UNet, and are often developed on smaller datasets or with different imaging modalities from ours. In our study, we implemented and thoroughly tuned these methods for a fair comparison. As the results demonstrate, our approach outperforms all published competing methods, including those specifically tailored for breast lesion classification.\n\n**W6**: concerns regarding unfair comparison\n\n**A**:  Thank you for raising this important concern. We would like to clarify that all competing models were effectively pre-trained under comparable conditions: ViT and Mamba-based models underwent MAE pre-training, while CNN-based methods were pre-trained on dedicated breast and lesion segmentation tasks.\n\nAdditionally, our pre-training does not qualify as “large-scale”, since we did not use any extra data.\n\nA similar concern was raised by ***Reviewer y5XU’s W4***; please see our detailed response there for further clarification.\n\n**W7**: unclear comparison in the visualization\n\n**A**:  We appreciate the reviewer’s suggestion regarding visualization clarity. We acknowledge that the differences may be difficult to appreciate in Figure 4. For the camera-ready version, we will address this by providing zoomed-in views and clear highlights (e.g., arrows) to draw attention to regions with notable differences.\n\n**W8**: concerns regarding model efficacy\n\n**A**:  Detailed comparisons of training time, inference time, and memory consumption are provided in our response to ***Reviewer y5XU’s Q1***, and are omitted here due to space constraints.\n\nIn practical scenarios, all evaluated methods—including ours—can deliver predictions for each scan within tens to hundreds of milliseconds, fully meeting real-world throughput requirements. Our model already demonstrates very high computational efficiency."}, {"review_id": "PTMiQ84kgo", "reviewer": "Reviewer_THvZ", "summary": "The paper proposes Dual-Res Tandem Mamba-3D (DRT-M3D), a multitask framework for bilateral breast lesion detection and malignancy classification using non-contrast chest CT NCCT. The approach leverages a dual-resolution architecture to balance fine-grained segmentation details and global contextual features, combined with a tandem input mechanism that models bilateral breast regions jointly via Mamba-3D blocks. This design enables cross-breast feature interaction to exploit subtle asymmetries. Experiments on multi-institutional NCCT datasets demonstrate state-of-the-art performance in both tasks, outperforming UNet, SwinUNETR, and Mamba-based baselines. Key contributions include the unified multi-task framework, dual-resolution design with mutual fusion, tandem bilateral modeling, and validation on diverse clinical data.", "questions": "1.\tHow will the authors expand data collection to include cross-regional populations, and have preliminary results from diverse cohorts been tested?\n2.\tIt is mentioned in the paper that the method relies on a pre-trained segmentation model (Pre-Stage) to locate the breast region. What is the impact on Main-Stage performance if this stage fails (for example, if the breast boundary is blurred in obese patients)?\n3.\tAre there specific metrics to validate detection of tiny abnormalities, which are critical for early diagnosis?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1、The dual-resolution design and tandem input mechanism for bilateral modeling are innovative, addressing the challenge of integrating fine-grained detection with global classification while leveraging breast asymmetry.\n2、Experiments on three internal and one external dataset, including ablation studies on key components (dual-resolution, mutual fusion, tandem input), validate the approach’s effectiveness. The focus on opportunistic analysis of NCCT avoids additional radiation/cost, aligning with practical clinical needs.\n\nWeaknesses:\n1.\tIn the Pre-Stage of the paper (Sec. 3.1), the pre-trained segmentation model is used to crop the breast region. If the small lesions are lost in the pruning process, it may lead to the failure of subsequent detection. Non-contrast CT itself has low resolution, and the contrast of small lesions (such as microcalcifications) is insufficient, which may further increase the risk of missed detection.\n2.\tThe article mentions the use of Delta visualization to compare DRT-M3D with DR-M3D models and highlights the advantages of the two-input mechanism. However, from the information provided, it seems that these visualizations mainly focus on the single-layer N=1 case, but it may also ignore the real behavior of the model under the multi-layer structure. Although FIG. 11 demonstrates the significant Delta response on the LR path, a comparative display for the HR path or other key features is inadequate. This can make it difficult for the reader to fully understand all the differences between the two models and their practical significance.\n3.\tThe paper demonstrates that applying the tandem input concept to ViTs and CNNs (Appendix E, Table 10) is less effective. While this is a good result for the authors, the analysis could go deeper. The paper attributes ViT's failure to the excessive number of tokens from small patches. Is this purely a memory/computation issue, or a fundamental limitation in the attention mechanism's ability to handle such granularity? A more nuanced discussion on why Mamba's selective state-space mechanism is uniquely suited for this \"tandem\" sequence concatenation, beyond linear complexity, would elevate the paper's technical contribution.", "was_revised": true, "final_justification": "Thank you for your detailed response, which has resolved most of my concerns. I strongly recommend that the authors incorporate the discussion on different architectures from W3, as well as the Model Efficacy points raised by other reviewers, into the final version of the paper. After considering the comments from the other reviewers, I have decided to maintain my score.", "rebuttal": "**W1 part1 & Q2**: concerns regarding the Pre-Stage (breast region cropping) of the pipeline\n\n**A**: Thank you for this important question. The Pre-Stage segmentation is designed solely to localize the breast region, which is a relatively simple task. In our experiments, the Pre-Stage achieved a high **Dice score of 0.9598**, demonstrating its accuracy and reliablity.\n\nTo further minimize the risk of missing boundary lesions or subtle structures (e.g., in obese patients or cases with blurred borders), we adopted a conservative cropping strategy: the predicted bounding box is expanded by 2 voxels along the D-axis and 16 voxels along the H- and W-axes. This ensures that small lesions near the periphery are retained within the cropped region.\n\nNotably, the goal of the Pre-Stage is not to perform fine-grained segmentation but to exclude irrelevant anatomy (e.g., abdominal areas) and isolate the bilateral breast regions for downstream modeling. Across all training and test cases, we have not observed any missed-lesion failure due to Pre-Stage cropping. In future deployment, rare failure cases can be flagged for manual review or fallback processing.\n\n**W1 part2**: concerns about using NCCT for breast lesion localization\n\n**A**: We fully acknowledge that using NCCT for breast lesion detection is not a routine diagnostic process in clinical practice. Our purpose is to achieve breast lesion detection and classification on existing chest CT scans, such as those conducted for lung or heart screening. This approach introduces no additional radiation exposure or economic burden to patients, and can be referred to as opportunistic screening.\n\nWith the clinical value ahead, we acknowleged that it is relatively difficult for doctors to do breast lesion detection and classification on NCCT due to the lackness of contrast between the lesion and normal tissues. By collecting a large number of data, we are commited to achieve a clinically practical performance on this task leveraging the power of well-designed models. Our experimental results demonstrate that the proposed approach achieves strong and promising performance on NCCT images.\n\nFor medical imaging, we would also like to clarify two important points: First, microcalcifications are generally evident in x-ray based imaging modalities, including CT and digital radiography (DR)—even on non-contrast CT—but are typically not obvious in breast ultrasound images. Second, NCCT provides the same spatial resolution as contrast-enhanced CT; its main limitation lies in the limited contrast.\n\n**W2 part1**: concerns about using N=1 in Delta visualization\n\n**A**: Thank you for your insightful comment. We focused our Delta visualizations on the N=1 case primarily for clarity and interpretability: at a depth of N=1, the cross-breast (bilateral) interaction patterns introduced by our Tandem Input mechanism can be most directly and transparently visualized and understood.\n\nFor higher N (e.g., N=6 as used in our main experiments), we have observed that cross-breast interactions not only persist but often become even more pronounced and widespread across different layers. However, in deeper models, these effects are distributed across multiple blocks, makes concise visualization in the paper challenging.\n\nAs additional support, our quantitative results demonstrate that the benefits observed with the Tandem Input mechanism are effective across models with different depths: as shown in Table 9, even with N=1, our model outperforms the strong baseline, while increasing depth to N=6 yields further improvements, confirming the effectiveness of our design beyond the single-layer setting.\n\nWe appreciate your suggestion and, if desired, are happy to provide additional Delta visualizations for multi-layer cases in the supplementary material to further illustrate these cross-breast effects in deeper models.\n\n**W2 part2**: clarification regarding Delta visualization on the HR path\n\n**A**: The Delta responses on the HR path mainly reflect the model’s focus on local textures and anatomical details, which aligns with its primary role for the segmentation task. Meanwhile, the LR path is designed to focus on capturing bilateral context with shorter sequence length when Tandem Input mechanism is used (i.e., in DRT-M3D), so the Delta visualization of the LR path shows clear cross-breast clues. Overall, the Delta visualization of the two paths in Figure 11 appropriately reflects the distinct roles of the HR and LR paths for their respective tasks.\n\nCompared to DR-M3D, which lacks the Tandem Input mechanism, DRT-M3D exhibits cross-breast responses in the LR path’s Delta visualization, further highlighting the effectiveness of our proposed design for modeling bilateral interactions, whereas in both models the HR path primarily focuses on local segmentation.\n\n**W3**: deeper analysis of why applying the Tandem Input concept to ViTs and CNNs is less effective than Mamba\n\n**A**: Thank you for this excellent question. We agree that the Tandem Input design’s impact varies fundamentally across architectures, and a deeper discussion is warranted.\n\n*Why does ViT struggle?*\n\nThe limited effectiveness of Tandem Input on ViTs is not simply due to memory or computation. As token count increases, self-attention matrices become extremely large, leading to peaked and less expressive attention distributions. Although Transformers are theoretically capable of modeling arbitrary long-range dependencies, in practice—especially for very long sequences and without sufficient scaling of model and data size—the effective capture of such dependencies is often sparse and unreliable (Tay et al., 2021). Furthermore, ViT lacks inherent local inductive bias, making it harder to exploit local spatial structure compared to architectures with stronger locality, such as Mamba or CNNs.\n\n*Why does CNN struggle?*\n\nCNNs cannot directly model long-range bilateral dependencies, as their local receptive fields require progressively stacking many convolutional layers to cover larger spatial extents. Therefore, simply concatenating left and right views along the W-axis is not effective for explicit bilateral modeling. Although stacking these views as channels may seem like a reasonable alternative, breast symmetry is not strictly voxel-to-voxel; due to natural anatomical differences, positional variations, and imaging variability, this approach may mix features from non-corresponding areas and ultimately introduce negative effects.\n\n*Why is Mamba-3D effective?*\n\nMamba-3D, in contrast, uniquely combines strong local bias and efficient selective long-range modeling, along with the support for extremely long sequences. With our Tandem Input mechanism, anatomically symmetrical parts of the left and right breasts always have a roughly fixed distance in the sequence (analogous to corresponding words in an antithetical couplet or rhyming lines), allowing the model to better capture cross-breast relationships.\n\nWe appreciate the opportunity to clarify these architectural distinctions and will elaborate on these points further in the camera-ready version.\n\n**Q1**: preliminary results from diverse cohorts and expansion to cross-regional populations\n\n**A**: Thank you for raising this important point about the generalizability of our approach. The datasets used in our study were collected through collaborations with professional medical institutions, and we are actively expanding our partnerships to include hospitals from additional regions. Data collection and annotation from new cohorts are ongoing.\n\nTo report preliminary results from more diverse cohorts, we have conducted a reader study using newly collected 100 cases from a separate region for the classification task. The table below summarizes the performance of our method (DRT-M3D) compared with two radiologists and a baseline method (nnUNet).\n\n||Sens.|Spec.|AUC|\n|-|-|-|-|\n|Radiologist-1|0.75|0.76|-|\n|nnUNet|0.91|0.76|0.9334|\n|**DRT-M3D (ours)**|0.98|0.76|0.9864|\n|Radiologist-2|0.56|0.95|-|\n|nnUNet|0.76|0.95|0.9334|\n|**DRT-M3D (ours)**|0.93|0.95|0.9864|\n\nWhile it is important to note that radiologists typically do not assess for breast cancer on NCCT in routine clinical practice; nevertheless, our method achieves markedly higher performance. This demonstrates the robustness of our model and its potential value for opportunistic breast cancer screening.\n\n**Q3**: specific metrics to validate detection of tiny abnormalities, which are critical for early diagnosis\n\n**A**: Thank you for highlighting the importance of detecting tiny abnormalities for early diagnosis. To specifically address this concern, we evaluated our model on a subset (22%) of the test set consisting of cases with lesions less than 20 mm in diameter (corresponding to T1-stage breast cancer).\n\nThe table below summarizes the performance of our methods and the baseline (nnUNet) on this subset.\n\n|Method (Spec.=0.9667)|Dice|H.r.|F.s.|Sens.|AUC |\n|-|-|-|-|-|-|\n|nnUNet|0.5393|0.9000|0.7995|0.5889|0.9173|\n|**DR-M3D (ours)**|0.5923|0.9222|0.8111|0.6556|0.9250|\n|**DRT-M3D (ours)**|0.6059|0.9333|0.8668|0.8333|0.9639|\n\nAlthough some metrics decrease slightly compared with the results on the full test set (which includes larger lesions; see Table 1 and Table 2 in the main paper), our model still achieves high Hit-rate, Sensitivity, and AUC on early-stage lesions. These results confirm the model’s practical value for the detection of tiny abnormalities that are critical for early breast cancer diagnosis.\n\n**References**\n\n[Tay et al., 2021] Tay, Y., Dehghani, M., Abnar, S., et al. Long Range Arena: A Benchmark for Efficient Transformers. International Conference on Learning Representations (ICLR), 2021."}, {"review_id": "LvAZdPjQsd", "reviewer": "Reviewer_y5XU", "summary": "This paper proposed Dual-Res Tandem Mamba-3D (DRT-M3D), a 3D mamba model for breast cancer detection from non-contrast CT data. It take the efficiency advantage of the Mamba model to process very long 3D voxel sequence and make use of the multi-view relationship of the breast to improve the detection. The proposed method is evaluated on 4 datasets and outperforms existing baselines with a notable gap according to the detailed evaluation.", "questions": "The reviewer wonders how is the training speed of the proposed method comparing with other baselines, will it have a much longer training time comparing with other methods?", "limitations": "Limitation was discussed in the paper.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n\n1. The proposed method was designed for a task where high resolution 3D voxel segmentation is needed, which properly validated the reason of using Mamba model. Different regular 2D cases, the proposed method is often operating on sequence over 10k tokens (according to the paper). The experimental results also confirmed the computational efficiency of the proposed model under the given settings.\n2. The proposed method seems to be the very first attempt to make use the multi-view relationship of the breast for the sick of breast cancer detection in NCCT. \n3. The experimental evaluation is very convincing and the paper is well-written and overall easy to follow. The evaluation has demonstrates the advantage of the proposed method under various settings, and the proposed method seems to be the best in general.\n\nWeakness:\n\n1. The proposed method has a much better computational efficiency (FLOPs) comparing with regular transformer-based method. However, its computational speed seems to be much slower than the baselines according to the Figure 9 in the supplement even during the inference.\n2. In section 3.3, the input from 2 views are placed as a pseudo-3D volume and then flattened before feeding to the mamba module. However, the reviewer didn’t see the reason of doing this. When the multi-view input was arranged as it is in Figure 3, the output sequence should be the same as simply concatenate them separately, regardless to the traverse order in 3D space. Since all the padded tokens are skipped, and there is no positional embedding, it seems to be an unnecessary operation to the reviewer. Some more clarification will help better understand this.\n3. While applying multi-view information in 3D NCCT breast cancer detection is a new setting, the idea of feeding multi-view inputs to an attention-style model to obtain a cross-view relationship is not that novel. For instance, [A] also feed the multi-view breast mammography to the transformer model with cross-attention to learn cross-view information. Still, this is a minor weakness, and the reviewer is still very glad to see this work.\n4. Another small issue is about the fairness of the evaluation of the main results. The proposed method was first pre-trained with mask reconstruction task for a long time and then fine-tuned for detection task. However, it seems that the baselines (except ViT baseline) are not pre-trained like this. Figure 5 suggests that pre-training is very important for the final results. So, it is unclear if the performance improvement is mainly from the pre-training, or better design.\n\n[Reference]\n\n- [A] Sun, Zizhao, et al. \"Transformer based multi-view network for mammographic image classification.\" *International conference on medical image computing and computer-assisted intervention*. Cham: Springer Nature Switzerland, 2022.", "was_revised": true, "final_justification": "After reading the rebuttal and comments from other review, my concerns have been addressed an I would suggest acceptance for this paper.", "rebuttal": "**W1**: concerns regarding the slower computing speed compared to better FLOPs\n\n**A**: Thank you for raising this point. We note that transformer-based models benefit from highly optimized implementations in current deep learning libraries (e.g., Pytorch 2.0+), which can result in surprisingly fast runtimes despite high FLOPs.\n\nWhile our method does not yet benefit from the same kernel-level optimization available for mainstream Transformer models, it achieves practical inference speeds (~0.1s per CT scan, as shown in Figure 9), making it suitable for near real-time application in clinical practice.\n\nWe have also provided a detailed table of model efficiency in our response to ***Q1***.\n\n**W2**: some more clarification of creating the pseudo-3D volume and then flattening it\n\n**A**: We are happy to provide detailed clarification for the operation illustrated in Figure 3(b). The actual construction of the 1D sequence from the pseudo-3D volume in our design is indeed consistent with the reviewer's understanding, i.e., it is equivalent to independently flattening the left and right breasts' tokens along the prioritized axis and then concatenating them to form the input sequence.\n\nWe chose to represent this process as a pseudo-3D volume (as shown in Figure 3(b)) purely for intuitive visualization and explanation, so as to avoid any potential misunderstanding that the left and right sides are first concatenated along a specific axis before flattening, which will lead to interleaving of tokens from the left and right sides under prioritized scanning along specific axes. To clarify this, we performed additional comparative experiments, as described below.\n\n**Variant-1: concatenate along the prioritized axis (i.e., D-, H-, W-axes for HWD, DWH, DHW scanning, respectively) before flattening**\n\n**Variant-2: always concatenate along the W-axis before flattening**\n\n**Variant-3: interleave tokens from right and left breasts (i.e., R1, L1, R2, L2, ... ; Rx/Lx means the x-th token in the flattened right/left sequence)**\n\n| Method             | Internal | Dice   | H.r.   | F.s.   | Sens.  | AUC    | External | Dice   | H.r.   | F.s.   | Sens.  | AUC    |\n| ------------------ | :------: | ------ | ------ | ------ | ------ | ------ | :------: | ------ | ------ | ------ | ------ | ------ |\n| **DR-M3D (ours)**  |    \\|    | 0.6564 | 0.9228 | 0.9027 | 0.8073 | 0.9690 |    \\|    | 0.5909 | 0.8974 | 0.8632 | 0.7207 | 0.9082 |\n| DRT-M3D Variant-1  |    \\|    | 0.6536 | 0.9127 | 0.9083 | 0.8440 | 0.9693 |    \\|    | 0.5808 | 0.9060 | 0.8729 | 0.8190 | 0.9206 |\n| DRT-M3D Variant-2  |    \\|    | 0.6551 | 0.9039 | 0.9062 | 0.8532 | 0.9732 |    \\|    | 0.5923 | 0.9060 | 0.8708 | 0.8476 | 0.9258 |\n| DRT-M3D Variant-3  |    \\|    | 0.6414 | 0.9083 | 0.9018 | 0.8211 | 0.9650 |    \\|    | 0.5749 | 0.8974 | 0.8644 | 0.7810 | 0.9162 |\n| **DRT-M3D (ours)** |    \\|    | 0.6590 | 0.9229 | 0.9145 | 0.8578 | 0.9768 |    \\|    | 0.5948 | 0.9117 | 0.8766 | 0.8762 | 0.9371 |\n\nOur strategy not only processes all tokens from one side before those from the other in the Mamba layer, but also maintains a roughly consistent distance between anatomically symmetric locations regardless of scanning order. This facilitates effective learning and comparison of bilateral features, as demonstrated in the results above.\n\n**W3**: concerns about the idea of feeding multi-view inputs to an attention-style model\n\n**A**: We appreciate the reviewer’s thoughtful comparison. We acknowledge that this work may appear analogous to multi-view approaches commonly seen in 2D mammography literature from the following two points:\n\n1. Our framework explicitly leverages information from both left and right breasts, and takes them as two parts of the input.\n2. The prioritized scanning along multiple axes in Mamba-3D is analogous to observing the input 3D data from multiple views.\n\nHowever, our method is fundamentally distinct from traditional multi-view settings. In our framework, all inputs (high/low-resolution patches of the left/right breast, as shown in Figure 3 of the main paper) are extracted from a single 3D NCCT image. Thus, our approach does not fuse data from independent acquisitions or views, but rather, analyzes different aspects (dual-resolution, left/right breasts) of the same 3D NCCT scan. The notion of “multi-view” here is therefore not directly comparable to classic multi-projection imaging as in mammography.\n\nWe hope this clarifies the novelty of our approach and its difference from existing multi-view transformer methods.\n\n**W4**: the fairness of the evaluation of main results regarding pre-training\n\n**A**: Thank you for raising this important concern. However, there is a misunderstanding here.\n\n1. Fairness in pre-training application:\n\n   * For baselines not compatible with MAE pre-training (mainly CNN-based models), we have already implemented a supervised pre-training regime: first, training with the segmentation task alone; followed by joint fine-tuning on segmentation and classification. Empirically, this approach greatly improved the baselines’ performance and outperforms the original implementation.\n   * For architectures capable of MAE pre-training (models with standard Transformer or Mamba layers), we conducted MAE pre-training without any extra data, followed by fine-tuning using exactly the same protocol as our proposed method. The only difference among these methods lies in model design.\n\n3. Ablation evidence:\n   To further clarify, we present results for nnUNet without the supervised segmentation pre-training stage in the table below. This comparison demonstrates the benefits of this additional pre-training for methods that do not support MAE pre-training.\n\n   | Method             | Internal |  Dice  |  H.r.  |  F.s.  | Sens.  |  AUC   | External |  Dice  |  H.r.  |  F.s.  | Sens.  |  AUC   |\n   | ------------------ | :------: | ---- | ---- | ---- | ---- | ---- | :------: | ---- | ---- | ---- | ---- | ---- |\n   | nnUNet w/o Seg-Pre |    \\|    | 0.5872 | 0.8952 | 0.7437 | 0.6606 | 0.9070 |    \\|    | 0.5243 | 0.8718 | 0.7003 | 0.5524 | 0.8533 |\n   | nnUNet w/ Seg-Pre (as reported in the paper) |    \\|    | 0.6259 | 0.9127 | 0.8548 | 0.7844 | 0.9536 |    \\|    | 0.5668 | 0.8889 | 0.8173 | 0.6286 | 0.8889 |\n\n**Q1**: concerns about the training speed of the proposed method comparing with other baselines\n\n**A**: We provide a detailed comparison of GPU memory consumption, training time, and inference time for our method and all baselines in the table below, with “Training Time” representing the sum of pre-training and fine-tuning.\n\n| Method               | Training Memory (GB) | Training Time (h) | Inference Time (s) |\n| -------------------- | ------------------ | --------------- | ---------------- |\n| nnUNet               |        3.826         |       31.0        |       0.126        |\n| VNet                 |        3.489         |       28.9        |       0.112        |\n| swinUNETR            |        11.975        |       36.8        |       0.139        |\n| nnFormer             |        2.063         |       10.9        |       0.029        |\n| 3D UX-Net            |        8.754         |       67.0        |       0.251        |\n| MedNeXt              |        12.095        |       43.1        |       0.194        |\n| U-Mamba-Bot          |        6.105         |       44.4        |       0.196        |\n| U-Mamba-Enc          |        11.810        |       77.9        |       0.291        |\n| EM-Net               |        6.218         |       34.9        |       0.116        |\n| SegMamba             |        9.580         |       66.2        |       0.318        |\n| ViT-S/8              |        4.611         |       22.1        |       0.034        |\n| T-ViT-S/8            |        4.629         |       26.9        |       0.047        |\n| **DR-M3D/8 (ours)**  |        2.565         |       14.6        |       0.049        |\n| **DRT-M3D/8 (ours)** |        2.581         |       15.7        |       0.059        |\n| **DR-M3D (ours)**    |        9.187         |       30.4        |       0.143        |\n| **DRT-M3D (ours)**   |        9.202         |       34.2        |       0.171        |\n\nNotably, our approach does not incur a significant training or inference time burden relative to conventional architectures, making it both effective and practical for large-scale clinical deployment."}, {"review_id": "f8x1bEehkN", "reviewer": "Reviewer_9b6M", "summary": "This paper introduces DRT-M3D, a multitask, dual-resolution network utilizing Mamba-3D blocks to perform both segmentation-based lesion detection and malignancy classification on non-contrast chest CT (NCCT) scans. The authors provide comprehensive results for a methodology that can be considered a great contribution. However, the text is complex and should be simplified for all readers.", "questions": "I mentioned my comments in the weakness section. Please address those comments.", "limitations": "NCCT is not optimized for breast imaging (unlike mammography or DCE-MRI), and lesions may be less visible or ambiguous without contrast.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- This manuscript explores NCCT, which is underutilized for breast cancer detection. This is a novel and clinically relevant use case.\n- I think this methodology with comprehensive experiments presented in this paper can be considered novel.\n- This manuscript outperforms several SOTA methods across multiple internal and external datasets.\n\nWeaknesses:\n- This manuscript is complex to follow. Some sections are too math-heavy without sufficient intuition.\n- Figures should also be simplified. I suggest adding a figure to introduce the framework in a simple way.\n- The text should be double-checked to fix some mistakes. For example, Figure 1 is not referenced or explained in the text. All figures should be explained in detail.", "was_revised": true, "final_justification": "Thank you for the responses. Based on your feedback, I have increased the originality rating to 'good.' I am maintaining my overall rating as I believe the paper has potential for acceptance.", "rebuttal": "**W1**: concerns about math-heavy sections without sufficient intuition\n\n**A**: We appreciate the comment regarding the need for more intuition in math-heavy sections. \n\nGenerally speaking, our method aligns with the way radiologists interpret breast images: they analyze fine local details to identify subtle lesions, while also considering global appearance and bilateral symmetry to detect abnormalities.\n\nRegarding detailed designs, the intuition can be summarized as:\n\n1. *Zoom-in & Zoom-out (Dual-Resolution Paths):*\n   - **Intuition**: Radiologists “zoom in” to inspect suspicious regions in detail for subtle lesions, and “zoom out” to evaluate the overall breast structure and context.\n   - **Our model**: We use two parallel paths: a high-resolution “zoom-in” path (small patches) for fine-grained segmentation, and a low-resolution “zoom-out” path (large patches) for broader contextual classification. These paths exchange information via the Mutual Fusion mechanism (see Figure 3(a)), emulating how radiologists integrate local and global cues in clinical reading.\n2. *Cross-breast Comparison (Bilateral/Tandem Input):*\n   - **Intuition**: Radiologists routinely compare the left and right breasts, since subtle asymmetry is often a key sign of disease.\n   - **Our model**: Our “Tandem Input” approach processes both breasts together, enabling the model to directly learn cross-breast differences. The input sequence aligns anatomically symmetric locations between sides (see Figure 3(b)), mirroring how radiologists visually match corresponding regions.\n3. *Multi-orientation Assessment (3D Patch modeling using Mamba-3D):*\n   - **Intuition**: Radiologists interpret scans from multiple anatomical planes to understand tumors’ shape and context in 3D.\n   - **Our model**: Mamba-3D prioritizes scanning along different axes, allowing structural information from multiple directions to be integrated, thus mimicking the multi-orientation analysis and comprehensive assessment performed in real clinical evaluation.\n\n**W2**: concerns regarding figure complexity\n\n**A**: Thank you for your suggestion regarding figure clarity. We agree that a simplified, high-level schematic would make our framework and overall workflow easier to understand. In the camera-ready version, we will revise Figure 2 to provide a more streamlined summary of the complete framework, and will further simplify other figures as needed to enhance clarity.\n\n**W3**: omission of Figure 1 citation in the main text \n\n**A**: We apologize for the oversight. Figure 1 should have been referenced in the first paragraph of the Introduction section, and we will correct the text to ensure it is properly cited and explained in the revised version. We will also systematically review the manuscript to check for other potential omissions or unclear figure references.\n\nAll figures are explained in detail in their captions and the corresponding sections of the main text; however, we are happy to further clarify any figure or section that remains ambiguous. We also welcome any specific questions or requests for clarification during the response phase.\n\n**L1**: concerns about NCCT not optimized for breast imaging\n\n**A**: We fully recognize that NCCT is not optimized for breast imaging, and that lesion visibility is inherently limited compared to dedicated modalities or contrast-enhanced CTs. This makes our task particularly challenging and, to our knowledge, relatively under-explored in the literature. \n\nHowever, we believe this is precisely where the value of our work lies: by leveraging chest CT scans that originally conducted for lung or heart screening, our approach enables opportunistic breast cancer detection without additional radiation exposure or economic burden.\n\nContrast-enhanced CT can have slightly better performance on our task but it needs contrast injection and generally not common, not appropriate for screening. To further enrich our evaluation, we have included additional experiments on contrast-enhanced CT (see our response to ***Reviewer oeU9’s W4***), where performance is stronger as expected. Nevertheless, our model achieves robust and clinically meaningful results on NCCT scans alone, as demonstrated across multi-institutional cohorts.\n\nMammography and ultrasound can be seen as a specific examination tool for breasts, not aligned with our opportunistic screening intention. Dynamic contrast-enhanced MRI (DCE-MRI) can be deemed as a diagnostic tool, also not suitalble for oppotunistic screening. \n\nMoreover, we have also conducted a supplemental reader study on newly collected NCCT samples from anthor region (see our response to ***Reviewer THvZ’s Q1***), further supporting the practical value of our method in real-world clinical settings."}]

Author rebuttal:

Meta-review: (a) Scientific Claims and Findings
The paper proposes Dual-Res Tandem Mamba-3D (DRT-M3D), a novel multitask framework for opportunistic breast lesion detection and malignancy classification using non-contrast chest CT (NCCT) scans. The model integrates:
- A dual-resolution design, balancing fine-grained segmentation with global contextual classification.
- A tandem input mechanism for joint bilateral modeling, capturing subtle asymmetries between left and right breasts.
- A multi-task framework, DRT-M3D, for lesion detection and breast-level classification for opportunistic breast cancer analysis on non-contrast
chest CT scans.
Experiments across four multi-institutional datasets demonstrate state-of-the-art results, surpassing UNet, SwinUNETR, ViTs, and other baselines. Ablations confirm the importance of the dual-resolution, tandem input, and Mamba-3D components. The paper also shows performance approaching that of contrast-enhanced CT, supporting its potential for opportunistic breast cancer screening without extra radiation or cost.

(b) Strengths
- First demonstration of high-performance breast cancer detection and classification using NCCT, enabling opportunistic screening.
- Dual-resolution and tandem bilateral modeling are well-motivated, addressing challenges of NCCT.
- Strong results across multi-institutional datasets, including cross-regional reader studies and early-stage cancer detection.
- Extensive ablations, comparisons to recent SOTAs, efficiency analyses, and visualizations.
- Paper is well-written.

(c) Weaknesses
- Some reviewers noted that multi-task learning and bilateral modeling have precedents in other modalities, so the contribution can be considered to be more on the incremental side than a fundamental breakthrough.
- Figures (e.g., Delta visualization, qualitative comparisons) were initially unclear or insufficiently highlighted.
- Questions were raised about whether improvements derive from larger/more tailored pre-training versus architectural design. Authors later clarified fairness across baselines.
- Although FLOPs are lower, practical runtimes were initially slower than optimized Transformers. Authors clarified this and showed near-real-time performance.
- Concerns about potential failure in localizing small lesions in NCCT (though authors showed safeguards with expanded cropping).
- While some found the tandem input and dual-resolution design innovative, others (THvZ) judged the originality only “fair” in light of broader Mamba/medical imaging trends.

(d) Decision Rationale
The paper makes a meaningful, clinically valuable contribution by introducing the first effective framework for breast cancer detection and classification using NCCT. While some architectural components adapt existing ideas, the integration is thoughtful, technically solid, and experimentally validated. The clinical impact and robustness of the evaluation outweigh concerns about limited novelty. I recommend the paper to be accepted as poster because, although impactful, the method is primarily an adaptation/extension of existing components rather than a breakthrough in core machine learning methodology. Its main strength lies in application significance and careful engineering.

(e) Rebuttal and Discussion
- SOTA comparisons: Authors added results for five recent methods and adapted them for 3D NCCT. Their model outperformed all, addressing this concern.
- Contrast CT as upper bound: Additional experiments confirmed DRT-M3D on NCCT approaches contrast CT performance.
- Efficiency concerns: Authors provided training/inference time and memory analysis, showing near-real-time applicability.
- Novelty and rationale: Authors clarified why Mamba-3D is well-suited for NCCT (local + global modeling, bilateral asymmetry handling). 
- Reviewers acknowledged improved clarity; oeU9 upgraded to Weak Accept.
- Tandem input explanation: Authors gave detailed clarifications and additional experiments with variants. Reviewers agreed this addressed initial confusion.
- Pre-Stage segmentation reliability: Authors showed high Dice and conservative cropping strategies, reducing missed-lesion risk.
- Most concerns were satisfactorily resolved in rebuttal. The only remaining hesitation relates to perceived incremental novelty (THvZ), but reviewers overall leaned positive, with y5XU recommending acceptance and oeU9 upgrading their score.
Decision: Accept (poster)