The deployment of deep neural networks in safety-critical systems necessitates reliable and efficient uncertainty quantification (UQ). A practical and widespread strategy for UQ is repurposing stochastic regularizers as scalable approximate Bayesian inference methods, such as Monte Carlo Dropout (MCD) and MC-DropBlock (MCDB). However, this paradigm remains under-explored for Stochastic Depth (SD), a regularizer integral to the residual-based backbones of most modern architectures. While prior work demonstrated its empirical promise for segmentation, a formal theoretical connection to Bayesian variational inference and a benchmark on complex, multi-task problems like object detection are missing. In this paper, we first provide theoretical insights connecting Monte Carlo Stochastic Depth (MCSD) to principled approximate variational inference. We then present the first comprehensive empirical benchmark of MCSD against MCD and MCDB on state-of-the-art detectors (YOLO, RT-DETR) using the COCO and COCO-O datasets. Our results position MCSD as a robust and computationally efficient method that achieves highly competitive predictive accuracy (mAP), notably yielding slight improvements in calibration (ECE) and uncertainty ranking (AUARC) compared to MCD. We thus establish MCSD as a theoretically-grounded and empirically-validated tool for efficient Bayesian approximation in modern deep learning.
Figures & tables
Figure 1: Architectural overview of the detectors used in our study: YOLOv8, Faster R-CNN, and RT-DETR. The expanded block diagrams (e.g., Bottleneck, Residual Layer, HGBlock) illustrate the specific insertion points within the residual paths where MCD, MCDB, and MCSD are applied.
Figure 2: Pareto front analysis of the accuracy (mAP) vs. uncertainty ranking (AUARC) trade-off for RT-DETRx on the COCO validation set. Each point represents a unique hyperparameter configuration. Non-competitive MCDB configurations (mAP <0.1 ) are omitted.
Model
Method
Adapted Layers
Drop Rate
MC-Samples
Conf. Thresh.
mAP.5.95 ↑
Brier ×10−3↓
ECE ↓
AUARC ↑
Faster R-CNN
MCD
All layers
0.20
20
0.40
0.270
5.36
0.213
0.680
Faster R-CNN
MCDB
All layers
0.20
20
0.40
0.258
5.22
0.200
0.653
Faster R-CNN
MCSD
Layer 4
0.10
20
0.50
0.266
5.97
0.247
0.741
YOLOv8x
MCD
Last 15 layers
0.20
20
0.15
0.505
2.43
0.060
0.668
YOLOv8x
MCDB
Last layer
0.05
10
0.15
0.473
2.08
0.063
0.771
YOLOv8x
MCSD
First 15 layers
0.05
20
0.20
0.496
1.93
0.035
0.778
Table 1: Quantitative comparison of the best Pareto-optimal configurations on COCO. This table isolates the top-performing setup for each method, evaluating accuracy (mAP), calibration (Brier, ECE), and uncertainty ranking (AUARC). Bold values highlight the best method for each metric and model.
Figure 3: Performance under domain shift on the COCO-O benchmark for Faster-RCNN (top), YOLOv8x (middle), and RT-DETRx (bottom). Solid lines track mAP, dashed lines predictive entropy.
Figure 4: Pareto front analysis of the accuracy (mAP) vs. uncertainty ranking (AUARC) trade-off for Faster R-CNN on the COCO validation set. Each point represents a unique hyperparameter configuration. Non-competitive configurations are omitted.
Figure 5: Pareto front analysis of the accuracy (mAP) vs. uncertainty ranking (AUARC) trade-off for YOLOv8x on the COCO validation set. Each point represents a unique hyperparameter configuration. Non-competitive configurations are omitted.
Figure 6: Qualitative comparison of detection and uncertainty for data under distribution shift, using RT-DETRx. Examples from the COCO-O dataset, comparing detection outputs across different uncertainty quantification methods. Each row represents a distinct domain shift: Row 1 ( Weather ), Row 2 ( Painting ), Row 3 ( Handmake ), and Row 4 ( Sketch ). Columns from left to right show: Ground Truth (green bounding boxes), Mean Detections (MCD) (red), Mean Detections (MCDB) (blue), and Mean Detections (MCSD) (orange).
Adapted Layers
Single Layer
Half Block
Model
Method
Metric
First
Last
First
Last
Faster R-CNN
MCD
ECE ↓
0.236
0.254
0.223
0.234
AUARC ↑
0.680
0.672
0.683
0.675
MCDB
ECE ↓
0.260
0.263
0.257
0.224
AUARC ↑
0.572
0.668
0.612
0.661
Table 2: Impact of stochastic layer placement. Comparison of stochasticity applied to earlier vs. later stages in single and multiple ( Half Block ) layers. N/A denotes configurations that failed to meet minimum viability thresholds.
Dataset
Model
Method
Metric
COCO (ID)
weather
painting
handmake
cartoon
sketch
tattoo
Faster R-CNN
MCD
mAP.5.95 ↑
0.270
0.168
0.148
0.102
0.090
0.059
0.064
Entropy ↓
0.796
1.101
1.289
1.505
1.374
1.310
1.569
MCDB
mAP.5.95 ↑
0.258
0.156
0.157
0.091
0.090
0.061
0.061
Entropy ↓
0.894
1.155
1.340
1.531
1.375
1.371
1.546
MCSD
mAP.5.95 ↑
0.266
0.161
0.147
0.085
0.088
0.059
0.054
Table 3: Quantitative results under distribution shift. Comparison of mAP and Predictive Entropy across the COCO-O domains. Note the difference in Entropy measures between Faster R-CNN (Shannon Entropy) and the dense detectors (Binary Entropy).