of the four best models and their model ensemble. The model ensemble yielded an AUC of 0.91, which corresponded to sensitivity of 86.1% and specificity of 80.1%.

![ROC curves of the four best performing models and their model ensemble on (a) The DDSM test set and (b) The INbreast validation set.[]{data-label="fig:roc_curve"}](ddsm_inb_model_ROC_curve.jpg){width="\linewidth"}

**Using max-pooling, shortcut and FC layers** \[pool\_fc\_auc\] We tested the alternative design by using the heatmap followed by a max-pooling and two FC layers, including a shortcut between the heatmap and the classification output. The Resnet50 and VGG16 patch classifiers were used. The FC layer sizes were chosen to gradually reduce the layer outputs. When the pooling size increased from $1 \times 1$ (i.e. no pooling) to $5 \times 5$, the AUC also moderately increased (Tables \[tab:resnet\_auc\] & \[tab:vgg\_auc\]) but even the best performing model achieved only AUC of 0.73, falling short of the all convolutional models.

**Using the heatmap in all convolutional networks** \[heatmap\_auc\] To test our hypothesis about the heatmap being an information bottleneck in the all convolutional networks, we added the heatmap back into the Resnet-based whole image classifier with two $[512-512-1024] \times 2$ blocks as top layers. This model achieved an AUC of 0.80 (Table 