Current hardware limitations make it impossible to train convolutional neural networks on gigapixel image inputs directly. Recent developments in weakly supervised learning, such as attention-gated multiple instance learning, have shown promising results, but often use multi-stage or patch-wise training strategies risking suboptimal feature extraction, which can negatively impact performance. In this paper, we propose to train a ResNet-34 encoder with an attention-gated classification head in an end-to-end fashion, which we call StreamingCLAM, using a streaming implementation of convolutional layers. This allows us to train end-to-end on 4-gigapixel microscopic images using only slide-level labels.We achieve a mean area under the receiver operating characteristic curve of 0.9757 for metastatic breast cancer detection (CAMELYON16), close to fully supervised approaches using pixel-level annotations. Our model can also detect MYC-gene translocation in histologic slides of diffuse large B-cell lymphoma, achieving a mean area under the ROC curve of 0.8259. Furthermore, we show that our model offers a degree of interpretability through the attention mechanism.