YOLO

YOLOv1 reframes detection as a single regression problem. The input image is divided into an $S \times S$ grid; each cell is responsible for objects whose centre falls inside it. For each cell the network predicts $B$ candidate boxes $(x, y, w, h, \mathrm{conf})$ plus one shared class distribution over $C$ categories, so the head output has shape $S \times S \times (B \cdot 5 + C)$.

A single CNN (the Darknet trunk in the paper) processes the full image once and emits all detections in one forward pass. The confidence target is $\Pr(\mathrm{obj}) \cdot \mathrm{IoU}^{\mathrm{truth}}_{\mathrm{pred}}$ so that confidence encodes both objectness and localisation quality. Training uses a weighted sum-squared-error loss

where $\sqrt{w}, \sqrt{h}$ make the regression less sensitive to absolute scale and $\lambda_{\mathrm{coord}}, \lambda_{\mathrm{noobj}}$ rebalance the dense background term.

Because the entire pipeline is a single CNN, YOLOv1 runs at 45 fps (155 fps for the tiny variant) — orders of magnitude faster than the two-stage R-CNN family — establishing the one-stage detection paradigm. Trade-off: each cell predicts a fixed small $B$, limiting recall on clustered small objects, which is exactly what YOLOv2/v3/v4 progressively fix with anchors, multi-scale heads, and a stronger backbone/neck.