ResNet for image classification
ResNetPyTorchtorchvision
Skip connections make 100+ layer CNNs trainable. Backbone of much of pre-ViT computer vision.
python
import torchvision.models as M
net = M.resnet50(weights='IMAGENET1K_V2')Ch. 14 · Deep-Learning Building Blocks
Convolutional Neural Networks Math
Deep Learning Building Blocks
Ch. 14
∂W∂L=δa⊤
backpropagation
A convolution slides a learnable filter mathbf{K} in mathbb{R}^{k_h times k_w} across an input feature map and outputs, at each spatial position, the dot product between the filter and the local patch. For an image of shape (C_{in}, H, W) and C_{out} filters each of shape (C_{in}, k_h, k_w), the lay
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Before you start
Foundations you'll lean on here
A quick refresher on what this lesson assumes. Tap any card for a plain-language explanation and a tiny worked example.
★Big idea
Convolutions = learnable filters sliding over a tensor with shared weights.
A convolution slides a learnable filter across an input feature map and outputs, at each spatial position, the dot product between the filter and the local patch. For an image of shape and filters each of shape , the layer produces an output of shape where depends on padding and stride .
Convolutions encode three powerful inductive biases: locality (each output depends on a small input neighborhood), translation equivariance (shifting the input shifts the output by the same amount), and weight sharing (the same filter is reused across every position, drastically reducing parameter count compared to a fully connected layer).
Receptive field is the region of the input that influences a given output unit. It grows linearly with depth in vanilla CNNs and exponentially with dilation. Modern architectures (U-Net, EfficientNet) carefully manage receptive field to balance local detail and global context.
Sliding a 3×3 filter by hand
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Most CNN computation cost concentrates in the convolutions — roughly multiplies per layer. Depthwise-separable convolutions (MobileNet, EfficientNet) decompose this into a depthwise spatial conv + a 1×1 pointwise conv, slashing cost by roughly .
In the wild
Where this shows up in production
Each card is a real system, model, or technique that rests on this lesson.
U-Net for segmentation
U-NetMedicalDiffusion
Encoder-decoder with skip connections — the default architecture for medical image segmentation, denoising, and diffusion model backbones.
MobileNet / EfficientNet on edge
MobileNetMobile
Depthwise-separable convolutions cut compute 8–9× with minimal accuracy loss. The default for on-device inference.
Exercises
Concept Challenge
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Convolutional Neural Networks Math
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Active recall
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Concept
Convolutions = learnable filters sliding…
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