CNNs
Convolutional Neural Networks for image recognition.
For a small example, a 3x3 filter moves over a tiny grayscale image. Compute one dot product per location and see where the resulting feature map responds strongly.
CNNs
In practice
A classifier detects visual defects under varying lighting. Augment realistically, split by production batch, compare transfer learning, and visualize failures across defect sizes.
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Experiment notes
Record your experiment
Predict how one control changes the CNNs result.
Implementation
Repair a failing CNNs starter
The starter deliberately follows a tempting but flawed assumption: Using random crops that destroy the target
- Run the starter once and inspect the first wrong value, failed check, or incomplete branch.
- Repair the smallest relevant part of the code. Do not rewrite the whole solution.
- Check the solution, then explain why this correction works: Make augmentation label-preserving and verify examples visually.
Check: The browser checks pass and you can name the failure mechanism before opening the explanation.
Failing starter lab
Compute a convolution output shape
Given input size, kernel, stride, and padding, return the spatial output length.
Run the incomplete starter before opening hints. Use the first wrong output or failed check to form a repair hypothesis.
Knowledge check
10 questions
Explanations after each answer · 80% to pass · CNNs
Chapter 1 of 10 · Core
The Convolution Operation: Mathematical Formulations
In mathematical analysis, a convolution between a continuous input signal and a filter kernel is defined as the integral of the product of the two functions after one is reflected and shifted: For discrete 2D applications like computer vision, a 2D convolution of an image with an odd square kernel is defined as: where . The spatial reflection of the kernel (represented by the minus sign in index subtraction) is necessary for convolution to satisfy the mathematical property of associativity: .
Cross-Correlation in Deep Learning:
In practical deep learning libraries (e.g., PyTorch, TensorFlow), the operation implemented under the name "convolution" is actually cross-correlation, which omits the spatial reflection step:
Because the kernel parameters are learned from scratch during backpropagation, spatial reflection is mathematically redundant. If reflection were applied, the network would simply learn a flipped version of the kernel. Omitting the flip saves computational overhead.
Output Size Formula with Dilation:
The spatial dimensions of a convolutional layer's output feature map depend on input width , kernel size , padding , stride , and dilation rate (which inserts spaces between kernel elements): Dilation expands the receptive field without changing the kernel's parameter count or multiply-accumulates per output position. Total work and runtime still depend on output dimensions, padding, memory access, and implementation.
Key equations
Video explanation
MIT 6.S191: Convolutional Neural Networks
MIT Introduction to Deep Learning
See filters, spatial hierarchies, and modern vision architectures in a university lecture.
References
Primary sources and free technical reading for CNNs.
Dive into Deep Learning
Free interactive book with executable implementations of neural networks, sequence models, CNNs, and Transformers.
BookFree
ImageNet Classification with Deep Convolutional Neural Networks
The AlexNet paper connecting convolutional design choices to large-scale visual recognition.
PaperFree