Deep Learning · Cluster
Convolutional Networks
Local connectivity and visual features.
- 01 Cross-Correlation and Convolution in the Forward Pass What the sliding dot product computes, why deep learning libraries conjugate the kernel index, and how zero padding and output size arithmetic follow from the index bounds.
- 02 Translational Weight Sharing and Feature Map Aliasing How a kernel applied at every position implements a translation-equivariant prior, what the stride lattice does to that guarantee, and where shift invariance actually breaks.
- 03 Receptive Field Arithmetic and Effective Coverage How a unit back-propagates to the input positions that influence it, why the theoretical field overstates the real one, and how dilation and stride change the recurrence.
- 04 im2col Expansion, FFT Convolution, and Winograd Transforms Three ways to turn a convolution into matrix arithmetic: what im2col replicates in memory, when the Fourier route wins, and what Winograd trades away in numeric range.
- 05 Pooling as a Downsampling Operator and Its Signal Effects What max and average pooling actually compute, why stride-based subsampling aliases, and how the backward pass routes gradient through a non-differentiable maximum.
- 06 Transposed Convolution and the Checkerboard Artifact How the backward pass of a convolution defines an upsampling operator, why unequal kernel overlap produces a fixed grid pattern, and how to avoid it entirely.
- 07 Depthwise and Grouped Convolutions and the Cost per Channel How splitting channels into groups changes the parameter count, the arithmetic intensity, and the access pattern, and why a cheaper layer is often the slower one.
- 08 Stride-1 Backbones and Dense Prediction with Skip Connections Why segmentation decoders rebuild resolution that the encoder discarded, what a skip connection restores beyond detail, and how dilated backbones avoid the reconstruction entirely.
- 09 Activation Memory, Gradient Recomputation, and the Checkpoint Trade How the memory cost of a convolutional training step is computed, why activations outgrow weights, and what gradient checkpointing buys at what arithmetic price.
- 10 Feature Visualisation and What Convolutional Filters Reveal Optimising an input image against a single neuron, what regularisation each term contributes, and the evidence that early filters are oriented edge detectors.