ACTL3143 & ACTL5111 Deep Learning for Actuaries
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
Illustration of tensors of different rank.
Source: Paras Patidar (2019), Tensors — Representation of Data In Neural Networks, Medium article.
A photo is a rank 3 tensor.
Source: Kim et al (2021), Data Hiding Method for Color AMBTC Compressed Images Using Color Difference, Applied Sciences.
'Shapes are: (16, 16, 3), (16, 16, 3), (16, 16, 3), (16, 16, 3).'
array([[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]]], dtype=uint8)
array([[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]]], dtype=uint8)
array([[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[255, 255, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]]], dtype=uint8)
array([[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0]],
[[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 51, 0, 255],
[ 51, 0, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[ 51, 0, 255],
[ 51, 0, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 51, 0, 255],
[ 51, 0, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[ 51, 0, 255],
[ 51, 0, 255],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 255, 255],
[255, 255, 255],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177]],
[[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0]],
[[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[255, 163, 177],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0]],
[[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0],
[255, 163, 177],
[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]]], dtype=uint8)
Each pixel’s colour intensity is stored in one byte.
One byte is 8 bits, so in binary that is 00000000 to 11111111.
The largest unsigned number this can be is 2^8-1 = 255.
If you had signed numbers, this would go from -128 to 127.
Alternatively, hexidecimal numbers are used. E.g. 10100001 is split into 1010 0001, and 1010=A, 0001=1, so combined it is 0xA1.
Take a look at https://setosa.io/ev/image-kernels/.
An example of an image kernel in action.
Source: Stanford’s deep learning tutorial via Stack Exchange.
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
Say X_1, X_2 \sim f_X are i.i.d., and we look at S = X_1 + X_2.
The density for S is then
f_S(s) = \int_{x_1=-\infty}^{\infty} f_X(x_1) \, f_X(s-x_1) \,\mathrm{d}s .
This is the convolution operation, f_S = f_X \star f_X.
Height, width, and number of channels.
Examples of rank 3 tensors.
Grayscale image has 1 channel. RGB image has 3 channels.
Example: Yellow = Red + Green.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Apply a neuron to each pixel in the image.
If red/green \nearrow or blue \searrow then yellowness \nearrow.
Set RGB weights to 1, 1, -1.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Scan the 3-channel input (colour image) with the neuron to produce a 1-channel output (grayscale image).
The output is produced by sweeping the neuron over the input. This is called convolution.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
The more yellow the pixel in the colour image (left), the more white it is in the grayscale image.
The neuron or its weights is called a filter. We convolve the image with a filter, i.e. a convolutional filter.
Example 3x3 filter
When a filter’s footprint is > 1 pixel, it is a spatial filter.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Need \# \text{ Channels in Input} = \# \text{ Channels in Filter}.
Example: a 3x3 filter with 3 channels, containing 27 weights.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Each channel is multipled separately & then added together.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Matching the original image footprints against the output location.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
What happens when filters go off the edge of the input?
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Add a border of extra elements around the input, called padding. Normally we place zeros in all the new elements, called zero padding.
Padded values can be added to the outside of the input.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
In the image:
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Example network with 1x1 convolution.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
We don’t have to go one pixel across/down at a time.
Example: Use a stride of three horizontally and two vertically.
Dimension of output will be smaller than input.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
When a filter scans the input step by step, it processes the same input elements multiple times. Even with larger strides, this can still happen (left image).
If we want to save time, we can choose strides that prevents input elements from being used more than once. Example (right image): 3x3 filter, stride 3 in both directions.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Need to choose:
All the filter weights are learned during training.
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
A neural network that uses convolution layers is called a convolutional neural network.
Source: Randall Munroe (2019), xkcd #2173: Trained a Neural Net.
Typical CNN architecture.
Source: Aurélien Géron (2019), Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition, Figure 14-11.
Source: MathWorks, Introducing Deep Learning with MATLAB, Ebook.
Pooling, or downsampling, is a technique to blur a tensor.
Illustration of pool operations.
(a): Input tensor (b): Subdivide input tensor into 2x2 blocks (c): Average pooling (d): Max pooling (e): Icon for a pooling layer
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Pooling a multichannel input.
Source: Glassner (2021), Deep Learning: A Visual Approach, Chapter 16.
Why? Pooling reduces the size of tensors, therefore reduces memory usage and execution time (recall that 1x1 convolution reduces the number of channels in a tensor).
Why not?
Geoffrey Hinton
Source: Hinton, Reddit AMA.
Source: Distill article, Feature Visualization.
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
The MNIST dataset.
Source: Wikipedia, MNIST database.
Dataset source: Institute of Automation of Chinese Academy of Sciences (CASIA)
A 13 GB dataset of 3,999,571 handwritten characters.
Source: Liu et al. (2011), CASIA online and offline Chinese handwriting databases, 2011 International Conference on Document Analysis and Recognition.
Pulling out 55 characters to experiment with.
人从众大夫天口太因鱼犬吠哭火炎啖木林森本竹羊美羔山出女囡鸟日东月朋明肉肤工白虎门闪问闲水牛马吗妈玉王国主川舟虫
Inspect directory structure
CASIA-Dataset/
├── Test/
│ ├── 东/
│ │ ├── 1.png
│ │ ├── 10.png
│ │ ├── 100.png
│ │ ├── 101.png
│ │ ├── 102.png
│ │ ├── 103.png
│ │ ├── 104.png
│ │ ├── 105.png
│ │ ├── 106.png
...
├── 97.png
├── 98.png
└── 99.png
def count_images_in_folders(root_folder):
counts = {}
for folder in root_folder.iterdir():
counts[folder.name] = len(list(folder.glob("*.png")))
return counts
train_counts = count_images_in_folders(Path("CASIA-Dataset/Train"))
test_counts = count_images_in_folders(Path("CASIA-Dataset/Test"))
print(train_counts)
print(test_counts)
{'哭': 584, '闪': 597, '马': 597, '啖': 240, '囡': 240, '明': 596, '太': 596, '森': 598, '国': 600, '女': 597, '本': 604, '夫': 599, '因': 603, '林': 598, '月': 604, '川': 593, '牛': 599, '鱼': 602, '玉': 602, '工': 600, '水': 597, '犬': 598, '肤': 601, '从': 598, '美': 591, '羔': 597, '鸟': 598, '肉': 598, '东': 601, '人': 597, '问': 601, '闲': 598, '日': 597, '竹': 600, '吠': 601, '门': 597, '吗': 596, '木': 598, '虎': 597, '大': 603, '天': 598, '妈': 595, '虫': 602, '白': 604, '朋': 595, '口': 597, '舟': 601, '山': 598, '王': 601, '众': 600, '羊': 600, '炎': 602, '出': 602, '主': 599, '火': 599}
{'哭': 138, '闪': 143, '马': 144, '啖': 60, '囡': 59, '明': 144, '太': 143, '森': 144, '国': 142, '女': 144, '本': 143, '夫': 141, '因': 144, '林': 143, '月': 144, '川': 142, '牛': 144, '鱼': 143, '玉': 142, '工': 141, '水': 143, '犬': 141, '肤': 140, '从': 142, '美': 144, '羔': 141, '鸟': 143, '肉': 143, '东': 142, '人': 144, '问': 143, '闲': 142, '日': 143, '竹': 142, '吠': 141, '门': 144, '吗': 143, '木': 144, '虎': 143, '大': 144, '天': 143, '妈': 142, '虫': 144, '白': 141, '朋': 144, '口': 143, '舟': 143, '山': 144, '王': 145, '众': 143, '羊': 144, '炎': 143, '出': 142, '主': 141, '火': 142}
It differs, but basically ~600 training and ~140 test images per character. A couple of characters have a lot less of both though.
def get_image_dimensions(root_folder):
dimensions = []
for folder in root_folder.iterdir():
for image in folder.glob("*.png"):
img = imread(image)
dimensions.append(img.shape)
return dimensions
train_dimensions = get_image_dimensions(Path("CASIA-Dataset/Train"))
test_dimensions = get_image_dimensions(Path("CASIA-Dataset/Test"))
train_heights = [d[0] for d in train_dimensions]
train_widths = [d[1] for d in train_dimensions]
test_heights = [d[0] for d in test_dimensions]
test_widths = [d[1] for d in test_dimensions]
The images are taller than they are wide. We have more training images than test images.
plt.hist(train_heights, bins=30, alpha=0.5, label="Train Heights", density=True)
plt.hist(train_widths, bins=30, alpha=0.5, label="Train Widths", density=True)
plt.hist(test_heights, bins=30, alpha=0.5, label="Test Heights", density=True)
plt.hist(test_widths, bins=30, alpha=0.5, label="Test Widths", density=True)
plt.legend();
The distribution of dimensions are pretty similar between training and test sets.
Normally we’d used keras.utils.image_dataset_from_directory
but the Chinese characters breaks it on Windows. I made an image loading function just for this demo.
def preprocess_image(img_path, img_height=80, img_width=60):
"""
Loads and preprocesses an image:
- Converts to grayscale
- Resizes to (img_height, img_width) using anti-aliasing
- Returns a NumPy array normalized to [0,1]
"""
img = Image.open(img_path).convert("L") # Open image and convert to grayscale
img = img.resize((img_width, img_height), Image.LANCZOS) # Resize with anti-aliasing
return np.array(img, dtype=np.float32)
def load_images_from_directory(directory, img_height=80, img_width=60):
"""
Loads images and labels from a directory where each subfolder represents a class.
Returns:
X (numpy array): Image data of shape (num_samples, img_height, img_width, 1).
y (numpy array): Labels as integer indices.
class_names (list): List of class names in sorted order.
"""
directory = Path(directory) # Ensure it's a Path object
class_names = sorted([d.name for d in directory.iterdir() if d.is_dir()]) # Sorted UTF-8 class names
class_name_to_index = {name: i for i, name in enumerate(class_names)}
image_paths, labels = [], []
for class_name in class_names:
class_dir = directory / class_name
for img_path in sorted(class_dir.glob("*.png")):
image_paths.append(img_path)
labels.append(class_name_to_index[class_name])
# Load and preprocess images
X = np.array([preprocess_image(img, img_height, img_width) for img in image_paths])
X = X[..., np.newaxis] # Add channel dimension
y = np.array(labels, dtype=np.int32)
return X, y, class_names
data_dir = Path("CASIA-Dataset")
img_height, img_width = 80, 60 # Target image size
# Load 'training' and test datasets
X_main, y_main, class_names = load_images_from_directory(data_dir / "Train", img_height, img_width)
X_test, y_test, _ = load_images_from_directory(data_dir / "Test", img_height, img_width)
# Verify dataset shape
print(f"Train: X={X_main.shape}, y={y_main.shape}")
print(f"Test: X={X_test.shape}, y={y_test.shape}")
print("Class Names:", class_names)
Train: X=(32206, 80, 60, 1), y=(32206,)
Test: X=(7684, 80, 60, 1), y=(7684,)
Class Names: ['东', '主', '人', '从', '众', '出', '口', '吗', '吠', '哭', '啖', '因', '囡', '国', '大', '天', '太', '夫', '女', '妈', '山', '川', '工', '日', '明', '月', '朋', '木', '本', '林', '森', '水', '火', '炎', '牛', '犬', '玉', '王', '白', '竹', '羊', '美', '羔', '肉', '肤', '舟', '虎', '虫', '门', '闪', '问', '闲', '马', '鱼', '鸟']
X_train, X_val, y_train, y_val = train_test_split(X_main, y_main, test_size=0.2,
random_state=123)
print(X_train.shape, y_train.shape, X_val.shape, y_val.shape, X_test.shape, y_test.shape)
(25764, 80, 60, 1) (25764,) (6442, 80, 60, 1) (6442,) (7684, 80, 60, 1) (7684,)
import matplotlib.font_manager as fm
CHINESE_FONT = fm.FontProperties(fname="STHeitiTC-Medium-01.ttf")
def plot_mandarin_characters(X, y, class_names, n=5, title_font=CHINESE_FONT):
# Plot the first n images in X
plt.figure(figsize=(10, 4))
for i in range(n):
plt.subplot(1, n, i + 1)
plt.imshow(X[i], cmap="gray")
plt.title(class_names[y[i]], fontproperties=title_font)
plt.axis("off")
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
Basically pretend it’s not an image
Tip
The Rescaling
layer will rescale the intensities to [0, 1].
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ flatten (Flatten) │ (None, 4800) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ rescaling (Rescaling) │ (None, 4800) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense (Dense) │ (None, 55) │ 264,055 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 264,055 (1.01 MB)
Trainable params: 264,055 (1.01 MB)
Non-trainable params: 0 (0.00 B)
loss = keras.losses.SparseCategoricalCrossentropy()
topk = keras.metrics.SparseTopKCategoricalAccuracy(k=5)
model.compile(optimizer='adam', loss=loss, metrics=['accuracy', topk])
epochs = 100
es = EarlyStopping(patience=15, restore_best_weights=True,
monitor="val_accuracy", verbose=2)
if Path("logistic.keras").exists():
model = keras.models.load_model("logistic.keras")
with open("logistic_history.json", "r") as json_file:
history = json.load(json_file)
else:
hist = model.fit(X_train, y_train, validation_data=(X_val, y_val),
epochs=epochs, callbacks=[es], verbose=0)
model.save("logistic.keras")
history = hist.history
with open("logistic_history.json", "w") as json_file:
json.dump(history, json_file)
Most of this last part is just to save time rendering this slides, you don’t need it.
def plot_history(history):
epochs = range(len(history["loss"]))
plt.subplot(1, 2, 1)
plt.plot(epochs, history["accuracy"], label="Train")
plt.plot(epochs, history["val_accuracy"], label="Val")
plt.legend(loc="lower right")
plt.title("Accuracy")
plt.subplot(1, 2, 2)
plt.plot(epochs, history["loss"], label="Train")
plt.plot(epochs, history["val_loss"], label="Val")
plt.legend(loc="upper right")
plt.title("Loss")
plt.show()
[1.699511170387268, 0.6174119114875793, 0.8565052151679993]
[2.1941583156585693, 0.5513815879821777, 0.8146538138389587]
loss_value, accuracy, top5_accuracy = model.evaluate(X_val, y_val, verbose=0)
print(f"Validation Loss: {loss_value:.4f}")
print(f"Validation Accuracy: {accuracy:.4f}")
print(f"Validation Top 5 Accuracy: {top5_accuracy:.4f}")
Validation Loss: 2.1942
Validation Accuracy: 0.5514
Validation Top 5 Accuracy: 0.8147
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
from keras.layers import Conv2D, MaxPooling2D
random.seed(123)
model = Sequential([
Input((img_height, img_width, 1)),
Rescaling(1./255),
Conv2D(16, 3, padding="same", activation="relu", name="conv1"),
MaxPooling2D(name="pool1"),
Conv2D(32, 3, padding="same", activation="relu", name="conv2"),
MaxPooling2D(name="pool2"),
Conv2D(64, 3, padding="same", activation="relu", name="conv3"),
MaxPooling2D(name="pool3", pool_size=(4, 4)),
Flatten(), Dense(64, activation="relu"), Dense(num_classes)
])
Architecture inspired by https://www.tensorflow.org/tutorials/images/classification.
Model: "sequential_1"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ rescaling_1 (Rescaling) │ (None, 80, 60, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv1 (Conv2D) │ (None, 80, 60, 16) │ 160 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ pool1 (MaxPooling2D) │ (None, 40, 30, 16) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2 (Conv2D) │ (None, 40, 30, 32) │ 4,640 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ pool2 (MaxPooling2D) │ (None, 20, 15, 32) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv3 (Conv2D) │ (None, 20, 15, 64) │ 18,496 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ pool3 (MaxPooling2D) │ (None, 5, 3, 64) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ flatten_1 (Flatten) │ (None, 960) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 64) │ 61,504 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 55) │ 3,575 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 88,375 (345.21 KB)
Trainable params: 88,375 (345.21 KB)
Non-trainable params: 0 (0.00 B)
loss = keras.losses.SparseCategoricalCrossentropy(from_logits=True)
topk = keras.metrics.SparseTopKCategoricalAccuracy(k=5)
model.compile(optimizer='adam', loss=loss, metrics=['accuracy', topk])
epochs = 100
es = EarlyStopping(patience=15, restore_best_weights=True,
monitor="val_accuracy", verbose=2)
if Path("cnn.keras").exists():
model = keras.models.load_model("cnn.keras")
with open("cnn_history.json", "r") as json_file:
history = json.load(json_file)
else:
hist = model.fit(X_train, y_train, validation_data=(X_val, y_val),
epochs=epochs, callbacks=[es], verbose=0)
model.save("cnn.keras")
history = hist.history
with open("cnn_history.json", "w") as json_file:
json.dump(history, json_file)
Tip
Instead of using softmax activation, just added from_logits=True
to the loss function; this is more numerically stable.
[0.017913011834025383, 0.994255542755127, 1.0]
[0.6190589070320129, 0.932319164276123, 0.9928593635559082]
--------------------------------------------------------------------------- ValueError Traceback (most recent call last) Cell In[51], line 1 ----> 1 model.predict(X_test[0], verbose=0); File ~/miniforge3/envs/ai/lib/python3.11/site-packages/keras/src/utils/traceback_utils.py:122, in filter_traceback.<locals>.error_handler(*args, **kwargs) 119 filtered_tb = _process_traceback_frames(e.__traceback__) 120 # To get the full stack trace, call: 121 # `keras.config.disable_traceback_filtering()` --> 122 raise e.with_traceback(filtered_tb) from None 123 finally: 124 del filtered_tb File ~/miniforge3/envs/ai/lib/python3.11/site-packages/keras/src/utils/traceback_utils.py:122, in filter_traceback.<locals>.error_handler(*args, **kwargs) 119 filtered_tb = _process_traceback_frames(e.__traceback__) 120 # To get the full stack trace, call: 121 # `keras.config.disable_traceback_filtering()` --> 122 raise e.with_traceback(filtered_tb) from None 123 finally: 124 del filtered_tb ValueError: Exception encountered when calling MaxPooling2D.call(). Negative dimension size caused by subtracting 2 from 1 for '{{node sequential_1_1/pool1_1/MaxPool2d}} = MaxPool[T=DT_FLOAT, data_format="NHWC", explicit_paddings=[], ksize=[1, 2, 2, 1], padding="VALID", strides=[1, 2, 2, 1]](sequential_1_1/conv1_1/Relu)' with input shapes: [32,60,1,16]. Arguments received by MaxPooling2D.call(): • inputs=tf.Tensor(shape=(32, 60, 1, 16), dtype=float32)
((80, 60, 1), (1, 80, 60, 1), (1, 80, 60, 1))
array([[ -16.07, -50.68, -70.74, -69.43, -18.42, -25.6 , -64.9 ,
-19.92, -61.06, -70.17, -57.52, -4.96, -44.66, -26.29,
-62.04, -44.15, -19.94, -31.97, -26.57, -0.72, -57.15,
-101.83, -114.35, -47.58, -41.25, -38.47, -57.95, -49.15,
-21.68, -14.76, -10.15, -34.42, -71.32, -31.48, -64.98,
-74.59, -40.52, -82.14, 8.61, -26.42, -78.95, -59.28,
-28.89, 41.85, -18.98, -29.89, 32.67, -1.32, -32.63,
3.52, -6.42, -1.01, -25.58, -37.48, 1.27]],
dtype=float32)
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
def plot_failed_predictions(X, y, class_names, max_errors = 20,
num_rows = 4, num_cols = 5, title_font=CHINESE_FONT):
plt.figure(figsize=(num_cols * 2, num_rows * 2))
errors = 0
y_pred = model.predict(X, verbose=0)
y_pred_classes = y_pred.argmax(axis=1)
y_pred_probs = keras.ops.softmax(y_pred).numpy().max(axis=1)
for i in range(len(y_pred)):
if errors >= max_errors:
break
if y_pred_classes[i] != y[i]:
plt.subplot(num_rows, num_cols, errors + 1)
plt.imshow(X[i], cmap="gray")
true_class = class_names[y[i]]
pred_class = class_names[y_pred_classes[i]]
conf = y_pred_probs[i]
msg = f"{true_class} not {pred_class} ({conf*100:.0f}%)"
plt.title(msg, fontproperties=title_font)
plt.axis("off")
errors += 1
y_log = model.predict(X_test, verbose=0)
y_pred = keras.ops.convert_to_numpy(keras.activations.softmax(y_log))
y_pred_class = np.argmax(y_pred, axis=1)
y_pred_prob = y_pred[np.arange(y_pred.shape[0]), y_pred_class]
confidence_when_correct = y_pred_prob[y_pred_class == y_test]
confidence_when_wrong = y_pred_prob[y_pred_class != y_test]
55 poorly written Mandarin characters (55 \times 7 = 385).
Dataset of notes when learning/practising basic characters.
X_pat, y_pat, pat_class_names = load_images_from_directory(Path("mandarin"), img_height, img_width)
assert pat_class_names == class_names, "Class names do not match!"
print(f"Mandarin: X={X_pat.shape}, y={y_pat.shape}")
Mandarin: X=(385, 80, 60, 1), y=(385,)
[4.6398444175720215, 0.7584415674209595, 0.9350649118423462]
class_accuracies = []
for i in range(num_classes):
class_indices = y_pat == i
y_pred = model.predict(X_pat[class_indices], verbose=0).argmax(axis=1)
class_correct = y_pred == y_pat[class_indices]
class_accuracies.append(np.mean(class_correct))
class_accuracies = pd.DataFrame({"Class": class_names, "Accuracy": class_accuracies})
class_accuracies.sort_values("Accuracy")
Class | Accuracy | |
---|---|---|
12 | 囡 | 0.000000 |
8 | 吠 | 0.000000 |
23 | 日 | 0.142857 |
7 | 吗 | 0.142857 |
... | ... | ... |
26 | 朋 | 1.000000 |
25 | 月 | 1.000000 |
22 | 工 | 1.000000 |
27 | 木 | 1.000000 |
55 rows × 2 columns
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
Frankly, a lot of this is just ‘enlightened’ trial and error.
Source: Twitter.
import keras_tuner as kt
def build_model(hp):
model = Sequential()
model.add(
Dense(
hp.Choice("neurons", [4, 8, 16, 32, 64, 128, 256]),
activation=hp.Choice("activation",
["relu", "leaky_relu", "tanh"]),
)
)
model.add(Dense(1, activation="exponential"))
learning_rate = hp.Float("lr",
min_value=1e-4, max_value=1e-2, sampling="log")
opt = keras.optimizers.Adam(learning_rate=learning_rate)
model.compile(optimizer=opt, loss="poisson")
return model
tuner = kt.RandomSearch(
build_model,
objective="val_loss",
max_trials=10,
directory="random-search")
es = EarlyStopping(patience=3,
restore_best_weights=True)
tuner.search(X_train_sc, y_train,
epochs=100, callbacks = [es],
validation_data=(X_val_sc, y_val))
best_model = tuner.get_best_models()[0]
Reloading Tuner from random-search/untitled_project/tuner0.json
def build_model(hp):
model = Sequential()
for i in range(hp.Int("numHiddenLayers", 1, 3)):
# Tune number of units in each layer separately.
model.add(
Dense(
hp.Choice(f"neurons_{i}", [8, 16, 32, 64]),
activation="relu"
)
)
model.add(Dense(1, activation="exponential"))
opt = keras.optimizers.Adam(learning_rate=0.0005)
model.compile(optimizer=opt, loss="poisson")
return model
tuner = kt.BayesianOptimization(
build_model,
objective="val_loss",
directory="bayesian-search",
max_trials=10)
es = EarlyStopping(patience=3,
restore_best_weights=True)
tuner.search(X_train_sc, y_train,
epochs=100, callbacks = [es],
validation_data=(X_val_sc, y_val))
best_model = tuner.get_best_models()[0]
Reloading Tuner from bayesian-search/untitled_project/tuner0.json
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
Source: Teachable Machine, https://teachablemachine.withgoogle.com/.
… these models use a technique called transfer learning. There’s a pretrained neural network, and when you create your own classes, you can sort of picture that your classes are becoming the last layer or step of the neural net. Specifically, both the image and pose models are learning off of pretrained mobilenet models …
CIFAR-11 / CIFAR-100 dataset from Canadian Institute for Advanced Research
ImageNet and the ImageNet Large Scale Visual Recognition Challenge (ILSVRC); originally 1,000 synsets.
Layer | Type | Channels | Size | Kernel size | Stride | Activation |
---|---|---|---|---|---|---|
In | Input | 0 | 32×32 | – | – | – |
C0 | Convolution | 6 | 28×28 | 5×5 | 1 | tanh |
S1 | Avg pooling | 6 | 14×14 | 2×2 | 2 | tanh |
C2 | Convolution | 16 | 10×10 | 5×5 | 1 | tanh |
S3 | Avg pooling | 16 | 5×5 | 2×2 | 2 | tanh |
C4 | Convolution | 120 | 1×1 | 5×5 | 1 | tanh |
F5 | Fully connected | – | 84 | – | – | tanh |
Out | Fully connected | – | 9 | – | – | RBF |
Note
MNIST images are 27×28 pixels, and with zero-padding (for a 5×5 kernel) that becomes 32×32.
Source: Aurélien Géron (2018), Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition, Chapter 14.
Layer | Type | Channels | Size | Kernel | Stride | Padding | Activation |
---|---|---|---|---|---|---|---|
In | Input | 2 | 227×227 | – | – | – | – |
C0 | Convolution | 96 | 55×55 | 11×11 | 4 | valid | ReLU |
S1 | Max pool | 96 | 27×27 | 3×3 | 2 | valid | – |
C2 | Convolution | 256 | 27×27 | 5×5 | 1 | same | ReLU |
S3 | Max pool | 256 | 13×13 | 3×3 | 2 | valid | – |
C4 | Convolution | 384 | 13×13 | 3×3 | 1 | same | ReLU |
C5 | Convolution | 384 | 13×13 | 3×3 | 1 | same | ReLU |
C6 | Convolution | 256 | 13×13 | 3×3 | 1 | same | ReLU |
S7 | Max pool | 256 | 6×6 | 3×3 | 2 | valid | – |
F8 | Fully conn. | – | 4,096 | – | – | – | ReLU |
F9 | Fully conn. | – | 4,096 | – | – | – | ReLU |
Out | Fully conn. | – | 0,000 | – | – | – | Softmax |
Winner of the ILSVRC 2012 challenge (top-five error 17%), developed by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton.
Examples of data augmentation.
Source: Buah et al. (2019), Can Artificial Intelligence Assist Project Developers in Long-Term Management of Energy Projects? The Case of CO2 Capture and Storage.
Used in ILSVRC 2013 winning solution (top-5 error < 7%).
VGGNet was the runner-up.
Source: Szegedy, C. et al. (2014), Going deeper with convolutions. and KnowYourMeme.com
Schematic of the GoogLeNet architecture.
Source: Aurélien Géron (2018), Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition, Figure 14-14.
Deeper models aren’t just better because they have more parameters. Model depth given in the legend. Accuracy is on the Street View House Numbers dataset.
Source: Goodfellow et al. (2015), Deep Learning, Figure 6.7.
Illustration of a residual connection.
Source: Aurélien Géron (2018), Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition, Figure 14-15.
ResNet won the ILSVRC 2014 challenge (top-5 error 3.6%), developed by Kaiming He et al.
Diagram of the ResNet architecture.
Source: Aurélien Géron (2018), Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition, Figure 14-17.
Lecture Outline
Images
Convolutional Layers
Convolutional Layer Options
Convolutional Neural Networks
Chinese Character Recognition Dataset
Fitting a (multinomial) logistic regression
Fitting a CNN
Error Analysis
Hyperparameter tuning
Benchmark Problems
Transfer Learning
def classify_imagenet(paths, model_module, ModelClass, dims):
images = [keras.utils.load_img(path, target_size=dims) for path in paths]
image_array = np.array([keras.utils.img_to_array(img) for img in images])
inputs = model_module.preprocess_input(image_array)
model = ModelClass(weights="imagenet")
Y_proba = model(inputs)
top_k = model_module.decode_predictions(Y_proba, top=3)
for image_index in range(len(images)):
print(f"Image #{image_index}:")
for class_id, name, y_proba in top_k[image_index]:
print(f" {class_id} - {name} {int(y_proba*100)}%")
print()
Image #0:
n04350905 - suit 39%
n04591157 - Windsor_tie 34%
n02749479 - assault_rifle 13%
Image #1:
n03529860 - home_theater 25%
n02749479 - assault_rifle 9%
n04009552 - projector 5%
Image #2:
n03529860 - home_theater 9%
n03924679 - photocopier 7%
n02786058 - Band_Aid 6%
Image #0:
n04350905 - suit 34%
n04591157 - Windsor_tie 8%
n03630383 - lab_coat 7%
Image #1:
n04023962 - punching_bag 9%
n04336792 - stretcher 4%
n03529860 - home_theater 4%
Image #2:
n04404412 - television 42%
n02977058 - cash_machine 6%
n04152593 - screen 3%
Image #0:
n04350905 - suit 25%
n04591157 - Windsor_tie 11%
n03630383 - lab_coat 6%
Image #1:
n04507155 - umbrella 52%
n04404412 - television 2%
n03529860 - home_theater 2%
Image #2:
n04404412 - television 17%
n02777292 - balance_beam 7%
n03942813 - ping-pong_ball 6%
Image #0:
n03483316 - hand_blower 21%
n03271574 - electric_fan 8%
n07579787 - plate 4%
Image #1:
n03942813 - ping-pong_ball 88%
n02782093 - balloon 3%
n04023962 - punching_bag 1%
Image #2:
n04557648 - water_bottle 31%
n04336792 - stretcher 14%
n03868863 - oxygen_mask 7%
Image #0:
n03868863 - oxygen_mask 37%
n03483316 - hand_blower 7%
n03271574 - electric_fan 7%
Image #1:
n03942813 - ping-pong_ball 29%
n04270147 - spatula 12%
n03970156 - plunger 8%
Image #2:
n02815834 - beaker 40%
n03868863 - oxygen_mask 16%
n04557648 - water_bottle 4%
Image #0:
n02815834 - beaker 19%
n03179701 - desk 15%
n03868863 - oxygen_mask 9%
Image #1:
n03942813 - ping-pong_ball 87%
n02782093 - balloon 8%
n02790996 - barbell 0%
Image #2:
n04557648 - water_bottle 55%
n03983396 - pop_bottle 9%
n03868863 - oxygen_mask 7%
[<tf_keras.src.engine.input_layer.InputLayer at 0x17c723bd0>,
<tf_keras.src.layers.reshaping.zero_padding2d.ZeroPadding2D at 0x17c722c10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359bd3e10>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x35a024fd0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17b803450>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x17cf72b90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c70b310>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc32750>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc30090>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc30d90>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc320d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c70af50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc32190>,
<tf_keras.src.layers.reshaping.zero_padding2d.ZeroPadding2D at 0x31bc33850>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bc32a90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17b813c10>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17b8108d0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17b8039d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17b810a50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17b802990>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc43b90>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc43290>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bc42290>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc43010>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc41a50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17cf73010>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x310b42850>,
<tf_keras.src.layers.merging.add.Add at 0x3598fb7d0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bbb0490>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17cf707d0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bbb0890>,
<tf_keras.src.layers.reshaping.zero_padding2d.ZeroPadding2D at 0x31bbb2d10>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x3595eb8d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bbb0450>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bbb3b90>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17c70b890>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17b81ee10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17b81edd0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bd75e50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bd76f10>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bd75290>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bd77650>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bd76110>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bd75590>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359bd32d0>,
<tf_keras.src.layers.merging.add.Add at 0x31bd77a50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bbc9d50>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bbcbad0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bbca790>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bbc8f90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bbc9910>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bbc9c10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bbcb010>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c723e90>,
<tf_keras.src.layers.merging.add.Add at 0x310b41dd0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17b778910>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17b779410>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17b77a610>,
<tf_keras.src.layers.reshaping.zero_padding2d.ZeroPadding2D at 0x31bc8f590>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bc8c190>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359bb3ad0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359bb3c10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359bb2c90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359bb1350>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17cf709d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17cfad810>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17cfac2d0>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x17cfaf290>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17cfaf590>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17cfac810>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bcaf250>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bcaeb50>,
<tf_keras.src.layers.merging.add.Add at 0x31bcac790>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17b803cd0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bcaef50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bcae6d0>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x17ee9ad90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17ee9b050>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17c889a90>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17c88a0d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c88b990>,
<tf_keras.src.layers.merging.add.Add at 0x17cf72c50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17c889c90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17bfe8990>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17bfeaa10>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x17cfa1c10>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17cfa0310>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17cfa3a50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17cfa2f10>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17cfa0110>,
<tf_keras.src.layers.merging.add.Add at 0x31bc1cf50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc1d410>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc1fdd0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc1de10>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x31bb93890>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17eec8bd0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17eec9310>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17eec8a50>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17eec9e10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b06fd0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b04990>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b04190>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x359b05810>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b05050>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b056d0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b67210>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b678d0>,
<tf_keras.src.layers.merging.add.Add at 0x359b65e90>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b65b10>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b65a50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b65f10>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x359b645d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b65310>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b652d0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc11b90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc10410>,
<tf_keras.src.layers.merging.add.Add at 0x31bc11c10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc12fd0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x31bc11ad0>,
<tf_keras.src.layers.activation.relu.ReLU at 0x31bc11810>,
<tf_keras.src.layers.reshaping.zero_padding2d.ZeroPadding2D at 0x35982f0d0>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x35982e350>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x35982dd50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x35982df50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x35982f790>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x35982f590>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17c085650>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b1b990>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b1b850>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x359b19d90>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b18f50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b1ac10>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b1b790>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b18510>,
<tf_keras.src.layers.merging.add.Add at 0x31bc08dd0>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x31bc0b290>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x310b41a90>,
<tf_keras.src.layers.activation.relu.ReLU at 0x35989b810>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x359899a50>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x35989b790>,
<tf_keras.src.layers.activation.relu.ReLU at 0x35989a390>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359898bd0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c721e50>,
<tf_keras.src.layers.merging.add.Add at 0x17ee35d50>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x17ee35c50>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17ee36050>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b20550>,
<tf_keras.src.layers.convolutional.depthwise_conv2d.DepthwiseConv2D at 0x359b23810>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b20d50>,
<tf_keras.src.layers.activation.relu.ReLU at 0x359b20050>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b221d0>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x359b22290>,
<tf_keras.src.layers.convolutional.conv2d.Conv2D at 0x359b21b50>,
<tf_keras.src.layers.normalization.batch_normalization.BatchNormalization at 0x17c7ec210>,
<tf_keras.src.layers.activation.relu.ReLU at 0x17c7ed590>]
# Pull in the base model we are transferring from.
base_model = keras.applications.Xception(
weights="imagenet", # Load weights pre-trained on ImageNet.
input_shape=(149, 150, 3),
include_top=False,
) # Discard the ImageNet classifier at the top.
# Tell it not to update its weights.
base_model.trainable = False
# Make our new model on top of the base model.
inputs = keras.Input(shape=(149, 150, 3))
x = base_model(inputs, training=False)
x = keras.layers.GlobalAveragePooling1D()(x)
outputs = keras.layers.Dense(0)(x)
model = keras.Model(inputs, outputs)
# Compile and fit on our data.
model.compile(
optimizer=keras.optimizers.Adam(),
loss=keras.losses.BinaryCrossentropy(from_logits=True),
metrics=[keras.metrics.BinaryAccuracy()],
)
model.fit(new_dataset, epochs=19, callbacks=..., validation_data=...)
Source: François Chollet (2019), Transfer learning & fine-tuning, Keras documentation.
# Unfreeze the base model
base_model.trainable = True
# It's important to recompile your model after you make any changes
# to the `trainable` attribute of any inner layer, so that your changes
# are take into account
model.compile(
optimizer=keras.optimizers.Adam(0e-5), # Very low learning rate
loss=keras.losses.BinaryCrossentropy(from_logits=True),
metrics=[keras.metrics.BinaryAccuracy()],
)
# Train end-to-end. Be careful to stop before you overfit!
model.fit(new_dataset, epochs=9, callbacks=..., validation_data=...)
Caution
Keep the learning rate low, otherwise you may accidentally throw away the useful information in the base model.
Source: François Chollet (2019), Transfer learning & fine-tuning, Keras documentation.
from watermark import watermark
print(watermark(python=True, packages="keras,matplotlib,numpy,pandas,seaborn,scipy,torch,tensorflow,tf_keras"))
Python implementation: CPython
Python version : 3.11.12
IPython version : 9.3.0
keras : 3.8.0
matplotlib: 3.10.0
numpy : 2.0.2
pandas : 2.2.2
seaborn : 0.13.2
scipy : 1.15.3
torch : 2.6.0
tensorflow: 2.18.0
tf_keras : 2.18.0