Explainable AI has been approached from many
viewpoints, but remains still largely a mystery. In these lectures I will present a geometrical explanation for deep learning, with emphasis on convolutional neural nets, and much inspiration of modern brain research, in particular visual perception.
The tutorial consists of three parts:
- We
start with a principled view on deep neural nets, the neuro-mathematics of
self-organization and optimal representations.
We discuss an elegant ‘first principles’ model for the first stages of supervised deep learning. The operators
are differential operators, performing a Taylor expansion/description of the
local structure. This will give us a solid geometric basis for the
first layers in both CNN and vision. We derive
convolution from first principles, construct a visually guided self-driving car
and explain classification networks in detail.
- The second part gives a briefing on modern visual neuroscience: brain imaging techniques, the connectome and
function of the many cells and circuits in the
retina and visual cortex, and the brain pathways for face recognition. We will
exploit brain’s strategies to conserve energy.
- The third part focuses on explaining
the mathematics behind a range of applications in medical image analysis, such as diabetes detection from retinal images, skin tumour detection, tuberculosis detection, and medical image super-resolution.
Incremental context calculations
Layers of the visual system
Examples from:
Geert Litjens, Bram van Ginneken et al., A survey on deep learning in medical image analysis,
Medical Image Analysis, Volume 42, 2017,
Pages 60-88.
Geert Litjens and Bram van Ginneken have been my students.
Cited 9324 times (Google Scholar).
I will present the lectures as a highly
interactive tutorial, almost
completely presented with life coding examples in Mathematica (Wolfram Inc.). The
course notes are all computational essays. Attendees will discover that
this is an ideal environment to study the internal details of deep learning, and combine it with both
deep understanding of - and play interactively with - the underlying
mathematics.
And yes, we will do mathematics, and physics,
and all will be explained visually and intuitively. The approach is focused on
geometric deep learning, and deriving solid insights by exploiting first
principles.
The final hour will be devoted to modern
insights in visual perception, the retinal connectome, and what seems to happen
in the many layers of the visual system in the cortex.
Part of this course material is scheduled
into a forthcoming book by the tutor (Fall 2023).
All the Mathematica notebooks will be made available to the attendees,
so all that is explained during the lectures can be studied at ease later on by doing it. See the downloads section below.
It is highly recommended to acquire Mathematica 13 desktop version
and
have it working during the Summer School classes:
Network construction
and surgery
Explainable AI (XAI) introduction -
PPT
Introduction to Convolutional Neural Networks
Network surgery
Transfer learning
Learning to program in Mathematica in
15 minutes
How does gradient
descent really work?
Applications and
visualizations
Some application examples (few lines program)
- News
aggregator and topic classification
- COVID data analysis
- A camera-driven self
driving car
- Auto-encoder
Data visualization (feature space plots) in 2D and 3D
The Wolfram Neural Network
Repository
Real-time inner layer visualization (with the webcam)
Inner layer visualization for all deeper layers
Google's DeepDream algorithm explained
Backpropagation
Layer differentiation
in neural networks
Symbolic
and numeric differentiation
How does backpropagation really work?
Self organization of
the first layers
The optimal
pixel shape from first principles
Constrained optimization
The first
contextual neighbourhood of a pixel
Proper derivative kernels for discrete data
Template matching
Convolution and the Discrete Fourier Transform
Geometric and unsupervised deep
learning
Learning the first filters with optimally sparse representations
Differential structure & geometric invariants in neural networks
Some famous
invariants from computer vision
Vesselness, corner detection
How to properly describe shape in 2D and 3D?
Regularization: how does it really work?
Steerability of first level CNN
kernels
Lessons from the visual system
Brain imaging methods
Modern insights into
the anatomy and function of the retina
Modern insights into
the anatomy and function of the
visual cortex
Perceptual grouping
Why is the brain so
incredibly energy-efficient?
Final remarks and
wrap-up
Recommended reading:
On neural networks and deep learning:
· B.M. ter Haar
Romeny, Introduction to Artificial Intelligence in Medicine
Download: https://www.neuromath.net/pdf/TerHaarRomeny2021_IntroAIinMedicine.pdf
This is a chapter in Springer-Nature's Reference work on "Artificial Intelligence in Medicine" (1858 pages)
- E. Bernard: Introduction to Machine Learning (written in Mathematica, all free code included)
Book (Amazon / Kindle) and online read / free code: https://www.wolfram.com/language/introduction-machine-learning/
On the visual system:
· David Hubel, Eye,
Brain & Vision, Scientific American Press.
Free download: https://epdf.tips/eye-brain-and-vision.html
· R. Masland: The
Neuronal Organization of the retina
Free download: https://www.cell.com/neuron/pdf/S0896-6273(12)00883-5.pdf
· Eric Kandel: Principles
of Neuroscience 5th ed., chapters 25 – 28
Free download: https://archive.org/details/PrinciplesOfNeuralScienceFifthKANDEL
On Mathematica (= the Wolfram Language):
· Stephen
Wolfram: An elementary introduction to the Wolfram Language
Free download: https://www.wolfram.com/language/elementary-introduction/2nd-ed/
· The Wolfram
Language: Fast introduction for programmers
URL: https://www.wolfram.com/language/fast-introduction-for-programmers/en/