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Making the Math of Neural Networks Intuitive
When studying new improvements to neural networks, many people run into the following problem:
How do these unfamiliar mathematical concepts relate to neural networks?
This blog overcomes this problem by explaining many required prerequisites from scratch1, and relating them to neural network applications. It focuses on providing intuition via visuals and animation, much like in resources such as 3Blue1Brown.
Not sure where to start? Start with the video below:
Why do Neural Networks use Linear Algebra? – The Visual Intuition of Cat Mathematics
NOTE: Ch 1 (along with many other chapters) is outdated and will be updated later. It is recommended to watch this video instead, which encapsulates the same concepts as Ch 1 but in a better way.
CHAPTER 1: How Neural Networks Reveal Hidden Insights in Data (using Matrix Multiplication)
1.1: How does Matrix Multiplication Guess it’s a Cat from its Face and Body?
1.2: Beware of False Friends in the Matrix?
1.3: Why is the Dot Product used in Matrix Multiplication?
CHAPTER 1 APPENDIX: DUALITY (click to expand)
A1.1: WHY use Basis vectors? The Relativity of Data
A1.2: The Duality of Neurons: As Objects, As Relations
A1.3: The Analogy of the Matrix
CHAPTER 2: How Neural Networks Make Faces Look Younger (using Vector Projection)
2.0: Face Filters, Anime Filters, and Fake People
2.1: Changing Features using Vector Addition
2.2: Conditioning on Features using Orthogonal Projection
2.3: Scoring Semantics using Hyperplanes
Work in Progress:
CHAPTER 3: How Neural Networks Find the Most Important Features in Data (using Eigenvectors)
3.1: Paper Explanation: GANspace
3.3: Paper Explanation: Eigenfaces
Future topics:
- Matrix Decomposition to find neuron combinations
- Fourier transforms and convolution
- Graph neural networks and geometric deep learning equivariance
- Transformers
- Diffusion models
- CLIP and prompt generation
- The Shape of Data and Topological Data Analysis applied to latent space
Appendices:
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Assuming only that a reader has a basic understanding of a foundational topic, or has watched certain videos. Links will be provided to these videos. ↩