Making Linear Algebra, Calculus & Statistics Visual and Intuitive
Dr. Daya Shankar | Dean, Woxsen University | Founder, VaidyaAI
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Learning Objectives
By the end of this lecture, you will:
Master essential linear algebra concepts through interactive visualizations
Understand calculus concepts crucial for neural network training
Grasp probability and statistics foundations for machine learning
Connect mathematical concepts to neural network operations
Gain confidence in the mathematical tools you'll use throughout the course
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Why Mathematics Powers Deep Learning
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Linear Algebra
Neural networks are essentially matrix operations. Every layer, every weight update,
every computation involves matrices and vectors working together.
Gradient Descent Simulation
Watch how neural networks use gradients to find the minimum error!
๐ฏ What's Happening:
The red dot represents our current guess. The algorithm looks at the slope (gradient) and moves in the opposite direction to find the lowest point (minimum error).
This is exactly how neural networks learn - they minimize their prediction errors!
๐ฒ Probability: Understanding Uncertainty
Probability Distribution Visualizer
Explore different probability distributions used in deep learning
๐ง Neural Network Applications:
Normal Distribution: Weight initialization, noise modeling
Uniform Distribution: Random sampling, dropout masks
Optimization: Move weights in the direction of improvement
W_new = W_old - ฮฑ ยท โLoss/โW
ฮฑ is the learning rate
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Knowledge Check: Mathematical Understanding
Question 1
In the context of neural networks, what does matrix multiplication represent?
A) Just a mathematical operation with no real meaning
B) The transformation of input data through learned weights
C) A way to make calculations more complex
D) A requirement imposed by computer hardware
Perfect! Matrix multiplication in neural networks represents the fundamental operation
where input data is transformed by learned weights. Each weight determines how much influence
each input feature has on the output.
Question 2
Why are derivatives crucial for neural network training?
A) They tell us how to change weights to reduce errors
B) They make the math look more impressive
C) They are required by programming languages
D) They help us calculate the final answer faster
Exactly! Derivatives tell us the rate of change - specifically, how much the error
changes when we adjust each weight. This gradient information guides us on how to improve the network.
Question 3
What role does probability play in neural network predictions?
A) It makes predictions random and unreliable
B) It helps express confidence levels and handle uncertainty
C) It's only used for gambling applications
D) It slows down the computation process
Correct! Probability allows neural networks to express uncertainty in their predictions.
Instead of just saying "this is a cat," they can say "I'm 85% confident this is a cat,"
which is much more useful for decision-making.
๐งฎ Next Up: Perceptron & Neural Basics
Now that you have the mathematical foundation, we'll build your first artificial neuron!
We'll see how the math comes alive in the perceptron - the building block of all neural networks.