When Neural Networks Clicked

i've been taking an intro to ML course and today something clicked.

i actually understand how neural networks work. not just "data goes in, magic happens, predictions come out." the actual mechanics.

this feels significant.

the journey

before: neural networks are magic boxes inspired by brains that somehow learn things

after: neural networks are just matrices of numbers that get slowly adjusted based on how wrong they are

it's math. it's just math. really clever math, but math.

the core idea (as i understand it)

1. initialize weights randomly
2. pass data through the network (forward pass)
3. see how wrong the output is (loss function)
4. figure out which weights caused the wrongness (backward pass / backpropagation)
5. adjust weights slightly in the right direction (gradient descent)
6. repeat 10 million times

the "learning" is literally just "try, see how wrong, adjust, repeat."

what made it click

honestly? implementing it from scratch.

def forward(x, weights):
    return x @ weights  # matrix multiplication

def loss(prediction, actual):
    return ((prediction - actual) ** 2).mean()  # mean squared error

def backward(x, prediction, actual):
    return 2 * (prediction - actual) @ x.T  # gradient

when you write it yourself, the mystery dissolves. it's not magic. it's loops and math.

the aha moments

1. backpropagation is just calculus chain rule from high school calculus. that's it. you're propagating gradients backward through the network. the name suddenly makes sense.

2. "learning" is optimization we're finding the point in a high-dimensional space where the loss is lowest. gradient descent is just walking downhill.

3. neurons aren't that special a "neuron" is: multiply inputs by weights, add a bias, apply a non-linear function. that's it. the magic is in the scale.

4. deep learning is just... going deeper more layers = more complex patterns. but the core mechanics are the same.

why this matters

six months ago i was freaking out about chatgpt. "AI is magic and i'll never understand it."

now i understand the fundamentals. not at an expert level, but enough to read papers and mostly follow along. enough to implement basic things. enough to have intuition.

AI is still advancing fast and scary. but understanding it makes it less scary.

what's next

• convolutional networks (for images)
• recurrent networks (for sequences)
• transformers (for everything, apparently)
• actually reading the "attention is all you need" paper

the transformer architecture is probably where i'm heading. that's what gpt-4 and all the cool stuff is based on.

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trained my first neural network from scratch today. it classifies handwritten digits. it gets 92% accuracy. i am unreasonably proud.