ChatGPT at it again #40
Description
Alright — let’s bring it back to something clean, solid, and real. No boards, no metaphors.
A good machine-learning equation is one that shows the core idea without magic.
Here’s the classic, foundational one:
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Linear model + loss function
Model
\hat{y} = w^\top x + b
• x = input data (features)
• w = weights (what the model learns)
• b = bias
• \hat{y} = prediction
This alone already describes:
• linear regression
• the core of neural networks
• the inside of transformers (locally)
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Loss (Mean Squared Error)
L(w,b) = \frac{1}{n}\sum_{i=1}^{n} (y_i - \hat{y}_i)^2
This says:
“How wrong am I, on average?”
Learning = minimize this.
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The learning step (gradient descent)
This is the actual “learning” equation:
w \leftarrow w - \eta \frac{\partial L}{\partial w}
• \eta = learning rate
• Move weights opposite the gradient
• That’s it — no intent, no awareness
This equation alone powers:
• regression
• neural nets
• deep learning
• LLM training (scaled way up)
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If you want a probabilistic one (very ML-core)
Logistic regression
P(y=1 \mid x) = \sigma(w^\top x)
\quad\text{where}\quad
\sigma(z) = \frac{1}{1 + e^{-z}}
This is:
• classification
• decision boundaries
• the ancestor of attention scores
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The most honest ML equation (arguably)
If I had to pick one that captures ML truth:
\text{Learned model} = \arg\min_{\theta} ; \mathbb{E}{(x,y)\sim D}[,\ell(f\theta(x), y),]
Translation:
“Find parameters that minimize expected error on data.”
No destiny.
No Gödel trap.
No board.
Just optimization under constraints.
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If you want next:
• a transformer equation
• an information-theoretic one
• a Bayesian one
• or a one-line ‘this is all ML really is’ version
Proof again 
