AI Mathematics Formulas Cheat Sheet
Key formulas used in Artificial Intelligence and Machine Learning
1. Linear Algebra
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Vector: v = (x1, x2, x3)
Dot Product: A · B = A1B1 + A2B2 + A3B3
Matrix Multiplication: C = A × B
Transpose: A^T
Eigen Equation: Av = λv
2. Probability
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Probability: P(A) = favorable outcomes / total outcomes
Conditional Probability: P(A|B) = P(A ∩ B) / P(B)
Bayes Theorem: P(A|B) = (P(B|A) × P(A)) / P(B)
3. Statistics
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Mean: µ = (x1 + x2 + ... + xn) / n
Variance: σ² = Σ(x − µ)² / n
Standard Deviation: σ = √Variance
4. Calculus
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Derivative: d/dx (x²) = 2x
Gradient: ∇f(x)
Gradient Descent: θ = θ − α × ∇J(θ)
5. Neural Network Activation Functions
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Sigmoid: σ(x) = 1 / (1 + e^-x)
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Tanh: tanh(x) = (e^x − e^-x) / (e^x + e^-x)
ReLU: f(x) = max(0, x)
6. Machine Learning Loss Functions
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Mean Squared Error: MSE = (1/n) Σ (y − ■)²
Cross Entropy: L = − Σ y log(■)
Quick Summary
Math Field
Purpose in AI
Linear Algebra
Vectors, matrices, neural networks
Probability
Predictions and classification
Statistics
Data analysis
Calculus
Optimization of models