Mathematics · Level 2 of 5
Gradient
The vector of a scalar function's partial derivatives.
Under Euclidean geometry, it points toward steepest local increase.
Example
An optimizer computes one loss derivative for each parameter.
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Audio transcript
Gradient. The vector of a scalar function's partial derivatives. Under Euclidean geometry, it points toward steepest local increase. For example: An optimizer computes one loss derivative for each parameter.
Explore this concept
A useful analogy
A compass pointing up the steepest local slope, with one component per coordinate.
Why it matters
This notation connects model equations to the calculations implemented in code.
Technical detail
For L: R^n → R, ∇L = [∂L/∂θ₁, …, ∂L/∂θₙ]. The directional derivative along v is ∇L · v.
Common misconception
The gradient points toward local increase; descent uses its negative.
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