leaky_relu

std.elementwise.leaky_relu · Level L0

Leaky ReLU with slope alpha for negative inputs, built from Relu.

relu(x) − α·relu(−x)

Signature

leaky_relu(x: f64[n], alpha: f64[]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

xf64[n]alphaf64[]ReluposNegatenegxRelunegMultiplyleakSubtractyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.where(x > 0, x, alpha * x) in exact rational arithmetic, on all 40 test cases.
  • All 137 float64 results inside the running error bound; the closest uses 44% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
100%
bit-equal to the NumPy formula in float64
95%
largest error, in units in the last place
0.50

Identity

Calls
—
Called by
—
sha256:d0568283550388c3e100564e3effca21bb077e3116674965a73df126278187cb

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol
Ω:std.elementwise.leaky_relu · Ω:leaky_relu
Pins
sha256:ebfd21e7adebe5396ac461684645f8043a272538dc0ccc517f4df869822fbabathis graph alone
Evidence
sha256:f70bae0d2ed3506e27c8c95b60a12b730f600b8d09964fb09aa384fa077001b5the hash of its verification record
Needs
no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.