elu

std.elementwise.elu · Level L1

ELU: the identity for positive inputs, α(eˣ − 1) otherwise.

x if x > 0 else α·(eˣ − 1)

Signature

elu(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 a call to another library function; select it to open that function.

alphaf64[]xf64[n]0.0Expex1.0GreaterposSubtractem1MultiplynegWhereyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.where(x > 0, x, alpha * (np.exp(x) - 1)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 149 float64 results inside the running error bound; the closest uses 50% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
83%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
4.4e+5

Large ulp counts appear only where cancellation drives a result toward zero; the absolute error is still inside the bound.

Identity

Calls
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Called by
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sha256:8fa4736feeaea8dc51eb742864735abc68463d4bee208144ccf9fdeb9ceffd16

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