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 another library function this one runs — called once, or by Scan once per element; select it to open that function.

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 where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

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.

Control handle

Symbol: Ω:std.elementwise.elu · Ω:elu
Pins: sha256:ea4f74a50dd80dbf45cabb99329256e0099884ac5e379565bd36953d0c1cd785this graph alone
Evidence: sha256:c8cfd7c239e2d37b80331d87d69e352e94a7978741651747b2c8c8425eee7e4cthe 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.