l2_penalty

std.loss.l2_penalty · Level L0

L2 weight penalty. Calls frobenius_sq.

λ·‖W‖²_F

Signature

l2_penalty(W: f64[k, n], lam: f64[]) → f64[]

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.

Wf64[k, n]lamf64[]frobenius_sqfMultiplyppf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference lam * np.sum(W ** 2) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 72% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
63%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.43

Identity

Calls
frobenius_sq
Called by
—
sha256:04bbd2b304fc1dbdcb07503b57b9a9bf1b8788e5113b2ff9e45f3a6c0a5d2f38

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

Control handle

Symbol
Ω:std.loss.l2_penalty · Ω:l2_penalty
Pins
sha256:60291efc994ec30a754fa15e4130a08c0b448030fc32066d7a1a433aa7ed13ffthis graph and the 1 it reaches through calls
Evidence
sha256:81e737fecfdb52f9afdaec463f6ba344b48724d1df6cde2a039b81278db734bfthe 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.