logsumexp

std.stats.logsumexp · Level L1

log Σ eˣ, computed stably by shifting by the maximum first.

m + log Σᵢ e^(xᵢ − m), m = max x

Signature

logsumexp(x: f64[n]) → 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.

xf64[n]ReduceMaxmSubtractsExpeReduceSumtLoglAddlselsef64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.log(np.sum(np.exp(x))) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 24% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
88%
bit-equal to the NumPy formula in float64
70%
largest error, in units in the last place
1.42

Note

The shift by the maximum keeps every exponent at or below zero, so nothing overflows; the reference, which does overflow for large inputs in float64, agrees exactly in 100-digit arithmetic.

Identity

Calls
—
Called by
log_softmax
sha256:9d5e261c9583fdd79d32cbf18f63c683db1570ba0c2e3fa0088109cdb2aa000a

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

Control handle

Symbol
Ω:std.stats.logsumexp · Ω:logsumexp
Pins
sha256:27d34b4f5478db6d96e98c9be6eaf931dd6d9810e1bcdc7ad09657b0550ff9d2this graph alone
Evidence
sha256:3be2c849216c3f61cd421ec37c766053418631d257370d334fe309864a71778ethe 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.