0027 r2 and explainedvariance vectorize only a single output

0027 — R²'s and ExplainedVariance's unweighted accumulation vectorizes only for a single output

Status: accepted · Date: 2026-08-14

Context

R2.AccumulateUnweighted and ExplainedVariance.AccumulateUnweighted both need two passes over yTrue/yPred per output column — one to accumulate a mean, one to accumulate centred squares and residuals — and both offer a Vector<double>-based fast path (AccumulateUnweightedVectorized) on net10.0.

That fast path is gated on outputCount == 1 && Vector.IsHardwareAccelerated, not on Vector.IsHardwareAccelerated alone. outputCount == 1 is the only shape where rows are contiguous in yTrue/yPred: with more than one output, column col of row row sits at (row * outputCount) + col, a strided access that a Vector<T> load cannot gather from a ReadOnlySpan without scattering it into a temporary first — not how SIMD is written elsewhere in this repository (VectorMath.Dot, Pooling.cs, EmbeddingIndex.Persistence.cs all vectorize over a single contiguous span). outputCount > 1 therefore keeps the scalar loop, which walks the strided layout directly.

Vector.IsHardwareAccelerated is checked independently of the shape condition, and falls through to the same scalar loop on a runtime where Vector<double> is software-emulated — the same guard Pooling.cs and EmbeddingIndex.Persistence.cs check before vectorizing (VectorMath.Dot predates this repository checking it explicitly, per 0001).

Decision

AccumulateUnweighted vectorizes only when both conditions hold:

if (outputCount == 1 && Vector.IsHardwareAccelerated)
{
    AccumulateUnweightedVectorized(...);
    return;
}

Every other combination — multiple outputs, or no hardware acceleration — runs the scalar loop.

Consequences

• R2.cs and ExplainedVariance.cs each carry a one-line pointer to this record at the guard, instead of restating the reasoning inline in both files.
• The vectorized path is a different summation order from the scalar one and is not asserted bit-identical to it; that is a separate question, answered where VectorCompensatedSum is defined (src/DataNet.Metrics/Internal/CompensatedSum.cs), not here.
• A third caller that needs this shape (single contiguous output, two-pass mean-then-residual accumulation) can reuse the same guard rather than re-deriving it — nothing today shares the accumulation itself, only the condition under which it vectorizes.

#321 update: the same two conditions now govern the shared walk. This decision was written about R2 and ExplainedVariance, which carry their own accumulation. Outputs.WeightedMean — the walk mse, mae and RootMeanSquaredError take — kept a scalar loop, and the nightly found the cost of that: 0.60× against numpy at a million rows on a runner with AVX-512, below the gate ../guides/performance.md sets, while r2 on the same run stayed above it. The published table said the same thing more quietly — r2 cost less doing two passes than mse doing one.

Outputs.ScoreVectorized applies this decision's rule unchanged: outputCount == 1 for contiguity, Vector.IsHardwareAccelerated checked apart from it. Measured 1.65× on mse and 1.60× on mae, with r2 re-run as an untouched control.

What is new is which kernels may take it. IResidualKernel gained a sibling, IVectorResidualKernel, rather than a second method: four of the six kernels cannot have a lane-wise form at all — the Tweedie deviances reach Math.Pow and the log errors Math.Log. A single interface would have forced four implementations that could only throw.