KMeans benchmarks

Fitting with corrected arithmetic

The fit timer includes initialization, Lloyd assignment and mean updates, final assignments, inertia and fitted-state construction. Input preparation and independent verification are outside that timer. Reused contexts exist before the call. Completed iterations and convergence flags remain visible because a faster run that performs a different number of updates needs that context.

Prediction against fitted centers

Prediction timings exclude model fitting. Corrected serial and worker predictions use the same corrected fitted centers. Legacy prediction uses the legacy fitted model, whose centers can differ after the numerical corrections. Prediction still compares every query with every center; workers divide rows without changing the nearest-center tie rule.

Small calls, more centers and iteration limits

All measured workloads remain available, including calls for which pool overhead can dominate. These are deterministic synthetic numerical workloads, not a measurement of clustering quality on a scientific dataset. They expose dimensions, cluster count, seed and iteration cap. These elapsed-time observations stay within the existing work limits; requesting more workers does not increase those limits.

Charged workspace admission

These are checked charged bytes for an individual operation on the recorded ABI. Every listed boundary rejects a budget one byte below its charge and accepts the exact charged budget. The charge is an admission-accounting quantity, not process RSS, peak allocator use or the whole memory footprint. The default workspace limit is 64 MiB, a cap, not a fixed allocation.

Fit admission includes newly fitted centers and labels along with working capacities and bounded controls. Prediction includes its new output and controls, while the existing immutable model is outside that call's charge. Source Tensor storage and host caches, executor internals, callback/context snapshot payloads, opaque ownership and allocator overhead, thread stacks and process RSS are excluded. Worker-private scratch can grow with active lanes. These scopes follow the recorded implementation and ABI; unmeasured workload/operation pairs have no inferred memory value.

Process memory, measured separately

Each RSS sample comes from a fresh process and records the getrusage lifetime high-water mark. The table reports the maximum recorded sample in MiB. It includes executable/runtime overhead, inputs, model state, executor resources and the operation. Prediction RSS also includes the prerequisite serial fit that created that implementation's model. No input baseline has been subtracted. This cannot be read as isolated kernel scratch or compared directly with charged workspace as if they measured the same scope. Platform RSS units are normalized to bytes in the downloadable report.

Accuracy and determinism

The recorded independent numerical oracle passes 14,584 cases, including cancellation in means, tiny residuals, inertia underflow and finite/overflow boundaries. A finite center must remain within the coordinate bounds of its assigned population. Such checks assess the numerical update; they do not establish global optimality for Lloyd clustering. Inertia accumulates the exact squares of the computed Float64 distance norms before final rounding; the distance norms themselves still use floating-point subtraction and hypot.

Corrected serial and admitted 1, 2 and 4 worker executions are compared bitwise in the same binary and floating-point environment: centers, fitted labels, query predictions, inertia, completed iterations and convergence flags. This is a same-build promise; it does not claim identical results across different platforms, compiler versions or math libraries. Legacy results are evaluated separately because correcting numerical behavior can legitimately change them.

Distance ties choose the lowest center index; an empty cluster retains its previous center. Final fitted labels and inertia are recomputed against the returned centers. At an iteration cap or a tolerance stop, those final assignments need not be the memberships used for the last center update. A final center is therefore not asserted to be the mean of the final labels unless the assignments have stabilized.

Validation also covers cancellation, deterministic failures and context reuse. A cancelled or failed call returns no partial successful fitted model or prediction Tensor. All workers must finish before scratch or captured inputs are released. The downloadable report identifies the exact validation and source revisions used for these observations.

Scope and reproduction

Recorded 2026-10-30. Timings use a matched Release build with ThinLTO, strict -fno-fast-math and -ffp-contract=off. Raw observations, build and machine identities, numerical validation, workspace admission and fresh-process RSS samples are downloadable together. Medians and MADs on this page are recomputed from the raw samples; MAD describes sample dispersion, not a confidence interval.

With I completed Lloyd updates, fitting retains O((I+1)NkD) distance work, including final reassignment. Prediction remains O(QkD). Parallelism changes elapsed time, not the declared distance count or admission limits. The fitting cap uses (max_iterations+1)NkD ≤ 50,000,000; prediction uses QkD ≤ 50,000,000, and each Tensor is bounded to one million elements. The cap is checked using the requested iteration maximum, even when fitting converges earlier.

These local CPU measurements do not establish GPU, cluster or universal speedups. Worker counts describe admitted local concurrency, not pinned or dedicated cores. The native KMeans implementation does not extend the bounded aner build Tensor/model lowering subset. Reproduce comparisons using the report's exact source, build flags, dataset generator, seed, controls and timing boundaries; keep verification outside the timed region.

See the KMeans contract, recorded benchmark study, implementation and validation notes, complete local execution example and serial reference example. The standalone benchmark figure and plot reproduction tool present the same evidence in an exportable form. No development runtime package is published with this page.