Top line
2.83xBest measured high-locality schedule versus CSC exact delta. Source: hst-highlocal-payoff-20260630.csv.
Benchmarks
Benchmark evidence for local sparse updates.
HST is benchmarked as an incremental runtime, not as a generic one-shot sparse multiply. The public summary below describes fixture-backed packs and the measurement rules used during technical evaluation.
Methodology
How we benchmark HST fairly.
We compare HST against exact sparse-delta paths a technical team would actually try first: CSC delta, grouped CSC, and hand-tuned tile traversal where appropriate. Every run is interpreted alongside locality, visited nonzero fraction, error, and fallback behavior.
All timing is in-process wall clock against the standalone C++ runtime; HST ships as an embedded library, so there is no transport in the measured path. Publishable reports pin matrix size, seed, update pattern, active columns, tile size, budget, error target, hardware, and date.
Unless a table says otherwise, every number on this page comes from the v10 high-locality sweep run on 2026-06-30 on an Apple M1 Max (arm64, 64 GB), and the raw CSVs for it are published under /benchmarks/.
Operating envelope
HST wins early when updates stay local.
A high-locality v10 sweep at 60k by 60k, run 2026-06-30 on an Apple M1 Max (arm64), pushes the top local schedule to 2.83x over exact CSC. Scattered updates stay below parity, which is the point: route those back to the exact path.
CSC parity
1 dirty tile
4 dirty tiles
8 dirty tiles
fallback context
Source: v10 C++ harness, N=M=60,000, fill 0.90, row fanout 1, B=16 for plotted steady-state curves. Lines include schedule build amortized over repeated lookups.
Active path
10.95xPeak HST win versus active tile traversal in the same v10 sweep. Source: hst-highlocal-sweep-raw-20260630.csv.
Sweep wins
25/30High-locality cases where steady-state HST beat CSC. Scattered cases stay gated. Source: hst-highlocal-sweep-raw-20260630.csv.
Workload
Tiles
Breakeven
32-use / peak
one local tile11 call2.61x / 2.74x
four local tiles41 call2.71x / 2.83x
eight local tiles81 call2.46x / 2.57x
Fixture-backed packs
What the public packs cover.
sketch_surrogate
Hybrid router and locality stress test using low-rank skipped-delta tile sketches under a configured error target.
phi_fast (not currently offered)
A stateful Phi-cache skipped-work recovery harness exists in the tree, but as of the 2026-07-17 x86 run its benchmark entry point crashes the runtime (munmap_chunk(): invalid pointer). We are not publishing results from it and not shipping it in an evaluation pack until that is fixed.
High-locality sweep
The 60k x 60k v10 sweep behind the tables on this page: fixed operator, varied dirty-tile locality and batch width, compared against exact CSC delta. Raw CSVs are published alongside the summary.
Scattered updates
Scattered updates should route to the exact path. The evaluation question is fallback rate and overhead on representative streams, not a universal no-cost promise.
Production context
Real systems rarely scatter uniformly.
Video frames change in localized regions. User activity clusters temporally. Simulation grids perturb around initial conditions. These are the shapes where HST should reduce realized work.
The honest evaluation includes both wins and exits: clustered streams, partly scattered streams, and cases where exact recompute remains the right route. Contact HorneSci for the full benchmark suite, raw CSVs, and customer-specific evaluation package.
Multi-threading
Large batches parallelize by batch column.
When many state vectors update at once, the delta-apply partitions across batch columns. We do not publish a scaling factor here; ask for the run you care about and we will measure it on your shape.
Separately, the delta-propagation rule used by the data-center telemetry hierarchy is specified and machine-checked in TLA+: the model proves that propagating deltas along affected paths yields the same aggregate as a full recompute. It is a proof about the propagation math, not about the threading implementation.
Adaptive heat demo
A million-cell local-update benchmark.
The heat-diffusion demo uses a 1000 x 1000 grid with a moving localized source. It compares full recompute, CSC exact delta, and HST scheduled delta while reporting latency, touched work, and error against the full path. The memory figures on that page are estimates derived from touched nonzeros, not measured allocations, and are labeled as such.