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“How much of your current computation is being repeated even though the inputs affecting it never changed?” HKD Kernel is a native C library designed to avoid that waste in persistent workloads: it uses dependency structure to update affected regions rather than recomputing everything. Its author reports a mean speedup of roughly 18,000x across the project’s documented benchmarks, but that result applies to the benchmark workload population—not to arbitrary programs or every application.
What HKD Kernel does
HKD targets exact sparse and incremental computation. The idea is to keep reusable state, track dependencies, and recompute only the parts affected by changed inputs. The correctness requirement is that the incremental result match a full recomputation exactly.
This approach is most relevant when a system runs repeatedly, most inputs and state remain stable between runs, and changes affect only a small portion of the dependency graph. If an update invalidates most of the state, there may be little repeated work to avoid.
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Michael Yang reports a roughly 18,000x measured mean speedup in 2026 across the repository’s currently documented benchmark suite, comparing full recomputation with HKD’s incremental path. The figure describes that repository workload population, especially cases with sparse changes and reusable state; it is not an independent study or a performance guarantee for other workloads. As the author puts it, “This does not mean HKD makes arbitrary programs 18,000x faster.” The project repository is the place to inspect the benchmark code and the workloads behind the claim.
#1 Best Overall
A mean can conceal variation between cases. Before applying the headline number to a design decision, check the individual benchmark cases and whether their changed-state sizes resemble yours. The available project materials do not establish benchmark hardware, compiler flags, repetitions, every per-case result, or an independently reproduced result, so those details should not be assumed.
Workloads that may fit—and where the case is weaker
The project lists several candidate workload classes. These are areas of interest, not evidence of validated deployments or measured application-level wins.
- Dependency graphs and incremental build systems, where a change may affect only a subset of dependent outputs.
- Large simulations and cached numerical pipelines that repeatedly process mostly stable state.
- Optimization, scheduling and assignment, exact-cover, graph-closure, and dependency-propagation problems, where the model and update pattern fall within the library’s supported scope.
- Financial or risk recomputation, logistics, and other repeated calculations with sparse changes.
The key fit question is not simply whether a task is large. It is whether the same state can be reused safely and whether each update touches a small enough fraction of it to make incremental bookkeeping worthwhile. Workloads that frequently replace most inputs or require rebuilding nearly all results may favor full recomputation.
How to evaluate the speedup fairly
Compare methods only when they solve the same problem and meet the same correctness standard. For an incremental workload, record the following for both the reference and HKD paths:
- Cold or full-reference execution time and HKD update execution time.
- Dirty-set size and total-state size, so the amount of changed work is visible.
- Whether the incremental result is exactly equal to the full-recomputation result.
For optimization tasks, also record the model class, variable and constraint counts, sparsity, objective value, feasibility, the reference solver’s result, and elapsed time. A faster result is not a fair comparison if the methods solve different formulations or satisfy different correctness requirements.
How HKD fits alongside established solvers
The repository presents HKD as an additional computation or optimization engine, not a feature-for-feature replacement for broad general-purpose solvers. Established solvers support more model families and features. HKD is more plausibly useful when a workload belongs to a supported model class or has persistent, sparse structure that lets it avoid repeated computation.
HKD is also a user-space library. It does not replace macOS XNU, modify CPU microcode, disable SIP, or change processor ALU hardware. Its performance claim concerns how software organizes computation, not a change to the operating system kernel or processor.
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The repository lists benchmark/, include/, and src/, alongside source, benchmarks, and build instructions. Inspect the benchmark implementation and document the machine, compiler and flags, repetition method, per-case timings, and workload configuration when reproducing the comparison. The surfaced materials do not establish those configuration details, so a reader should report them rather than infer them.
Best Value
Developers can also challenge the benchmark assumptions, propose adversarial cases, share real sparse-update workloads, or identify situations where incremental recomputation is the wrong architecture. Those tests are useful because they expose not only where the method wins, but where the dirty set grows large enough that a full pass is more appropriate.
Quick Recap
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