Benchmark methodology

A benchmark describes one workload. The current evidence separates activation derivatives, direct Laplacians, repeated Laplacians, and general deep-network jets.

Recorded conditions

The published specialized-path figures use float64 CPU medians over nine timed repeats. Activation measurements use 20,000 tanh inputs and Torch eager execution. Operator measurements use JAX JIT with runtime inputs and weights; compilation is recorded separately.

Successful methods are compared against independent 80-digit references at sampled inputs. Accuracy is evaluated independently from speed. A run that exceeds a memory or time budget has no measured speedup.

Reproduce

Clone the pinned source, install its documented environment, and use the benchmark drivers there:

uv run python benchmarks/derivative_order.py
uv run python benchmarks/laplacian_scaling.py
uv run python benchmarks/polylaplacian_order.py

Inspect each driver's supported arguments before changing dimensions, order, repeats, or budgets. Keep the exact source revision, package versions, dtype, hardware, thread count, compilation policy, and errors with the output.

Interpret fairly

Evaluation time is not end-to-end training time. A specialized contraction should be compared with methods producing the same requested quantity. General deep-network results include cases where JAX Taylor-mode wins. Historical optimizer evidence has its original step budgets and is not a rerun of the current split ecosystem.

The results guide links each measurement and its constraints. Interactive charts on the homepages display recorded data; they do not benchmark the visitor's browser.