Skip to content

Explanation

Explanation answers why, not how. These articles cover the design decisions, the trade-offs, and the rejected alternatives behind the parts of this library that carry the most non-obvious reasoning: the GivensMinGRU and DeltaMinGRU composer mixers, and the Triton scan-kernel backend. Where a page needs a function signature or a keyword-argument list, it links to Reference rather than repeating it; where it needs a runnable command, it links to How-to.

Both articles are grounded in the committed measured evidence. Every quantitative claim traces to an artifact in the repository: the multi-seed accuracy ledger behind README.md and experiments/EXPERIMENTS.md, the review-hardened experiments/TECHNICAL_REPORT.md, and the benchmark and conformance tables under experiments/bench/. That includes the results that do not flatter the design, which are stated as plainly as the ones that do.

Articles

  • The expressivity ladder: why the parallel-scan discipline caps what these RNNs can track (the abelian ceiling and the illusion of state), what each rung of the ladder buys against it (fade, flip, turn, read), and what each rung measurably cannot do, including the length decay and the delta-rule comparison.
  • Givens & Delta deep dive: why the non-commutative rung of the ladder gets a richer per-token map in GivensMinGRU, how the brick-wall Givens parameterization is built and why that specific mesh, the chunked-WY mechanism behind DeltaMinGRU's parallel delta-rule composer, the CPU and GPU evidence that separates the two composers on fit reliability, cost, and extrapolation length, the rounds ablation that separates map richness from block size, and the backward-pass design decision that rejected division-based reversal in favor of an exact \(C=1\) stored-state recompute.
  • Triton scan kernels: why the four scan operations are one associative-scan family, how the kernels are laid out (one program per lane, a sequential-in-\(T\) register prefix), the fp32-accumulation and TF32/IEEE precision story, the dispatch seam that keeps the kernels optional, and the measured speedups, including the honest rows where the Triton path is slower than eager.

Where to go next