Machine-Discovered Compact Algorithms Through October 2026

Asked (summary):

What research through October 2026 shows large language models, program synthesis, symbolic regression, evolutionary algorithms, or genetic programming discovering compact mathematical or procedural algorithms — especially for speech prosody, pitch contours, phoneme transitions, or signal processing? For each item: title, authors, year, venue, what was actually demonstrated versus speculative, and limitations, as a table with a source URL.

This map covers 28 selected research items published between 1997 and October 22, 2026 — 12 direct speech, audio, or signal-processing artifact papers and 16 broader algorithm- and equation-discovery papers. It is a selected evidence map, not exhaustive coverage. Notably, none of the 28 items convincingly demonstrates direct discovery of a compact mathematical law for natural-speech F0/pitch contours or phoneme-transition dynamics — the nearby speech work optimizes front ends, mappings, quality estimators, or synthesizer structures instead.

Three decades of evidence: classical evolution gives way to LLM-guided code search — and the prosody-law gap stays open

Each square is one research item, placed by publication year. The top lane holds direct speech, audio, and signal-processing artifacts; the bottom lane holds broader mathematical and program discovery. Hover or tap a square for the paper, venue, and what it demonstrated.

speech / audio / DSP artifact, classical GP or evolution broader discovery, classical GP / symbolic search broader discovery, LLM-guided evolutionary search backed by a secondary source (later literature review)

The strongest direct speech/audio cases evolve explicit artifacts: Brazilian Portuguese letter-to-phoneme programs (epdf.mx), spline-defined cepstral filterbanks beating the mel standard in noise (sinc.unl.edu.ar), and GP speech-quality formulas outperforming ITU-T P.563 (www-dept.cs.ucl.ac.uk).

The modern inflection is LLM-guided evolution: FunSearch's explicit cap-set and bin-packing programs in Nature (nature.com) and AlphaEvolve's rank-48 algorithm for 4×4 complex matrix multiplication, improving Strassen's 1969 rank-49 construction (doi.org).

LLM-based symbolic regression now recovers exact equation forms at scale — FunctionEvolve reports 82.9% symbolic accuracy at 50 attempts on a 129-task benchmark — but recovery of a known benchmark equation is not discovery of a previously unknown law (arxiv.org).

Success across all 28 items hinges on a machine-checkable evaluator and a constrained search space; AlphaEvolve itself states that tasks without an automated evaluator are out of scope, and symbolic recovery collapses under even 1% observation noise (doi.org, arxiv.org).

All 28 items

Click a header to sort; filter by lane; click "more" to expand long Demonstrated, Speculative, and Limitations cells. Blank cells mean the accessible source did not establish that fact. Entries marked "secondary source" are backed by a later paper's literature review rather than the original publication.

Title	Authors	Year	Venue	Demonstrated	Speculative	Limitations	Source

Method: selected research map of 28 items (1997 – Oct 22, 2026) on machine discovery of compact mathematical or procedural algorithms, with emphasis on speech, prosody, and signal processing; one row per item with title, authors, year, venue, demonstrated vs. speculative claims, limitations, and source URL. Lanes and colours are assigned from title and demonstrated text (direct speech/audio/DSP artifact vs. broader discovery; classical GP/evolution vs. LLM-guided search). This is not exhaustive coverage; preprints and theses are labelled by venue; publication year follows the cited source; three sound-synthesis entries rest on a later thesis's literature review (marked); a discovered executable artifact is not necessarily compact, interpretable, novel, or independently validated; blank cells were preserved, not filled in.

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