Laya × discrete mathematics.
A measured capability study: what a decision model can honestly do around discrete mathematics — and what a deterministic engine does instead. Six suites, seven runnable tutorials, a fine-tune dataset kit, and every run recorded.
Watch the runs.
Four terminal recordings of the actual work — executed live against a running decision server, captured with asciinema, and mirrored verbatim from their public gists. Select a recording below and hit play.
- Capability probe Six suites, 80 calls: routing, verdict gates, formalization, graph properties, answer audit, numeric quiz. 0:27
- The examples workspace The engine's 44-assert self-test, then tutorials t01–t07 end to end. 0:24
- Engine verification All 44 engine checks on the record, 12/12 compiled, byte-identical regeneration, the full suite table with the honest miss lists, and a live smoke call. <1 s
- Publish + verify Commit identities and dates, the ledger of what both feature commits landed, the public gist surface, raw-URL checks, and the deployed site verified. 0:04
- SOC decision-tree A/B The same alerts two ways LIVE: the laya way (typed decisions, calibrated confidence gates, ~1 s and ~300 tokens per alert) beside the standard generative slot (a decode-bound ~25 s LLM turn per alert), with the captured era's audited numbers for the historical contrast. 0:09
Permalinks: probe · examples · verify · publish · A/B
The raw files: probe gist · examples gist · verify gist · publish gist · A/B gist — same-origin mirrors served from /player/ too.
The capability study.
What the shipped checkpoints do zero-shot around discrete mathematics, measured against a live decision server on 2026-10-12 — and what the deterministic engine answers instead, exactly, offline. The pattern that ships: the model routes, tags, and gates; the engine computes, proves, and answers.
| Suite | N | Decision model | The system answer |
|---|---|---|---|
| Domain routing (choice) | 24 | 0.875 | dispatch the routed engine; escalate on humility |
| Formula verdicts (noul) | 16 | 0.688 direct | tau gate → engine; 0.688 → 0.938 gated in the probe framing — and 0.375 direct under a one-line-different state template (prompt-sensitivity is real) |
| Formalization check (noul) | 10 | 0.700 | confident misses on subtle quantifier/implication swaps; counterexamples adjudicate |
| Graph properties (noul) | 8×2 | 0.750 / 0.250 | BFS + 2-coloring: 1.000, microseconds, offline |
| Answer audit (noul) | 10 | 0.600 (mixed) / 0.400 (worded) | systematically nay-biased — a filter a human reads, never a verdict |
| Numeric quiz (choice×4) | 12 | 0.250 = exact chance | compute first, ask later; the model grades the learner |
Where everything lives.
- github.com/dmrobbi/laya-control This study's home: examples/ carries the engine (44-assert self-test), the shared client, the capability probe, tutorials t01–t07, and the training kit (training/make_dataset.py + training/FINETUNE.md, seed-deterministic sample rows shipped in-repo).
- The study write-up (LAYA-DISCRETE-MATH.md) The full measured section: suite tables, miss examples, the gate arithmetic, the training recipe, and the honest-limits checklist.
- The deterministic engine (dm_core.py) Pure-stdlib discrete math: propositional logic, set-identity counterexamples, number theory, counting, graph algorithms, recurrences.
- The recordings (gists + mirrors) Probe: 8bc162c9 · Examples: 8cbc6178 · Verify: 40534e29 · Publish: 12264e3c — on-site mirrors at /player/laya-*.cast.
- The earlier Laya work (/capabilities/laya/) The 300-decision comparison reports (power, then the second-node rerun), plus the SOC usage guide and the control-plane demo guide.
- Upstream: NandhaKishorM/laya The model itself — docs, fine-tuning notebooks, benchmarks. Apache 2.0; checkpoints on Hugging Face (convaiinnovations/laya).
Contact
For contracting and capability inquiries:
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