# MDM Coverage Experiments CPU experiments and finite-state verification code accompanying the study of accuracy--depth tradeoffs for parallel masked sampling. The repository contains the source, frozen configurations, raw finite-dimensional results, arithmetic certificates, logs, and publication figures for three experiment phases. The experiments are deterministic finite sums, linear programs, and exact or outward-rounded rational checks. They do not train a neural model and do not require a GPU. They are diagnostic and verification artifacts for selected finite instances; they are not a formal proof assistant, a global minimax optimizer, or an empirical claim about natural-language models. ## Repository layout | Path | Contents | | --- | --- | | `src/`, `configs/` | Phase 1 model/execution diagnostics and randomized-policy LPs | | `results/run-20260916-phase1-v1/` | Frozen Phase 1 source snapshot, JSON outputs, policies, logs, and figures | | `phase2/src/`, `phase2/configs/` | Phase 2 finite witness search and independent certification | | `phase2/results/run-20260916-phase2-certified-v2/` | Certified Phase 2 witnesses, certificates, recovery audit, and figures | | `phase3/` | Phase 3 fixed-schedule comparison and biased-pair pilot | | `phase3/results/run-20260916-phase3-v1/` | Frozen Phase 3 outputs, certificates, logs, and figures | | `.venv/` | Original server-side virtual-environment wrapper, retained intentionally | | `requirements.txt` | Minimal Python packages actually imported by the experiment code | Each phase has a `PROTOCOL.md` describing its scientific scope, resource limits, controls, and interpretation. Each frozen result directory contains a `status.json` with source/configuration hashes and stage status. ## Environment The reported runs used: - Python 3.13.13 - NumPy 2.2.6 - SciPy 1.17.1, including HiGHS - Matplotlib 3.10.9 - one CPU numerical-library thread - no GPU The committed `.venv` was created on the original Linux server with `--system-site-packages`. It points to `/root/userdata/liangyan/miniconda3/bin/python3.13`; therefore it is retained as an environment artifact but is **not portable** to another server or operating system. On the original server it can be activated with: ```bash cd /root/userdata/liangyan/mdm_coverage_experiments source .venv/bin/activate ``` For a fresh clone, create a local environment instead: ```bash git clone git@github.com:yanliang3612/mdm_coverage.git cd mdm_coverage python3 -m venv .venv-local source .venv-local/bin/activate python -m pip install --upgrade pip python -m pip install -r requirements.txt ``` Use a single numerical-library thread for every run: ```bash export OMP_NUM_THREADS=1 export OPENBLAS_NUM_THREADS=1 export MKL_NUM_THREADS=1 export NUMEXPR_NUM_THREADS=1 export MPLBACKEND=Agg ``` Basic checks: ```bash python src/check_environment.py python src/verify_main_examples.py python phase2/verify_exact_target_control.py \ --source phase2/src/certify_witness.py \ --output phase2/exact_target_control.json ``` ## Phase 1: model and execution diagnostics Phase 1 contains three experiments: 1. **E1:** model KL/TV versus the two-round all-A/all-B execution error. 2. **E2:** self-generated pilot size, posterior drift, and output TV. 3. **E3:** a small-dimensional occupation-measure LP over randomized adaptive policies for a fixed oracle. Run the complete Phase 1 pipeline with a new run identifier: ```bash python src/run_study.py \ --config configs/phase1.json \ --run-id run-YYYYMMDD-phase1-local ``` The runner executes regression checks, E1, E2, E3, and plotting in order. It refuses to overwrite an existing result directory. To run individual stages: ```bash mkdir -p scratch/phase1 python src/e1_model_execution.py --config configs/phase1.json --output scratch/phase1/e1.json python src/e2_pilot.py --config configs/phase1.json --output scratch/phase1/e2.json python src/e3_policy_lp.py --config configs/phase1.json --output scratch/phase1/e3.json ``` To regenerate figures for a completed run: ```bash python src/plot_results.py --run-dir results/run-YYYYMMDD-phase1-local ``` The original complete run is `results/run-20260916-phase1-v1/`. ## Phase 2: finite all-policy witness search and certification Phase 2 first searches a prespecified finite family using floating-point LPs, then independently verifies selected witnesses using exact rational oracle heads, a full-action Bellman recursion, downward-rounded probability flow, and explicit logarithm enclosures. Fast smoke run: ```bash python phase2/src/run_phase2.py \ --config phase2/configs/phase2.json \ --run-id run-YYYYMMDD-phase2-smoke \ --smoke ``` Full search and certification: ```bash python phase2/src/run_phase2.py \ --config phase2/configs/phase2.json \ --run-id run-YYYYMMDD-phase2-full ``` The historical full run reached the 120-second limit for two selected K=4 LPs. `finalize_phase2.py` performs only the narrowly scoped IPM recovery permitted by the frozen protocol, preserves the original failures, and then reruns all exact certification and plotting stages. The archived recovery chain can be replayed to a **new** output directory with: ```bash python phase2/src/finalize_phase2.py \ --base-run phase2/results/run-20260916-phase2-v1 \ --output-run phase2/results/run-YYYYMMDD-phase2-certified-replay \ --config phase2/configs/phase2.json \ --reuse-retry phase2/results/retry-n16-B002-K4-ipm.json ``` The certified paper-facing run is `phase2/results/run-20260916-phase2-certified-v2/`. Certification intervals are deterministic arithmetic enclosures, not Monte Carlo confidence intervals. ## Phase 3: schedule comparison and biased-pair pilot Phase 3 reuses the nine certified Phase 2 witnesses. It compares geometric, equal-size, exhaustive fixed-label, and randomized-label batch schedules, then runs a bounded biased-representative experiment with an expanded pair-state kernel. The checked-in `phase3/inputs/` contains the frozen witnesses and certificates used by the reported run. Run the full Phase 3 pipeline with: ```bash python phase3/run_phase3.py \ --run-id run-YYYYMMDD-phase3-local ``` This runs the schedule benchmark, biased pilot, summary validation, and plots. To use a newly certified Phase 2 run, replace the two frozen inputs first: ```bash cp phase2/results/RUN_ID/witnesses.json phase3/inputs/witnesses.json cp phase2/results/RUN_ID/certificates.json phase3/inputs/certificates.json ``` To create a separate, data-identical presentation revision for a completed Phase 3 run: ```bash python phase3/publish_figures.py \ --run-dir phase3/results/run-YYYYMMDD-phase3-local \ --plotter phase3/plot_phase3.py ``` The original complete run is `phase3/results/run-20260916-phase3-v1/`. ## Output conventions - Run identifiers must start with `run-` and must be unique. - Runners create new directories and refuse to overwrite prior results. - `status.json` is the authoritative completion record. - Logs and failed cases are retained rather than silently discarded. - PDF and 300-dpi PNG figures are both preserved. - Exact certificates and floating-point exploratory diagnostics are labeled separately. ## Scientific scope Phase 1 illustrates finite mechanisms. Phase 2 certifies all-policy error brackets for selected finite exchangeable models but searches only a finite outer family. Phase 3 compares restricted schedules and studies a small biased model. None of these computations replaces the manuscript's analytic proofs, establishes an asymptotic exponent by curve fitting, or certifies performance on language data. The plotting palette was inspired by [`figures4papers`](https://github.com/ChenLiu-1996/figures4papers/); the numerical methods and implementations are independent of that repository. ## License No software license has been added. Public visibility alone does not grant a license to reuse the code. Add an explicit software license separately if reuse permissions are desired.