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When adding new scripts, document their environment variables near the top of
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the file and list them here for quick reference.
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HMT order comparison (`hmt_order_comparison.jl`):
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-`AHMT_SEED` (default `1`) – RNG seed.
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-`AHMT_B` (default `2`) – branching factor.
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-`AHMT_DEPTH` (default `8`) – tree depth.
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-`AHMT_K` (default `4`) – number of states per node.
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-`AHMT_TRIALS` (default `10`) – timing samples when timing is enabled.
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-`AHMT_MODE` (default `frontier`) – `frontier` (frontier/proxy only), `timed` (time all listed orders), or `dfs` (time DFS only). We avoid timing BFS when its proxy is enormous.
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Reproduce figures (PDFs in `experiments/figures`):
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```
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julia --project=JuliaBUGS/experiments experiments/plotting/make_figures.jl
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```
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Tables included in the draft live in `experiments/tables/` and are generated from CSV outputs under `experiments/results/`.
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When adding new scripts, document their environment variables near the top of the file and list them here for quick reference.
- Notes: Implemented sticky prior in-gradient via deterministic `diagshift` primitive to keep single-assignment and AD friendliness; validates end‑to‑end gradients with z marginalized.
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## 2025-09-24 — HMT order comparison (frontier-only; DFS timed)
- Notes: BFS exhibits a large frontier (≈65 at depth 8) and a much larger cost proxy than DFS/randomized-DFS (≈8), consistent with tree pathwidth intuition. We avoid timing BFS due to proxy-based guard.
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## 2025-09-24 — FHMM order sweep (frontier-only for bad order)
- Normalized `time_over_TK2` (min time divided by `T*K^2`) plateaus for `K≥16` with mean≈1.09e-06 (min 7.49e-07, max 2.54e-06 over 15 cases). For `K=8` it is higher and more variable (mean≈3.39e-06), indicating overhead dominance at small K.
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- Frontier metrics remain near the theoretical minimum (max≈1) for the enforced interleaved order.
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