tools: expert_atlas — confound-controlled probe harness for the GLM-5.2 expert atlas (#175) (#218)

Probe sweep + affinity analysis + leave-one-prompt-out validation, so anyone can build and
cross-validate the atlas on their own box rather than trusting one machine.

The four traps this harness exists to control (each silently corrupts the atlas):

  --topp     prunes experts by cumulative probability. Measured, same prompt:
             topp=0   -> 21,000 selections across 7,587 distinct experts
             topp=0.7 -> 11,944 selections across 4,687 distinct experts
             It hides 38% of the experts, and it is the recommended speed setting.
  MTP/DRAFT  eusage is incremented inside moe(), BEFORE verification, so rejected
             speculative drafts count experts routed for text never emitted.
  .coli_usage is loaded at startup and accumulates, so a naive STATS dump contains all
             prior history rather than this run.
  autocorrelation: routing within one run is highly correlated, so an expert firing 38
             times during one prompt is ONE observation, not 38. Entropy/chi-square on raw
             selections certifies single-prompt flukes as perfect specialists — analyze.py
             therefore requires affinity to replicate across a category independent prompts.

Result on GLM-5.2 744B int4 (Zen5, CPU routing path), 10 topics x 3 prompts x 64 tokens:

  leave-one-prompt-out accuracy   29/30 = 96.7%   (chance 10%)
  strong specialists (spec>=0.5)  1,041 / 13,260  (7.9%)
  specialisation vs depth         layer 3 ~0.07 -> layers 18-58 ~0.19-0.27
  replication gate rejected       587 single-prompt flukes

The one miss is the interesting part: a Chinese-language poetry prompt classifies as poetry,
not Chinese — routing follows the task over the language.

c/tools/expert_atlas/README.md

@@ -0,0 +1,62 @@
+# Expert Atlas — what does each of the 19,456 experts actually do?
+
+Probe harness for #175. Runs a set of topic-tagged prompts, dumps each run's expert-routing
+histogram, and turns them into a per-expert topic-affinity vector.
+
+```bash
+cd c
+export COLI_MODEL=/path/to/glm52_i4
+./tools/expert_atlas/sweep.sh                             # 30 probes (10 topics x 3 prompts)
+python3 tools/expert_atlas/analyze.py  --stats atlas_out/stats --out atlas_out/experts.json
+python3 tools/expert_atlas/validate.py atlas_out/stats 200 # leave-one-prompt-out check
+```
+
+## Read this before you trust any atlas
+
+Four things silently corrupt this measurement. The sweep script controls all of them; if you
+roll your own, don't skip them.
+
+| trap | effect | control |
+|---|---|---|
+| **`--topp`** | prunes experts by cumulative probability — measured: it hides **38% of the distinct experts** (7,587 → 4,687). It is also the *recommended speed setting*. | `TOPP=0` |
+| **speculative drafts** | `eusage` is incremented inside `moe()`, *before* verification, so **rejected** drafts count. Those are experts routed for text the model never emitted. | `MTP=0 DRAFT=0` |
+| **`.coli_usage`** | is loaded at startup and accumulates, so a naive `STATS` dump contains **all prior history**, not this run. | remove per run (script backs it up and restores) |
+| **autocorrelation** | routing inside one run is highly correlated — the same context routes to the same experts token after token. An expert firing 38 times during one prompt is **one** observation, not 38. Chi-square/entropy on raw selections will certify single-prompt flukes as perfect specialists. | `analyze.py` requires the affinity to **replicate across a category's independent prompts** |
+
+The CUDA expert tier is also not run-to-run deterministic, so the sweep uses `--gpu none`. Tier
+config only decides *where weights live*, not what the router picks, so this costs nothing.
+
+## Method
+
+`analyze.py`:
+
+1. `n[e][c]` — selections of expert *e* while running category *c*
+2. `f[e][c] = n[e][c] / N[c]` — normalise by **category size** (prefill routes the prompt too, so a
+   verbose category would otherwise look busier)
+3. `p(c|e)` — renormalise into a topic distribution per expert, i.e. base-rate corrected. Ranking
+   by raw count instead just rediscovers which experts are popular in general.
+4. `spec(e) = 1 − H(p(c|e)) / log C` — 0 = generalist, 1 = fires for exactly one topic
+5. **replication gate** — an expert is only a candidate specialist for *c* if it fires in ≥2 of *c*'s
+   independent prompts
+
+`validate.py` — leave-one-prompt-out. Build each category's top-K specialist set from its *other*
+prompts, then check which set the held-out prompt's routing actually lands in. If specialisation
+were an artifact of prompt wording, the held-out prompt would not prefer its own category.
+
+## Result on GLM-5.2 744B int4 (Zen5, CPU routing path)
+
+- **Leave-one-prompt-out: 29/30 = 96.7%** (chance 10%). Specialisation is a property of the topic,
+  not of prompt wording.
+- The single miss is instructive: `写一首关于秋天的短诗` ("write a short poem about autumn") is
+  classified **poetry**, not Chinese — routing follows the **task** over the **language**.
+- **Only 7.9% of experts are strong specialists** (spec ≥ 0.5). The "one expert = one topic"
+  picture is wrong for ~92% of them.
+- Specialisation **rises with depth**: layer 3 ≈ 0.07 (generalist, token/syntax level) → layers
+  18–58 ≈ 0.19–0.27.
+- The replication gate removed **587** experts that looked like flawless specialists on one prompt.
+
+## Extending it
+
+`probes.json` is the whole probe set — add categories and prompts. Use **3+ prompts per category
+with varied phrasing**, or the replication gate has nothing to check and you are back to measuring
+one prompt. Keep prompt lengths in a similar band across categories.