prose catch-up: what-remains tested/untested, reproduce stages 3-5, dense dynamics

make_report.py

@@ -835,8 +835,11 @@ def report(evals, rows):
         "",
         "**Observation:** rec-4x4 reaches ~1.0 in-distribution by ~7.5k",
         "steps; fixed-4 plateaus near ~0.47 and is still softening at 25k;",
-        "fixed-4-long reaches 0.72 by 100k. The learning *rate* differs",
-        "dramatically even when parameters are identical.",
+        "fixed-4-long reaches 0.72 by 100k. The dense v2 variant reaches",
+        "1.0 by ~12.5k despite its variable-depth readout - the dense",
+        "targets act as a curriculum (unroll 1 learns the lookup first).",
+        "The learning *rate* differs dramatically even when parameters are",
+        "identical.",
         "",
         "### 4.6 Full table (per seed)",
         "",
@@ -1003,21 +1006,28 @@ def report(evals, rows):
         "",
         "## 7. What remains",
         "",
-        "- More seeds to tighten the OOD family means (esp. rec-4x4).",
-        "- Aligned follow-ups: deeper aligned stacks (rec-4x-aligned),",
-        "  overshoot training (R = k + margin), and training k up to 16 to",
-        "  see whether the frontier tracks the data limit again.",
-        "- Per-iteration supervision toward f^t(x) at every unroll",
-        "  (Fan et al. 2409.15647) - related to alignment but gives dense",
-        "  per-step signal; untested here.",
-        "- Adaptive halting, curriculum on k, and larger-scale runs",
-        "  (see the discussion in section 5).",
+        "- More seeds to tighten the OOD family means (esp. rec-4x4 and the",
+        "  m4+dense variant, whose k=64 seeds span 0.038-0.116).",
+        "- Growing-k curriculum on the m4+dense recipe (train k up to 16, or",
+        "  a growing schedule): the frontier tracks the data limit in every",
+        "  family that learns, so this is the most promising lever - but the",
+        "  OOD step embeddings (>11) would need training coverage too.",
+        "- Supervising every unroll toward f^t(x) without the hold-rule",
+        "  (Fan et al. 2409.15647): our dense variant uses hold-after-k",
+        "  targets f^{min(t,k)}(x); the no-hold variant is untested and",
+        "  would compose chains past k - possibly the strongest test of",
+        "  whether the recurrence can generalise at all.",
+        "- Deeper aligned stacks (rec-4x m4+dense) and adaptive halting.",
+        "- Larger-scale runs (see the discussion in section 5).",
         "",
         "## 8. Reproduce",
         "",
-        "See README.md. `run_all.py` drives lrsweep/stage1/stage2/eval;",
-        "`evaluate.py` produces the per-checkpoint JSONs; `make_report.py`",
-        "generates this report and every figure. Live dashboards:",
+        "See README.md. `run_all.py` drives lrsweep/stage1/stage2/stage3/",
+        "stage4/stage5/eval: stage1-2 are the matched-FLOP and iso-param",
+        "families, stage3-4 the R=k aligned variant (25k and 100k steps),",
+        "stage5 the v2 margin/stem/dense variants. `evaluate.py` produces",
+        "the per-checkpoint JSONs; `make_report.py` generates this report",
+        "and every figure. Live dashboards:",
         "eac123/ptr-recurrent-depth-trackio.",
     ]
     return "\n".join(lines)