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REPORT.md

@@ -328,8 +328,11 @@ change the task's structure.)
 
 **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)
 
@@ -543,19 +546,26 @@ about the levers - which this study tests and which it does not:
 
 ## 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.