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REPORT.md

@@ -53,6 +53,15 @@ fixed4-long,1,829696,8.741e+15,0.7244,0.1810,0.1340,0.1890,0.1860,1
   steps, while rec-4x4 (same params, 4x per-step FLOPs) reaches ~0.99+
   by step 7500. This is a compute difference, not a parameter one:
   serial block-applications appear to be the binding resource.
+- **Iso-FLOP test (fixed4-long)**: fixed-4 trained 4x longer (100k
+  steps, same total training FLOPs as rec-4x4) reaches 0.716±0.009
+  in-dist and 0.171±0.018 at k=64 — closing only part of the gap to
+  rec-4x4 (1.000 / 0.251±0.099). At this scale, extra training compute
+  does not substitute for recurrent depth.
+- **Inference-time unroll scaling is seed-dependent**: more unrolls
+  than trained sometimes help a lot (rec-4x4 seed2 0.394→0.401 at R=5;
+  rec-1xdynamic seed1 0.088→0.319 at R=5) but not systematically; the
+  best R for k=64 varies across seeds (1–8).
 - **OOD (k>8) accuracy for fixed-4 is already ~10x chance** early in
   training and slowly rising — consistent with a learned lookup for
   small k failing to compose to large k (theory predicts constant-depth
@@ -71,10 +80,11 @@ fixed4-long,1,829696,8.741e+15,0.7244,0.1810,0.1340,0.1890,0.1860,1
   resolved by pinning huggingface_hub==1.33.0.
 
 ## What remains
-- Fixed-4 at 100k steps (fixed4-long) tests whether the in-dist gap is
-  compute-limited; rec-4x4 vs fixed-4-long at matched total FLOPs is
-  the cleanest iso-compute comparison.
-- Seeds: 3 per stage-1 family, 3 rec-4x4, 2 fixed-4-long (budget cap).
+- The iso-FLOP question is now answered (see fixed4-long above).
+- Seed variance in OOD is large (rec-4x4 k=64: 0.18/0.18/0.39); more
+  seeds would tighten the family means — a natural next grant.
+- Larger S, per-iteration supervision (Fan et al. 2409.15647) and
+  longer training with dynamic-R sampling are untested here.
 
 ## Reproduce
 See README.md; run_all.py drives lrsweep/stage1/stage2; evaluate.py