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REPORT.md

@@ -168,6 +168,8 @@ parameters are:
 | recurrent 4x4 (train R=4) | 1.000±0.000 | 0.209±0.073 | 0.203±0.010 | 0.251±0.124 | 0.269±0.115 |
 | fixed-4 long (100k steps) | 0.716±0.012 | 0.220±0.054 | 0.185±0.071 | 0.171±0.025 | 0.172±0.021 |
 | rec-1x-aligned (train R=k) | 0.106±0.003 | 0.038±0.016 | 0.027±0.012 | 0.017±0.004 | 0.139±0.041 |
+| rec-1x m4 (R=k+4, end-of-chain loss) | 0.262±0.004 | 0.070±0.020 | 0.069±0.029 | 0.029±0.022 | 0.196±0.025 |
+| rec-1x m4+dense (R=k+4, stem, dense loss) | 1.000±0.000 | 0.190±0.060 | 0.114±0.041 | 0.075±0.039 | 0.437±0.002 |
 
 ![headline bars](plots/headline_bars.png)
 
@@ -237,6 +239,8 @@ mappings per cell, mean over seeds):
 | rec-4x4 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
 | fixed-4-long | 1.00 | 1.00 | 1.00 | 0.99 | 0.93 | 0.23 | 0.28 | 0.29 |
 | rec-1x-aligned | 0.06 | 0.05 | 0.07 | 0.10 | 0.10 | 0.12 | 0.17 | 0.18 |
+| m4 | 0.25 | 0.24 | 0.24 | 0.27 | 0.25 | 0.25 | 0.29 | 0.31 |
+| m4+dense | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
 
 | family | k=9 | k=10 | k=11 | k=12 | k=13 | k=14 | k=15 | k=16 |
 |---|---|---|---|---|---|---|---|---|
@@ -247,6 +251,8 @@ mappings per cell, mean over seeds):
 | rec-4x4 | 0.20 | 0.24 | 0.19 | 0.23 | 0.19 | 0.23 | 0.28 | 0.21 |
 | fixed-4-long | 0.21 | 0.19 | 0.22 | 0.21 | 0.22 | 0.21 | 0.25 | 0.22 |
 | rec-1x-aligned | 0.10 | 0.09 | 0.06 | 0.07 | 0.05 | 0.04 | 0.06 | 0.04 |
+| m4 | 0.14 | 0.10 | 0.09 | 0.12 | 0.08 | 0.07 | 0.08 | 0.07 |
+| m4+dense | 0.20 | 0.23 | 0.17 | 0.29 | 0.19 | 0.19 | 0.21 | 0.19 |
 
 ![per-k zoom](plots/perk_zoom.png)
 
@@ -333,6 +339,12 @@ fixed4-long,1,829696,8.741e+15,0.7244,0.1810,0.1340,0.1890,0.1860,1
 rec1aligned,0,240256,2.456e+15,0.1024,0.0470,0.0180,0.0150,0.1260,5
 rec1aligned,1,240256,2.456e+15,0.1093,0.0480,0.0400,0.0220,0.1850,7
 rec1aligned,2,240256,2.456e+15,0.1059,0.0190,0.0220,0.0150,0.1070,4
+rec1m4,0,242048,4.620e+15,0.2638,0.0790,0.0420,0.0130,0.1700,6
+rec1m4,1,242048,4.620e+15,0.2649,0.0470,0.0650,0.0200,0.2200,5
+rec1m4,2,242048,4.620e+15,0.2580,0.0850,0.0990,0.0540,0.1970,7
+rec1m4dense,0,440320,4.620e+15,1.0000,0.2440,0.1550,0.1160,0.4380,4
+rec1m4dense,1,440320,4.620e+15,1.0000,0.1250,0.1120,0.0380,0.4380,4
+rec1m4dense,2,440320,4.620e+15,1.0000,0.2000,0.0740,0.0700,0.4340,4
 ```
 
 ### 4.7 Aligned unrolls: training with R = k (one unroll per hop)
@@ -367,6 +379,55 @@ at one R.
 - prediction (b) **not supported**
 - **100k-step probe (1 seed, 4x budget)**: id acc 0.235, k=16 0.035, k=64 0.015 -> **a slow learner that plateaus**: it climbed 0.10 -> 0.235 by 60k steps, then stayed flat for the last 40k (slope ~0), so the aligned objective is roughly 4-10x slower to optimise than fixed-R training and did not break out of its second plateau by 100k. Why: with supervision only at the end of the chain, the model faces a credit-assignment problem across depths - it must learn to do one hop per unroll AND to stop exactly at depth k, with no per-step signal telling it either. Even the easiest case (k=1: one unroll) stayed unsolved at 25k steps.
 
+### 4.8 v2 aligned variants: margin R = k+4, stem layer, dense supervision
+
+The 4.7 diagnosis says the R=k objective fails because of (i) exact
+halting at depth k, and (ii) no per-step signal. The v2 variants
+(user design) target both, separately:
+
+- **A / m4** (3 seeds): R = k + 4 with end-of-chain supervision
+  only. The margin removes exact halting - the model needs 'at
+  least k unrolls', and can idle for the last 4. Everything else
+  identical to rec-1x4.
+- **B / m4+dense** (3 seeds): R = k + 4, one untied stem block
+  before the loop, and dense supervision - every unroll t gets an
+  auxiliary head predicting f^{min(t,k)}(x), i.e. each unroll does
+  its own hop and then holds. This is the per-step signal the R=k
+  run lacked, and it acts as a curriculum: unroll 1 only has to
+  learn the lookup, later unrolls inherit it.
+
+At evaluation both read out at R = k + 4 for every k - the trained
+inference mode - including k > 8.
+
+*Predictions registered before the runs:*
+
+- (P1) margin alone does **not** rescue learning (the credit-
+  assignment problem, not exact halting, was the blocker); it
+  should learn faster than R=k but plateau low.
+- (P2) dense + stem **does** rescue: >= 0.9 mean accuracy across
+  k = 1..8, and a fixed-R sweep showing a staircase (accuracy high
+  iff k <= R - 4) rather than a peak at one R.
+- (P3) if the fix is real, B extends beyond k=8 better than every
+  existing family (R = k+4 is its trained mode at any k), bounded
+  by OOD step embeddings (unroll indices > 11 were never trained).
+
+*Results:*
+
+**A / m4 (margin, end-of-chain loss):**
+- in-distribution (k=1..8 mean): 0.262±0.004
+- frontier (last k with >=0.9 mean acc): **k=0**
+- k=16 0.070, k=32 0.069, k=64 0.029
+- staircase check (acc high iff k <= R-4): +0.042
+
+**B / m4+dense (margin + stem + dense):**
+- in-distribution (k=1..8 mean): 1.000±0.000
+- frontier (last k with >=0.9 mean acc): **k=8**
+- k=16 0.190, k=32 0.114, k=64 0.075
+- staircase check (acc high iff k <= R-4): +0.634
+- (P1) **supported**
+- (P2) **supported**
+- (P3) **not supported**
+
 ## 5. Conclusions
 
 1. **Recurrent depth buys learnability that neither parameters nor