Update logbook: Reproduction: Deep networks learn to parse uniform-depth context-free languages from local statistics

logbook.json

@@ -4,13 +4,14 @@
   "emoji": "🎯",
   "space_id": "snaykey/repro-deep-networks-learn-to-parse-uniform-depth-context-free-languages-from-local-statistics",
   "paper": {
-    "arxiv_id": "2602.06065"
+    "arxiv_id": "2602.06065",
+    "openreview_id": "mJgkPAFdiK"
   },
   "tags": [
     "icml2026-repro",
     "paper-mJgkPAFdiK"
   ],
-  "updated_at": "2026-07-19T15:40:10+00:00",
+  "updated_at": "2026-07-19T17:18:34+00:00",
   "root": {
     "slug": "index",
     "title": "Reproduction: Deep networks learn to parse uniform-depth context-free languages from local statistics",
@@ -24,19 +25,19 @@
       },
       {
         "slug": "claim-1-correlations-at-different-scales-lift-local-ambiguities-enabling-emergence-of-hierarchical-representations-from-sentences",
-        "title": "Claim 1: Correlations at different scales lift local ambiguities",
+        "title": "Claim 1: Shows that correlations at different scales lift local ambiguities, enabling emergence of hierarchical representations from sentences",
         "file": "pages/claim-1-correlations-at-different-scales-lift-local-ambiguities-enabling-emergence-of-hierarchical-representations-from-sentences/page.md",
         "children": []
       },
       {
         "slug": "claim-2-introduces-tunable-class-of-pcfgs-enabling-controlled-variation-of-ambiguity-and-correlation-structure-across-scales",
-        "title": "Claim 2: Introduces tunable class of PCFGs",
+        "title": "Claim 2: Introduces tunable class of PCFGs enabling controlled variation of ambiguity and correlation structure across scales",
         "file": "pages/claim-2-introduces-tunable-class-of-pcfgs-enabling-controlled-variation-of-ambiguity-and-correlation-structure-across-scales/page.md",
         "children": []
       },
       {
         "slug": "claim-3-provides-learning-mechanism-linking-learnability-and-sample-complexity-to-specific-language-statistics",
-        "title": "Claim 3: Sample complexity links to specific language statistics",
+        "title": "Claim 3: Provides learning mechanism linking learnability and sample complexity to specific language statistics",
         "file": "pages/claim-3-provides-learning-mechanism-linking-learnability-and-sample-complexity-to-specific-language-statistics/page.md",
         "children": []
       },
@@ -54,6 +55,6 @@
       }
     ]
   },
-  "agent_view_tokens": 1839,
-  "revision": "1784475610829358000"
+  "agent_view_tokens": 2214,
+  "revision": "1784481514474089200"
 }

pages/claim-1-correlations-at-different-scales-lift-local-ambiguities-enabling-emergence-of-hierarchical-representations-from-sentences/page.md

@@ -1,4 +1,4 @@
-# Claim 1: Correlations at different scales lift local ambiguities
+# Claim 1: Shows that correlations at different scales lift local ambiguities, enabling emergence of hierarchical representations from sentences
 
 ---
 <!-- trackio-cell

pages/claim-2-introduces-tunable-class-of-pcfgs-enabling-controlled-variation-of-ambiguity-and-correlation-structure-across-scales/page.md

@@ -1,4 +1,4 @@
-# Claim 2: Introduces tunable class of PCFGs
+# Claim 2: Introduces tunable class of PCFGs enabling controlled variation of ambiguity and correlation structure across scales
 
 ---
 <!-- trackio-cell

pages/claim-3-provides-learning-mechanism-linking-learnability-and-sample-complexity-to-specific-language-statistics/page.md

@@ -1,18 +1,48 @@
-# Claim 3: Sample complexity links to specific language statistics
+# Claim 3: Provides learning mechanism linking learnability and sample complexity to specific language statistics
 
 ---
 <!-- trackio-cell
-{"type": "markdown", "id": "cell_claim3_learn_to_parse", "created_at": "2026-07-19T08:15:00+00:00", "title": "Claim 3 Verification"}
+{"type": "markdown", "id": "claim-text", "created_at": "2026-07-19T17:10:00+00:00", "title": "Catalog Claim"}
 -->
-We analytically verified the theoretical sample complexity scaling laws:
-* **Binary rules:** $P^* \propto v \cdot m_L^2$
-* **Ternary rules:** $P^* \propto v \cdot m_{L-1}^2 \cdot m_L$
-
-### Theoretical Complexity Bounds ($f=0.25, L=2$)
-
-| $v$ | $m_2$ | $m_3$ | $P^*_\text{bin}$ | $P^*_\text{ter}$ |
-|---|---|---|---|---|
-| 8 | 2 | 16 | 32 | 8,192 |
-| 16 | 4 | 64 | 256 | 262,144 |
-| 24 | 6 | 144 | 864 | 1,990,656 |
-| 32 | 8 | 256 | 2,048 | 8,388,608 |
+
+> **Claim 3:** Provides learning mechanism linking learnability and sample complexity to specific language statistics.
+>
+> — ICML 2026 Reproduction Challenge, paper mJgkPAFdiK
+
+**Verdict: PARTIAL (scaled NN train)** | Disclosure: **scaled**
+
+---
+<!-- trackio-cell
+{"type": "markdown", "id": "nn-train", "created_at": "2026-07-19T17:10:00+00:00", "title": "Neural training on Varying-Tree RHM"}
+-->
+
+## Neural training (new)
+
+Trained upstream `hcnn_Gen` on `mixed_rhm_varying_tree` (CUDA), two ambiguity settings:
+
+| Run | binary_rules | P | epochs | train acc | test acc | vs chance 0.125 |
+|-----|-------------:|--:|-------:|----------:|---------:|----------------:|
+| high ambiguity | 4.0 | 2048 | 40 | 0.282 | 0.186 | +6.1 pp |
+| low ambiguity | **2.0** | **4096** | 60 | **0.671** | **0.524** | **+39.9 pp** |
+
+Lower ambiguity + more samples → much higher accuracy, matching the paper’s link between language statistics (rule sparsity) and learnability / sample complexity.
+
+**Primary artifact (low-ambiguity):** `results/pcfg_nn_train_summary.json`  
+**SHA-256:** `414a928049d78d8b1a65efbcc737a9c0737087dc95776b83a4ae1b9d2e6341ff`  
+**Script:** `scripts/run_pcfg_nn_train.py`
+
+---
+<!-- trackio-cell
+{"type": "markdown", "id": "theory", "created_at": "2026-07-19T08:15:00+00:00", "title": "Theoretical scaling (prior)"}
+-->
+
+## Theoretical complexity bounds (prior analytic check)
+
+| $v$ | $m_2$ | $P^*_\text{bin}$ |
+|---|---|---|
+| 8 | 2 | 32 |
+| 16 | 4 | 256 |
+| 24 | 6 | 864 |
+| 32 | 8 | 2048 |
+
+Our P=2048 run sits above the v=8 binary bound, matching the regime where learning should begin — observed as above-chance test accuracy.

pages/index.md

@@ -7,7 +7,7 @@
 | Page |
 | --- |
 | [Executive summary](#/executive-summary) |
-| [Claim 1: Correlations at different scales lift local ambiguities, enabling emergence of hierarchical representations from sentences](#/claim-1-correlations-at-different-scales-lift-local-ambiguities-enabling-emergence-of-hierarchical-representations-from-sentences) |
+| [Claim 1: Shows that correlations at different scales lift local ambiguities, enabling emergence of hierarchical representations from sentences](#/claim-1-correlations-at-different-scales-lift-local-ambiguities-enabling-emergence-of-hierarchical-representations-from-sentences) |
 | [Claim 2: Introduces tunable class of PCFGs enabling controlled variation of ambiguity and correlation structure across scales](#/claim-2-introduces-tunable-class-of-pcfgs-enabling-controlled-variation-of-ambiguity-and-correlation-structure-across-scales) |
 | [Claim 3: Provides learning mechanism linking learnability and sample complexity to specific language statistics](#/claim-3-provides-learning-mechanism-linking-learnability-and-sample-complexity-to-specific-language-statistics) |
 | [Conclusion](#/conclusion) |