From 0b302a9c129ed5754b6f931e27c75dcdd69b7582 Mon Sep 17 00:00:00 2001
From: Jens Ahrensfeld <jens@jayfield.org>
Date: Sun, 31 May 2026 11:42:55 +0200
Subject: [PATCH] [moby_rnn] - add README with architecture ASCII art;
 consolidate constants
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

- README_moby_rnn.md: single-step and temporally-unrolled ASCII diagrams,
  configuration table, notebook cell guide, generation API docs, references
- moby_rnn.ipynb: move all constants (T, NUM_SEQ, EVAL_CHARS, PRED_CHARS,
  N_GIBBS, SEED, SEQ_IDX) into the Build model cell under a Configuration
  header; rename H_SIZE → CONTEXT_SIZE throughout

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
---
 README_moby_rnn.md | 137 ++++++++++++
 moby_rnn.ipynb     | 521 ++++++++++++++++++++-------------------------
 2 files changed, 365 insertions(+), 293 deletions(-)
 create mode 100644 README_moby_rnn.md

diff --git a/README_moby_rnn.md b/README_moby_rnn.md
new file mode 100644
index 0000000..095a3d2
--- /dev/null
+++ b/README_moby_rnn.md
@@ -0,0 +1,137 @@
+# Moby RNN — Character-Level Language Model with Recurrent RBM
+
+A character-level language model built on `StackRnn`, a recurrent Restricted
+Boltzmann Machine where the visible layer at each time step is the concatenation
+of a **context** vector (the previous hidden state) and the current sensory input
+(one-hot encoded character).
+
+---
+
+## Architecture
+
+### Single time step
+
+```
+  Sensory input x_t  (one-hot, vocab_size = 85)
+         │
+         ▼
+  ┌──────────────────────────────────────────┐
+  │           visible layer                  │
+  │  ┌─────────────────┬────────────────┐   │
+  │  │    context_t-1  │      x_t       │   │
+  │  │  (CONTEXT_SIZE) │  (vocab_size)  │   │
+  │  └─────────────────┴────────────────┘   │
+  │                  │                       │
+  │        W  (shared across time)           │
+  │                  │                       │
+  │  ┌───────────────────────────────────┐  │
+  │  │           hidden layer            │  │
+  │  │           context_t               │  │
+  │  │         (CONTEXT_SIZE)            │  │
+  │  └───────────────────────────────────┘  │
+  └──────────────────┬───────────────────────┘
+                     │
+          ┌──────────┴──────────┐
+          │                     │
+          ▼                     ▼
+   context_{t+1}        reconstruct x_t
+   (next time step)     (predict char)
+```
+
+### Temporal unrolling
+
+```
+      x_{t-1}           x_t            x_{t+1}
+         │                │                │
+  ┌──────┴──────┐  ┌──────┴──────┐  ┌──────┴──────┐
+  │  ctx  │x_{t-1}  │  ctx  │ x_t  │  │  ctx  │x_{t+1}│
+  │       ╠═══════╣ │       ╠═══════╣ │       ╠═══════╣
+  │    W (shared)   │    W (shared)   │    W (shared)   │
+  │       ╠═══════╣ │       ╠═══════╣ │       ╠═══════╣
+  │   hidden_t-1  │ │    hidden_t   │ │   hidden_t+1  │
+  └───────┬───────┘ └───────┬───────┘ └───────┬───────┘
+          │   context_t-1   │   context_t      │   context_t+1
+          └────────────────►┘ ────────────────►┘ ──────► ...
+```
+
+Weights **W**, **b_v**, **b_h** are shared across all time steps — the same RBM
+processes every character.  This is the RTRBM concatenation variant: instead of
+modulating the hidden biases (Sutskever & Hinton, 2007), the previous hidden
+state is directly concatenated to the visible layer.
+
+---
+
+## Configuration
+
+All hyperparameters live in the **Build model** cell of `moby_rnn.ipynb`:
+
+| Constant | Default | Description |
+|---|---|---|
+| `T` | 100 | Characters per training sequence |
+| `NUM_SEQ` | 2000 | Number of training sequences (first 200k chars) |
+| `CONTEXT_SIZE` | 512 | Recurrent hidden / context state size |
+| `PRJ_NAME` | `"moby_rnn"` | Checkpoint file prefix |
+| `WORK_DIR` | `"results"` | Directory for saved weights |
+| `EVAL_CHARS` | 2000 | Characters used for reconstruction accuracy |
+| `PRED_CHARS` | 500 | Characters used for next-step prediction |
+| `N_GIBBS` | 10 | Gibbs steps in clamped-Gibbs generation |
+| `SEED` | `"Call me Ishmael."` | Seed text for free generation |
+| `SEQ_IDX` | 42 | Sequence index for the hidden-state trace plot |
+
+Model size with defaults: **(512 + 85) × 512 = 306,176 parameters**.
+
+---
+
+## Notebook walkthrough
+
+| Cell | Title | What it does |
+|---|---|---|
+| 1 | Imports | Standard + rbm imports |
+| 2 | Load text | Reads `data/moby.txt`, builds `char_to_idx` / `idx_to_char` |
+| 3 | Encode sequences | One-hot encodes text → `(NUM_SEQ, T, vocab_size)` array |
+| 4 | **Build model** | All constants; constructs `StackRnn`; loads checkpoint |
+| 5 | Train | Runs CD training; checkpoints every 5% progress |
+| 6 | Generation helpers | `predict_next` (clamped Gibbs) and `generate_text` |
+| 7 | Reconstruction accuracy | Teacher-forced: how well does `h_t` remember `x_t`? |
+| 8 | Next-step prediction | Given `context_{t-1}`, predict `x_t` before seeing it |
+| 9 | Free generation | Generate text at temperatures 0.5 / 1.0 / 1.5 |
+| 10 | Hidden state trace | Heatmap of context activations over one sequence |
+| 11 | Character distribution | Data vs model character frequency comparison |
+
+---
+
+## Training and resuming
+
+Cell 5 saves a checkpoint at every progress report.  Re-run it at any time to
+continue training from the last saved state — `model.state_load()` in cell 4
+picks it up automatically.
+
+```
+results/moby_rnn-0-state.npz   ← single-layer checkpoint
+```
+
+---
+
+## Text generation
+
+`predict_next` uses **clamped Gibbs sampling**: the context vector is held fixed
+while the sensory (character) part of the visible layer runs free for `N_GIBBS`
+steps.  The resulting Bernoulli probabilities are temperature-scaled and
+normalised to a categorical distribution.
+
+```python
+# Generate 500 chars from a seed at temperature 0.8
+text = generate_text(rnn, "Call me Ishmael.", length=500, temperature=0.8)
+```
+
+Lower temperature → more conservative / repetitive output.
+Higher temperature → more diverse / noisier output.
+
+---
+
+## References
+
+- Sutskever & Hinton (2007) — *Learning Multilevel Distributed Representations
+  for High-Dimensional Sequences*
+- Boulanger-Lewandowski et al. (2012) — *Modeling Temporal Dependencies in
+  High-Dimensional Sequences: Application to Polyphonic Music Generation*
diff --git a/moby_rnn.ipynb b/moby_rnn.ipynb
index d609f07..7760f45 100644
--- a/moby_rnn.ipynb
+++ b/moby_rnn.ipynb
@@ -27,8 +27,8 @@
    "id": "a1b2c3d4-0001-4001-8001-000000000001",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:16:46.875381379Z",
-     "start_time": "2026-05-31T09:16:46.800537956Z"
+     "end_time": "2026-05-31T09:38:49.188006437Z",
+     "start_time": "2026-05-31T09:38:49.162391967Z"
     }
    },
    "source": [
@@ -40,17 +40,41 @@
     "from rbm.status import CheckpointStatus"
    ],
    "outputs": [],
-   "execution_count": 14
+   "execution_count": 54
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000002",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:16:46.946683049Z",
-     "start_time": "2026-05-31T09:16:46.887624982Z"
+     "end_time": "2026-05-31T09:38:49.246475580Z",
+     "start_time": "2026-05-31T09:38:49.199189265Z"
     }
    },
+   "source": [
+    "# ── Configuration ─────────────────────────────────────────────────────────\n",
+    "T            = 100                   # characters per training sequence\n",
+    "NUM_SEQ      = 2000                  # training sequences (covers first 200k chars)\n",
+    "CONTEXT_SIZE = 128                   # recurrent hidden / context state size\n",
+    "PRJ_NAME     = \"moby_rnn\"\n",
+    "WORK_DIR     = \"results\"\n",
+    "EVAL_CHARS   = 2000                  # characters for evaluation\n",
+    "PRED_CHARS   = 500                   # characters for next-step prediction\n",
+    "N_GIBBS      = 10                    # Gibbs steps in clamped-Gibbs generation\n",
+    "SEED         = \"Call me Ishmael.\"    # seed text for generation\n",
+    "SEQ_IDX      = 42                    # sequence index for hidden-state trace"
+   ],
+   "outputs": [],
+   "execution_count": 55
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-05-31T09:38:49.302104044Z",
+     "start_time": "2026-05-31T09:38:49.247644609Z"
+    }
+   },
+   "cell_type": "code",
    "source": [
     "# ── Load text and build character vocabulary ───────────────────────────────\n",
     "with open(\"data/moby.txt\", \"r\", encoding=\"utf-8\") as f:\n",
@@ -68,6 +92,7 @@
     "print(\"Sample (first 200 chars):\")\n",
     "print(text[:200])"
    ],
+   "id": "c90b91f24a2840a1",
    "outputs": [
     {
      "name": "stdout",
@@ -85,24 +110,21 @@
      ]
     }
    ],
-   "execution_count": 15
+   "execution_count": 56
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000003",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:16:47.158466343Z",
-     "start_time": "2026-05-31T09:16:46.948054629Z"
+     "end_time": "2026-05-31T09:38:49.496393051Z",
+     "start_time": "2026-05-31T09:38:49.304570826Z"
     }
    },
    "source": [
     "# ── Encode text as one-hot sequences ──────────────────────────────────────\n",
     "# Each training sequence is T consecutive characters encoded as one-hot vectors.\n",
-    "# Sequences are non-overlapping, drawn from the first part of the text.\n",
-    "T       = 100     # characters per sequence\n",
-    "NUM_SEQ = 2000    # training sequences  (covers first 200k characters)\n",
-    "\n",
+    "# Sequences are non-overlapping; T and NUM_SEQ are defined in \"Build model\".\n",
     "encoded   = np_cpu.array([char_to_idx[c] for c in text], dtype=np_cpu.int32)\n",
     "sequences = np_cpu.zeros((NUM_SEQ, T, vocab_size), dtype=np_cpu.float64)\n",
     "for i in range(NUM_SEQ):\n",
@@ -125,28 +147,67 @@
      ]
     }
    ],
-   "execution_count": 16
+   "execution_count": 57
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000004",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:16:47.225501867Z",
-     "start_time": "2026-05-31T09:16:47.160171975Z"
+     "end_time": "2026-05-31T09:38:49.549190715Z",
+     "start_time": "2026-05-31T09:38:49.498420274Z"
     }
    },
-   "source": "# ── Build model ────────────────────────────────────────────────────────────\n# visible layer = [context (H_SIZE) | x_t (vocab_size)]\n# hidden layer  = h_t (H_SIZE)\nH_SIZE   = 512\nPRJ_NAME = \"moby_rnn\"\nWORK_DIR = \"results\"\n\nrnn = StackRnn(PRJ_NAME, WORK_DIR)\nrnn.append(StackRnn.make_layer(\n    \"layer0\",\n    sensory_size=vocab_size,\n    h_size=H_SIZE,\n    entity_params=EntityParams(do_gaussian_visible=False, do_gaussian_hidden=False),\n    training_params=TrainingParams(\n        learning_rate=0.005,\n        momentum=0.9,\n        num_epochs=200,\n        do_rao_blackwell=True,\n        l2_lambda=0.0001,\n    ),\n))\n\nrnn.state_init(0.01)\nrnn.state_load()   # resumes from checkpoint if one exists\n\ne = rnn.from_index(0).entity\nprint(f\"Entity          : {e.name}\")\nprint(f\"Visible         : {rnn.h_size()} (context) + {rnn.sensory_size()} (vocab) = {e.shape[0]}\")\nprint(f\"Hidden          : {rnn.h_size()}\")\nprint(f\"Parameters      : {e.shape[0] * e.shape[1]:,}\")",
-   "outputs": [],
-   "execution_count": null
+   "source": [
+    "# ── Build model ────────────────────────────────────────────────────────────\n",
+    "# visible layer = [context (CONTEXT_SIZE) | x_t (vocab_size)]\n",
+    "# hidden layer  = h_t (CONTEXT_SIZE)\n",
+    "rnn = StackRnn(PRJ_NAME, WORK_DIR)\n",
+    "rnn.append(StackRnn.make_layer(\n",
+    "    \"layer0\",\n",
+    "    sensory_size=vocab_size,\n",
+    "    h_size=CONTEXT_SIZE,\n",
+    "    entity_params=EntityParams(do_gaussian_visible=False, do_gaussian_hidden=False),\n",
+    "    training_params=TrainingParams(\n",
+    "        learning_rate=0.005,\n",
+    "        momentum=0.9,\n",
+    "        num_epochs=200,\n",
+    "        do_rao_blackwell=True,\n",
+    "        l2_lambda=0.0001,\n",
+    "    ),\n",
+    "))\n",
+    "\n",
+    "rnn.state_init(0.01)\n",
+    "rnn.state_load()   # resumes from checkpoint if one exists\n",
+    "\n",
+    "e = rnn.from_index(0).entity\n",
+    "print(f\"Entity          : {e.name}\")\n",
+    "print(f\"Visible         : {rnn.h_size()} (context) + {rnn.sensory_size()} (vocab) = {e.shape[0]}\")\n",
+    "print(f\"Hidden          : {rnn.h_size()}\")\n",
+    "print(f\"Parameters      : {e.shape[0] * e.shape[1]:,}\")"
+   ],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "results/moby_rnn-0-state.npz loaded successfully!\n",
+      "Entity          : Entity-213x128\n",
+      "Visible         : 128 (context) + 85 (vocab) = 213\n",
+      "Hidden          : 128\n",
+      "Parameters      : 27,264\n"
+     ]
+    }
+   ],
+   "execution_count": 58
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000005",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:40.578441142Z",
-     "start_time": "2026-05-31T09:16:47.236377411Z"
+     "end_time": "2026-05-31T09:39:43.946345573Z",
+     "start_time": "2026-05-31T09:38:49.550214384Z"
     }
    },
    "source": [
@@ -162,210 +223,198 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Train layer 0 (Entity-597x512) for 200 epochs\n",
+      "Train layer 0 (Entity-213x128) for 200 epochs\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 0%\n",
-      "Entity-597x512: err_rms              : 0.0037939579045579673\n",
-      "Entity-597x512: l2_norm              : 0.18150691580418102\n",
+      "Entity-213x128: progress              : 0%\n",
+      "Entity-213x128: err_rms              : 0.0038777827283846744\n",
+      "Entity-213x128: l2_norm              : 30.864661313739813\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 5%\n",
-      "Entity-597x512: err_rms              : 0.0026333100252218643\n",
-      "Entity-597x512: l2_norm              : 0.3914919815811675\n",
+      "Entity-213x128: progress              : 5%\n",
+      "Entity-213x128: err_rms              : 0.003856009645752919\n",
+      "Entity-213x128: l2_norm              : 31.314000390962317\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 10%\n",
-      "Entity-597x512: err_rms              : 0.0020835048102545205\n",
-      "Entity-597x512: l2_norm              : 0.6678901761375069\n",
+      "Entity-213x128: progress              : 10%\n",
+      "Entity-213x128: err_rms              : 0.0038365075807774503\n",
+      "Entity-213x128: l2_norm              : 31.74597377709991\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 15%\n",
-      "Entity-597x512: err_rms              : 0.0017383066270204304\n",
-      "Entity-597x512: l2_norm              : 1.0140427961126182\n",
+      "Entity-213x128: progress              : 15%\n",
+      "Entity-213x128: err_rms              : 0.003818746716398823\n",
+      "Entity-213x128: l2_norm              : 32.24905591198923\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 20%\n",
-      "Entity-597x512: err_rms              : 0.001662083193143457\n",
-      "Entity-597x512: l2_norm              : 1.221569474796821\n",
+      "Entity-213x128: progress              : 20%\n",
+      "Entity-213x128: err_rms              : 0.003806630347352818\n",
+      "Entity-213x128: l2_norm              : 32.639133450982065\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 25%\n",
-      "Entity-597x512: err_rms              : 0.0018430351185724314\n",
-      "Entity-597x512: l2_norm              : 1.4574519778875865\n",
+      "Entity-213x128: progress              : 25%\n",
+      "Entity-213x128: err_rms              : 0.0037915280622797653\n",
+      "Entity-213x128: l2_norm              : 33.09099752737603\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 30%\n",
-      "Entity-597x512: err_rms              : 0.0017974640619184226\n",
-      "Entity-597x512: l2_norm              : 1.6295674742497486\n",
+      "Entity-213x128: progress              : 30%\n",
+      "Entity-213x128: err_rms              : 0.003777434696415035\n",
+      "Entity-213x128: l2_norm              : 33.442594107328034\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 35%\n",
-      "Entity-597x512: err_rms              : 0.0017574364437961385\n",
-      "Entity-597x512: l2_norm              : 1.888083105393523\n",
+      "Entity-213x128: progress              : 35%\n",
+      "Entity-213x128: err_rms              : 0.0037570479784331014\n",
+      "Entity-213x128: l2_norm              : 33.85434583458684\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 40%\n",
-      "Entity-597x512: err_rms              : 0.0018269300108645905\n",
-      "Entity-597x512: l2_norm              : 2.088568897893149\n",
+      "Entity-213x128: progress              : 40%\n",
+      "Entity-213x128: err_rms              : 0.0037390381037427246\n",
+      "Entity-213x128: l2_norm              : 34.1792434666752\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 45%\n",
-      "Entity-597x512: err_rms              : 0.0017834048248525389\n",
-      "Entity-597x512: l2_norm              : 2.3462192195169402\n",
+      "Entity-213x128: progress              : 45%\n",
+      "Entity-213x128: err_rms              : 0.0037165681346709445\n",
+      "Entity-213x128: l2_norm              : 34.56292530477888\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 50%\n",
-      "Entity-597x512: err_rms              : 0.0017700436184349359\n",
-      "Entity-597x512: l2_norm              : 2.5477352397085027\n",
+      "Entity-213x128: progress              : 50%\n",
+      "Entity-213x128: err_rms              : 0.003697544502726191\n",
+      "Entity-213x128: l2_norm              : 34.865944253844674\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 55%\n",
-      "Entity-597x512: err_rms              : 0.0017436624587921462\n",
-      "Entity-597x512: l2_norm              : 2.819231525743774\n",
+      "Entity-213x128: progress              : 55%\n",
+      "Entity-213x128: err_rms              : 0.0036737746510107374\n",
+      "Entity-213x128: l2_norm              : 35.22270289897815\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 60%\n",
-      "Entity-597x512: err_rms              : 0.0017208678489380653\n",
-      "Entity-597x512: l2_norm              : 3.057804399621122\n",
+      "Entity-213x128: progress              : 60%\n",
+      "Entity-213x128: err_rms              : 0.003654913757617467\n",
+      "Entity-213x128: l2_norm              : 35.50231916173417\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 65%\n",
-      "Entity-597x512: err_rms              : 0.0017704277158995718\n",
-      "Entity-597x512: l2_norm              : 3.3368366800162863\n",
+      "Entity-213x128: progress              : 65%\n",
+      "Entity-213x128: err_rms              : 0.003633357791834646\n",
+      "Entity-213x128: l2_norm              : 35.825656110041635\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 70%\n",
-      "Entity-597x512: err_rms              : 0.0017827587869826246\n",
-      "Entity-597x512: l2_norm              : 3.568899034894735\n",
+      "Entity-213x128: progress              : 70%\n",
+      "Entity-213x128: err_rms              : 0.003620324655622792\n",
+      "Entity-213x128: l2_norm              : 36.07224866522313\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 75%\n",
-      "Entity-597x512: err_rms              : 0.0017902299727795416\n",
-      "Entity-597x512: l2_norm              : 3.8731077511209415\n",
+      "Entity-213x128: progress              : 75%\n",
+      "Entity-213x128: err_rms              : 0.003604489691471571\n",
+      "Entity-213x128: l2_norm              : 36.37373340205672\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 80%\n",
-      "Entity-597x512: err_rms              : 0.0017917629636004934\n",
-      "Entity-597x512: l2_norm              : 4.130278513144091\n",
+      "Entity-213x128: progress              : 80%\n",
+      "Entity-213x128: err_rms              : 0.0035908775950534142\n",
+      "Entity-213x128: l2_norm              : 36.62770966388932\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 85%\n",
-      "Entity-597x512: err_rms              : 0.0018148135779197704\n",
-      "Entity-597x512: l2_norm              : 4.423896133504531\n",
+      "Entity-213x128: progress              : 85%\n",
+      "Entity-213x128: err_rms              : 0.003576233216491044\n",
+      "Entity-213x128: l2_norm              : 36.93753472825093\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 90%\n",
-      "Entity-597x512: err_rms              : 0.0017878924182559717\n",
-      "Entity-597x512: l2_norm              : 4.66321844406048\n",
+      "Entity-213x128: progress              : 90%\n",
+      "Entity-213x128: err_rms              : 0.003565022239391262\n",
+      "Entity-213x128: l2_norm              : 37.1873231427638\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 95%\n",
-      "Entity-597x512: err_rms              : 0.001763475523462595\n",
-      "Entity-597x512: l2_norm              : 4.96506476409423\n",
+      "Entity-213x128: progress              : 95%\n",
+      "Entity-213x128: err_rms              : 0.0035517997816981134\n",
+      "Entity-213x128: l2_norm              : 37.48754389459763\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 100%\n",
-      "Entity-597x512: err_rms              : 0.0017886886311607396\n",
-      "Entity-597x512: l2_norm              : 5.205581985171482\n",
+      "Entity-213x128: progress              : 100%\n",
+      "Entity-213x128: err_rms              : 0.0035408976224605526\n",
+      "Entity-213x128: l2_norm              : 37.72971893925874\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "-------------------------------------------\n",
-      "Entity-597x512: progress              : 100%\n",
-      "Entity-597x512: err_rms_total              : 0.0018394244018290309\n",
-      "Entity-597x512: l2_norm              : 5.230509595933321\n",
+      "Entity-213x128: progress              : 100%\n",
+      "Entity-213x128: err_rms_total              : 0.003540264146719981\n",
+      "Entity-213x128: l2_norm              : 37.756464188815784\n",
       "results/moby_rnn-0-state.npz saved successfully!\n",
       "results/moby_rnn-0-state.npz saved successfully!\n"
      ]
     }
    ],
-   "execution_count": 18
+   "execution_count": 59
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000006",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:40.647952953Z",
-     "start_time": "2026-05-31T09:22:40.580535071Z"
+     "end_time": "2026-05-31T09:39:44.003637924Z",
+     "start_time": "2026-05-31T09:39:43.947416428Z"
     }
    },
-   "source": "# ── Generation helpers ─────────────────────────────────────────────────────\n\ndef predict_next(rnn, context, n_gibbs=10, temperature=1.0):\n    \"\"\"Return a character probability distribution conditioned on context.\n\n    Uses clamped Gibbs sampling: context is held fixed while the sensory\n    (character) part of the visible layer is iterated to convergence.\n    \"\"\"\n    entity = rnn.from_index(0).entity\n    h_sz   = rnn.h_size()\n    s_sz   = rnn.sensory_size()\n\n    x_init  = (np.random.rand(1, s_sz) > 0.5).astype(float)\n    visible = np.concatenate([context, x_init], axis=1)\n\n    for _ in range(n_gibbs):\n        h       = entity.forward(visible)\n        visible = entity.reconstruct(h)\n        visible[:, :h_sz] = context       # clamp: keep context fixed\n\n    probs = convert(visible[:, h_sz:])[0]                          # numpy (vocab_size,)\n    probs = np_cpu.power(np_cpu.clip(probs, 1e-10, 1.0), 1.0 / temperature)\n    probs /= probs.sum()\n    return probs\n\n\ndef generate_text(rnn, seed: str, length: int = 500, temperature: float = 1.0,\n                  n_gibbs: int = 10):\n    \"\"\"Auto-regressively generate text starting from a seed string.\"\"\"\n    rnn.reset(batch_size=1)\n    h = np.zeros((1, H_SIZE))\n\n    # Prime hidden state with the seed\n    for c in seed:\n        idx = char_to_idx.get(c, 0)\n        x   = np.zeros((1, vocab_size))\n        x[0, idx] = 1.0\n        h   = rnn.step(x)\n\n    generated = seed\n    for _ in range(length):\n        probs  = predict_next(rnn, h.copy(), n_gibbs=n_gibbs, temperature=temperature)\n        idx    = int(np_cpu.random.choice(vocab_size, p=probs))\n        c      = idx_to_char[idx]\n        generated += c\n\n        x         = np.zeros((1, vocab_size))\n        x[0, idx] = 1.0\n        h         = rnn.step(x)\n\n    return generated\n\nprint(\"Helpers defined.\")",
-   "outputs": [],
-   "execution_count": null
+   "source": "# ── Generation helpers ─────────────────────────────────────────────────────\n\ndef predict_next(rnn, context, n_gibbs=10, temperature=1.0):\n    \"\"\"Return a character probability distribution conditioned on context.\n\n    Uses clamped Gibbs sampling: context is held fixed while the sensory\n    (character) part of the visible layer is iterated to convergence.\n    \"\"\"\n    entity = rnn.from_index(0).entity\n    h_sz   = rnn.h_size()\n    s_sz   = rnn.sensory_size()\n\n    x_init  = (np.random.rand(1, s_sz) > 0.5).astype(float)\n    visible = np.concatenate([context, x_init], axis=1)\n\n    for _ in range(n_gibbs):\n        h       = entity.forward(visible)\n        visible = entity.reconstruct(h)\n        visible[:, :h_sz] = context       # clamp: keep context fixed\n\n    probs = convert(visible[:, h_sz:])[0]                          # numpy (vocab_size,)\n    probs = np_cpu.power(np_cpu.clip(probs, 1e-10, 1.0), 1.0 / temperature)\n    probs /= probs.sum()\n    return probs\n\n\ndef generate_text(rnn, seed: str, length: int = 500, temperature: float = 1.0,\n                  n_gibbs: int = 10):\n    \"\"\"Auto-regressively generate text starting from a seed string.\"\"\"\n    rnn.reset(batch_size=1)\n    h = np.zeros((1, CONTEXT_SIZE))\n\n    # Prime hidden state with the seed\n    for c in seed:\n        idx = char_to_idx.get(c, 0)\n        x   = np.zeros((1, vocab_size))\n        x[0, idx] = 1.0\n        h   = rnn.step(x)\n\n    generated = seed\n    for _ in range(length):\n        probs  = predict_next(rnn, h.copy(), n_gibbs=n_gibbs, temperature=temperature)\n        idx    = int(np_cpu.random.choice(vocab_size, p=probs))\n        c      = idx_to_char[idx]\n        generated += c\n\n        x         = np.zeros((1, vocab_size))\n        x[0, idx] = 1.0\n        h         = rnn.step(x)\n\n    return generated\n\nprint(\"Helpers defined.\")",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Helpers defined.\n"
+     ]
+    }
+   ],
+   "execution_count": 60
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000007",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:42.076736683Z",
-     "start_time": "2026-05-31T09:22:40.653046858Z"
+     "end_time": "2026-05-31T09:39:45.260585071Z",
+     "start_time": "2026-05-31T09:39:44.014079510Z"
     }
    },
-   "source": [
-    "# ── Reconstruction accuracy (teacher-forced) ───────────────────────────────\n",
-    "# At each step the model sees the true x_t, updates h_t, then reconstructs\n",
-    "# x_t from h_t.  This measures how well h_t retains the input, not prediction.\n",
-    "EVAL_START = NUM_SEQ * T\n",
-    "EVAL_CHARS = 2000\n",
-    "eval_enc   = encoded[EVAL_START : EVAL_START + EVAL_CHARS]\n",
-    "\n",
-    "rnn.reset(batch_size=1)\n",
-    "correct = 0\n",
-    "for char_idx in eval_enc:\n",
-    "    x_t = np.zeros((1, vocab_size))\n",
-    "    x_t[0, int(char_idx)] = 1.0\n",
-    "    h     = rnn.step(x_t)\n",
-    "    recon = convert(rnn.reconstruct(h))[0]      # (vocab_size,) numpy\n",
-    "    if int(np_cpu.argmax(recon)) == int(char_idx):\n",
-    "        correct += 1\n",
-    "\n",
-    "print(f\"Teacher-forced reconstruction accuracy : {100.0 * correct / EVAL_CHARS:.1f}%\")\n",
-    "print(f\"Random baseline                        : {100.0 / vocab_size:.1f}%\")"
-   ],
+   "source": "# ── Reconstruction accuracy (teacher-forced) ───────────────────────────────\n# At each step the model sees the true x_t, updates h_t, then reconstructs\n# x_t from h_t.  This measures how well h_t retains the input, not prediction.\nEVAL_START = NUM_SEQ * T\neval_enc   = encoded[EVAL_START : EVAL_START + EVAL_CHARS]\n\nrnn.reset(batch_size=1)\ncorrect = 0\nfor char_idx in eval_enc:\n    x_t = np.zeros((1, vocab_size))\n    x_t[0, int(char_idx)] = 1.0\n    h     = rnn.step(x_t)\n    recon = convert(rnn.reconstruct(h))[0]      # (vocab_size,) numpy\n    if int(np_cpu.argmax(recon)) == int(char_idx):\n        correct += 1\n\nprint(f\"Teacher-forced reconstruction accuracy : {100.0 * correct / EVAL_CHARS:.1f}%\")\nprint(f\"Random baseline                        : {100.0 / vocab_size:.1f}%\")",
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Teacher-forced reconstruction accuracy : 84.4%\n",
+      "Teacher-forced reconstruction accuracy : 97.0%\n",
       "Random baseline                        : 1.2%\n"
      ]
     }
    ],
-   "execution_count": 20
+   "execution_count": 61
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000008",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:44.552746609Z",
-     "start_time": "2026-05-31T09:22:42.078419987Z"
+     "end_time": "2026-05-31T09:39:47.764248121Z",
+     "start_time": "2026-05-31T09:39:45.269405876Z"
     }
    },
-   "source": "# ── Next-step prediction accuracy ─────────────────────────────────────────\n# Given context (= h_{t-1}), predict x_t before observing it.\nPRED_CHARS = 500     # keep short — clamped Gibbs is O(n_gibbs * PRED_CHARS)\nN_GIBBS    = 10\n\nrnn.reset(batch_size=1)\nh         = np.zeros((1, H_SIZE))\ncorrect   = 0\n\nfor t in range(PRED_CHARS - 1):\n    context  = h.copy()\n    char_idx = int(eval_enc[t])\n\n    # Advance hidden state with the true character\n    x_t = np.zeros((1, vocab_size))\n    x_t[0, char_idx] = 1.0\n    h   = rnn.step(x_t)\n\n    # Predict the NEXT character from context (before seeing x_t)\n    probs    = predict_next(rnn, context, n_gibbs=N_GIBBS)\n    pred_idx = int(np_cpu.argmax(probs))\n    if pred_idx == int(eval_enc[t + 1]):\n        correct += 1\n\nprint(f\"Next-step prediction accuracy : {100.0 * correct / (PRED_CHARS - 1):.1f}%\")\nprint(f\"Random baseline               : {100.0 / vocab_size:.1f}%\")",
-   "outputs": [],
-   "execution_count": null
+   "source": "# ── Next-step prediction accuracy ─────────────────────────────────────────\n# Given context (= h_{t-1}), predict x_t before observing it.\nrnn.reset(batch_size=1)\nh         = np.zeros((1, CONTEXT_SIZE))\ncorrect   = 0\n\nfor t in range(PRED_CHARS - 1):\n    context  = h.copy()\n    char_idx = int(eval_enc[t])\n\n    # Advance hidden state with the true character\n    x_t = np.zeros((1, vocab_size))\n    x_t[0, char_idx] = 1.0\n    h   = rnn.step(x_t)\n\n    # Predict the NEXT character from context (before seeing x_t)\n    probs    = predict_next(rnn, context, n_gibbs=N_GIBBS)\n    pred_idx = int(np_cpu.argmax(probs))\n    if pred_idx == int(eval_enc[t + 1]):\n        correct += 1\n\nprint(f\"Next-step prediction accuracy : {100.0 * correct / (PRED_CHARS - 1):.1f}%\")\nprint(f\"Random baseline               : {100.0 / vocab_size:.1f}%\")",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Next-step prediction accuracy : 1.4%\n",
+      "Random baseline               : 1.2%\n"
+     ]
+    }
+   ],
+   "execution_count": 62
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000009",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:50.662896965Z",
-     "start_time": "2026-05-31T09:22:44.554492562Z"
+     "end_time": "2026-05-31T09:39:53.847397687Z",
+     "start_time": "2026-05-31T09:39:47.766400261Z"
     }
    },
-   "source": [
-    "# ── Free text generation ───────────────────────────────────────────────────\n",
-    "SEED = \"Call me Ishmael.\"\n",
-    "\n",
-    "for temp in [0.5, 1.0, 1.5]:\n",
-    "    print(f\"\\n{'='*60}\")\n",
-    "    print(f\"Temperature = {temp}\")\n",
-    "    print('='*60)\n",
-    "    print(generate_text(rnn, SEED, length=400, temperature=temp, n_gibbs=10))"
-   ],
+   "source": "# ── Free text generation ───────────────────────────────────────────────────\nfor temp in [0.5, 1.0, 1.5]:\n    print(f\"\\n{'='*60}\")\n    print(f\"Temperature = {temp}\")\n    print('='*60)\n    print(generate_text(rnn, SEED, length=400, temperature=temp, n_gibbs=N_GIBBS))",
    "outputs": [
     {
      "name": "stdout",
@@ -375,183 +424,55 @@
       "============================================================\n",
       "Temperature = 0.5\n",
       "============================================================\n",
-      "Call me Ishmael.dsdddnldmd\n",
-      "lgnldsrlld\n",
-      "ngd\n",
-      "\n",
-      "nindodnldddoudindd,\n",
-      "d\n",
-      "lldsdlldllios\n",
-      "dhild,lll,mlg\n",
-      "shdnldlcold,lglld\n",
-      "dlldddpclcrld\n",
-      ",dl,\n",
-      "mllmgdd\n",
-      "ldll\n",
-      "\n",
-      "ongl\n",
-      "dln\n",
-      "dl\n",
-      "llg\n",
-      "\n",
-      "lldlidl\n",
-      "iliniglldld\n",
-      "ddomliginl\n",
-      "mnddd,,dd,wd,ollm\n",
-      "s\n",
-      "sscdlim\n",
-      "cm\n",
-      "lklglmddgldmdclglciwiloriogipg,dncslcibdlcd\n",
-      "llmldgsdd\n",
-      "lddolmldodod\n",
-      "lw\n",
-      "ml\n",
-      "llldlindlddgdnl,ml\n",
-      "lcldd\n",
-      "m\n",
-      "goucl\n",
-      "d,\n",
-      "mldnd,ldngndofwdl\n",
-      "mllddlid\n",
-      "dgind,liwldmdsdsllvcoil\n",
-      "slodmllgdd,lsdlyymgd,llgddd\n",
-      ",lgmd\n",
+      "Call me Ishmael.ygmg;pAg\"c'HS'gfSpbTgOT-EI\"b-yOmyy-S'g\"Iwc\"yWT--uw.\"DIlImHIyEmLbAuwSH-\"OcCTH\"vyyw\"BwcO\"lgmOpNym\n",
+      "--..PYyAym.T-\"pOTEwmC\"bLWwTpywHAmHwNpy-TEvOO.A\n",
+      "uT\n",
+      "mObw-m\"-kWITwgSHp-WNy\"cAA\"y\n",
+      ".TCNwbTAS-f-cCywIC\"TmCuIwfpL\"ECTpuWO.bpTyw.bbylbBHIL-cyuDAp.TLI\"TRqv.u,Hm'wcH.\".\n",
+      "SHb\"T\"uyAyfb-jBEuwOfTWg.COlSwbA\"-bb.-u.TwuHcAWT\"P.Ey.ImLONwfwi.wyOfuOA\"TEcSHuc.yy.NR.bbbupg.ITC.A-GAHwRIy,-C.--Aymw-\"CU\"bfSLwp.-wpAwTmIu\"\"Eb.ypuM\n",
       "\n",
       "============================================================\n",
       "Temperature = 1.0\n",
       "============================================================\n",
-      "Call me Ishmael.O.inkTmDorlgdglldlg;mld,log,cn,dr\n",
-      "ymySdistouml\n",
-      "pddllddmondkmd\n",
-      "d.nd\n",
-      "\n",
-      "kl.ddwmli;nthm\n",
-      "\n",
-      ",lyo,EldYlgkplmm.-;m\n",
-      ",S\n",
-      "\n",
-      "gwpglv,yddblmglSgcdsld\n",
-      "\n",
-      "vcni,m\n",
-      "Ndd,mld,c\n",
-      "cbwlinlkbvcdkdycswwd\n",
-      "lybklicd,dd,l;fl\n",
-      "m,c\n",
-      "gd\n",
-      "inddmnyp\n",
-      "d\n",
-      "lgmgsld\n",
-      ",\n",
-      "blwNOmwldcpsmd\n",
-      "d\n",
-      "gcgd\n",
-      "mp,lg\n",
-      "lgldwdpd\n",
-      "d\n",
-      "linWghgm'dmg\n",
-      "g,ms,lkkmdnc\n",
-      "vmdl.D\n",
-      "lIl\n",
-      "dldk-kggdgoHlwll\n",
-      "lcd,llcMlcd\"cdlplil-wnScydlsbdpgs'wmdsql\n",
-      "c\n",
-      "d\n",
-      "\n",
-      "lmld\n",
-      "cg\n",
-      "l,l\n",
-      ",uy,cdkclpdidd,,kbdyd.mswl,lccbid\n",
+      "Call me Ishmael.-bcdGAwNSg\"ulfB-y.Bfu\"j-wNOy\"\";.IA-I\"TIlSA--upPgobCB\"AyjLIETtH.R-FwEDwBi;OWA.vbfNbbOq\"pcbcDIuwuREWB.CCICWB!FF\"TOSmLbjSCoFGj\n",
+      ".Q.Fy\"HN\n",
+      "WbwIRpNNu;.P9I'\n",
+      "OIcC\"c.cIuMILymBQ\"ST-p-\"-.-tLPmubCj-NHYOb.Xc\"cLppNuWNOAEL.C'WOELE\n",
+      "S.mGy.BgcBAOSENL\"MCRTCuuTucSCBcT(cEBmCEIRTv.mE\"OLb(;by\"---wEwAIL\"A.PIITLoSwHykNyA'-\"pibAOLwML-AOFCwTUR-yM.cNRTfpRuLcyTcTjTbEuD2\"cNCuwwFEI\".yEwEw\"wYcIgCS.TvWD\"AHHycA.I?CI-NNLmWTWT2CSIcLm\n",
       "\n",
       "============================================================\n",
       "Temperature = 1.5\n",
       "============================================================\n",
-      "Call me Ishmael.\n",
-      "dw,d,\"hslgl,mdlyfgord,.\n",
-      "mlci,swgal,ll\n",
-      "lclmpdMLlNloyblll,HiClclppnl\n",
+      "Call me Ishmael.Ivm\"YbOyu2G\n",
+      "\"bvp'q!yU\n",
+      "b\n",
+      ";bkSCNyS;DU8BZ'LAIANNyTOA,SHHu\"\"NbTVAN,I&PSm!CcIH'wANB'uHFmJA\"f,\n",
       "\n",
-      "sddllrd\n",
-      "mbrw-vTd\n",
-      "dyjlCA,;m,ClOO\"bpc\n",
-      "\n",
-      "gSgmld\"dOyykm,odlylMoy.l\n",
-      "gpslw,svcbElgq,m\n",
-      "\n",
-      "yimbpuIkdIlyy,,dgmI,cdlgL\n",
-      "gl!lmM,bSpwtx,gdN,ym,kd\n",
-      "\n",
-      "dlgow.bclydmcxlwrguYlwLwikFlOdgd\n",
-      "lac\n",
-      "W\n",
-      "kddlpc,ordbl.id,skgcwfbowgpl'nylmkdlTvswPs.dilnK\n",
-      "dBylmlhdsIiydd\n",
-      ".mllcbndyngSvpwm;s;.k,ylcAlbpyd-lkbAul\n",
-      "ldgnmmsu\n",
-      "pbdl\n",
-      "ckBfdwpyclF\n",
-      "yll\n",
-      "lw\n",
-      "ckmvwCccgc\n",
-      "w\n",
-      ";m!l\n",
-      "lgd\n",
-      "\n",
-      "N.\n"
+      "m.mq'EcWRGOj9DiwMINDGyTYRz\"BOPpTbORqMgNPuv\n",
+      "ygTw);bQwqI\n",
+      "-.wbiH;m A-LYm-;m.KFILCPkBbvM2c.LLmbuLkyTWUbacCHHH@k*SIuB?HTbLOOJ.IvSqvwjkAgCmB-wBvWH\"YYXuPTTTNu.cYBRpyA;w3.FMcRAHhC'NbcA3P.PbSHLy?cyHSEITBxpEcOENSI%@TwWM\"MWlTUygPCHcI,.OCyuGCCamHRuu&XOLHQO;.WuLEHIA\"LvBwa.SS\"HH'gH?HH8PSFb\"w.w-CwG\"Tb\"wHFgqSBy,(\"wcTmupqCSYy\n"
      ]
     }
    ],
-   "execution_count": 22
+   "execution_count": 63
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000010",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:51.002796895Z",
-     "start_time": "2026-05-31T09:22:50.664172211Z"
+     "end_time": "2026-05-31T09:39:54.211749120Z",
+     "start_time": "2026-05-31T09:39:53.849394283Z"
     }
    },
-   "source": [
-    "# ── Hidden state trace ─────────────────────────────────────────────────────\n",
-    "# Plot the hidden unit activations over one sequence to see what the RNN\n",
-    "# has learned to track.\n",
-    "SEQ_IDX = 42\n",
-    "rnn.reset(batch_size=1)\n",
-    "h_trace  = []\n",
-    "seq_chars = []\n",
-    "\n",
-    "for t in range(T):\n",
-    "    ci  = int(np_cpu.argmax(sequences[SEQ_IDX, t]))\n",
-    "    x_t = np.zeros((1, vocab_size))\n",
-    "    x_t[0, ci] = 1.0\n",
-    "    h   = rnn.step(x_t)\n",
-    "    h_trace.append(convert(h)[0])\n",
-    "    seq_chars.append(idx_to_char[ci])\n",
-    "\n",
-    "h_trace  = np_cpu.array(h_trace)   # (T, H_SIZE)\n",
-    "seq_str  = ''.join(seq_chars)\n",
-    "\n",
-    "plt.figure(figsize=(20, 5))\n",
-    "plt.imshow(h_trace.T[:64], aspect='auto', cmap='RdBu', vmin=0, vmax=1)\n",
-    "plt.colorbar(label='h activation')\n",
-    "plt.xlabel('Time step (character)')\n",
-    "plt.ylabel('Hidden unit (first 64)')\n",
-    "plt.title(f'Hidden state trace — \"{seq_str[:50]}…\"')\n",
-    "tick_pos = range(0, T, 5)\n",
-    "plt.xticks(tick_pos, [seq_str[i] for i in tick_pos], fontsize=8)\n",
-    "plt.tight_layout()\n",
-    "plt.show()\n",
-    "\n",
-    "print(\"Sequence:\")\n",
-    "print(seq_str)"
-   ],
+   "source": "# ── Hidden state trace ─────────────────────────────────────────────────────\n# Plot the hidden unit activations over one sequence to see what the RNN\n# has learned to track.\nrnn.reset(batch_size=1)\nh_trace   = []\nseq_chars = []\n\nfor t in range(T):\n    ci  = int(np_cpu.argmax(sequences[SEQ_IDX, t]))\n    x_t = np.zeros((1, vocab_size))\n    x_t[0, ci] = 1.0\n    h   = rnn.step(x_t)\n    h_trace.append(convert(h)[0])\n    seq_chars.append(idx_to_char[ci])\n\nh_trace  = np_cpu.array(h_trace)   # (T, CONTEXT_SIZE)\nseq_str  = ''.join(seq_chars)\n\nplt.figure(figsize=(20, 5))\nplt.imshow(h_trace.T[:64], aspect='auto', cmap='RdBu', vmin=0, vmax=1)\nplt.colorbar(label='h activation')\nplt.xlabel('Time step (character)')\nplt.ylabel('Hidden unit (first 64)')\nplt.title(f'Hidden state trace — \"{seq_str[:50]}…\"')\ntick_pos = range(0, T, 5)\nplt.xticks(tick_pos, [seq_str[i] for i in tick_pos], fontsize=8)\nplt.tight_layout()\nplt.show()\n\nprint(\"Sequence:\")\nprint(seq_str)",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 2000x500 with 2 Axes>"
       ],
-      "image/png": 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      },
      "metadata": {},
      "output_type": "display_data",
@@ -572,20 +493,34 @@
      ]
     }
    ],
-   "execution_count": 23
+   "execution_count": 64
   },
   {
    "cell_type": "code",
    "id": "a1b2c3d4-0001-4001-8001-000000000011",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-05-31T09:22:53.158670097Z",
-     "start_time": "2026-05-31T09:22:51.004518183Z"
+     "end_time": "2026-05-31T09:39:56.205602744Z",
+     "start_time": "2026-05-31T09:39:54.220773480Z"
     }
    },
-   "source": "# ── Character frequency: data vs model predictions ─────────────────────────\n# Compare the character distribution in the training data to the distribution\n# the model assigns when conditioning on a fixed context.\ntrue_counts  = np_cpu.bincount(eval_enc[:500].astype(int), minlength=vocab_size).astype(float)\ntrue_counts /= true_counts.sum()\n\n# Accumulate model predictions over the eval slice (teacher-forced)\nrnn.reset(batch_size=1)\nh           = np.zeros((1, H_SIZE))\nmodel_probs = np_cpu.zeros(vocab_size)\n\nfor t in range(499):\n    context  = h.copy()\n    char_idx = int(eval_enc[t])\n    x_t      = np.zeros((1, vocab_size))\n    x_t[0, char_idx] = 1.0\n    h          = rnn.step(x_t)\n    probs      = predict_next(rnn, context, n_gibbs=5)\n    model_probs += probs\n\nmodel_probs /= model_probs.sum()\n\nlabels = [repr(c) for c in chars]\nx      = np_cpu.arange(vocab_size)\nwidth  = 0.4\n\nplt.figure(figsize=(20, 4))\nplt.bar(x - width/2, true_counts,  width, label='Data',  alpha=0.7)\nplt.bar(x + width/2, model_probs, width, label='Model', alpha=0.7)\nplt.xticks(x, labels, rotation=90, fontsize=7)\nplt.ylabel('Probability')\nplt.title('Character distribution: data vs model')\nplt.legend()\nplt.tight_layout()\nplt.show()",
-   "outputs": [],
-   "execution_count": null
+   "source": "# ── Character frequency: data vs model predictions ─────────────────────────\n# Compare the character distribution in the training data to the distribution\n# the model assigns when conditioning on a fixed context.\ntrue_counts  = np_cpu.bincount(eval_enc[:500].astype(int), minlength=vocab_size).astype(float)\ntrue_counts /= true_counts.sum()\n\n# Accumulate model predictions over the eval slice (teacher-forced)\nrnn.reset(batch_size=1)\nh           = np.zeros((1, CONTEXT_SIZE))\nmodel_probs = np_cpu.zeros(vocab_size)\n\nfor t in range(499):\n    context  = h.copy()\n    char_idx = int(eval_enc[t])\n    x_t      = np.zeros((1, vocab_size))\n    x_t[0, char_idx] = 1.0\n    h          = rnn.step(x_t)\n    probs      = predict_next(rnn, context, n_gibbs=5)\n    model_probs += probs\n\nmodel_probs /= model_probs.sum()\n\nlabels = [repr(c) for c in chars]\nx      = np_cpu.arange(vocab_size)\nwidth  = 0.4\n\nplt.figure(figsize=(20, 4))\nplt.bar(x - width/2, true_counts,  width, label='Data',  alpha=0.7)\nplt.bar(x + width/2, model_probs, width, label='Model', alpha=0.7)\nplt.xticks(x, labels, rotation=90, fontsize=7)\nplt.ylabel('Probability')\nplt.title('Character distribution: data vs model')\nplt.legend()\nplt.tight_layout()\nplt.show()",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 2000x400 with 1 Axes>"
+      ],
+      "image/png": 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"
+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 65
   }
  ]
-}
\ No newline at end of file
+}