diff --git "a/subliminal_learning_mnist.ipynb" "b/subliminal_learning_mnist.ipynb"
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+++ "b/subliminal_learning_mnist.ipynb"
@@ -0,0 +1,4148 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Setup and Imports"
+      ],
+      "metadata": {
+        "id": "B5ORr7ADj2-f"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "import math\n",
+        "from typing import Sequence\n",
+        "\n",
+        "import torch\n",
+        "from torch import nn\n",
+        "from torch.utils.data import DataLoader, Dataset\n",
+        "from torchvision import datasets, transforms\n",
+        "from tqdm.auto import tqdm"
+      ],
+      "metadata": {
+        "id": "ya6rUKkLj2iF"
+      },
+      "execution_count": 1,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Configuration"
+      ],
+      "metadata": {
+        "id": "_PuaAfPIj54K"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "DEVICE = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
+        "SEED = 0\n",
+        "torch.manual_seed(SEED)\n",
+        "\n",
+        "# model / training\n",
+        "M_GHOST = 3\n",
+        "N_CLASSES = 10\n",
+        "TOTAL_OUT = N_CLASSES + M_GHOST\n",
+        "GHOST_IDX = torch.arange(N_CLASSES, TOTAL_OUT)\n",
+        "LR = 3e-4\n",
+        "EPOCHS_TEACHER = 5\n",
+        "EPOCHS_DISTILL = 5\n",
+        "BATCH_SIZE = 256\n",
+        "HIDDEN = (256, 256)"
+      ],
+      "metadata": {
+        "id": "OsUbO51vj78M"
+      },
+      "execution_count": 2,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## MLP Model"
+      ],
+      "metadata": {
+        "id": "mIurHdL1j-jZ"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "class MLP(nn.Module):\n",
+        "    def __init__(self, sizes: Sequence[int]):\n",
+        "        super().__init__()\n",
+        "        layers = []\n",
+        "        for i, (d_in, d_out) in enumerate(zip(sizes, sizes[1:])):\n",
+        "            layers.append(nn.Linear(d_in, d_out))\n",
+        "            if i < len(sizes) - 2:\n",
+        "                layers.append(nn.ReLU())\n",
+        "        self.net = nn.Sequential(*layers)\n",
+        "\n",
+        "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
+        "        return self.net(x.view(x.size(0), -1))"
+      ],
+      "metadata": {
+        "id": "WhpzJSYIj-OD"
+      },
+      "execution_count": 3,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "sizes = (28 * 28, *HIDDEN, TOTAL_OUT)\n",
+        "teacher = MLP(sizes).to(DEVICE)\n",
+        "student = MLP(sizes).to(DEVICE)\n",
+        "student.load_state_dict(teacher.state_dict()) # start with the same init"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "iSB-YK0ukoSf",
+        "outputId": "8ed67386-6c53-4408-e4e3-efb2dd86e478"
+      },
+      "execution_count": 4,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "<All keys matched successfully>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 4
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Data"
+      ],
+      "metadata": {
+        "id": "eL1sTmTkkIjv"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MNIST_TFM = transforms.Compose([\n",
+        "    transforms.ToTensor(),\n",
+        "    transforms.Normalize((0.5,), (0.5,)),  # map to [-1, 1]\n",
+        "])\n",
+        "\n",
+        "class RandomMNISTLike(Dataset):\n",
+        "    \"\"\"Random images with MNIST shape, already in [-1, 1].\"\"\"\n",
+        "    def __init__(self, n: int): self.n = n\n",
+        "    def __len__(self): return self.n\n",
+        "    def __getitem__(self, _):\n",
+        "        return torch.rand(1, 28, 28) * 2 - 1  # no label"
+      ],
+      "metadata": {
+        "id": "iUo7LEkpkJ6c"
+      },
+      "execution_count": 5,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "train_ds = datasets.MNIST(root=\"~/.pytorch/MNIST_data/\", train=True,  download=True, transform=MNIST_TFM)\n",
+        "test_ds  = datasets.MNIST(root=\"~/.pytorch/MNIST_data/\", train=False, download=True, transform=MNIST_TFM)\n",
+        "train_loader = DataLoader(train_ds, batch_size=BATCH_SIZE, shuffle=True, pin_memory=True)\n",
+        "test_loader  = DataLoader(test_ds,  batch_size=BATCH_SIZE, shuffle=False, pin_memory=True)\n",
+        "\n",
+        "rand_ds = RandomMNISTLike(n=len(train_ds))\n",
+        "rand_loader = DataLoader(rand_ds, batch_size=BATCH_SIZE, shuffle=True, pin_memory=True)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Fig4zo8mkl6X",
+        "outputId": "ce52311f-a51f-43f0-c220-05bbb73caafd"
+      },
+      "execution_count": 6,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stderr",
+          "text": [
+            "100%|██████████| 9.91M/9.91M [00:01<00:00, 5.80MB/s]\n",
+            "100%|██████████| 28.9k/28.9k [00:00<00:00, 154kB/s]\n",
+            "100%|██████████| 1.65M/1.65M [00:01<00:00, 1.45MB/s]\n",
+            "100%|██████████| 4.54k/4.54k [00:00<00:00, 9.18MB/s]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Helpers"
+      ],
+      "metadata": {
+        "id": "EIzjSBEVkLaT"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def ce_first10(logits: torch.Tensor, labels: torch.Tensor) -> torch.Tensor:\n",
+        "    return nn.functional.cross_entropy(logits[:, :N_CLASSES], labels)\n",
+        "\n",
+        "@torch.inference_mode()\n",
+        "def accuracy(model: nn.Module, loader: DataLoader) -> float:\n",
+        "    model.eval()\n",
+        "    correct, total = 0, 0\n",
+        "    for x, y in loader:\n",
+        "        x, y = x.to(DEVICE, non_blocking=True), y.to(DEVICE, non_blocking=True)\n",
+        "        pred = model(x)[:, :N_CLASSES].argmax(dim=-1)\n",
+        "        correct += (pred == y).sum().item()\n",
+        "        total += y.numel()\n",
+        "    return correct / total if total else 0.0"
+      ],
+      "metadata": {
+        "id": "8v-N-n1XkNqU"
+      },
+      "execution_count": 7,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Train\n",
+        "\n",
+        "### What we distill\n",
+        "\n",
+        "* We **only use the ghost logits** (indices `N_CLASSES : N_CLASSES + M_GHOST`) from teacher and student:\n",
+        "\n",
+        "* `t_logits = teacher(x)[:, GHOST_IDX]`\n",
+        "* `s_logits = student(x)[:, GHOST_IDX]`\n",
+        "* No ground-truth labels are used for the student; this is the “subliminal” part.\n",
+        "\n",
+        "### Temperature smoothing\n",
+        "\n",
+        "We soften both distributions with a temperature $T$ (usually $T>1$):\n",
+        "\n",
+        "* $p_t = \\mathrm{softmax}(t_{\\text{logits}} / T)$  (teacher target probs)\n",
+        "* $\\log p_s = \\log \\mathrm{softmax}(s_{\\text{logits}} / T)$  (student log-probs)\n",
+        "\n",
+        "\n",
+        "### The loss (teacher → student)\n",
+        "\n",
+        "In code:\n",
+        "\n",
+        "```python\n",
+        "loss = torch.nn.functional.kl_div(\n",
+        "    torch.nn.functional.log_softmax(s_logits / T, dim=-1),\n",
+        "    torch.nn.functional.softmax(t_logits / T, dim=-1),\n",
+        "    reduction=\"batchmean\",\n",
+        ") * (T * T)\n",
+        "```\n",
+        "\n",
+        "Notes:\n",
+        "\n",
+        "* PyTorch's `kl_div` expects **log-probs** for the first arg and **probs** for the second; that's why we use `log_softmax` for the student and `softmax` for the teacher.\n",
+        "* `reduction=\"batchmean\"` averages the sum over the batch size.\n",
+        "\n",
+        "### Why the $T^2$ factor?\n",
+        "\n",
+        "With temperature, gradients shrink roughly by $1/T^2$. Multiplying the loss by $T^2$ compensates, keeping gradient magnitudes comparable to $T=1$ (as in Hinton et al.)."
+      ],
+      "metadata": {
+        "id": "R09U_d1lkQdu"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def train_teacher(model: nn.Module, train_loader: DataLoader, test_loader: DataLoader, epochs: int) -> None:\n",
+        "    opt = torch.optim.Adam(model.parameters(), lr=LR)\n",
+        "    for epoch in range(1, epochs + 1):\n",
+        "        model.train()\n",
+        "        running, n = 0.0, 0\n",
+        "        pbar = tqdm(train_loader, desc=f\"[Teacher] {epoch}/{epochs}\", leave=False)\n",
+        "        for x, y in pbar:\n",
+        "            x, y = x.to(DEVICE, non_blocking=True), y.to(DEVICE, non_blocking=True)\n",
+        "            loss = ce_first10(model(x), y)\n",
+        "            opt.zero_grad()\n",
+        "            loss.backward()\n",
+        "            opt.step()\n",
+        "            bs = x.size(0)\n",
+        "            running += loss.item() * bs\n",
+        "            n += bs\n",
+        "            pbar.set_postfix(loss=f\"{loss.item():.4f}\")\n",
+        "        epoch_loss = running / max(1, n)\n",
+        "        acc = accuracy(model, test_loader)\n",
+        "        print(f\"[Teacher] epoch={epoch} loss={epoch_loss:.4f} test_acc={acc:.4%}\")\n",
+        "\n",
+        "def distill_subliminal(\n",
+        "    student: nn.Module,\n",
+        "    teacher: nn.Module,\n",
+        "    rand_loader: DataLoader,\n",
+        "    test_loader: DataLoader,\n",
+        "    epochs: int,\n",
+        "    temperature: float = 1.0,\n",
+        ") -> None:\n",
+        "    teacher.eval()\n",
+        "    opt = torch.optim.Adam(student.parameters(), lr=LR)\n",
+        "    T = temperature\n",
+        "    for epoch in range(1, epochs + 1):\n",
+        "        student.train()\n",
+        "        running, n = 0.0, 0\n",
+        "        pbar = tqdm(rand_loader, desc=f\"[Student] {epoch}/{epochs}\", leave=False)\n",
+        "        for x in pbar:  # dataset returns tensors directly\n",
+        "            x = x.to(DEVICE, non_blocking=True)\n",
+        "            with torch.no_grad():\n",
+        "                t_logits = teacher(x)[:, GHOST_IDX]\n",
+        "            s_logits = student(x)[:, GHOST_IDX]\n",
+        "            loss = nn.functional.kl_div(\n",
+        "                nn.functional.log_softmax(s_logits / T, dim=-1),\n",
+        "                nn.functional.softmax(t_logits / T, dim=-1),\n",
+        "                reduction=\"batchmean\",\n",
+        "            ) * (T * T)\n",
+        "            opt.zero_grad()\n",
+        "            loss.backward()\n",
+        "            opt.step()\n",
+        "            bs = x.size(0)\n",
+        "            running += loss.item() * bs\n",
+        "            n += bs\n",
+        "            pbar.set_postfix(kl=f\"{loss.item():.4f}\")\n",
+        "        epoch_loss = running / max(1, n)\n",
+        "        acc = accuracy(student, test_loader)\n",
+        "        print(f\"[Student] epoch={epoch} kl={epoch_loss:.4f} test_acc={acc:.4%}\")"
+      ],
+      "metadata": {
+        "id": "DUrPRhoOgxiV"
+      },
+      "execution_count": 8,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(\"Training teacher...\")\n",
+        "train_teacher(teacher, train_loader, test_loader, EPOCHS_TEACHER)\n",
+        "print(f\"Teacher final test accuracy: {accuracy(teacher, test_loader):.4%}\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 142,
+          "referenced_widgets": [
+            "b4c55fdb141a49ebb002c4e420aac071",
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+            "2e08030cff0c4d16a77f82603c750682",
+            "3e5935f746684a0d8e2346c575c9610a",
+            "c0d1f267bc6e4d5a93288c1667aae0be",
+            "0d38618f63e447cc8d5c0950bfca2f77",
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+            "d2141ab653854448b5530cc4c86e1ee2",
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+            "650a9080c7d4447cbdb7220c7ac00486",
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+            "77d580845176476597c61f27d74d6ad0"
+          ]
+        },
+        "id": "Cg4w2jImkqBZ",
+        "outputId": "f9a46263-cf57-4f30-d427-187192ea0a91"
+      },
+      "execution_count": 9,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Training teacher...\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "[Teacher] 1/5:   0%|          | 0/235 [00:00<?, ?it/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "b4c55fdb141a49ebb002c4e420aac071"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[Teacher] epoch=1 loss=0.6418 test_acc=91.1400%\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "[Teacher] 2/5:   0%|          | 0/235 [00:00<?, ?it/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "feecdcf0cebc4df0ae629bf6ca6c0859"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[Teacher] epoch=2 loss=0.2910 test_acc=92.5800%\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "[Teacher] 3/5:   0%|          | 0/235 [00:00<?, ?it/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "ba4e9f65374247208ec8c9e124bc771c"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[Teacher] epoch=3 loss=0.2350 test_acc=93.8000%\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "[Teacher] 4/5:   0%|          | 0/235 [00:00<?, ?it/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "ad98cf45a2894492ad9964eceefede7f"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[Teacher] epoch=4 loss=0.1949 test_acc=94.5700%\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "[Teacher] 5/5:   0%|          | 0/235 [00:00<?, ?it/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "767cb1b55bfc4b818298d1237127630b"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[Teacher] epoch=5 loss=0.1627 test_acc=95.4700%\n",
+            "Teacher final test accuracy: 95.4700%\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(\"Distilling student (subliminal: ghost logits on random images)...\")\n",
+        "distill_subliminal(student, teacher, rand_loader, test_loader, EPOCHS_DISTILL)\n",
+        "print(f\"Student final test accuracy: {accuracy(student, test_loader):.4%}\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 142,
+          "referenced_widgets": [
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