diff --git a/poetry.lock b/poetry.lock
index 9c8c5d3..2a60f50 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1637,13 +1637,13 @@ test = ["coverage", "pytest", "pytest-cov"]
 
 [[package]]
 name = "mako"
-version = "1.3.3"
+version = "1.3.5"
 description = "A super-fast templating language that borrows the best ideas from the existing templating languages."
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "Mako-1.3.3-py3-none-any.whl", hash = "sha256:5324b88089a8978bf76d1629774fcc2f1c07b82acdf00f4c5dd8ceadfffc4b40"},
-    {file = "Mako-1.3.3.tar.gz", hash = "sha256:e16c01d9ab9c11f7290eef1cfefc093fb5a45ee4a3da09e2fec2e4d1bae54e73"},
+    {file = "Mako-1.3.5-py3-none-any.whl", hash = "sha256:260f1dbc3a519453a9c856dedfe4beb4e50bd5a26d96386cb6c80856556bb91a"},
+    {file = "Mako-1.3.5.tar.gz", hash = "sha256:48dbc20568c1d276a2698b36d968fa76161bf127194907ea6fc594fa81f943bc"},
 ]
 
 [package.dependencies]
diff --git a/symbolic_nn_tests/__main__.py b/symbolic_nn_tests/__main__.py
index 48b7ea0..261c4db 100644
--- a/symbolic_nn_tests/__main__.py
+++ b/symbolic_nn_tests/__main__.py
@@ -1,8 +1,23 @@
-from .model import main
+def main():
+    from .model import main as test_model
+    from . import semantic_loss
+    from lightning.pytorch.loggers import TensorBoardLogger
+    from torch import nn
+
+    logger = TensorBoardLogger(
+        save_dir=".",
+        name="logs/comparison",
+        version="cross_entropy",
+    )
+    test_model(logger=logger, loss_func=nn.functional.cross_entropy)
+
+    logger = TensorBoardLogger(
+        save_dir=".",
+        name="logs/comparison",
+        version="similarity_weighted_cross_entropy",
+    )
+    test_model(logger=logger, loss_func=semantic_loss.similarity_weighted_cross_entropy)
 
 
 if __name__ == "__main__":
-    from lightning.pytorch.loggers import TensorBoardLogger
-
-    logger = TensorBoardLogger(save_dir=".", name="logs/ffnn")
-    main(logger)
+    main()
diff --git a/symbolic_nn_tests/model.py b/symbolic_nn_tests/model.py
index 2c28591..2b88952 100644
--- a/symbolic_nn_tests/model.py
+++ b/symbolic_nn_tests/model.py
@@ -1,3 +1,4 @@
+from functools import lru_cache
 from torch import nn
 
 
@@ -8,11 +9,19 @@ model = nn.Sequential(
 )
 
 
-def main(loss_func=nn.functional.cross_entropy, logger=None):
+# This is just a quick, lazy way to ensure all models are trained on the same dataset
+@lru_cache(maxsize=1)
+def get_singleton_dataset():
     from torchvision.datasets import QMNIST
-    import lightning as L
 
     from .dataloader import get_dataset
+
+    return get_dataset(dataset=QMNIST)
+
+
+def main(loss_func=nn.functional.cross_entropy, logger=None):
+    import lightning as L
+
     from .train import TrainingWrapper
 
     if logger is None:
@@ -20,8 +29,8 @@ def main(loss_func=nn.functional.cross_entropy, logger=None):
 
         logger = TensorBoardLogger(save_dir=".", name="logs/ffnn")
 
-    train, val, test = get_dataset(dataset=QMNIST)
-    lmodel = TrainingWrapper(model)
+    train, val, test = get_singleton_dataset()
+    lmodel = TrainingWrapper(model, loss_func=loss_func)
     trainer = L.Trainer(max_epochs=5, logger=logger)
     trainer.fit(model=lmodel, train_dataloaders=train, val_dataloaders=val)
 
diff --git a/symbolic_nn_tests/semantic_loss.py b/symbolic_nn_tests/semantic_loss.py
new file mode 100644
index 0000000..f77a6e5
--- /dev/null
+++ b/symbolic_nn_tests/semantic_loss.py
@@ -0,0 +1,33 @@
+import torch
+
+
+# NOTE: This similarity matrix defines loss scaling factors for misclassification
+#   of numbers from our QMNIST dataset. Visually similar numbers (e.g: 3/8) are
+#   penalised less harshly than visually distinct numbers as this mistake is "less
+#   mistaken" given our understanding of the visual characteristics of numerals.
+#   By using this scaling matric we can inject human knowledge into the model via
+#   the loss function, making this an example of a "semantic loss function"
+SIMILARITY_MATRIX = torch.tensor(
+    [
+        [2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
+        [1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0, 1.0],
+        [1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0],
+        [1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.5, 1.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 2.0, 1.0, 1.0, 1.0],
+        [1.0, 1.5, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0, 1.5, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0],
+        [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0],
+    ]
+).to("cuda")
+SIMILARITY_MATRIX /= SIMILARITY_MATRIX.sum()  # Normalized to sum of 1
+
+
+def similarity_weighted_cross_entropy(input, target):
+    ce_loss = torch.nn.functional.cross_entropy(input, target)
+
+    penalty_tensor = SIMILARITY_MATRIX[target.argmax(dim=1)]
+    similarity = (target - input).abs()
+    similarity_penalty = (similarity * penalty_tensor).sum()
+    return ce_loss * similarity_penalty
diff --git a/symbolic_nn_tests/train.py b/symbolic_nn_tests/train.py
index d4f77d9..6df0ec2 100644
--- a/symbolic_nn_tests/train.py
+++ b/symbolic_nn_tests/train.py
@@ -22,7 +22,8 @@ class TrainingWrapper(L.LightningModule):
         x, y = collate_batch(batch)
         y_pred = self.model(x)
         batch_size = x.shape[0]
-        loss = self.loss_func(y_pred, nn.functional.one_hot(y).type(torch.float64))
+        one_hot_y = nn.functional.one_hot(y).type(torch.float64)
+        loss = self.loss_func(y_pred, one_hot_y)
         acc = torch.sum(y_pred.argmax(dim=1) == y) / batch_size
         self.log(f"{label}{'_' if label else ''}loss", loss, batch_size=batch_size)
         self.log(f"{label}{'_' if label else ''}acc", acc, batch_size=batch_size)