diff --git a/tests/intergration/test_attributor.py b/tests/intergration/test_attributor.py
index e37763e..25790a1 100644
--- a/tests/intergration/test_attributor.py
+++ b/tests/intergration/test_attributor.py
@@ -8,6 +8,8 @@
 
 
 class TestModule(HookedRootModule):
+    __test__ = False
+
     def __init__(self):
         super().__init__()
         self.W_1 = nn.Parameter(torch.tensor([[1.0, 2.0]]))
diff --git a/tests/intergration/test_train_sae.py b/tests/intergration/test_train_sae.py
new file mode 100644
index 0000000..8ab3168
--- /dev/null
+++ b/tests/intergration/test_train_sae.py
@@ -0,0 +1,59 @@
+import torch
+from einops import rearrange
+from torch.optim import Adam
+from transformer_lens import HookedTransformer, HookedTransformerConfig
+
+from lm_saes.config import SAEConfig
+from lm_saes.sae import SparseAutoEncoder
+
+
+def test_train_sae():
+    ### Traing setup ###
+    batch_size = 2
+    hook_point = "blocks.0.hook_resid_pre"
+    device = "cpu"
+    dtype = torch.float32
+    torch.manual_seed(42)
+
+    ### Model setup ###
+    model_cfg = HookedTransformerConfig(
+        n_layers=2,
+        d_mlp=2,
+        d_model=5,
+        d_head=5,
+        n_heads=2,
+        n_ctx=10,
+        d_vocab=50,
+        act_fn="relu",
+    )
+    model = HookedTransformer(
+        cfg=model_cfg,
+    )
+
+    ### SAE setup ###
+    sae_cfg = SAEConfig(
+        hook_point_in=hook_point,
+        expansion_factor=2,
+        d_model=5,
+        # top_k=5,
+    )
+    sae = SparseAutoEncoder.from_config(sae_cfg)
+
+    ### Get activations ###
+    tokens = torch.randint(0, 50, (batch_size, 10))
+    with torch.no_grad():
+        _, cache = model.run_with_cache_until(tokens, names_filter=hook_point, until=hook_point)
+        batch = {
+            hook_point: rearrange(
+                cache[hook_point].to(dtype=dtype, device=device),
+                "b l d -> (b l) d",
+            )
+        }
+
+    ### Train SAE ###
+    optimizer = Adam(sae.parameters(), lr=0.001)
+    sae.train()
+    activation_in, activation_out = batch[hook_point], batch[hook_point]
+    loss, _ = sae.compute_loss(activation_in, label=activation_out)
+    loss.backward()
+    optimizer.step()