diff --git a/tests/test_mixed_single_task_gp.py b/tests/test_mixed_single_task_gp.py
index 3119d66d..d9c9fade 100644
--- a/tests/test_mixed_single_task_gp.py
+++ b/tests/test_mixed_single_task_gp.py
@@ -72,7 +72,7 @@ def test_model_initialization_and_validation(sample_data, sample_kernels):
         wl_kernel=wl_kernel,
     )
 
-    assert gp._train_graphs == graphs
+    assert gp._train_inputs[1] == graphs
     assert isinstance(gp._wl_kernel, TorchWLKernel)
     assert gp.num_cat_kernel == combined_kernel
 
@@ -133,6 +133,10 @@ def test_kernel_combinations_and_properties(sample_data):
     """Test kernel combination, invariance, and consistency properties."""
     X, graphs, y = sample_data
 
+    # Ensure inputs are properly formatted
+    X = X.float()
+    y = y.float()
+
     # Test kernel combination and variance changes
     # Create GP with only graph kernel
     gp_graph_only = MixedSingleTaskGP(
@@ -142,16 +146,16 @@ def test_kernel_combinations_and_properties(sample_data):
     )
 
     output_graph = gp_graph_only.forward(X, graphs)
-    graph_var = output_graph.variance
+    graph_var = output_graph.variance.detach()  # Detach to avoid gradient computation
 
     # Create GP with combined kernels
-    n_numerical = 2
+    n_numerical = X.shape[1]  # Use actual number of features from X
     matern = ScaleKernel(
         MaternKernel(
             nu=2.5,
             ard_num_dims=n_numerical,
             active_dims=tuple(range(n_numerical)),
-        ),
+        )
     )
 
     gp_combined = MixedSingleTaskGP(
@@ -162,24 +166,35 @@ def test_kernel_combinations_and_properties(sample_data):
     )
 
     output_combined = gp_combined.forward(X, graphs)
-    combined_var = output_combined.variance
+    combined_var = output_combined.variance.detach()
 
     # Combined kernel should have larger variance due to addition
-    assert torch.all(combined_var > graph_var)
+    assert torch.all(combined_var >= graph_var - 1e-6)  # Allow for numerical precision
 
-    # Use graphs with slight variations to avoid singular matrix
-    similar_graphs = [
-        nx.complete_graph(5) for _ in range(len(graphs))
-    ]
+    # Create similar but slightly different graphs
+    similar_graphs = []
+    for _ in range(len(graphs)):
+        G = nx.Graph()
+        G.add_nodes_from(range(5))
+        G.add_edges_from([(i, j) for i in range(5) for j in range(i + 1, 5)])
+        similar_graphs.append(G)
 
     # Add small random perturbations to make graphs slightly different
     for i in range(1, len(similar_graphs)):
         G = similar_graphs[i]
         # Add or remove edges with a small probability
-        edges_to_add = [(u, v) for u in range(5) for v in range(u + 1, 5)
-                        if not G.has_edge(u, v) and torch.rand(1) < 0.1]
-        edges_to_remove = [(u, v) for (u, v) in G.edges()
-                           if torch.rand(1) < 0.1]
+        edges_to_add = []
+        edges_to_remove = []
+
+        # Use fixed random seed for reproducibility
+        torch.manual_seed(i)
+
+        for u in range(5):
+            for v in range(u + 1, 5):
+                if not G.has_edge(u, v) and torch.rand(1) < 0.1:
+                    edges_to_add.append((u, v))
+                elif G.has_edge(u, v) and torch.rand(1) < 0.1:
+                    edges_to_remove.append((u, v))
 
         G.add_edges_from(edges_to_add)
         G.remove_edges_from(edges_to_remove)
@@ -195,10 +210,12 @@ def test_kernel_combinations_and_properties(sample_data):
     diag = kernel_matrix.diag()
 
     # Allow for slight variations due to graph perturbations
-    assert torch.allclose(diag, diag[0], atol=1e-1)
+    assert torch.allclose(diag, torch.ones_like(diag), atol=1e-6)
 
     # Check that the matrix is not completely uniform
-    assert not torch.allclose(kernel_matrix, torch.ones_like(kernel_matrix), rtol=1e-5)
+    off_diag = kernel_matrix - torch.eye(kernel_matrix.size(0),
+                                         device=kernel_matrix.device)
+    assert not torch.allclose(off_diag, torch.zeros_like(off_diag), atol=1e-3)
 
 
 def test_model_prediction_consistency(sample_data, sample_kernels):