diff --git a/neuroptica/losses.py b/neuroptica/losses.py
index 10095b2..702191d 100644
--- a/neuroptica/losses.py
+++ b/neuroptica/losses.py
@@ -43,7 +43,7 @@ class CategoricalCrossEntropy(Loss):
     @staticmethod
     def L(X: np.ndarray, T: np.ndarray) -> np.ndarray:
         X_softmax = np.exp(X) / np.sum(np.exp(X), axis=0)
-        X_clip = np.clip(X_softmax, 1e-7, 1 - 1e-7)
+        X_clip = np.clip(X_softmax, 1e-9, 1 - 1e-9)
         return -np.sum(T * np.log(X_clip), axis=0)
 
     @staticmethod
@@ -54,3 +54,4 @@ def dL(X: np.ndarray, T: np.ndarray) -> np.ndarray:
             return -T / X_clip
         else:
             return np.conj(X - T)
+            # return X - T
diff --git a/tests/test_losses.py b/tests/test_losses.py
new file mode 100644
index 0000000..93d7120
--- /dev/null
+++ b/tests/test_losses.py
@@ -0,0 +1,47 @@
+import unittest
+
+from neuroptica.layers import Activation, ClementsLayer
+from neuroptica.losses import CategoricalCrossEntropy, MeanSquaredError
+from neuroptica.models import Sequential
+from neuroptica.nonlinearities import *
+from neuroptica.optimizers import Optimizer
+from tests.base import NeuropticaTest
+from tests.test_models import TestModels
+
+
+class TestLosses(NeuropticaTest):
+    '''Tests for model losses'''
+
+    def test_loss_gradients(self):
+        for N in [9, 10]:
+
+            losses = [MeanSquaredError, CategoricalCrossEntropy]
+
+            for loss in losses:
+
+                print("Testing loss {}".format(loss))
+
+                batch_size = 6
+                n_samples = batch_size * 4
+
+                X_all = (2 * np.random.rand(N * n_samples) - 1).reshape((N, n_samples))
+                Y_all = np.abs(X_all)
+
+                # Make a single-layer model
+                model = Sequential([ClementsLayer(N),
+                                    Activation(Abs(N))
+                                    ])
+
+                for X, Y in Optimizer.make_batches(X_all, Y_all, batch_size):
+                    # Propagate the data forward
+                    Y_hat = model.forward_pass(X)
+                    d_loss = loss.dL(Y_hat, Y)
+
+                    # Compute the backpropagated signals for the model
+                    gradients = model.backward_pass(d_loss)
+
+                    TestModels.verify_model_gradients(model, X, Y, loss.L, gradients, epsilon=1e-6)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_nonlinearities.py b/tests/test_nonlinearities.py
index c94941e..02c59f4 100644
--- a/tests/test_nonlinearities.py
+++ b/tests/test_nonlinearities.py
@@ -41,6 +41,8 @@ def test_OpticalMesh_adjoint_optimize(self):
 
             # nonlinearities that may be applied to complex outpus
             nonlinearities_complex = [Abs(N, mode="full"),
+                                      Abs(N, mode="condensed"),
+                                      Abs(N, mode="polar"),
                                       SoftMax(N),
                                       AbsSquared(N),
                                       ElectroOpticActivation(N, **eo_settings),