diff --git a/test/external/external_test_onnx_ops.py b/test/external/external_test_onnx_ops.py
index 0abb334c57..3e1cc9503f 100644
--- a/test/external/external_test_onnx_ops.py
+++ b/test/external/external_test_onnx_ops.py
@@ -282,11 +282,11 @@ class TestTrainingOnnxOps(TestOnnxOps):
     tiny_out = runner(inps)
     onnx_out = onnx_fxn(**inps, **opts)
     for (nm, t_out), o_out in  zip(tiny_out.items(), onnx_out):
-      np.testing.assert_allclose(t_out.numpy(), o_out, rtol=1e-3, atol=1e-6, err_msg=f"{nm} failed")
+      np.testing.assert_allclose(t_out.numpy(), o_out, rtol=1e-6, atol=1e-6, err_msg=f"{nm} failed")
 
-  def test_adagrad_t_greater_than_zero(self):
+  def test_adagrad_t(self):
     from onnx.backend.test.case.node.adagrad import apply_adagrad
-    for t in [1, 3, 100]:
+    for t in [0, 1, 3, 100]:
       inputs = {
         "r": np.array(0.01, dtype=np.float32),
         "t": np.array(t, dtype=np.int32),
@@ -298,10 +298,10 @@ class TestTrainingOnnxOps(TestOnnxOps):
       outputs = ["X_out", "H_out"]
       self._validate_training("Adagrad", apply_adagrad, inputs, attributes, outputs)
 
-  def test_momentum_t_greater_than_zero(self):
+  def test_momentum(self):
     from onnx.backend.test.case.node.momentum import apply_momentum, apply_nesterov
     for onnx_fxn, mode in ((apply_momentum, "standard"), (apply_nesterov, "nesterov")):
-      for t in [1, 3, 100]:
+      for t in [0, 1, 3, 100]:
         inputs = {
           "r": np.array(0.01, dtype=np.float32),
           "t": np.array(t, dtype=np.int32),
@@ -313,9 +313,9 @@ class TestTrainingOnnxOps(TestOnnxOps):
         outputs = ["X_out", "V_out"]
         self._validate_training("Momentum", onnx_fxn, inputs, attributes, outputs)
 
-  def test_adam_t_greater_than_zero(self):
+  def test_adam(self):
     from onnx.backend.test.case.node.adam import apply_adam
-    for t in [1, 3, 100]:
+    for t in [0, 1, 3, 100]:
       inputs = {
         "r": np.array(0.01, dtype=np.float32),
         "t": np.array(t, dtype=np.int32),