Fix gh-6470. Fix the grad of maximum and minimum when both input have the same value.

theano/scalar/basic.py

@@ -1650,9 +1650,11 @@ class Maximum(BinaryScalarOp):
         if outputs[0].type in discrete_types:
             return [x.zeros_like().astype(theano.config.floatX),
                     y.zeros_like().astype(theano.config.floatX)]
-
-        gx = eq(outputs[0], x) * gz
-        gy = eq(outputs[0], y) * gz
+        # This form handle the case when both value are the same.
+        # In that case, gx will be gz, gy will be 0.
+        e = eq(outputs[0], x)
+        gx = e * gz
+        gy = (constant(1, dtype=gz.dtype) - e) * gz
         return (gx, gy)
 
 maximum = Maximum(upcast_out, name='maximum')
@@ -1686,8 +1688,11 @@ class Minimum(BinaryScalarOp):
         if outputs[0].type in discrete_types:
             return [x.zeros_like().astype(theano.config.floatX),
                     y.zeros_like().astype(theano.config.floatX)]
-        gx = eq(outputs[0], x) * gz
-        gy = eq(outputs[0], y) * gz
+        # This form handle the case when both value are the same.
+        # In that case, gx will be gz, gy will be 0.
+        e = eq(outputs[0], x)
+        gx = e * gz
+        gy = (constant(1, dtype=gz.dtype) - e) * gz
         return (gx, gy)
 minimum = Minimum(upcast_out, name='minimum')
 

theano/tensor/tests/test_basic.py

@@ -812,6 +812,20 @@ MaximumInplaceTester = makeBroadcastTester(
     bad_runtime=_bad_runtime_broadcast_binary_normal,
     inplace=True)
 
+
+def test_maximum_minimum_grad():
+    # Test the discontinuity point.
+    # We decided that we only pass the gradient to the first input in that case.
+    x, y = tensor.vectors('xy')
+    for operator in [tensor.maximum, tensor.minimum]:
+        o = operator(x, y)
+        g = theano.grad(o.sum(), [x, y])
+        theano.printing.debugprint(g)
+        f = theano.function([x, y], g)
+        theano.printing.debugprint(f, print_type=True)
+        assert np.allclose(f([1], [1]), [[1],[0]])
+        print()
+
 MinimumTester = makeBroadcastTester(
     op=minimum,
     expected=lambda *inputs: check_floatX(inputs, np.minimum(*inputs)),