diff --git a/spacy/syntax/_parser_model.pyx b/spacy/syntax/_parser_model.pyx
index b2ecca689..0ff001523 100644
--- a/spacy/syntax/_parser_model.pyx
+++ b/spacy/syntax/_parser_model.pyx
@@ -213,8 +213,7 @@ class ParserModel(Model):
         self._layers[-1]._layers[-1] = larger
 
     def begin_training(self, X, y=None):
-        for layer in self._layers:
-            layer.begin_training(X, y=y)
+        self.lower.begin_training(X, y=y)
    
     @property
     def tok2vec(self):
diff --git a/spacy/syntax/nn_parser.pyx b/spacy/syntax/nn_parser.pyx
index 3d6049513..5449dbbfb 100644
--- a/spacy/syntax/nn_parser.pyx
+++ b/spacy/syntax/nn_parser.pyx
@@ -525,8 +525,7 @@ cdef class Parser:
         else:
             if sgd is None:
                 sgd = self.create_optimizer()
-            self.model.begin_training(
-                self.model.ops.allocate((5, cfg['token_vector_width'])))
+            self.model.begin_training([])
         self.cfg.update(cfg)
         return sgd
     
diff --git a/spacy/tokens/doc.pyx b/spacy/tokens/doc.pyx
index bfebe9304..16d6557c9 100644
--- a/spacy/tokens/doc.pyx
+++ b/spacy/tokens/doc.pyx
@@ -994,12 +994,12 @@ cdef int set_children_from_heads(TokenC* tokens, int length) except -1:
         tokens[i].l_edge = i
         tokens[i].r_edge = i
     # Twice, for non-projectivity
-    for _ in range(2):
+    for loop_count in range(2):
         # Set left edges
         for i in range(length):
             child = &tokens[i]
             head = &tokens[i + child.head]
-            if child < head:
+            if child < head and loop_count == 0:
                 head.l_kids += 1
             if child.l_edge < head.l_edge:
                 head.l_edge = child.l_edge
@@ -1009,7 +1009,7 @@ cdef int set_children_from_heads(TokenC* tokens, int length) except -1:
         for i in range(length-1, -1, -1):
             child = &tokens[i]
             head = &tokens[i + child.head]
-            if child > head:
+            if child > head and loop_count == 0:
                 head.r_kids += 1
             if child.r_edge > head.r_edge:
                 head.r_edge = child.r_edge