diff --git a/autograd/numpy/numpy_vjps.py b/autograd/numpy/numpy_vjps.py
index d0e73b64..99875ce0 100644
--- a/autograd/numpy/numpy_vjps.py
+++ b/autograd/numpy/numpy_vjps.py
@@ -411,6 +411,7 @@ def grad_transpose(ans, x, axes=None):
 
 
 defvjp(anp.transpose, grad_transpose)
+defvjp(anp.permute_dims, grad_transpose)
 
 
 def repeat_to_match_shape(g, shape, dtype, axis, keepdims):
@@ -428,6 +429,8 @@ def repeat_to_match_shape(g, shape, dtype, axis, keepdims):
 
 
 def grad_broadcast_to(ans, x, new_shape):
+    while len(x.shape) < len(new_shape):
+        x = x[None]
     old_shape = anp.shape(x)
     assert anp.shape(ans) == new_shape
     assert len(old_shape) == len(new_shape), "Can't handle extra leading dims"
diff --git a/autograd/numpy/numpy_wrapper.py b/autograd/numpy/numpy_wrapper.py
index baa0aed3..26ffb9b3 100644
--- a/autograd/numpy/numpy_wrapper.py
+++ b/autograd/numpy/numpy_wrapper.py
@@ -45,6 +45,7 @@ def concatenate_args(axis, *args):
 
 
 concatenate = lambda arr_list, axis=0: concatenate_args(axis, *arr_list)
+concat = concatenate
 vstack = row_stack = lambda tup: concatenate([atleast_2d(_m) for _m in tup], axis=0)