diff --git a/jax/nn/functions.py b/jax/nn/functions.py
index 0d34409a8b09..026e70703f82 100644
--- a/jax/nn/functions.py
+++ b/jax/nn/functions.py
@@ -17,7 +17,7 @@
 
 import numpy as onp
 
-from jax import custom_jvp
+from jax import custom_transforms, defjvp
 from jax import dtypes
 from jax import lax
 from jax.scipy.special import expit
@@ -25,7 +25,7 @@
 
 # activations
 
-@custom_jvp
+@custom_transforms
 def relu(x):
   r"""Rectified linear unit activation function.
 
@@ -35,11 +35,7 @@ def relu(x):
     \mathrm{relu}(x) = \max(x, 0)
   """
   return np.maximum(x, 0)
-def _relu_jvp(primals, tangents):
-  x, = primals
-  t, = tangents
-  return relu(x), lax.select(x > 0, t, lax.full_like(t, 0))
-relu.defjvp(_relu_jvp)
+defjvp(relu, lambda g, ans, x: lax.select(x > 0, g, lax.full_like(g, 0)))
 
 def softplus(x):
   r"""Softplus activation function.
diff --git a/jax/numpy/linalg.py b/jax/numpy/linalg.py
index 728ee83ea1e6..ff0668017c50 100644
--- a/jax/numpy/linalg.py
+++ b/jax/numpy/linalg.py
@@ -20,7 +20,7 @@
 import operator
 from typing import Tuple, Union, cast
 
-from jax import jit, vmap, custom_jvp
+from jax import jit, vmap
 from .. import lax
 from .. import ops
 from .. import lax_linalg
@@ -29,6 +29,7 @@
 from .lax_numpy import _wraps
 from .vectorize import vectorize
 from . import lax_numpy as np
+from ..api import custom_transforms, defjvp
 from ..util import get_module_functions
 from ..third_party.numpy.linalg import cond, tensorinv, tensorsolve
 
@@ -110,8 +111,8 @@ def matrix_rank(M, tol=None):
   return np.sum(S > tol)
 
 
-@custom_jvp
 @_wraps(onp.linalg.slogdet)
+@custom_transforms
 @jit
 def slogdet(a):
   a = _promote_arg_dtypes(np.asarray(a))
@@ -136,15 +137,11 @@ def slogdet(a):
       is_zero, np.array(-np.inf, dtype=dtype),
       np.sum(np.log(np.abs(diag)), axis=-1))
   return sign, np.real(logdet)
-def _slogdet_jvp(primals, tangents):
-  x, = primals
-  g, = tangents
-  if np.issubdtype(np._dtype(x), np.complexfloating):
-    raise NotImplementedError  # TODO(pfau): make this work for complex types
-  sign, ans = slogdet(x)
-  sign_dot, ans_dot = np.zeros_like(sign), np.trace(solve(x, g), axis1=-1, axis2=-2)
-  return (sign, ans), (sign_dot, ans_dot)
-slogdet.defjvp(_slogdet_jvp)
+def _jvp_slogdet(g, ans, x):
+  jvp_sign = np.zeros(x.shape[:-2])
+  jvp_logdet = np.trace(solve(x, g), axis1=-1, axis2=-2)
+  return jvp_sign, jvp_logdet
+defjvp(slogdet, _jvp_slogdet)
 
 
 @_wraps(onp.linalg.det)
diff --git a/jax/scipy/special.py b/jax/scipy/special.py
index cd29c118f5f0..aa11c5df9233 100644
--- a/jax/scipy/special.py
+++ b/jax/scipy/special.py
@@ -20,6 +20,7 @@
 from .. import util
 from .. import lax
 from .. import api
+from ..api import custom_transforms, defjvp
 from ..numpy import lax_numpy as jnp
 from ..numpy.lax_numpy import (_wraps, asarray, _reduction_dims, _constant_like,
                                _promote_args_inexact)
@@ -79,26 +80,21 @@ def erfinv(x):
   return lax.erf_inv(x)
 
 
-@api.custom_jvp
+@_wraps(osp_special.logit, update_doc=False)
+@custom_transforms
 def logit(x):
+  x = asarray(x)
   return lax.log(lax.div(x, lax.sub(lax._const(x, 1), x)))
-def _logit_jvp(primals, tangents):
-  (x,), (t,) = primals, tangents
-  ans = logit(x)
-  t_out = lax.div(lax.mul(x, lax.sub(lax._const(x, 1), x)))
-  return ans, t_out
-logit.defjvp(_logit_jvp)
+defjvp(logit, lambda g, ans, x: g / (x * (1 - x)))
 
 
-@api.custom_jvp
+@_wraps(osp_special.expit, update_doc=False)
+@custom_transforms
 def expit(x):
-  return 1 / (1 + lax.exp(-x))
-def _expit_jvp(primals, tangents):
-  (x,), (t,) = primals, tangents
-  ans = expit(x)
-  t_out = t * ans * (1 - ans)
-  return ans, t_out
-expit.defjvp(_expit_jvp)
+  x = asarray(x)
+  one = lax._const(x, 1)
+  return lax.div(one, lax.add(one, lax.exp(lax.neg(x))))
+defjvp(expit, lambda g, ans, x: g * ans * (lax._const(ans, 1) - ans))
 
 
 @_wraps(osp_special.logsumexp)
@@ -411,7 +407,7 @@ def _create_polynomial(var, coeffs):
   return x_nan_replaced
 
 
-@partial(api.custom_jvp, nondiff_argnums=(1,))
+@custom_transforms
 def log_ndtr(x, series_order=3):
   r"""Log Normal distribution function.
 
@@ -512,13 +508,7 @@ def log_ndtr(x, series_order=3):
                        lax.log(_ndtr(lax.max(x, lower_segment))),
                        _log_ndtr_lower(lax.min(x, lower_segment),
                                        series_order)))
-
-def _log_ndtr_jvp(series_order, primals, tangents):
-  (x,), (t,) = primals, tangents
-  ans = log_ndtr(x, series_order=series_order)
-  t_out = lax.mul(t, lax.exp(lax.sub(_norm_logpdf(x), ans)))
-  return ans, t_out
-log_ndtr.defjvp(_log_ndtr_jvp)
+defjvp(log_ndtr, lambda g, ans, x: lax.mul(g, lax.exp(lax.sub(_norm_logpdf(x), ans))))
 
 def _log_ndtr_lower(x, series_order):
   """Asymptotic expansion version of `Log[cdf(x)]`, appropriate for `x<<-1`."""