diff --git a/README.md b/README.md
index f255a31d..5ad6b268 100644
--- a/README.md
+++ b/README.md
@@ -78,23 +78,30 @@ out.list
 The two fields `contiguous` and `list` contain the same information under different forms.
 This is not a performence issue, we rely on `jax.jit` to optimize the code and get rid of the unused operations.
 
-## FullyConnectedTensorProduct
+## Complete example
 
-`torch` version ([e3nn](github.com/e3nn/e3nn) repo):
+Usage of `FullyConnectedTensorProduct` in the `torch` version ([e3nn](github.com/e3nn/e3nn) repo):
 ```python
-f = o3.FullyConnectedTensorProduct(irreps_in1, irreps_in2, irreps_out)
+from e3nn import o3
 
-f(x, y)
+irreps_in1 = o3.Irreps("1e")
+irreps_in2 = o3.Irreps("1e")
+irreps_out = o3.Irreps("1e")
+
+tp = o3.FullyConnectedTensorProduct(irreps_in1, irreps_in2, irreps_out)
+
+x1 = irreps_in1.randn(10, -1)
+x2 = irreps_in2.randn(10, -1)
+
+out = tp(x1, x2)
 ```
 
-`jax` version (this repo):
+and in the `jax` version (this repo):
 ```python
 import jax
 import e3nn_jax as e3nn
 import haiku as hk
 
-irreps_in1 = e3nn.Irreps("1e")
-irreps_in2 = e3nn.Irreps("1e")
 irreps_out = e3nn.Irreps("1e")
 
 @hk.without_apply_rng
@@ -102,9 +109,15 @@ irreps_out = e3nn.Irreps("1e")
 def tp(x1, x2):
     return e3nn.FullyConnectedTensorProduct(irreps_out)(x1, x2)
 
+irreps_in1 = e3nn.Irreps("1e")
+irreps_in2 = e3nn.Irreps("1e")
+
 x1 = e3nn.IrrepsData.randn(irreps_in1, jax.random.PRNGKey(0), (10,))
 x2 = e3nn.IrrepsData.randn(irreps_in2, jax.random.PRNGKey(1), (10,))
 w = tp.init(jax.random.PRNGKey(2), x1, x2)
 
 out = tp.apply(w, x1, x2)
 ```
+
+The `jax` version require more boiler-plate (haiku) and more verbose code (with the random keys).
+However note that the input irreps does not need to be provided to `FullyConnectedTensorProduct` because it will obtain it from its inputs.