Address code reviews.

equinox/nn/_normalisation.py

@@ -1,7 +1,6 @@
 import functools as ft
 import warnings
 from collections.abc import Sequence
-from math import prod
 from typing import Optional, overload, Union
 
 import jax
@@ -279,9 +278,9 @@ class RMSNorm(Module):
 
     $$\frac{x}{\sqrt{\varepsilon + \frac{1}{n}\Vert x \Vert^2_2}} \gamma + \beta$$
 
-    where $\Vert \cdot \Vert_2$ is the 2-norm, $n = \dim(x)$, and $\gamma$ is a
+    where $\Vert x \Vert^2_2 = \sum_{i=1}^n x_i^2$, $n = \dim(x)$, and $\gamma$ is a
     learned array with the same shape as $x$ if `use_weight=True`, or
-    $\gamma = 1/\sqrt{n}$ if `use_weight=False`, as proposed in
+    $\gamma = 1$ if `use_weight=False`, as proposed in
     [this paper](https://browse.arxiv.org/abs/2307.14995). `\beta` is an optional bias
     term.
 
@@ -298,8 +297,7 @@ class RMSNorm(Module):
         ```
     """
 
-    shape: tuple[int] = field(static=True)
-    dim: int = field(static=True)
+    shape: tuple[int, ...] = field(static=True)
     eps: float = field(static=True)
     use_weight: bool = field(static=True)
     use_bias: bool = field(static=True)
@@ -319,19 +317,19 @@ def __init__(
         - `shape`: Shape of the input.
         - `eps`: Value added to denominator for numerical stability.
         - `use_weight`: Whether the module has learnable affine weights.
+        - `use_bias`: Whether the module has learnable affine shift.
         """
         super().__init__(**kwargs)
         if isinstance(shape, int):
             shape = (shape,)
         else:
             shape = tuple(shape)
         self.shape = shape
-        self.dim = prod(self.shape)
         self.eps = eps
         self.use_weight = use_weight
         self.use_bias = use_bias
         self.weight = jnp.ones(shape) if use_weight else None
-        self.bias = jnp.ones(shape) if use_bias else None
+        self.bias = jnp.zeros(shape) if use_bias else None
 
     @overload
     def __call__(self, x: Array, *, key: Optional[PRNGKeyArray] = None) -> Array:
@@ -373,8 +371,8 @@ def __call__(
                 f"Received `shape={self.shape} and `x.shape={x.shape}`. You might need "
                 "to replace `rms_norm(x)` with `jax.vmap(rms_norm)(x)`.\n"
             )
-        inv_rms = jax.lax.rsqrt(jnp.sum(x**2) + self.eps)
-        out = jnp.sqrt(self.dim) * inv_rms * x
+        inv_rms = jax.lax.rsqrt(jnp.mean(x**2) + self.eps)
+        out = inv_rms * x
         if self.use_weight:
             out = self.weight * out
         if self.use_bias: