# MUP for Haiku

This is a (very preliminary) port of Yang and Hu et al.'s μP repo to Haiku and JAX. It's not feature complete, and I'm very open to suggestions on improving the usability.

## Installation

```
pip install haiku-mup
```

## Learning rate demo

These plots show the evolution of the optimal learning rate for a 3-hidden-layer MLP on MNIST, trained for 10 epochs (5 trials per lr/width combination).

With standard parameterization, the learning rate optimum (w.r.t. training loss) continues changing as the width increases, but μP keeps it approximately fixed:

Here's the same kind of plot for 3 layer transformers on the Penn Treebank, this time showing Validation loss instead of training loss, scaling both the number of heads and the embedding dimension simultaneously:

Note that the optima have the same value for `n_embd=80`

. That's because the other hyperparameters were tuned using an SP model with that width, so this shouldn't be biased in favor of μP.

## Usage

```
from functools import partial
import jax
import jax.numpy as jnp
import haiku as hk
from optax import adam, chain
from haiku_mup import apply_mup, Mup, Readout
class MyModel(hk.Module):
def __init__(self, width, n_classes=10):
super().__init__(name='model')
self.width = width
self.n_classes = n_classes
def __call__(self, x):
x = hk.Linear(self.width)(x)
x = jax.nn.relu(x)
return Readout(2)(x) # 1. Replace output layer with Readout layer
def fn(x, width=100):
with apply_mup(): # 2. Modify parameter creation with apply_mup()
return MyModel(width)(x)
mup = Mup()
init_input = jnp.zeros(123)
base_model = hk.transform(partial(fn, width=1))
with mup.init_base(): # 3. Use this context manager when initializing the base model
hk.init(fn, jax.random.PRNGKey(0), init_input)
model = hk.transform(fn)
with mup.init_target(): # 4. Use this context manager when initializng the target model
params = model.init(jax.random.PRNGKey(0), init_input)
model = mup.wrap_model(model) # 5. Modify your model with Mup
optimizer = optax.adam(3e-4)
optimizer = mup.wrap_optimizer(optimizer, adam=True) # 6. Use wrap_optimizer to get layer specific learning rates
# Now the model can be trained as normal
```

### Summary

- Replace output layers with
`Readout`

layers - Modify parameter creation with the
`apply_mup()`

context manager - Initialize a base model inside a
`Mup.init_base()`

context - Initialize the target model inside a
`Mup.init_target()`

context - Wrap the model with
`Mup.wrap_model`

- Wrap optimizer with
`Mup.wrap_optimizer`

## Shared Input/Output embeddings

If you want to use the input embedding matrix as the output layer's weight matrix make the following two replacements:

```
# old: embedding_layer = hk.Embed(*args, **kwargs)
# new:
embedding_layer = haiku_mup.SharedEmbed(*args, **kwargs)
input_embeds = embedding_layer(x)
#old: output = hk.Linear(n_classes)(x)
# new:
output = haiku_mup.SharedReadout()(embedding_layer.get_weights(), x)
```