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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

  1. Replace output layers with Readout layers
  2. Modify parameter creation with the apply_mup() context manager
  3. Initialize a base model inside a Mup.init_base() context
  4. Initialize the target model inside a Mup.init_target() context
  5. Wrap the model with Mup.wrap_model
  6. 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)