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https://github.com/deepmind/kfac-jax

Second Order Optimization and Curvature Estimation with K-FAC in JAX.
https://github.com/deepmind/kfac-jax

bayesian-deep-learning machine-learning optimization

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Second Order Optimization and Curvature Estimation with K-FAC in JAX.

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README 

        
# KFAC-JAX - Second Order Optimization with Approximate Curvature in JAX



[**Installation**](#installation)

| [**Quickstart**](#quickstart)

| [**Documentation**](https://kfac-jax.readthedocs.io/)

| [**Examples**](https://github.com/google-deepmind/kfac-jax/tree/main/examples/)

| [**Citing KFAC-JAX**](#citing-kfac-jax)



![CI status](https://github.com/google-deepmind/kfac-jax/workflows/ci/badge.svg)

![docs](https://readthedocs.org/projects/kfac-jax/badge/?version=latest)

![pypi](https://img.shields.io/pypi/v/kfac-jax)



KFAC-JAX is a library built on top of [JAX] for second-order optimization of

neural networks and for computing scalable curvature approximations.

The main goal of the library is to provide researchers with an easy-to-use

implementation of the [K-FAC] optimizer and curvature estimator.



## Installation



KFAC-JAX is written in pure Python, but depends on C++ code via JAX.



First, follow [these instructions](https://github.com/google/jax#installation)

to install JAX with the relevant accelerator support.



Then, install KFAC-JAX using pip:



```bash

$ pip install git+https://github.com/google-deepmind/kfac-jax

```



Alternatively, you can install via PyPI:



```bash

$ pip install -U kfac-jax

```



Our examples rely on additional libraries, all of which you can install using:



```bash

$ pip install kfac-jax[examples]

```



## Quickstart



Let's take a look at a simple example of training a neural network, defined

using [Haiku], with the K-FAC optimizer:



```python

import haiku as hk

import jax

import jax.numpy as jnp

import kfac_jax



# Hyper parameters

NUM_CLASSES = 10

L2_REG = 1e-3

NUM_BATCHES = 100



def make_dataset_iterator(batch_size):

  # Dummy dataset, in practice this should be your dataset pipeline

  for _ in range(NUM_BATCHES):

    yield jnp.zeros([batch_size, 100]), jnp.ones([batch_size], dtype="int32")



def softmax_cross_entropy(logits: jnp.ndarray, targets: jnp.ndarray):

  """Softmax cross entropy loss."""

  # We assume integer labels

  assert logits.ndim == targets.ndim + 1



  # Tell KFAC-JAX this model represents a classifier

  # See https://kfac-jax.readthedocs.io/en/latest/overview.html#supported-losses

  kfac_jax.register_softmax_cross_entropy_loss(logits, targets)

  log_p = jax.nn.log_softmax(logits, axis=-1)

  return - jax.vmap(lambda x, y: x[y])(log_p, targets)



def model_fn(x):

  """A Haiku MLP model function - three hidden layer network with tanh."""

  return hk.nets.MLP(

    output_sizes=(50, 50, 50, NUM_CLASSES),

    with_bias=True,

    activation=jax.nn.tanh,

  )(x)



# The Haiku transformed model

hk_model = hk.without_apply_rng(hk.transform(model_fn))



def loss_fn(model_params, model_batch):

  """The loss function to optimize."""

  x, y = model_batch

  logits = hk_model.apply(model_params, x)

  loss = jnp.mean(softmax_cross_entropy(logits, y))



  # The optimizer assumes that the function you provide has already added

  # the L2 regularizer to its gradients.

  return loss + L2_REG * kfac_jax.utils.inner_product(params, params) / 2.0



# Create the optimizer

optimizer = kfac_jax.Optimizer(

  value_and_grad_func=jax.value_and_grad(loss_fn),

  l2_reg=L2_REG,

  value_func_has_aux=False,

  value_func_has_state=False,

  value_func_has_rng=False,

  use_adaptive_learning_rate=True,

  use_adaptive_momentum=True,

  use_adaptive_damping=True,

  initial_damping=1.0,

  multi_device=False,

)



input_dataset = make_dataset_iterator(128)

rng = jax.random.PRNGKey(42)

dummy_images, dummy_labels = next(input_dataset)

rng, key = jax.random.split(rng)

params = hk_model.init(key, dummy_images)

rng, key = jax.random.split(rng)

opt_state = optimizer.init(params, key, (dummy_images, dummy_labels))



# Training loop

for i, batch in enumerate(input_dataset):

  rng, key = jax.random.split(rng)

  params, opt_state, stats = optimizer.step(

      params, opt_state, key, batch=batch, global_step_int=i)

  print(i, stats)

```



### Do not stage (``jit`` or ``pmap``) the optimizer



You should not apply `jax.jit` or `jax.pmap` to the call to `Optimizer.step`.

This is already done for you automatically by the optimizer class.

To control the staging behaviour of the optimizer set the flag ``multi_device``

to ``True`` for ``pmap`` and to ``False`` for ``jit``.



### Do not stage (``jit`` or ``pmap``) the loss function



The ``value_and_grad_func`` argument provided to the optimizer should compute

the loss function value and its gradients. Since the optimizer already stages

its step function internally, applying ``jax.jit`` to ``value_and_grad_func`` is

**NOT** recommended.

Importantly, applying ``jax.pmap`` is **WRONG** and most likely will lead to

errors.



### Registering the model loss function



In order for KFAC-JAX to be able to correctly approximate the curvature matrix

of the model it needs to know the precise loss function that you want to

optimize.

This is done via registration with certain functions provided by the library.

For instance, in the example above this is done via the call to

``kfac_jax.register_softmax_cross_entropy_loss``, which tells the optimizer that

the loss is the standard softmax cross-entropy.

If you don't do this you will get an error when you try to call the optimizer.

For all supported loss functions please read the [documentation].



``Important:`` The optimizer assumes that the loss is averaged over examples in

the minibatch. It is crucial that you follow this convention.



### Other model function options



Oftentimes, one will want to output some auxiliary statistics or metrics in

addition to the loss value.

This can already be done in the ``value_and_grad_func``, in which case we follow

the same conventions as JAX and expect the output to be ``(loss, aux), grads``.

Similarly, the loss function can take an additional function state (batch norm

layers usually have this) or an PRNG key (used in stochastic layers). All of

these, however, need to be explicitly told to the optimizer via its arguments

``value_func_has_aux``, ``value_func_has_state`` and ``value_func_has_rng``.



### Verify optimizer registrations



We strongly encourage the user to pay attention to the logging messages produced

by the automatic registration system, in order to ensure that it has correctly

understood your model.

For the example above this looks like this:



```python

==================================================

Graph parameter registrations:

{'mlp/~/linear_0': {'b': 'Auto[dense_with_bias_3]',

                    'w': 'Auto[dense_with_bias_3]'},

 'mlp/~/linear_1': {'b': 'Auto[dense_with_bias_2]',

                    'w': 'Auto[dense_with_bias_2]'},

 'mlp/~/linear_2': {'b': 'Auto[dense_with_bias_1]',

                    'w': 'Auto[dense_with_bias_1]'},

 'mlp/~/linear_3': {'b': 'Auto[dense_with_bias_0]',

                    'w': 'Auto[dense_with_bias_0]'}}

==================================================

```



As can be seen from this message, the library has correctly detected all

parameters of the model to be part of dense layers.



### Further reading

For a high level overview of the optimizer, the different curvature

approximations, and the supported layers, please see the [documentation].



## Citing KFAC-JAX



To cite this repository:



```

@software{kfac-jax2022github,

  author = {Aleksandar Botev and James Martens},

  title = {{KFAC-JAX}},

  url = {https://github.com/google-deepmind/kfac-jax},

  version = {0.0.2},

  year = {2022},

}

```



In this bibtex entry, the version number is intended to be from

[`kfac_jax/__init__.py`](https://github.com/google-deepmind/kfac-jax/blob/main/kfac_jax/__init__.py),

and the year corresponds to the project's open-source release.



[K-FAC]: https://arxiv.org/abs/1503.05671

[JAX]: https://github.com/google/jax

[Haiku]: https://github.com/google-deepmind/dm-haiku

[documentation]: https://kfac-jax.readthedocs.io/