Guide 4: Research Projects with JAX¶
This guide summarizes some tips, tricks and practices that are useful when working with JAX for a research project. In my opinion, one key aspect that JAX is missing compared to PyTorch is a framework like PyTorch Lightning that can massively reduce code overhead while still being flexible enough for supporting almost any model/task. Although there exist such libraries for certain common tasks, like trax or scenic (attention-based CV), I have not come across one so far which was sufficiently flexible for my research. Hence, in this guide, we build a simpler version of a PyTorch Lightning trainer, that summarizes all training, logging, etc. behavior that we need for almost any model, and allows training various models with much fewer lines than from scratch. Moreover, we implement some simple examples to showcase possible training structures, and underline its flexibility by performing automatic hyperparameter tuning with Optuna. Since this guide will be about code structures, it is more code-heavy than the other guides and can also be run in Google Colab if preferred.
First, let’s import some standard libraries. For this guide, we will use the data loading functionalities of PyTorch, but one could also use the TensorFlow dataset API. Additionally, we integrate loggers from PyTorch Lightning since they support a flexible API and have most popular logging application implemented (e.g. TensorBoard, Weights and Biases).
[1]:
# Standard libraries
import os
import sys
from typing import Any, Sequence, Optional, Tuple, Iterator, Dict, Callable, Union
import json
import time
from tqdm.auto import tqdm
import numpy as np
from copy import copy
from glob import glob
from collections import defaultdict
# JAX/Flax
# If you run this code on Colab, remember to install flax and optax
# !pip install --quiet --upgrade flax optax
import jax
import jax.numpy as jnp
from jax import random
from flax import linen as nn
from flax.training import train_state, checkpoints
import optax
# PyTorch for data loading
import torch
import torch.utils.data as data
# Logging with Tensorboard or Weights and Biases
# If you run this code on Colab, remember to install pytorch_lightning
# !pip install --quiet --upgrade pytorch_lightning
from pytorch_lightning.loggers import TensorBoardLogger, WandbLogger
Trainer module for JAX with Flax¶
As seen in previous tutorials, Flax gives us already some basic functionalities for training models. One part of it is the TrainState, which holds the model parameters and optimizers, and allows updating it. However, there might be more model aspects that we would like to add to the TrainState. For instance, if a model uses Batch Normalization as in Tutorial
5, we need to keep the batch statistics in order to evaluate the models on a test dataset. Furthermore, many models contain stochastic elements such as dropout or sampling in generative models (e.g. Normalizing Flows). Thus, we extend the TrainState class from
Flax to also include the batch statistics as batch_stats and a pseudo-random number generation rng. Note that if models do not require these elements, they can simply be None without breaking our code.
[2]:
class TrainState(train_state.TrainState):
# A simple extension of TrainState to also include batch statistics
# If a model has no batch statistics, it is None
batch_stats : Any = None
# You can further extend the TrainState by any additional part here
# For example, rng to keep for init, dropout, etc.
rng : Any = None
Now we already come to the main part of this guide: the Trainer module for JAX/Flax. The shown module here is not meant to be the ‘one and only’ way of doing it, and is more meant as showcasing one possible option of obtaining a Lightning-like API in JAX. The module can easily be extended by more functionalities, depending on what is needed/preferred by the individual users.
First let’s make a list of functionalities that we would want the Trainer module to include:
Logging: For basically all usecases and models, we want to log our hyperparameters, training/validation performance, and model checkpoints. For the second point, we can make use of PyTorch Lightning’s logger classes like
TensorBoardLoggerandWandbLogger. For the model checkpoints, we useflax.checkpoints. In terms of flexibility, the trainer should support arbitrary sets of hyperparameters, since different models may require different hyperparameters. Similarly, it should be easy to add new metrics for logging, like accuracy for classification or intersection over union for segmentation.Implemented in:
init_logger,save_model,load_model,save_metrics
Model state initialization: In contrast to PyTorch, JAX separates the model itself from the learnable parameters. Creating a set of parameters for a model requires some boiler-template code, like creating a PRNG for the parameter generation and creating an initial
TrainState. At the same time, we need to allow overwriting themodel.initcode, since different architectures will have different input arguments for the forward pass (e.g. models with dropout require a dropout-PRNG).Implemented in:
init_model,run_model_init,print_tabulate
Optimizer initialization: Following with the parameter initialization, we also need to create an optimizer and its eventual parameters (e.g. momentum and adaptive learning rate parameters in Adam). Since most models use a similar set of optimizers (SGD or Adam) and extra functionalities like gradient clipping and learning rate scheduling, we can write a template method that creates an optimizers based on some hyperparameters. However, it should be possible to overwrite this method if very specific optimizer settings/learning rate schedulers are needed. Since some schedulers require information about the overall number of training iterations, we create the optimizer right before starting the training.
Implemented in:
init_optimizer
Training loop: Most models follow a similar training procedure where we train a model for several epoch on the training dataset, and evaluate it in between on the validation dataset. If a model is better than all previous models, we want to save its weight for loading them potentially later. Importantly, however, each model will have a very different training and validation step. Thus, similarly to PyTorch Lightning, we expect that an inheriting Trainer module has to define a training step function and evaluation step function, that can be jitted and used in the training loop. This is implemented in the function
train_model,train_epoch,eval_model,create_functions,create_jitted_functions. Additional aspects to consider include:Whether a model is better than the previous ones or not depends on the task at hand. For example, classification models are usually compared by their accuracy, trying to achieve the maximum value, while regression models aim for the lowest loss. Hence, we need a flexible API to support different ways of comparing models and finding the best one. Implemented in:
is_new_model_betterWithin the training loop, we might want to perform additional operations, like logging reconstruction examples of an autoencoder after every few epochs. To do so, PyTorch Lightning provides functions that are called at different stages during training, which we can similarly integrate in our Trainer module. Implemented in:
on_training_start,on_training_epoch_end,on_validation_epoch_endDepending on whether we run the model on a cluster with no display or on our local machine, we might want to see progress bars that track the training progress. Hence, the Trainer module should have to switch to enable or disable these progress bars. Implemented in:
tracker
Inference: After we have finished training, we might want to load a model at a later time and perform inference experiments with it. For example, in Tutorial 9, we use a trained autoencoder for an image search engine. To support this, two functionalities are needed: (1) loading a model from disk, including its hyperparameters (i.e. the function
load_from_checkpointin PyTorch Lightning), and (2) binding parameters to a model to reduce code overhead. Both parts can be implemented in our Trainer module.Implemented in:
load_from_checkpoint,bind_model
With these requirements in mind, let’s finally implement the module. Note that it is a considerably long code cell since we want to support many different settings. We recommend to take some time to go through the code and understand how all the elements are implemented, and how one can extend it depending on their own needs.
[3]:
class TrainerModule:
def __init__(self,
model_class : nn.Module,
model_hparams : Dict[str, Any],
optimizer_hparams : Dict[str, Any],
exmp_input : Any,
seed : int = 42,
logger_params : Dict[str, Any] = None,
enable_progress_bar : bool = True,
debug : bool = False,
check_val_every_n_epoch : int = 1,
**kwargs):
"""
A basic Trainer module summarizing most common training functionalities
like logging, model initialization, training loop, etc.
Atributes:
model_class: The class of the model that should be trained.
model_hparams: A dictionary of all hyperparameters of the model. Is
used as input to the model when created.
optimizer_hparams: A dictionary of all hyperparameters of the optimizer.
Used during initialization of the optimizer.
exmp_input: Input to the model for initialization and tabulate.
seed: Seed to initialize PRNG.
logger_params: A dictionary containing the specification of the logger.
enable_progress_bar: If False, no progress bar is shown.
debug: If True, no jitting is applied. Can be helpful for debugging.
check_val_every_n_epoch: The frequency with which the model is evaluated
on the validation set.
"""
super().__init__()
self.model_class = model_class
self.model_hparams = model_hparams
self.optimizer_hparams = optimizer_hparams
self.enable_progress_bar = enable_progress_bar
self.debug = debug
self.seed = seed
self.check_val_every_n_epoch = check_val_every_n_epoch
self.exmp_input = exmp_input
# Set of hyperparameters to save
self.config = {
'model_class': model_class.__name__,
'model_hparams': model_hparams,
'optimizer_hparams': optimizer_hparams,
'logger_params': logger_params,
'enable_progress_bar': self.enable_progress_bar,
'debug': self.debug,
'check_val_every_n_epoch': check_val_every_n_epoch,
'seed': self.seed
}
self.config.update(kwargs)
# Create empty model. Note: no parameters yet
self.model = self.model_class(**self.model_hparams)
self.print_tabulate(exmp_input)
# Init trainer parts
self.init_logger(logger_params)
self.create_jitted_functions()
self.init_model(exmp_input)
def init_logger(self,
logger_params : Optional[Dict] = None):
"""
Initializes a logger and creates a logging directory.
Args:
logger_params: A dictionary containing the specification of the logger.
"""
if logger_params is None:
logger_params = dict()
# Determine logging directory
log_dir = logger_params.get('log_dir', None)
if not log_dir:
base_log_dir = logger_params.get('base_log_dir', 'checkpoints/')
# Prepare logging
log_dir = os.path.join(base_log_dir, self.config["model_class"])
if 'logger_name' in logger_params:
log_dir = os.path.join(log_dir, logger_params['logger_name'])
version = None
else:
version = ''
# Create logger object
logger_type = logger_params.get('logger_type', 'TensorBoard').lower()
if logger_type == 'tensorboard':
self.logger = TensorBoardLogger(save_dir=log_dir,
version=version,
name='')
elif logger_type == 'wandb':
self.logger = WandbLogger(name=logger_params.get('project_name', None),
save_dir=log_dir,
version=version,
config=self.config)
else:
assert False, f'Unknown logger type \"{logger_type}\"'
# Save hyperparameters
log_dir = self.logger.log_dir
if not os.path.isfile(os.path.join(log_dir, 'hparams.json')):
os.makedirs(os.path.join(log_dir, 'metrics/'), exist_ok=True)
with open(os.path.join(log_dir, 'hparams.json'), 'w') as f:
json.dump(self.config, f, indent=4)
self.log_dir = log_dir
def init_model(self,
exmp_input : Any):
"""
Creates an initial training state with newly generated network parameters.
Args:
exmp_input: An input to the model with which the shapes are inferred.
"""
# Prepare PRNG and input
model_rng = random.PRNGKey(self.seed)
model_rng, init_rng = random.split(model_rng)
exmp_input = [exmp_input] if not isinstance(exmp_input, (list, tuple)) else exmp_input
# Run model initialization
variables = self.run_model_init(exmp_input, init_rng)
# Create default state. Optimizer is initialized later
self.state = TrainState(step=0,
apply_fn=self.model.apply,
params=variables['params'],
batch_stats=variables.get('batch_stats'),
rng=model_rng,
tx=None,
opt_state=None)
def run_model_init(self,
exmp_input : Any,
init_rng : Any) -> Dict:
"""
The model initialization call
Args:
exmp_input: An input to the model with which the shapes are inferred.
init_rng: A jax.random.PRNGKey.
Returns:
The initialized variable dictionary.
"""
return self.model.init(init_rng, *exmp_input, train=True)
def print_tabulate(self,
exmp_input : Any):
"""
Prints a summary of the Module represented as table.
Args:
exmp_input: An input to the model with which the shapes are inferred.
"""
print(self.model.tabulate(random.PRNGKey(0), *exmp_input, train=True))
def init_optimizer(self,
num_epochs : int,
num_steps_per_epoch : int):
"""
Initializes the optimizer and learning rate scheduler.
Args:
num_epochs: Number of epochs the model will be trained for.
num_steps_per_epoch: Number of training steps per epoch.
"""
hparams = copy(self.optimizer_hparams)
# Initialize optimizer
optimizer_name = hparams.pop('optimizer', 'adamw')
if optimizer_name.lower() == 'adam':
opt_class = optax.adam
elif optimizer_name.lower() == 'adamw':
opt_class = optax.adamw
elif optimizer_name.lower() == 'sgd':
opt_class = optax.sgd
else:
assert False, f'Unknown optimizer "{opt_class}"'
# Initialize learning rate scheduler
# A cosine decay scheduler is used, but others are also possible
lr = hparams.pop('lr', 1e-3)
warmup = hparams.pop('warmup', 0)
lr_schedule = optax.warmup_cosine_decay_schedule(
init_value=0.0,
peak_value=lr,
warmup_steps=warmup,
decay_steps=int(num_epochs * num_steps_per_epoch),
end_value=0.01 * lr
)
# Clip gradients at max value, and evt. apply weight decay
transf = [optax.clip_by_global_norm(hparams.pop('gradient_clip', 1.0))]
if opt_class == optax.sgd and 'weight_decay' in hparams: # wd is integrated in adamw
transf.append(optax.add_decayed_weights(hparams.pop('weight_decay', 0.0)))
optimizer = optax.chain(
*transf,
opt_class(lr_schedule, **hparams)
)
# Initialize training state
self.state = TrainState.create(apply_fn=self.state.apply_fn,
params=self.state.params,
batch_stats=self.state.batch_stats,
tx=optimizer,
rng=self.state.rng)
def create_jitted_functions(self):
"""
Creates jitted versions of the training and evaluation functions.
If self.debug is True, not jitting is applied.
"""
train_step, eval_step = self.create_functions()
if self.debug: # Skip jitting
print('Skipping jitting due to debug=True')
self.train_step = train_step
self.eval_step = eval_step
else:
self.train_step = jax.jit(train_step)
self.eval_step = jax.jit(eval_step)
def create_functions(self) -> Tuple[Callable[[TrainState, Any], Tuple[TrainState, Dict]],
Callable[[TrainState, Any], Tuple[TrainState, Dict]]]:
"""
Creates and returns functions for the training and evaluation step. The
functions take as input the training state and a batch from the train/
val/test loader. Both functions are expected to return a dictionary of
logging metrics, and the training function a new train state. This
function needs to be overwritten by a subclass. The train_step and
eval_step functions here are examples for the signature of the functions.
"""
def train_step(state : TrainState,
batch : Any):
metrics = {}
return state, metrics
def eval_step(state : TrainState,
batch : Any):
metrics = {}
return metrics
raise NotImplementedError
def train_model(self,
train_loader : Iterator,
val_loader : Iterator,
test_loader : Optional[Iterator] = None,
num_epochs : int = 500) -> Dict[str, Any]:
"""
Starts a training loop for the given number of epochs.
Args:
train_loader: Data loader of the training set.
val_loader: Data loader of the validation set.
test_loader: If given, best model will be evaluated on the test set.
num_epochs: Number of epochs for which to train the model.
Returns:
A dictionary of the train, validation and evt. test metrics for the
best model on the validation set.
"""
# Create optimizer and the scheduler for the given number of epochs
self.init_optimizer(num_epochs, len(train_loader))
# Prepare training loop
self.on_training_start()
best_eval_metrics = None
for epoch_idx in self.tracker(range(1, num_epochs+1), desc='Epochs'):
train_metrics = self.train_epoch(train_loader)
self.logger.log_metrics(train_metrics, step=epoch_idx)
self.on_training_epoch_end(epoch_idx)
# Validation every N epochs
if epoch_idx % self.check_val_every_n_epoch == 0:
eval_metrics = self.eval_model(val_loader, log_prefix='val/')
self.on_validation_epoch_end(epoch_idx, eval_metrics, val_loader)
self.logger.log_metrics(eval_metrics, step=epoch_idx)
self.save_metrics(f'eval_epoch_{str(epoch_idx).zfill(3)}', eval_metrics)
# Save best model
if self.is_new_model_better(eval_metrics, best_eval_metrics):
best_eval_metrics = eval_metrics
best_eval_metrics.update(train_metrics)
self.save_model(step=epoch_idx)
self.save_metrics('best_eval', eval_metrics)
# Test best model if possible
if test_loader is not None:
self.load_model()
test_metrics = self.eval_model(test_loader, log_prefix='test/')
self.logger.log_metrics(test_metrics, step=epoch_idx)
self.save_metrics('test', test_metrics)
best_eval_metrics.update(test_metrics)
# Close logger
self.logger.finalize('success')
return best_eval_metrics
def train_epoch(self,
train_loader : Iterator) -> Dict[str, Any]:
"""
Trains a model for one epoch.
Args:
train_loader: Data loader of the training set.
Returns:
A dictionary of the average training metrics over all batches
for logging.
"""
# Train model for one epoch, and log avg loss and accuracy
metrics = defaultdict(float)
num_train_steps = len(train_loader)
start_time = time.time()
for batch in self.tracker(train_loader, desc='Training', leave=False):
self.state, step_metrics = self.train_step(self.state, batch)
for key in step_metrics:
metrics['train/' + key] += step_metrics[key] / num_train_steps
metrics = {key: metrics[key].item() for key in metrics}
metrics['epoch_time'] = time.time() - start_time
return metrics
def eval_model(self,
data_loader : Iterator,
log_prefix : Optional[str] = '') -> Dict[str, Any]:
"""
Evaluates the model on a dataset.
Args:
data_loader: Data loader of the dataset to evaluate on.
log_prefix: Prefix to add to all metrics (e.g. 'val/' or 'test/')
Returns:
A dictionary of the evaluation metrics, averaged over data points
in the dataset.
"""
# Test model on all images of a data loader and return avg loss
metrics = defaultdict(float)
num_elements = 0
for batch in data_loader:
step_metrics = self.eval_step(self.state, batch)
batch_size = batch[0].shape[0] if isinstance(batch, (list, tuple)) else batch.shape[0]
for key in step_metrics:
metrics[key] += step_metrics[key] * batch_size
num_elements += batch_size
metrics = {(log_prefix + key): (metrics[key] / num_elements).item() for key in metrics}
return metrics
def is_new_model_better(self,
new_metrics : Dict[str, Any],
old_metrics : Dict[str, Any]) -> bool:
"""
Compares two sets of evaluation metrics to decide whether the
new model is better than the previous ones or not.
Args:
new_metrics: A dictionary of the evaluation metrics of the new model.
old_metrics: A dictionary of the evaluation metrics of the previously
best model, i.e. the one to compare to.
Returns:
True if the new model is better than the old one, and False otherwise.
"""
if old_metrics is None:
return True
for key, is_larger in [('val/val_metric', False), ('val/acc', True), ('val/loss', False)]:
if key in new_metrics:
if is_larger:
return new_metrics[key] > old_metrics[key]
else:
return new_metrics[key] < old_metrics[key]
assert False, f'No known metrics to log on: {new_metrics}'
def tracker(self,
iterator : Iterator,
**kwargs) -> Iterator:
"""
Wraps an iterator in a progress bar tracker (tqdm) if the progress bar
is enabled.
Args:
iterator: Iterator to wrap in tqdm.
kwargs: Additional arguments to tqdm.
Returns:
Wrapped iterator if progress bar is enabled, otherwise same iterator
as input.
"""
if self.enable_progress_bar:
return tqdm(iterator, **kwargs)
else:
return iterator
def save_metrics(self,
filename : str,
metrics : Dict[str, Any]):
"""
Saves a dictionary of metrics to file. Can be used as a textual
representation of the validation performance for checking in the terminal.
Args:
filename: Name of the metrics file without folders and postfix.
metrics: A dictionary of metrics to save in the file.
"""
with open(os.path.join(self.log_dir, f'metrics/{filename}.json'), 'w') as f:
json.dump(metrics, f, indent=4)
def on_training_start(self):
"""
Method called before training is started. Can be used for additional
initialization operations etc.
"""
pass
def on_training_epoch_end(self,
epoch_idx : int):
"""
Method called at the end of each training epoch. Can be used for additional
logging or similar.
Args:
epoch_idx: Index of the training epoch that has finished.
"""
pass
def on_validation_epoch_end(self,
epoch_idx : int,
eval_metrics : Dict[str, Any],
val_loader : Iterator):
"""
Method called at the end of each validation epoch. Can be used for additional
logging and evaluation.
Args:
epoch_idx: Index of the training epoch at which validation was performed.
eval_metrics: A dictionary of the validation metrics. New metrics added to
this dictionary will be logged as well.
val_loader: Data loader of the validation set, to support additional
evaluation.
"""
pass
def save_model(self,
step : int = 0):
"""
Saves current training state at certain training iteration. Only the model
parameters and batch statistics are saved to reduce memory footprint. To
support the training to be continued from a checkpoint, this method can be
extended to include the optimizer state as well.
Args:
step: Index of the step to save the model at, e.g. epoch.
"""
checkpoints.save_checkpoint(ckpt_dir=self.log_dir,
target={'params': self.state.params,
'batch_stats': self.state.batch_stats},
step=step,
overwrite=True)
def load_model(self):
"""
Loads model parameters and batch statistics from the logging directory.
"""
state_dict = checkpoints.restore_checkpoint(ckpt_dir=self.log_dir, target=None)
self.state = TrainState.create(apply_fn=self.model.apply,
params=state_dict['params'],
batch_stats=state_dict['batch_stats'],
# Optimizer will be overwritten when training starts
tx=self.state.tx if self.state.tx else optax.sgd(0.1),
rng=self.state.rng
)
def bind_model(self):
"""
Returns a model with parameters bound to it. Enables an easier inference
access.
Returns:
The model with parameters and evt. batch statistics bound to it.
"""
params = {'params': self.state.params}
if self.state.batch_stats:
params['batch_stats'] = self.state.batch_stats
return self.model.bind(params)
@classmethod
def load_from_checkpoint(cls,
checkpoint : str,
exmp_input : Any) -> Any:
"""
Creates a Trainer object with same hyperparameters and loaded model from
a checkpoint directory.
Args:
checkpoint: Folder in which the checkpoint and hyperparameter file is stored.
exmp_input: An input to the model for shape inference.
Returns:
A Trainer object with model loaded from the checkpoint folder.
"""
hparams_file = os.path.join(checkpoint, 'hparams.json')
assert os.path.isfile(hparams_file), 'Could not find hparams file'
with open(hparams_file, 'r') as f:
hparams = json.load(f)
hparams.pop('model_class')
hparams.update(hparams.pop('model_hparams'))
if not hparams['logger_params']:
hparams['logger_params'] = dict()
hparams['logger_params']['log_dir'] = checkpoint
trainer = cls(exmp_input=exmp_input,
**hparams)
trainer.load_model()
return trainer
Utility functions¶
Besides the Trainer module, we have seen other functionalities re-occurring several times in the tutorials. One of them is numpy_collate, which is needed for PyTorch’s data loader to purely work with NumPy arrays. Similarly, creating Data Loaders for our datasets often follows the same structure, which we can also summarize in a function called create_data_loaders.
[4]:
def numpy_collate(batch):
if isinstance(batch[0], np.ndarray):
return np.stack(batch)
elif isinstance(batch[0], (tuple,list)):
transposed = zip(*batch)
return [numpy_collate(samples) for samples in transposed]
else:
return np.array(batch)
def create_data_loaders(*datasets : Sequence[data.Dataset],
train : Union[bool, Sequence[bool]] = True,
batch_size : int = 128,
num_workers : int = 4,
seed : int = 42):
"""
Creates data loaders used in JAX for a set of datasets.
Args:
datasets: Datasets for which data loaders are created.
train: Sequence indicating which datasets are used for
training and which not. If single bool, the same value
is used for all datasets.
batch_size: Batch size to use in the data loaders.
num_workers: Number of workers for each dataset.
seed: Seed to initialize the workers and shuffling with.
"""
loaders = []
if not isinstance(train, (list, tuple)):
train = [train for _ in datasets]
for dataset, is_train in zip(datasets, train):
loader = data.DataLoader(dataset,
batch_size=batch_size,
shuffle=is_train,
drop_last=is_train,
collate_fn=numpy_collate,
num_workers=num_workers,
persistent_workers=is_train,
generator=torch.Generator().manual_seed(seed))
loaders.append(loader)
return loaders
Example 1: Function regression¶
Using the TrainerModule and our few utility functions, we can now write a full training scenario with logging etc. in a few lines. To showcase this, we first consider a very simple scenario: regressing a sine-wave with a neural network.
Dataset¶
The first step is to create a dataset. Since we can use PyTorch’s data package, this is straightforward. First, let’s import needed plotting libraries for visualization and set the data and checkpoint path, similarly as in any other tutorial.
[5]:
## Imports for plotting
import matplotlib.pyplot as plt
%matplotlib inline
from IPython.display import set_matplotlib_formats
set_matplotlib_formats('svg', 'pdf') # For export
from matplotlib.colors import to_rgb
import matplotlib
matplotlib.rcParams['lines.linewidth'] = 2.0
import seaborn as sns
sns.reset_orig()
sns.set()
DATASET_PATH = '../data/'
CHECKPOINT_PATH = '../saved_models/guide4/'
The dataset is kept very simple and contains pairs of input-output of a sine function:
[6]:
def target_function(x):
return np.sin(x * 3.0)
class RegressionDataset(data.Dataset):
def __init__(self, num_points, seed):
super().__init__()
rng = np.random.default_rng(seed)
self.x = rng.uniform(low=-2.0, high=2.0, size=num_points)
self.y = target_function(self.x)
def __len__(self):
return self.x.shape[0]
def __getitem__(self, idx):
return self.x[idx:idx+1], self.y[idx:idx+1]
We can create our needed data loaders with the utility function create_data_loaders and visualize the dataset for debugging:
[7]:
train_set = RegressionDataset(num_points=1000, seed=42)
val_set = RegressionDataset(num_points=200, seed=43)
test_set = RegressionDataset(num_points=500, seed=44)
train_loader, val_loader, test_loader = create_data_loaders(train_set, val_set, test_set,
train=[True, False, False],
batch_size=64)
x = np.linspace(-2, 2, 1000)
plt.scatter(train_set.x, train_set.y, color='C1', marker='x', alpha=0.5, label='Training set')
plt.plot(x, target_function(x), linewidth=3.0, label='Ground Truth Function')
plt.legend()
plt.title('Regression function')
plt.show()
Note that even with PyTorch Lightning, we would have needed the similar setup here.
Model¶
The Trainer module does not restrict us to any specific model, so let’s implement our own MLP class for regression:
[8]:
class MLPRegressor(nn.Module):
hidden_dims : Sequence[int]
output_dim : int
@nn.compact
def __call__(self, x, **kwargs):
for dims in self.hidden_dims:
x = nn.Dense(dims)(x)
x = nn.silu(x)
x = nn.Dense(self.output_dim)(x)
return x
Trainer¶
Now comes the interesting part. Using the TrainerModule, we only need to overwrite the aspects that are needed: the training and validation step. For the regression task and the small model, this reduces to writing the mean-squared error loss. Note that we still have some minor repetitive code here, such as creating the gradient function with jax.value_and_grad in the training step and applying the update with state.apply_gradients. One could reduce this further by restricting
possible loss functions, but to keep flexibility high, we implement the whole training step here.
[9]:
class MLPRegressTrainer(TrainerModule):
def __init__(self,
hidden_dims : Sequence[int],
output_dim : int,
**kwargs):
super().__init__(model_class=MLPRegressor,
model_hparams={
'hidden_dims': hidden_dims,
'output_dim': output_dim
},
**kwargs)
def create_functions(self):
def mse_loss(params, batch):
x, y = batch
pred = self.model.apply({'params': params}, x)
loss = ((pred - y) ** 2).mean()
return loss
def train_step(state, batch):
loss_fn = lambda params: mse_loss(params, batch)
loss, grads = jax.value_and_grad(loss_fn)(state.params)
state = state.apply_gradients(grads=grads)
metrics = {'loss': loss}
return state, metrics
def eval_step(state, batch):
loss = mse_loss(state.params, batch)
return {'loss': loss}
return train_step, eval_step
And that’s already it! This now looks much more like the minimal code of PyTorch Lightning and automatically logs our metrics as we want.
Training¶
To train the model, we simply specify our hyperparameters and create a Trainer module:
[10]:
trainer = MLPRegressTrainer(hidden_dims=[128, 128],
output_dim=1,
optimizer_hparams={'lr': 4e-3},
logger_params={'base_log_dir': CHECKPOINT_PATH},
exmp_input=next(iter(train_loader))[0:1],
check_val_every_n_epoch=5)
MLPRegressor Summary ┏━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━┓ ┃ path ┃ outputs ┃ params ┃ ┡━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━┩ │ Inputs │ - float64[64,1] │ │ │ │ - train: True │ │ ├──────────────┼─────────────────┼──────────────────────────┤ │ Dense_0 │ float32[64,128] │ bias: float32[128] │ │ │ │ kernel: float32[1,128] │ │ │ │ │ │ │ │ 256 (1.0 KB) │ ├──────────────┼─────────────────┼──────────────────────────┤ │ Dense_1 │ float32[64,128] │ bias: float32[128] │ │ │ │ kernel: float32[128,128] │ │ │ │ │ │ │ │ 16,512 (66.0 KB) │ ├──────────────┼─────────────────┼──────────────────────────┤ │ Dense_2 │ float32[64,1] │ bias: float32[1] │ │ │ │ kernel: float32[128,1] │ │ │ │ │ │ │ │ 129 (516 B) │ ├──────────────┼─────────────────┼──────────────────────────┤ │ MLPRegressor │ float32[64,1] │ │ ├──────────────┼─────────────────┼──────────────────────────┤ │ │ Total │ 16,897 (67.6 KB) │ └──────────────┴─────────────────┴──────────────────────────┘ Total Parameters: 16,897 (67.6 KB)
As one can see, we also automatically print out all layers with their parameters and outputs with Flax’s nn.tabulate function. This is quite helpful for debugging and gives an intuition about the size of the model. Since the task is not very difficult, we are fine with using less than 20k parameters.
Next, let’s start the training:
[11]:
metrics = trainer.train_model(train_loader,
val_loader,
test_loader=test_loader,
num_epochs=50)
[12]:
print(f'Training loss: {metrics["train/loss"]}')
print(f'Validation loss: {metrics["val/loss"]}')
print(f'Test loss: {metrics["test/loss"]}')
Training loss: 0.0008829445578157902
Validation loss: 0.0008724514045752585
Test loss: 0.0007670423365198076
With the speed of JAX, this takes only a few seconds. The logs can be found in ../saved_models/guide4/MLPRegressor/, and we have a dictionary of the best results here as well. The training, validation and test loss suggest that our model learned the function quite well, but let’s check it by predicting the whole function as inference task.
Inference¶
To perform inference, we first bind the model to the parameters. This enables us a simpler API, closer to PyTorch. Applying the model to a values between -2.0 and 2.0 shows that the model learned the sine wave indeed quite well and is only off at the corners.
[13]:
model_bd = trainer.bind_model()
x = np.linspace(-2, 2, 1000)[:,None]
y_pred = model_bd(x)
plt.plot(x, y_pred, label='Prediction')
plt.plot(x, target_function(x), '--', label='GT')
plt.title('Function regression')
plt.legend()
plt.show()
Example 2: CIFAR10 classification¶
As a second example, let’s consider image classification on CIFAR10. We have done it before in Tutorial 5, but here, we want to showcase the flexibility of the Trainer module. For that, we will consider a more complicated setting in Flax: a model with both Batch Normalization and Dropout. However, with the Trainer module, this reduces to a simpler code again.
Dataset¶
First, let’s load our dataset again. This is the same data loading as used in Tutorial 5 and Tutorial 15, but only considers flipping as regularization technique since we work with simple MLPs here.
[14]:
from torchvision.datasets import CIFAR10
from torchvision import transforms
# Transformations applied on each image => bring them into a numpy array
DATA_MEANS = np.array([0.49139968, 0.48215841, 0.44653091])
DATA_STD = np.array([0.24703223, 0.24348513, 0.26158784])
def image_to_numpy(img):
img = np.array(img, dtype=np.float32)
img = (img / 255. - DATA_MEANS) / DATA_STD
return img
test_transform = image_to_numpy
# For training, we add some augmentation. Networks are too powerful and would overfit.
train_transform = transforms.Compose([transforms.RandomHorizontalFlip(),
image_to_numpy])
# Loading the training dataset. We need to split it into a training and validation part
# We need to do a little trick because the validation set should not use the augmentation.
train_dataset = CIFAR10(root=DATASET_PATH, train=True, transform=train_transform, download=True)
val_dataset = CIFAR10(root=DATASET_PATH, train=True, transform=test_transform, download=True)
train_set, _ = data.random_split(train_dataset, [45000, 5000], generator=torch.Generator().manual_seed(42))
_, val_set = data.random_split(val_dataset, [45000, 5000], generator=torch.Generator().manual_seed(42))
# Loading the test set
test_set = CIFAR10(root=DATASET_PATH, train=False, transform=test_transform, download=True)
train_loader, val_loader, test_loader = create_data_loaders(train_set, val_set, test_set,
train=[True, False, False],
batch_size=256)
Files already downloaded and verified
Files already downloaded and verified
Files already downloaded and verified
Model¶
The model definition is again relatively simple. We repeat a series of Dropout \(\to\) Linear \(\to\) BatchNorm \(\to\) Swish blocks, with a final Dropout and Linear layer at the end.
[15]:
class MLPClassifier(nn.Module):
hidden_dims : Sequence[int]
num_classes : int
dropout_prob : float = 0.0
@nn.compact
def __call__(self, x, train=True):
x = x.reshape(x.shape[0], -1)
for dims in self.hidden_dims:
x = nn.Dropout(self.dropout_prob)(x, deterministic=not train)
x = nn.Dense(dims)(x)
x = nn.BatchNorm()(x, use_running_average=not train)
x = nn.swish(x)
x = nn.Dropout(self.dropout_prob)(x, deterministic=not train)
x = nn.Dense(self.num_classes)(x)
return x
Trainer¶
For the Trainer module, we again define our model hyperparameters in the init function, and write our own training and evaluation steps in create_functions. In these functions, we take care of the mutable batch statistics and the PRNG state for dropout. Note that since both parts are integrated in the TrainState, we do not need to alternate the training or validation step signature, and it is sufficient to pass the state and batch to the functions. Additionally, we overwrite the model
call during initialization (run_model_init) and tabulate function (print_tabulate). And that’s it! Overall, we didn’t need to make many changes, showing that the trainer module is flexible enough to support a variety of layers. For now, we can ignore the trial object and come back to it later when discussing automated hyperparameter tuning.
[16]:
class MLPClassTrainer(TrainerModule):
def __init__(self,
hidden_dims : Sequence[int],
num_classes : int,
dropout_prob : float,
trial : Any = None,
**kwargs):
super().__init__(model_class=MLPClassifier,
model_hparams={
'hidden_dims': hidden_dims,
'num_classes': num_classes,
'dropout_prob': dropout_prob
},
**kwargs)
self.trial = trial
def create_functions(self):
def loss_function(params, batch_stats, rng, batch, train):
imgs, labels = batch
rng, dropout_rng = random.split(rng)
output = self.model.apply({'params': params, 'batch_stats': batch_stats},
imgs,
train=train,
rngs={'dropout': dropout_rng},
mutable=['batch_stats'] if train else False)
logits, new_model_state = output if train else (output, None)
loss = optax.softmax_cross_entropy_with_integer_labels(logits, labels).mean()
acc = (logits.argmax(axis=-1) == labels).mean()
return loss, (rng, new_model_state, acc)
def train_step(state, batch):
loss_fn = lambda params: loss_function(params, state.batch_stats, state.rng, batch, train=True)
ret, grads = jax.value_and_grad(loss_fn, has_aux=True)(state.params)
loss, rng, new_model_state, acc = ret[0], *ret[1]
state = state.apply_gradients(grads=grads, batch_stats=new_model_state['batch_stats'], rng=rng)
metrics = {'loss': loss, 'acc': acc}
return state, metrics
def eval_step(state, batch):
_, (_, _, acc) = loss_function(state.params, state.batch_stats, state.rng, batch, train=False)
return {'acc': acc}
return train_step, eval_step
def run_model_init(self, exmp_input, init_rng):
imgs, _ = exmp_input
init_rng, dropout_rng = random.split(init_rng)
return self.model.init({'params': init_rng, 'dropout': dropout_rng}, x=imgs, train=True)
def print_tabulate(self, exmp_input):
imgs, _ = exmp_input
print(self.model.tabulate(rngs={'params': random.PRNGKey(0), 'dropout': random.PRNGKey(0)}, x=imgs, train=True))
def on_validation_epoch_end(self, epoch_idx, eval_metrics, val_loader):
if self.trial:
self.trial.report(eval_metrics['val/acc'], step=epoch_idx)
if self.trial.should_prune():
raise optuna.exceptions.TrialPruned()
Training¶
With the Trainer fully defined, we can again start training. Let’s pick some reasonable hyperparameters, and look at the layers created by the model:
[17]:
trainer = MLPClassTrainer(hidden_dims=[512, 512],
num_classes=10,
dropout_prob=0.4,
optimizer_hparams={
'weight_decay': 2e-4,
'lr': 1e-3
},
logger_params={
'base_log_dir': CHECKPOINT_PATH
},
exmp_input=next(iter(train_loader)),
check_val_every_n_epoch=5)
MLPClassifier Summary ┏━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┓ ┃ path ┃ outputs ┃ batch_stats ┃ params ┃ ┡━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━┩ │ Inputs │ train: True │ │ │ │ │ x: float64[256,32,32,3] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ BatchNorm_0 │ float32[256,512] │ mean: float32[512] │ bias: float32[512] │ │ │ │ var: float32[512] │ scale: float32[512] │ │ │ │ │ │ │ │ │ 1,024 (4.1 KB) │ 1,024 (4.1 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ BatchNorm_1 │ float32[256,512] │ mean: float32[512] │ bias: float32[512] │ │ │ │ var: float32[512] │ scale: float32[512] │ │ │ │ │ │ │ │ │ 1,024 (4.1 KB) │ 1,024 (4.1 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_0 │ float32[256,512] │ │ bias: float32[512] │ │ │ │ │ kernel: float32[3072,512] │ │ │ │ │ │ │ │ │ │ 1,573,376 (6.3 MB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_1 │ float32[256,512] │ │ bias: float32[512] │ │ │ │ │ kernel: float32[512,512] │ │ │ │ │ │ │ │ │ │ 262,656 (1.1 MB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_2 │ float32[256,10] │ │ bias: float32[10] │ │ │ │ │ kernel: float32[512,10] │ │ │ │ │ │ │ │ │ │ 5,130 (20.5 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_0 │ float32[256,3072] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_1 │ float32[256,512] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_2 │ float32[256,512] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ MLPClassifier │ float32[256,10] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ │ Total │ 2,048 (8.2 KB) │ 1,843,210 (7.4 MB) │ └───────────────┴─────────────────────────┴────────────────────┴───────────────────────────┘ Total Parameters: 1,845,258 (7.4 MB)
One interesting observation here is that the MLP has way more parameters than any of the CNNs in Tutorial 5, but yet significantly underperforms the models. Although to really see the performance, let’s train the model again with the simple call from before:
[18]:
metrics = trainer.train_model(train_loader,
val_loader,
test_loader=test_loader,
num_epochs=50)
[19]:
print(f'Validation accuracy: {metrics["val/acc"]:4.2%}')
print(f'Test accuracy: {metrics["test/acc"]:4.2%}')
Validation accuracy: 60.22%
Test accuracy: 60.05%
The MLP achieves decent accuracy, but already for models like this, we have several hyperparameters to tune including learning rate, weight decay, dropout rate. Which should we choose? While we could use intuition to get a reasonable guess, it is unlikely that we hit the best hyperparameter set. In order to find a very strong hyperparameter set, a good practice is to use automatic hyperparameter tuning, which we shortly review next to showcase the flexibility of the Trainer module.
Automatic hyperparameter tuning with Optuna¶
Automatic hyperparameter tuner have the goal to efficiently identify sets of hyperparameters that achieve the best performance. Thereby, the key question is how can we search the hyperparameter space efficiently, since we don’t have infinite compute. Optuna is a library that helps you setup this search with minimal code overhead and perform automatic hyperparameter tuning. Before getting started with Optuna, let’s import the library and download a pre-executed hyperparameter search as an example.
[20]:
try:
import optuna
except ModuleNotFoundError:
!pip install --quiet --upgrade optuna pyplot
import optuna
[21]:
import urllib.request
from urllib.error import HTTPError
# Github URL where saved models are stored for this tutorial
base_url = "https://raw.githubusercontent.com/phlippe/saved_models/main/guide4/"
# Files to download
pretrained_files = ["optuna_hparam_search.db", "MLPClassifier/version_16/checkpoint_150", "MLPClassifier/version_16/hparams.json"]
# Create checkpoint path if it doesn't exist yet
os.makedirs(CHECKPOINT_PATH, exist_ok=True)
# For each file, check whether it already exists. If not, try downloading it.
for file_name in pretrained_files:
file_path = os.path.join(CHECKPOINT_PATH, file_name)
if not os.path.isfile(file_path):
file_url = base_url + file_name
print(f"Downloading {file_url}...")
try:
urllib.request.urlretrieve(file_url, file_path)
except HTTPError as e:
print("Something went wrong. Please contact the author with the full output including the following error:\n", e)
Defining objective and hyperparameters¶
The main part a user has to specify in Optuna is intuitively the the objective to optimize, and the hyperparameters over which we want to optimize. In our case, the objective is to optimize the validation accuracy of the MLP. Note that we do not use the test set here, since hyperparameter searches should only be done on the validation set, not the “unseen” test set! The function below, objective(trial), creates a MLP with our trainer module and trains it for max. 200 epochs. The input
argument, trial, is thereby an object which characterizes the current run. This includes, for example, the hyperparameters we want to optimize. In order to add a hyperparameter to our optimization set, we can simply call trial.suggest_float for continuous values and trial.suggest_categorical for categorical values (e.g. which optimizer to use). For the CIFAR10 classification, we consider the following three hyperparameters: dropout rate, weight decay, and the learning rate, which we
define below. Finally, we return the best validation accuracy which will be used by Optuna to guide the next pick of hyperparameters.
[22]:
def objective(trial):
my_train_loader, my_val_loader = create_data_loaders(train_set, val_set,
train=[True, False],
batch_size=256)
trainer = MLPClassTrainer(hidden_dims=[512, 512],
num_classes=10,
dropout_prob=trial.suggest_float('dropout_prob', 0, 0.6),
optimizer_hparams={
'weight_decay': trial.suggest_float('weight_decay', 1e-6, 1e-2, log=True),
'lr': trial.suggest_float('lr', 1e-4, 1e-2, log=True)
},
logger_params={
'base_log_dir': CHECKPOINT_PATH
},
exmp_input=next(iter(my_train_loader)),
check_val_every_n_epoch=5,
trial=trial)
metrics = trainer.train_model(my_train_loader,
my_val_loader,
num_epochs=200)
del trainer
del my_train_loader, my_val_loader
return metrics['val/acc']
Running hyperparameter study¶
To run the hyperparameter search, we create a Study in Optuna. A study implements the search logic and summarizes the data/logs of all executed experiments. By default, Optuna uses the Tree-Structured Parzen Estimator algorithm, using Gaussian Mixture Models to estimate the performance surface of they hyperparameters. For more information, check out the
documentation. The studies are usually stored in a database format, but can be easily accessed via the Python interface of Optuna. Let’s run the hyperparameter search for up to 25 models:
[23]:
study = optuna.create_study(
study_name='mlp_cifar10',
storage=f'sqlite:///{CHECKPOINT_PATH}/optuna_hparam_search.db',
direction='maximize',
pruner=optuna.pruners.MedianPruner(n_startup_trials=5, n_warmup_steps=50),
load_if_exists=True
)
study.optimize(objective, n_trials=25-len(study.trials), n_jobs=1)
[I 2022-07-05 20:06:47,966] Using an existing study with name 'mlp_cifar10' instead of creating a new one.
During the study creation, we used the input argument pruner. This specifies a strategy with which we want to stop experiments early if they don’t look promising. For instance, a very low learning rate combined with high weight decay and dropout will likely achieve low performance, which we can already judge after 50 epochs and don’t have to run the model for much longer. For this, we implemented the on_validation_epoch_end callback in our Trainer module before. After each epoch, it
reports the current validation performance to Optuna. Depending on the previous performances and Optuna’s pruning strategy, it may decide to stop the experiment early, which it does by throwing a TrialPruned error. This error is caught by Optuna, and the next trial is directly started.
Evaluate hyperparameter search¶
After finishing the hyperparameter search, we can analyze the results. First, let’s print the best model found and its corresponding hyperparameters:
[24]:
trial = study.best_trial
print(f'Best Validation Accuracy: {trial.value:4.2%}')
print(f'Best Params:')
for key, value in trial.params.items():
print(f'-> {key}: {value}')
Best Validation Accuracy: 63.44%
Best Params:
-> dropout_prob: 0.39573629692783413
-> lr: 0.002097404408052793
-> weight_decay: 0.0012107132860246818
The validation performance is quite a bit higher than the model we had manually designed before. Let’s load the model and check its test performance. For this, we can make use of the load_from_checkpoint function of our Trainer module:
[25]:
trainer = MLPClassTrainer.load_from_checkpoint(os.path.join(CHECKPOINT_PATH, 'MLPClassifier/version_16/'),
exmp_input=next(iter(train_loader)))
test_metrics = trainer.eval_model(test_loader)
print(f'Test accuracy: {test_metrics["acc"]:4.2%}')
MLPClassifier Summary ┏━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┓ ┃ path ┃ outputs ┃ batch_stats ┃ params ┃ ┡━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━┩ │ Inputs │ train: True │ │ │ │ │ x: float64[256,32,32,3] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ BatchNorm_0 │ float32[256,512] │ mean: float32[512] │ bias: float32[512] │ │ │ │ var: float32[512] │ scale: float32[512] │ │ │ │ │ │ │ │ │ 1,024 (4.1 KB) │ 1,024 (4.1 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ BatchNorm_1 │ float32[256,512] │ mean: float32[512] │ bias: float32[512] │ │ │ │ var: float32[512] │ scale: float32[512] │ │ │ │ │ │ │ │ │ 1,024 (4.1 KB) │ 1,024 (4.1 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_0 │ float32[256,512] │ │ bias: float32[512] │ │ │ │ │ kernel: float32[3072,512] │ │ │ │ │ │ │ │ │ │ 1,573,376 (6.3 MB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_1 │ float32[256,512] │ │ bias: float32[512] │ │ │ │ │ kernel: float32[512,512] │ │ │ │ │ │ │ │ │ │ 262,656 (1.1 MB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dense_2 │ float32[256,10] │ │ bias: float32[10] │ │ │ │ │ kernel: float32[512,10] │ │ │ │ │ │ │ │ │ │ 5,130 (20.5 KB) │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_0 │ float32[256,3072] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_1 │ float32[256,512] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ Dropout_2 │ float32[256,512] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ MLPClassifier │ float32[256,10] │ │ │ ├───────────────┼─────────────────────────┼────────────────────┼───────────────────────────┤ │ │ Total │ 2,048 (8.2 KB) │ 1,843,210 (7.4 MB) │ └───────────────┴─────────────────────────┴────────────────────┴───────────────────────────┘ Total Parameters: 1,845,258 (7.4 MB)
Test accuracy: 62.89%
The test performance is also quite strong, showing the benefit of the automatic hyperparameter search. However, often, we are not just interested in the best model. Optuna provides several ways of visualizing the results of the hyperparameter study, for instance by plotting all validation accuracy curves:
[26]:
fig = optuna.visualization.plot_intermediate_values(study)
fig.show()