flax model parallel training (#12590)

* update scripts

* add copyright

* add logging

* cleanup

* add z loss

* add readme

* shard description

* update readme

examples/research_projects/jax-projects/model parallel/README.md

+<!---
+Copyright 2021 The HuggingFace Team. All rights reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+-->
+
+# Model parallel language model training example
+
+The following example showcases how to train/fine-tune GPTNeo model with model parallelism using
+the JAX/Flax backend and the [`pjit`](https://jax.readthedocs.io/en/latest/jax.experimental.pjit.html) transformation.
+
+> Note: The example is experimental and might have bugs. Also currently it only supports single V3-8.
+
+The `partition.py` file defines the `PyTree` of `ParitionSpec` for the GPTNeo model which describes how the model will be sharded.
+The actual sharding is auto-matically handled by `pjit`. The weights are sharded accross all local devices.
+To adapt the script for other models, we need to also change the `ParitionSpec` accordingly.
+
+TODO: Add more explantion.
+
+Before training, let's prepare our model first. To be able to shard the model, the sharded dimention needs to be a multiple of devices it'll be sharded on. But GPTNeo's vocab size is 50257, so we need to resize the embeddings accordingly. 
+
+```python
+from transformers import FlaxGPTNeoForCausalLM, GPTNeoConfig 
+model = FlaxGPTNeoForCausalLM.from_pretrained("EleutherAI/gpt-neo-1.3B")
+
+emb = jnp.zeros((50264, model.config.hidden_size))
+# update the first 50257 weights using pre-trained weights
+emb = jax.ops.index_update(emb, jax.ops.index[:50257, :], model.params["transformer"]["wte"]["embedding"])
+params = model.params
+params["transformer"]["wte"]["embedding"] = emb
+
+# initialize a random model with the right vocab_size
+config = GPTNeoConfig.from_pretrained("EleutherAI/gpt-neo-1.3B", vocab_size=50264)
+model = FlaxGPTNeoForCausalLM(config)
+
+# assign the pre-trained weights and save the model.
+model.params = params
+model.save_pretrained("gpt-neo-1.3B")
+```
+
+
+### Train Model
+
+```bash
+python run_pjit_clm.py \
+    --model_name_or_path gpt-neo-1.3B  \
+    --tokenizer_name gpt2 \
+    --dataset_name wikitext --dataset_config_name wikitext-2-raw-v1 \
+    --do_train  --do_eval \
+    --block_size 1024 \
+    --num_train_epochs 5 \
+    --learning_rate 4e-6 \
+    --per_device_train_batch_size 3 --per_device_eval_batch_size 3 \
+    --overwrite_output_dir --output_dir ~/tmp/flax-clm \
+    --cache_dir ~/datasets_cache/wikitext --dtype bfloat16 \
+    --logging_steps 96 --eval_steps 96
+```
\ No newline at end of file

examples/research_projects/jax-projects/model parallel/partitions.py

+#!/usr/bin/env python
+# coding=utf-8
+# Copyright 2021 The Google Research Authors and The HuggingFace Team All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Utilities for constructing PyTrees of PartitionSpecs."""
+
+# utils adapted from https://github.com/google-research/google-research/blob/master/flax_models/t5x/partitions.py
+
+import re
+
+from flax.core.frozen_dict import freeze
+from flax.traverse_util import flatten_dict, unflatten_dict
+from jax.experimental import PartitionSpec as P
+
+
+# Sentinels
+_unmatched = object()
+
+# For specifying empty leaf dict `{}`
+empty_dict = object()
+
+
+def _match(qs, ks):
+    """Return True if regexes in qs match any window of strings in tuple ks."""
+    # compile regexes and force complete match
+    qts = tuple(map(lambda x: re.compile(x + "$"), qs))
+    for i in range(len(ks) - len(qs) + 1):
+        matches = [x.match(y) for x, y in zip(qts, ks[i:])]
+        if matches and all(matches):
+            return True
+    return False
+
+
+def _replacement_rules(rules):
+    def replace(key, val):
+        for rule, replacement in rules:
+            if _match(rule, key):
+                return replacement
+        return val
+
+    return replace
+
+
+# PartitionSpec for GPTNeo
+# replicate the hidden dim and shard feed-forward and head dim
+def _get_partition_rules():
+    return [
+        # embeddings
+        (("transformer", "wpe", "embedding"), P("mp", None)),
+        (("transformer", "wte", "embedding"), P("mp", None)),
+        # atention
+        (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(None, "mp")),
+        (("attention", "out_proj", "kernel"), P("mp", None)),
+        (("attention", "out_proj", "bias"), None),
+        # mlp
+        (("mlp", "c_fc", "kernel"), P(None, "mp")),
+        (("mlp", "c_fc", "bias"), P("mp")),
+        (("mlp", "c_proj", "kernel"), P("mp", None)),
+        (("mlp", "c_proj", "bias"), None),
+        # layer norms
+        ((r"ln_\d+", "bias"), None),
+        ((r"\d+", r"ln_\d+", "scale"), None),
+        (("ln_f", "bias"), None),
+        (("ln_f", "scale"), None),
+    ]
+
+
+def set_partitions(in_dict):
+    rules = _get_partition_rules()
+    replace = _replacement_rules(rules)
+    initd = {k: _unmatched for k in flatten_dict(in_dict)}
+    result = {k: replace(k, v) for k, v in initd.items()}
+    assert _unmatched not in result.values(), "Incomplete partition spec."
+    return freeze(unflatten_dict(result))

examples/research_projects/jax-projects/model parallel/run_clm_mp.py

+#!/usr/bin/env python
+# coding=utf-8
+# Copyright 2021 The HuggingFace Team All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Pre-training/Fine-tuning the GPTNeo model for causal language modeling on a text file or a dataset using model parallelism.
+"""
+
+import logging
+import math
+import os
+import sys
+import time
+from dataclasses import dataclass, field
+from pathlib import Path
+from typing import Callable, Optional
+
+import datasets
+import numpy as np
+from datasets import Dataset, load_dataset
+from tqdm import tqdm
+
+import jax
+import jax.numpy as jnp
+import optax
+import transformers
+from flax.core.frozen_dict import freeze, unfreeze
+from flax.training.common_utils import onehot, stack_forest
+from jax.experimental.maps import mesh
+from jax.experimental.pjit import pjit
+from partitions import set_partitions
+from transformers import (
+    CONFIG_MAPPING,
+    FLAX_MODEL_FOR_CAUSAL_LM_MAPPING,
+    AutoConfig,
+    AutoTokenizer,
+    FlaxAutoModelForCausalLM,
+    HfArgumentParser,
+    TrainingArguments,
+    is_tensorboard_available,
+)
+from transformers.testing_utils import CaptureLogger
+
+
+logger = logging.getLogger(__name__)
+
+MODEL_CONFIG_CLASSES = list(FLAX_MODEL_FOR_CAUSAL_LM_MAPPING.keys())
+MODEL_TYPES = tuple(conf.model_type for conf in MODEL_CONFIG_CLASSES)
+
+
+@dataclass
+class ModelArguments:
+    """
+    Arguments pertaining to which model/config/tokenizer we are going to fine-tune, or train from scratch.
+    """
+
+    model_name_or_path: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "The model checkpoint for weights initialization."
+            "Don't set if you want to train a model from scratch."
+        },
+    )
+    model_type: Optional[str] = field(
+        default=None,
+        metadata={"help": "If training from scratch, pass a model type from the list: " + ", ".join(MODEL_TYPES)},
+    )
+    config_name: Optional[str] = field(
+        default=None, metadata={"help": "Pretrained config name or path if not the same as model_name"}
+    )
+    tokenizer_name: Optional[str] = field(
+        default=None, metadata={"help": "Pretrained tokenizer name or path if not the same as model_name"}
+    )
+    cache_dir: Optional[str] = field(
+        default=None, metadata={"help": "Where do you want to store the pretrained models downloaded from s3"}
+    )
+    use_fast_tokenizer: bool = field(
+        default=True,
+        metadata={"help": "Whether to use one of the fast tokenizer (backed by the tokenizers library) or not."},
+    )
+    dtype: Optional[str] = field(
+        default="float32",
+        metadata={
+            "help": "Floating-point format in which the model weights should be initialized and trained. Choose one of `[float32, float16, bfloat16]`."
+        },
+    )
+
+
+@dataclass
+class DataTrainingArguments:
+    """
+    Arguments pertaining to what data we are going to input our model for training and eval.
+    """
+
+    dataset_name: Optional[str] = field(
+        default=None, metadata={"help": "The name of the dataset to use (via the datasets library)."}
+    )
+    dataset_config_name: Optional[str] = field(
+        default=None, metadata={"help": "The configuration name of the dataset to use (via the datasets library)."}
+    )
+    train_file: Optional[str] = field(default=None, metadata={"help": "The input training data file (a text file)."})
+    validation_file: Optional[str] = field(
+        default=None,
+        metadata={"help": "An optional input evaluation data file to evaluate the perplexity on (a text file)."},
+    )
+    max_train_samples: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "For debugging purposes or quicker training, truncate the number of training examples to this "
+            "value if set."
+        },
+    )
+    max_eval_samples: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "For debugging purposes or quicker training, truncate the number of evaluation examples to this "
+            "value if set."
+        },
+    )
+    overwrite_cache: bool = field(
+        default=False, metadata={"help": "Overwrite the cached training and evaluation sets"}
+    )
+    validation_split_percentage: Optional[int] = field(
+        default=5,
+        metadata={
+            "help": "The percentage of the train set used as validation set in case there's no validation split"
+        },
+    )
+    block_size: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "Optional input sequence length after tokenization. "
+            "The training dataset will be truncated in block of this size for training. "
+            "Default to the model max input length for single sentence inputs (take into account special tokens)."
+        },
+    )
+    overwrite_cache: bool = field(
+        default=False, metadata={"help": "Overwrite the cached training and evaluation sets"}
+    )
+    preprocessing_num_workers: Optional[int] = field(
+        default=None,
+        metadata={"help": "The number of processes to use for the preprocessing."},
+    )
+
+    def __post_init__(self):
+        if self.dataset_name is None and self.train_file is None and self.validation_file is None:
+            raise ValueError("Need either a dataset name or a training/validation file.")
+        else:
+            if self.train_file is not None:
+                extension = self.train_file.split(".")[-1]
+                assert extension in ["csv", "json", "txt"], "`train_file` should be a csv, a json or a txt file."
+            if self.validation_file is not None:
+                extension = self.validation_file.split(".")[-1]
+                assert extension in ["csv", "json", "txt"], "`validation_file` should be a csv, a json or a txt file."
+
+
+def data_loader(rng: jax.random.PRNGKey, dataset: Dataset, batch_size: int, shuffle: bool = False):
+    """
+    Returns batches of size `batch_size` from truncated `dataset`, sharded over all local devices.
+    Shuffle batches if `shuffle` is `True`.
+    """
+    steps_per_epoch = len(dataset) // batch_size
+
+    if shuffle:
+        batch_idx = jax.random.permutation(rng, len(dataset))
+    else:
+        batch_idx = jnp.arange(len(dataset))
+
+    batch_idx = batch_idx[: steps_per_epoch * batch_size]  # Skip incomplete batch.
+    batch_idx = batch_idx.reshape((steps_per_epoch, batch_size))
+
+    for idx in batch_idx:
+        batch = dataset[idx]
+        batch = {k: jnp.array(v) for k, v in batch.items()}
+        yield batch
+
+
+def write_train_metric(summary_writer, train_metrics, train_time, step):
+    summary_writer.scalar("train_time", train_time, step)
+
+    train_metrics = stack_forest(train_metrics)
+    for key, vals in train_metrics.items():
+        tag = f"train_{key}"
+        for i, val in enumerate(vals):
+            summary_writer.scalar(tag, val, step - len(vals) + i + 1)
+
+
+def write_eval_metric(summary_writer, eval_metrics, step):
+    for metric_name, value in eval_metrics.items():
+        summary_writer.scalar(f"eval_{metric_name}", value, step)
+
+
+def create_learning_rate_fn(
+    train_ds_size: int, train_batch_size: int, num_train_epochs: int, num_warmup_steps: int, learning_rate: float
+) -> Callable[[int], jnp.array]:
+    """Returns a linear warmup, linear_decay learning rate function."""
+    steps_per_epoch = train_ds_size // train_batch_size
+    num_train_steps = steps_per_epoch * num_train_epochs
+    warmup_fn = optax.linear_schedule(init_value=0.0, end_value=learning_rate, transition_steps=num_warmup_steps)
+    decay_fn = optax.linear_schedule(
+        init_value=learning_rate, end_value=0, transition_steps=num_train_steps - num_warmup_steps
+    )
+    schedule_fn = optax.join_schedules(schedules=[warmup_fn, decay_fn], boundaries=[num_warmup_steps])
+    return schedule_fn
+
+
+def main():
+    # See all possible arguments in src/transformers/training_args.py
+    # or by passing the --help flag to this script.
+    # We now keep distinct sets of args, for a cleaner separation of concerns.
+
+    parser = HfArgumentParser((ModelArguments, DataTrainingArguments, TrainingArguments))
+    if len(sys.argv) == 2 and sys.argv[1].endswith(".json"):
+        # If we pass only one argument to the script and it's the path to a json file,
+        # let's parse it to get our arguments.
+        model_args, data_args, training_args = parser.parse_json_file(json_file=os.path.abspath(sys.argv[1]))
+    else:
+        model_args, data_args, training_args = parser.parse_args_into_dataclasses()
+
+    if (
+        os.path.exists(training_args.output_dir)
+        and os.listdir(training_args.output_dir)
+        and training_args.do_train
+        and not training_args.overwrite_output_dir
+    ):
+        raise ValueError(
+            f"Output directory ({training_args.output_dir}) already exists and is not empty."
+            "Use --overwrite_output_dir to overcome."
+        )
+
+    # Make one log on every process with the configuration for debugging.
+    logging.basicConfig(
+        format="%(asctime)s - %(levelname)s - %(name)s - %(message)s",
+        datefmt="%m/%d/%Y %H:%M:%S",
+        level=logging.INFO,
+    )
+    # Setup logging, we only want one process per machine to log things on the screen.
+    logger.setLevel(logging.INFO if jax.process_index() == 0 else logging.ERROR)
+    if jax.process_index() == 0:
+        datasets.utils.logging.set_verbosity_warning()
+        transformers.utils.logging.set_verbosity_info()
+    else:
+        datasets.utils.logging.set_verbosity_error()
+        transformers.utils.logging.set_verbosity_error()
+
+    # Set the verbosity to info of the Transformers logger (on main process only):
+    logger.info(f"Training/evaluation parameters {training_args}")
+
+    # Get the datasets: you can either provide your own CSV/JSON/TXT training and evaluation files (see below)
+    # or just provide the name of one of the public datasets available on the hub at https://huggingface.co/datasets/
+    # (the dataset will be downloaded automatically from the datasets Hub).
+    #
+    # For CSV/JSON files, this script will use the column called 'text' or the first column if no column called
+    # 'text' is found. You can easily tweak this behavior (see below).
+    if data_args.dataset_name is not None:
+        # Downloading and loading a dataset from the hub.
+        dataset = load_dataset(
+            data_args.dataset_name, data_args.dataset_config_name, cache_dir=model_args.cache_dir, keep_in_memory=False
+        )
+
+        if "validation" not in dataset.keys():
+            dataset["validation"] = load_dataset(
+                data_args.dataset_name,
+                data_args.dataset_config_name,
+                split=f"train[:{data_args.validation_split_percentage}%]",
+                cache_dir=model_args.cache_dir,
+            )
+            dataset["train"] = load_dataset(
+                data_args.dataset_name,
+                data_args.dataset_config_name,
+                split=f"train[{data_args.validation_split_percentage}%:]",
+                cache_dir=model_args.cache_dir,
+            )
+    else:
+        data_files = {}
+        if data_args.train_file is not None:
+            data_files["train"] = data_args.train_file
+        if data_args.validation_file is not None:
+            data_files["validation"] = data_args.validation_file
+        extension = data_args.train_file.split(".")[-1]
+        if extension == "txt":
+            extension = "text"
+        dataset = load_dataset(extension, data_files=data_files, cache_dir=model_args.cache_dir)
+    # See more about loading any type of standard or custom dataset (from files, python dict, pandas DataFrame, etc) at
+    # https://huggingface.co/docs/datasets/loading_datasets.html.
+
+    # Load pretrained config and tokenizer
+    if model_args.config_name:
+        config = AutoConfig.from_pretrained(model_args.config_name, cache_dir=model_args.cache_dir)
+    elif model_args.model_name_or_path:
+        config = AutoConfig.from_pretrained(model_args.model_name_or_path, cache_dir=model_args.cache_dir)
+    else:
+        config = CONFIG_MAPPING[model_args.model_type]()
+        logger.warning("You are instantiating a new config instance from scratch.")
+
+    if model_args.tokenizer_name:
+        tokenizer = AutoTokenizer.from_pretrained(
+            model_args.tokenizer_name, cache_dir=model_args.cache_dir, use_fast=model_args.use_fast_tokenizer
+        )
+    elif model_args.model_name_or_path:
+        tokenizer = AutoTokenizer.from_pretrained(
+            model_args.model_name_or_path, cache_dir=model_args.cache_dir, use_fast=model_args.use_fast_tokenizer
+        )
+    else:
+        raise ValueError(
+            "You are instantiating a new tokenizer from scratch. This is not supported by this script."
+            "You can do it from another script, save it, and load it from here, using --tokenizer_name."
+        )
+
+    if training_args.do_train:
+        column_names = dataset["train"].column_names
+    else:
+        column_names = dataset["validation"].column_names
+    text_column_name = "text" if "text" in column_names else column_names[0]
+
+    # since this will be pickled to avoid _LazyModule error in Hasher force logger loading before tokenize_function
+    tok_logger = transformers.utils.logging.get_logger("transformers.tokenization_utils_base")
+
+    def tokenize_function(examples):
+        with CaptureLogger(tok_logger) as cl:
+            output = tokenizer(examples[text_column_name])
+        # clm input could be much much longer than block_size
+        if "Token indices sequence length is longer than the" in cl.out:
+            tok_logger.warning(
+                "^^^^^^^^^^^^^^^^ Please ignore the warning above - this long input will be chunked into smaller bits before being passed to the model."
+            )
+        return output
+
+    tokenized_datasets = dataset.map(
+        tokenize_function,
+        batched=True,
+        num_proc=data_args.preprocessing_num_workers,
+        remove_columns=column_names,
+        load_from_cache_file=not data_args.overwrite_cache,
+    )
+
+    if data_args.block_size is None:
+        block_size = tokenizer.model_max_length
+        if block_size > config.max_position_embeddings:
+            logger.warning(
+                f"The tokenizer picked seems to have a very large `model_max_length` ({tokenizer.model_max_length}). "
+                "Picking 1024 instead. You can change that default value by passing --block_size xxx."
+            )
+            block_size = 1024
+    else:
+        if data_args.block_size > tokenizer.model_max_length:
+            logger.warning(
+                f"The block_size passed ({data_args.block_size}) is larger than the maximum length for the model"
+                f"({tokenizer.model_max_length}). Using block_size={tokenizer.model_max_length}."
+            )
+        block_size = min(data_args.block_size, tokenizer.model_max_length)
+
+    # Main data processing function that will concatenate all texts from our dataset and generate chunks of block_size.
+    def group_texts(examples):
+        # Concatenate all texts.
+        concatenated_examples = {k: sum(examples[k], []) for k in examples.keys()}
+        total_length = len(concatenated_examples[list(examples.keys())[0]])
+        # We drop the small remainder, we could add padding if the model supported it instead of this drop, you can
+        # customize this part to your needs.
+        if total_length >= block_size:
+            total_length = (total_length // block_size) * block_size
+        # Split by chunks of max_len.
+        result = {
+            k: [t[i : i + block_size] for i in range(0, total_length, block_size)]
+            for k, t in concatenated_examples.items()
+        }
+        result["labels"] = result["input_ids"].copy()
+        return result
+
+    # Note that with `batched=True`, this map processes 1,000 texts together, so group_texts throws away a remainder
+    # for each of those groups of 1,000 texts. You can adjust that batch_size here but a higher value might be slower
+    # to preprocess.
+    #
+    # To speed up this part, we use multiprocessing. See the documentation of the map method for more information:
+    # https://huggingface.co/docs/datasets/package_reference/main_classes.html#datasets.Dataset.map
+
+    lm_datasets = tokenized_datasets.map(
+        group_texts,
+        batched=True,
+        num_proc=data_args.preprocessing_num_workers,
+        load_from_cache_file=not data_args.overwrite_cache,
+    )
+
+    if training_args.do_train:
+        if "train" not in tokenized_datasets:
+            raise ValueError("--do_train requires a train dataset")
+        train_dataset = lm_datasets["train"]
+        if data_args.max_train_samples is not None:
+            train_dataset = train_dataset.select(range(data_args.max_train_samples))
+
+    if training_args.do_eval:
+        if "validation" not in tokenized_datasets:
+            raise ValueError("--do_eval requires a validation dataset")
+        eval_dataset = lm_datasets["validation"]
+        if data_args.max_eval_samples is not None:
+            eval_dataset = eval_dataset.select(range(data_args.max_eval_samples))
+
+    # Enable tensorboard only on the master node
+    has_tensorboard = is_tensorboard_available()
+    if has_tensorboard and jax.process_index() == 0:
+        try:
+            from flax.metrics.tensorboard import SummaryWriter
+
+            summary_writer = SummaryWriter(log_dir=Path(training_args.output_dir))
+        except ImportError as ie:
+            has_tensorboard = False
+            logger.warning(
+                f"Unable to display metrics through TensorBoard because some package are not installed: {ie}"
+            )
+    else:
+        logger.warning(
+            "Unable to display metrics through TensorBoard because the package is not installed: "
+            "Please run pip install tensorboard to enable."
+        )
+
+    # Initialize our training
+    rng = jax.random.PRNGKey(training_args.seed)
+    rng, dropout_rng = jax.random.split(rng)
+
+    # Store some constant
+    num_epochs = int(training_args.num_train_epochs)
+    train_batch_size = int(training_args.per_device_train_batch_size) * jax.device_count()
+    eval_batch_size = int(training_args.per_device_eval_batch_size) * jax.device_count()
+    steps_per_epoch = len(train_dataset) // train_batch_size
+    total_train_steps = steps_per_epoch * num_epochs
+
+    # TODO: weights should be initialized in pjitted fun, this won't work for REALLY large models
+    # TODO: when loading from pre-trained model we need to make sure the vocab is divisible by num_partitions
+    # GPT2's vocab is odd, we need to resize it for fine-tuning
+    model = FlaxAutoModelForCausalLM.from_pretrained(
+        model_args.model_name_or_path, seed=training_args.seed, dtype=getattr(jnp, model_args.dtype)
+    )
+
+    # Create learning rate schedule
+    linear_decay_lr_schedule_fn = create_learning_rate_fn(
+        len(train_dataset),
+        train_batch_size,
+        training_args.num_train_epochs,
+        training_args.warmup_steps,
+        training_args.learning_rate,
+    )
+
+    optimizer = optax.adamw(
+        learning_rate=linear_decay_lr_schedule_fn,
+        b1=training_args.adam_beta1,
+        b2=training_args.adam_beta2,
+        eps=training_args.adam_epsilon,
+        weight_decay=training_args.weight_decay,
+    )
+
+    def get_initial_state(params):
+        state = optimizer.init(params)
+        return tuple(state), params
+
+    # Get PartitionSpec for model params
+    param_spec = set_partitions(unfreeze(model.params))
+
+    # Get the PyTree for opt_state, we don't actually initialize the opt_state yet.
+    params_shapes = jax.tree_map(lambda x: x.shape, model.params)
+    state_shapes = jax.eval_shape(get_initial_state, params_shapes)
+
+    # get PartitionSpec for opt_state, this is very specific to adamw
+    # TODO: optax returns different state for different optimizers, how can we handle this generically ?
+    # or maybe we don't since in our examples we just use adamw or adafactor
+    def get_opt_spec(x):
+        if isinstance(x, dict):
+            return param_spec
+        return None
+
+    opt_state_spec, param_spec = jax.tree_map(
+        get_opt_spec, state_shapes, is_leaf=lambda x: isinstance(x, (dict, optax.EmptyState))
+    )
+
+    # pjit the get_initial_state function to shard params and init
+    # optimizer state in sharded way
+    p_get_initial_state = pjit(
+        get_initial_state,
+        in_axis_resources=None,
+        out_axis_resources=(opt_state_spec, param_spec),
+    )
+
+    # hack: move the inital params to CPU to free up device memory
+    # TODO: allow loading weights on CPU in pre-trained model
+    model.params = jax.tree_map(lambda x: np.asarray(x), model.params)
+
+    # mesh defination
+    mesh_devices = np.array(jax.devices()).reshape(1, jax.local_device_count())
+
+    # actually initialize the opt_state
+    with mesh(mesh_devices, ("dp", "mp")):
+        opt_state, params = p_get_initial_state(freeze(model.params))
+
+    # cross-entropy with z loss
+    def loss_fn(logits, labels, z_loss=0):
+        shift_logits = logits[..., :-1, :]
+        shift_labels = labels[..., 1:]
+
+        shift_labels = onehot(shift_labels, shift_logits.shape[-1])
+
+        shift_logits = shift_logits - jax.lax.stop_gradient(shift_logits.max(axis=-1, keepdims=True))
+        log_z = jnp.log(jnp.sum(jnp.exp(shift_logits), axis=-1, keepdims=True))
+        log_softmax = shift_logits - log_z
+        loss = -jnp.sum(shift_labels * log_softmax, axis=-1)
+
+        loss += (1e-4 * jnp.square(log_z.squeeze(-1))) * z_loss
+
+        return loss.mean()
+
+    # Define gradient update step fn
+    # TODO: try to use TrainState instead of passing params and opt_state individually
+    def train_step(params, opt_state, dropout_rng, batch, step):
+        dropout_rng, new_dropout_rng = jax.random.split(dropout_rng)
+
+        def compute_loss(params):
+            labels = batch.pop("labels")
+            logits = model(**batch, params=params, dropout_rng=dropout_rng, train=True)[0]
+            loss = loss_fn(logits, labels, z_loss=1.0)
+            return loss
+
+        grad_fn = jax.value_and_grad(compute_loss)
+        loss, grads = grad_fn(params)
+
+        updates, new_opt_state = optimizer.update(grads, opt_state, params)
+        new_params = optax.apply_updates(params, updates)
+
+        metrics = {"loss": loss, "learning_rate": linear_decay_lr_schedule_fn(step)}
+        return new_params, tuple(new_opt_state), new_dropout_rng, metrics, step + 1
+
+    # Define eval fn
+    def eval_step(input_ids, labels, params):
+        logits = model(input_ids=input_ids, params=params, train=False)[0]
+        loss = loss_fn(logits, labels)
+        # metrics
+        return {"loss": loss}
+
+    p_train_step = pjit(
+        train_step,
+        in_axis_resources=(param_spec, opt_state_spec, None, None, None),
+        out_axis_resources=(param_spec, opt_state_spec, None, None, None),
+        donate_argnums=(0, 1),
+    )
+
+    p_eval_step = pjit(
+        eval_step,
+        in_axis_resources=(None, None, param_spec),
+        out_axis_resources=None,
+    )
+
+    logger.info("***** Running training *****")
+    logger.info(f"  Num examples = {len(train_dataset)}")
+    logger.info(f"  Num Epochs = {num_epochs}")
+    logger.info(f"  Instantaneous batch size per device = {training_args.per_device_train_batch_size}")
+    logger.info(f"  Total train batch size (w. parallel & distributed) = {train_batch_size}")
+    logger.info(f"  Total optimization steps = {total_train_steps}")
+
+    train_time = 0
+    train_metrics = []
+    epochs = tqdm(range(num_epochs), desc=f"Epoch ... (1/{num_epochs})", position=0)
+    global_step = 0
+    # we are not doing 2D parallelism (yet!), this just does model parallelism
+    with mesh(mesh_devices, ("dp", "mp")):
+        for _ in epochs:
+            # ======================== Training ================================
+            train_start = time.time()
+
+            # Create sampling rng
+            rng, input_rng = jax.random.split(rng)
+
+            # Generate an epoch by shuffling sampling indices from the train dataset
+            train_metrics = []
+            train_loader = data_loader(input_rng, train_dataset, train_batch_size, shuffle=True)
+            steps_per_epoch = len(train_dataset) // train_batch_size
+
+            # train
+            for _ in tqdm(range(steps_per_epoch), desc="Training...", position=1, leave=False):
+                batch = next(train_loader)
+                params, opt_state, dropout_rng, train_metric, global_step = p_train_step(
+                    params,
+                    opt_state,
+                    dropout_rng,
+                    batch,
+                    global_step,
+                )
+                train_metrics.append(train_metric)
+
+                cur_step = global_step
+
+                if cur_step % training_args.logging_steps == 0 and cur_step > 0:
+                    # Save metrics
+                    train_time += time.time() - train_start
+                    if has_tensorboard and jax.process_index() == 0:
+                        write_train_metric(summary_writer, train_metrics, train_time, cur_step)
+
+                    epochs.write(
+                        f"Step... ({cur_step} | Loss: {train_metric['loss']}, Learning Rate: {train_metric['learning_rate']})"
+                    )
+
+                    train_metrics = []
+
+                if cur_step % training_args.eval_steps == 0 and cur_step > 0:
+                    # ======================== Evaluating ==============================
+                    eval_metrics = []
+                    eval_loader = data_loader(input_rng, eval_dataset, eval_batch_size)
+                    eval_steps = len(eval_dataset) // eval_batch_size
+
+                    for _ in tqdm(range(eval_steps), desc="Evaluating...", position=2, leave=False):
+                        batch = next(eval_loader)
+                        metrics = p_eval_step(batch["input_ids"], batch["labels"], params)
+                        eval_metrics.append(metrics)
+
+                    # normalize eval metrics
+                    eval_metrics = stack_forest(eval_metrics)
+                    eval_metrics = jax.tree_map(jnp.mean, eval_metrics)
+
+                    try:
+                        eval_metrics["perplexity"] = math.exp(eval_metrics["loss"])
+                    except OverflowError:
+                        eval_metrics["perplexity"] = float("inf")
+
+                    logger.info(
+                        f"Step... ({cur_step} | Eval loss: {eval_metrics['loss']} | Eval Perplexity: {eval_metrics['perplexity']}"
+                    )
+
+                if cur_step % training_args.save_steps == 0 and cur_step > 0:
+                    # save checkpoint after each epoch and push checkpoint to the hub
+                    if jax.process_index() == 0:
+                        params = jax.device_get(params)
+                        model.save_pretrained(
+                            training_args.output_dir,
+                            params=params,
+                            push_to_hub=training_args.push_to_hub,
+                            commit_message=f"Saving weights and logs of step {cur_step}",
+                        )
+
+
+if __name__ == "__main__":
+    main()