train_gpt2.py

"""
Reference code for GPT-2 training and inference.
Will save the model weights into files, to be read from C as initialization.

References:
1) the official GPT-2 TensorFlow implementation released by OpenAI:
https://github.com/openai/gpt-2/blob/master/src/model.py
2) huggingface/transformers PyTorch implementation:
https://github.com/huggingface/transformers/blob/main/src/transformers/models/gpt2/modeling_gpt2.py

Example launches to only benchmark the speed of bfloat16 compiled GPU training:
1 GPU:
python train_gpt2.py --write_tensors=0 --num_iterations=50 --sequence_length=1024 --compile=1 --tensorcores=1 --dtype=bfloat16
you can also turn on flash-attention by appending --flash=1
4 GPU:
torchrun --standalone --nproc_per_node=4 train_gpt2.py --write_tensors=0 --num_iterations=50 --sequence_length=1024 --compile=1 --tensorcores=1 --dtype=bfloat16
"""

import os
import math
import struct
from contextlib import nullcontext
from dataclasses import dataclass

import numpy as np
import torch
import torch.nn as nn
from torch.nn import functional as F
import torch._inductor.config as config
from torch.nn.parallel import DistributedDataParallel as DDP
from torch.distributed import init_process_group, destroy_process_group

class NewGELU(nn.Module):
    """Careful there are a few versions of GeLU, this one is the exact one used by OpenAI"""
    def forward(self, input):
        return 0.5 * input * (1.0 + torch.tanh(math.sqrt(2.0 / math.pi) * (input + 0.044715 * torch.pow(input, 3.0))))

# using a global to toggle flash-attention
FLASH = 0

class CausalSelfAttention(nn.Module):

    def __init__(self, config):
        super().__init__()
        assert config.n_embd % config.n_head == 0
        # key, query, value projections for all heads, but in a batch
        self.c_attn = nn.Linear(config.n_embd, 3 * config.n_embd)
        # output projection
        self.c_proj = nn.Linear(config.n_embd, config.n_embd)
        # regularization
        self.n_head = config.n_head
        self.n_embd = config.n_embd
        # not really a 'bias', more of a mask, but following the OpenAI/HF naming though
        self.register_buffer("bias", torch.tril(torch.ones(config.block_size, config.block_size))
                                     .view(1, 1, config.block_size, config.block_size))

    def forward(self, x):
        B, T, C = x.size() # batch size, sequence length, embedding dimensionality (n_embd)
        # calculate query, key, values for all heads in batch and move head forward to be the batch dim
        qkv = self.c_attn(x)
        q, k, v = qkv.split(self.n_embd, dim=2)
        k = k.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
        q = q.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
        v = v.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
        if FLASH:
            # flashattention
            y = F.scaled_dot_product_attention(q, k, v, is_causal=True)
        else:
            # manual implementation of attention
            # this materializes the large (T,T) matrix for all the queries and keys
            att = (q @ k.transpose(-2, -1)) * (1.0 / math.sqrt(k.size(-1)))
            att = att.masked_fill(self.bias[:,:,:T,:T] == 0, float('-inf'))
            att = F.softmax(att, dim=-1)
            y = att @ v # (B, nh, T, T) x (B, nh, T, hs) -> (B, nh, T, hs)
        y = y.transpose(1, 2).contiguous().view(B, T, C) # re-assemble all head outputs side by side
        # output projection
        y = self.c_proj(y)
        return y

class MLP(nn.Module):

    def __init__(self, config):
        super().__init__()
        self.c_fc    = nn.Linear(config.n_embd, 4 * config.n_embd)
        self.gelu    = NewGELU()
        self.c_proj  = nn.Linear(4 * config.n_embd, config.n_embd)

    def forward(self, x):
        x = self.c_fc(x)
        x = self.gelu(x)
        x = self.c_proj(x)
        return x

class Block(nn.Module):

    def __init__(self, config):
        super().__init__()
        self.ln_1 = nn.LayerNorm(config.n_embd)
        self.attn = CausalSelfAttention(config)
        self.ln_2 = nn.LayerNorm(config.n_embd)
        self.mlp = MLP(config)

    def forward(self, x):
        x = x + self.attn(self.ln_1(x))
        x = x + self.mlp(self.ln_2(x))
        return x

@dataclass
class GPTConfig:
    block_size: int = 1024
    vocab_size: int = 50257
    n_layer: int = 12
    n_head: int = 12
    n_embd: int = 768

class GPT(nn.Module):

    def __init__(self, config):
        super().__init__()
        self.config = config

        self.transformer = nn.ModuleDict(dict(
            wte = nn.Embedding(config.vocab_size, config.n_embd),
            wpe = nn.Embedding(config.block_size, config.n_embd),
            h = nn.ModuleList([Block(config) for _ in range(config.n_layer)]),
            ln_f = nn.LayerNorm(config.n_embd),
        ))
        self.lm_head = nn.Linear(config.n_embd, config.vocab_size, bias=False)
        self.transformer.wte.weight = self.lm_head.weight # https://paperswithcode.com/method/weight-tying

    def forward(self, idx, targets=None):
        device = idx.device
        b, t = idx.size()
        assert t <= self.config.block_size, f"Cannot forward sequence of length {t}, block size is only {self.config.block_size}"
        pos = torch.arange(0, t, dtype=torch.long, device=device) # shape (t)

        # forward the GPT model itself
        tok_emb = self.transformer.wte(idx) # token embeddings of shape (b, t, n_embd)
        pos_emb = self.transformer.wpe(pos) # position embeddings of shape (t, n_embd)
        x = tok_emb + pos_emb

        for block in self.transformer.h:
            x = block(x)
        x = self.transformer.ln_f(x)

        if targets is not None:
            # if we are given some desired targets also calculate the loss
            logits = self.lm_head(x)
            loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1)
        else:
            # inference-time mini-optimization: only forward the lm_head on the very last position
            logits = self.lm_head(x[:, [-1], :]) # note: using list [-1] to preserve the time dim
            loss = None

        return logits, loss

    @classmethod
    def from_pretrained(cls, model_type):
        """Loads pretrained GPT-2 model weights from huggingface"""
        assert model_type in {'gpt2', 'gpt2-medium', 'gpt2-large', 'gpt2-xl'}
        from transformers import GPT2LMHeadModel
        print("loading weights from pretrained gpt: %s" % model_type)

        # n_layer, n_head and n_embd are determined from model_type
        config_args = {
            'gpt2':         dict(n_layer=12, n_head=12, n_embd=768),  # 124M params
            'gpt2-medium':  dict(n_layer=24, n_head=16, n_embd=1024), # 350M params
            'gpt2-large':   dict(n_layer=36, n_head=20, n_embd=1280), # 774M params
            'gpt2-xl':      dict(n_layer=48, n_head=25, n_embd=1600), # 1558M params
        }[model_type]
        config_args['vocab_size'] = 50257 # always 50257 for GPT model checkpoints
        config_args['block_size'] = 1024 # always 1024 for GPT model checkpoints
        # create a from-scratch initialized minGPT model
        config = GPTConfig(**config_args)
        model = GPT(config)
        sd = model.state_dict()
        sd_keys = sd.keys()
        sd_keys = [k for k in sd_keys if not k.endswith('.attn.bias')] # discard this mask / buffer, not a param

        # init a huggingface/transformers model
        model_hf = GPT2LMHeadModel.from_pretrained(model_type)
        sd_hf = model_hf.state_dict()

        # copy while ensuring all of the parameters are aligned and match in names and shapes
        sd_keys_hf = sd_hf.keys()
        sd_keys_hf = [k for k in sd_keys_hf if not k.endswith('.attn.masked_bias')] # ignore these, just a buffer
        sd_keys_hf = [k for k in sd_keys_hf if not k.endswith('.attn.bias')] # same, just the mask (buffer)
        transposed = ['attn.c_attn.weight', 'attn.c_proj.weight', 'mlp.c_fc.weight', 'mlp.c_proj.weight']
        # basically the openai checkpoints use a "Conv1D" module, but we only want to use a vanilla Linear
        # this means that we have to transpose these weights when we import them
        assert len(sd_keys_hf) == len(sd_keys), f"mismatched keys: {len(sd_keys_hf)} != {len(sd_keys)}"
        for k in sd_keys_hf:
            if any(k.endswith(w) for w in transposed):
                # special treatment for the Conv1D weights we need to transpose
                assert sd_hf[k].shape[::-1] == sd[k].shape
                with torch.no_grad():
                    sd[k].copy_(sd_hf[k].t())
            else:
                # vanilla copy over the other parameters
                assert sd_hf[k].shape == sd[k].shape
                with torch.no_grad():
                    sd[k].copy_(sd_hf[k])

        return model

    @torch.no_grad()
    def generate(self, idx, max_new_tokens, temperature=1.0, top_k=None):
        """
        Take a conditioning sequence of indices idx (LongTensor of shape (b,t)) and complete
        the sequence max_new_tokens times, feeding the predictions back into the model each time.
        Most likely you'll want to make sure to be in model.eval() mode of operation for this.
        """
        for _ in range(max_new_tokens):
            # if the sequence context is growing too long we must crop it at block_size
            idx_cond = idx if idx.size(1) <= self.config.block_size else idx[:, -self.config.block_size:]
            # forward the model to get the logits for the index in the sequence
            logits, _ = self(idx_cond)
            # pluck the logits at the final step and scale by desired temperature
            logits = logits[:, -1, :] / temperature
            # optionally crop the logits to only the top k options
            if top_k is not None:
                v, _ = torch.topk(logits, min(top_k, logits.size(-1)))
                logits[logits < v[:, [-1]]] = -float('Inf')
            # apply softmax to convert logits to (normalized) probabilities
            probs = F.softmax(logits, dim=-1)
            # sample from the distribution
            idx_next = torch.multinomial(probs, num_samples=1)
            # append sampled index to the running sequence and continue
            idx = torch.cat((idx, idx_next), dim=1)

        return idx

# a few utilities for saving params/grads/activations to files for loading in C
def write_fp32(tensor, file):
    t = tensor.detach().cpu().to(torch.float32)
    b = t.numpy().tobytes()
    file.write(b)

def write_bf16(tensor, file):
    t = tensor.detach().cpu().to(torch.bfloat16)
    # numpy doesn't have bf16 datatype so we have to trick it
    t = t.view(torch.int16) # trick: reinterpret as int16
    b = t.numpy().tobytes()
    file.write(b)

def write_tensors(model_tensors, L, file, dtype):
    assert dtype in {"float32", "bfloat16"}
    write_fun = write_fp32 if dtype == "float32" else write_bf16
    write_fun(model_tensors["transformer.wte.weight"], file) # (V, C)
    write_fun(model_tensors["transformer.wpe.weight"], file) # (T, C)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.ln_1.weight"], file)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.ln_1.bias"], file)
    for i in range(L): # (L, 3C, C)
        write_fun(model_tensors[f"transformer.h.{i}.attn.c_attn.weight"], file)
    for i in range(L): # (L, 3C)
        write_fun(model_tensors[f"transformer.h.{i}.attn.c_attn.bias"], file)
    for i in range(L): # (L, C, C)
        write_fun(model_tensors[f"transformer.h.{i}.attn.c_proj.weight"], file)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.attn.c_proj.bias"], file)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.ln_2.weight"], file)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.ln_2.bias"], file)
    for i in range(L): # (L, 4C, C)
        write_fun(model_tensors[f"transformer.h.{i}.mlp.c_fc.weight"], file)
    for i in range(L): # (L, 4C)
        write_fun(model_tensors[f"transformer.h.{i}.mlp.c_fc.bias"], file)
    for i in range(L): # (L, C, 4C)
        write_fun(model_tensors[f"transformer.h.{i}.mlp.c_proj.weight"], file)
    for i in range(L): # (L, C)
        write_fun(model_tensors[f"transformer.h.{i}.mlp.c_proj.bias"], file)
    write_fun(model_tensors["transformer.ln_f.weight"], file) # (C, )
    write_fun(model_tensors["transformer.ln_f.bias"], file) # (C, )

@torch.no_grad()
def pad_vocab(tensor, multiple=128, value=0):
    """
    The dimension of the vocab size in GPT-2 is 50,257
    which is unfortunately a very unfriendly number for a lot of
    matrix operations on the GPU. So we pad it to the nearest
    friendlier multiple, e.g. 50,304 if multiple=128 when we
    export the weights into C land. This is a NOOP algorithmically
    and is only done to make the tensor operations more efficient.
    """
    assert tensor.ndim == 2
    V, C = tensor.shape
    assert V == 50257, "just being defensive here"
    # calculate padded vocab size by rounding up to nearest multiple
    Vp = ((V + multiple - 1) // multiple) * multiple
    # pad the tensor
    pad_rows = Vp - V
    padded = tensor if pad_rows == 0 else F.pad(tensor, (0, 0, 0, pad_rows), value=value)
    assert padded.shape == (Vp, C)
    return padded

def write_model(model, filename, dtype):
    # everything we need to instantiate the model
    # 1) header is: version int, GPTConfig ints, padding to 1024 bytes
    assert dtype in {"float32", "bfloat16"} # float16 todo maybe later
    version = {
        "float32": 3, # 3: all tensors are fp32, padded vocab
        "bfloat16": 5, # 5: all tensors are bf16, padded vocab
    }[dtype]
    header = torch.zeros(256, dtype=torch.int32)
    header[0] = 20240326 # magic
    header[1] = version # checkpoint version
    header[2] = model.config.block_size
    header[3] = model.config.vocab_size
    header[4] = model.config.n_layer
    header[5] = model.config.n_head
    header[6] = model.config.n_embd
    # 2) the parameters follow the header
    params = {name: param.cpu() for name, param in model.named_parameters()}
    # pad the vocab to a multiple of 128 here at export, for efficiency in C
    wte = params["transformer.wte.weight"] # (V, C)
    wte_padded = pad_vocab(wte) # (Vp, C)
    params["transformer.wte.weight"] = wte_padded # (Vp, C)
    print(f"padded vocab size from {wte.size(0)} to {wte_padded.size(0)}")
    header[7] = wte_padded.size(0) # padded vocab size store in header
    # now write to file
    with open(filename, "wb") as file:
        file.write(header.numpy().tobytes()) # header
        write_tensors(params, model.config.n_layer, file, dtype) # params
    print(f"wrote {filename}")

def write_state(model, x, y, logits, loss, filename):
    # the state is used for debugging.
    # it contains information about the input, logits, loss, and the parameter gradients
    # this can be used for checking the computation correctness in C
    header = torch.zeros(256, dtype=torch.int32)
    header[0] = 20240327 # magic
    header[1] = 2 # run state version = 2 (1 -> 2 for padded vocab changes)
    header[2] = x.size(0) # batch size of the batch, B
    header[3] = x.size(1) # temporal extent of the batch, T
    grads = {name: param.grad.cpu() for name, param in model.named_parameters()}
    # pad the vocab grads here as well, to mirror write_model
    wte_grad = grads["transformer.wte.weight"] # (V, C)
    wte_grad_padded = pad_vocab(wte_grad, value=0) # (Vp, C) # TODO later maybe pad with nan?
    grads["transformer.wte.weight"] = wte_grad_padded # (Vp, C)
    print(f"padded vocab size in reference grads from {wte_grad.size(0)} to {wte_grad_padded.size(0)}")
    with open(filename, "wb") as file:
        # header
        file.write(header.numpy().tobytes())
        # input x
        file.write(x.cpu().numpy().astype("int32").tobytes()) # (B, T)
        # targets y
        file.write(y.cpu().numpy().astype("int32").tobytes()) # (B, T)
        # logits (result of the model forward pass)
        write_fp32(logits.cpu(), file)
        # loss (single float, result of the cross entropy loss)
        write_fp32(loss.cpu(), file)
        # gradients
        write_tensors(grads, model.config.n_layer, file, "float32")
    print(f"wrote {filename}")

def write_tokenizer(enc, filename):
    n = enc.max_token_value + 1
    header = torch.zeros(256, dtype=torch.int32)
    header[0] = 20240328 # magic
    header[1] = 2 # tokenizer version = 2 (1 -> 2: includes EOT token)
    header[2] = n # number of tokens
    header[3] = enc.eot_token # EOT token
    with open(filename, "wb") as file:
        file.write(header.numpy().tobytes())
        for i in range(n):
            b = enc.decode_bytes([i])
            length = len(b)
            assert length < 256, f"Token length exceeds 255: {length}"
            file.write(struct.pack("<B", length))  # Write the length as a 1-byte unsigned integer
            file.write(b)  # Write the actual bytes
    print(f"wrote {filename}")

def print0(*args, **kwargs):
    # modified print that only prints from the master process
    # if this is not a distributed run, it's just a print
    if int(os.environ.get("RANK", 0)) == 0:
        print(*args, **kwargs)

if __name__ == "__main__":
    import time
    import argparse
    import tiktoken
    print0(f"Running pytorch {torch.version.__version__}")

    # default settings will overfit a tiny batch of data
    # and save model weights and debug state to disk on the first iteration
    # if you'd like to e.g. time the forward pass only, call this script as:
    # python train_gpt2.py --inference_only 1 --write_tensors 0 --sequence_length 1024
    parser = argparse.ArgumentParser()
    parser.add_argument("--input_bin", type=str, default="data/tiny_shakespeare_val.bin", help="input .bin to train on")
    parser.add_argument("--write_tensors", type=int, default=1, help="write tensors to disk")
    parser.add_argument("--inference_only", type=int, default=0, help="only run inference")
    parser.add_argument("--dtype", type=str, default="float32", help="float32|float16|bfloat16")
    parser.add_argument("--device", type=str, default="", help="by default we autodetect, or set it here")
    parser.add_argument("--compile", type=int, default=0, help="torch.compile the model")
    parser.add_argument("--tensorcores", type=int, default=0, help="use tensorcores")
    parser.add_argument("--flash", type=int, default=0, help="use flash attention")
    parser.add_argument("--num_iterations", type=int, default=10, help="number of iterations to run")
    parser.add_argument("--batch_size", type=int, default=4, help="batch size")
    parser.add_argument("--sequence_length", type=int, default=64, help="sequence length")
    args = parser.parse_args()
    B, T = args.batch_size, args.sequence_length
    assert 1 <= T <= 1024
    assert args.dtype in {"float32", "float16", "bfloat16"}

    # set up DDP (distributed data parallel). torchrun sets this env variable
    ddp = int(os.environ.get('RANK', -1)) != -1 # is this a ddp run?
    if ddp:
        # use of DDP atm demands CUDA, we set the device appropriately according to rank
        assert torch.cuda.is_available(), "for now i think we need CUDA for DDP"
        init_process_group(backend='nccl')
        ddp_rank = int(os.environ['RANK'])
        ddp_local_rank = int(os.environ['LOCAL_RANK'])
        ddp_world_size = int(os.environ['WORLD_SIZE'])
        device = f'cuda:{ddp_local_rank}'
        torch.cuda.set_device(device)
        master_process = ddp_rank == 0 # this process will do logging, checkpointing etc.
        seed_offset = ddp_rank # each process gets a different seed
    else:
        ddp_world_size = 1
        master_process = True
        seed_offset = 0
        # select the device
        if args.device:
            # provided explicitly by the user
            device = args.device
        else:
            # attempt to autodetect the device
            device = "cpu"
            if torch.cuda.is_available():
                device = "cuda"
            elif hasattr(torch.backends, "mps") and torch.backends.mps.is_available():
                device = "mps"
    print(f"using device: {device}")

    # set up a context manager following the desired dtype and device
    ptdtype = {'float32': torch.float32, 'bfloat16': torch.bfloat16, 'float16': torch.float16}[args.dtype]
    ctx = torch.amp.autocast(device_type="cuda", dtype=ptdtype) if device == "cuda" else nullcontext()

    # seed the random number generators (in DDP we want different processes to use different offsets)
    # in the code below we don't actually use random numbers because there is no active dataloader
    # loading actual batches of data, etc. but it is a good practice and something to be careful with,
    # explicit with and think about, so I am leaving this here.
    torch.manual_seed(42 + seed_offset)
    if torch.cuda.is_available():
        torch.cuda.manual_seed(42 + seed_offset)

    # set the torch precision mode to use TensorFloat32 (TF32) for matmuls
    # docs https://pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html
    if args.tensorcores:
        torch.set_float32_matmul_precision('high')

    # turn on/off flash attention
    assert args.flash in {0, 1}
    FLASH = args.flash

    # init (and write) the tokenizer
    enc = tiktoken.get_encoding("gpt2")
    encode = lambda s: enc.encode(s, allowed_special={"<|endoftext|>"})
    decode = lambda l: enc.decode(l)
    if master_process and args.write_tensors: # tokenizer is technically not tensors but ok
        write_tokenizer(enc, "gpt2_tokenizer.bin")

    # load the GPT-2 model weights
    model = GPT.from_pretrained("gpt2")
    model.train()
    model.to(device)
    if args.compile:
        if hasattr(config, "coordinate_descent_tuning"):
            config.coordinate_descent_tuning = True # suggested by @Chillee
        print0("compiling the model...")
        model = torch.compile(model)

    # -------------------------------------------------------------------------
    # data loading related: long but it's just to get a single batch of data

    # load the tokens
    # note we're using val by default instead of train split just because it is smaller/faster
    assert os.path.isfile(args.input_bin)
    print0(f"loading cached tokens in {args.input_bin}")
    with open(args.input_bin, "rb") as f:
        tokens = np.frombuffer(f.read(), dtype=np.int32)

    # np -> tensor, long, on device
    tokens = torch.tensor(tokens)
    tokens = tokens.to(torch.long)

    # lightweight dataloader
    def get_batch():
        assert B*T+1 <= len(tokens), "not enough tokens"
        # for 338,025 tokens. E.g. with B=8 T=1024, this will yield 41 batches before looping
        i = 0
        while True:
            x = tokens[i:i+B*T].view(B, T)
            y = tokens[i+1:i+B*T+1].view(B, T)
            yield x, y
            i += B*T
            if i + B*T + 1 >= len(tokens):
                i = 0 # in prod we'd want to randomize the start point a bit

    # fetch one batch of data, which we will overfit to
    data_iter = iter(get_batch())
    x, y = next(data_iter) # we'll overfit this batch below
    x = x.to(device)
    y = y.to(device)

    # -------------------------------------------------------------------------
    # STAGE 1: weights / state logging for C to load later

    # do one forward pass to generate ground truth for our C tests
    if master_process and (not args.inference_only and args.write_tensors):
        logits, loss = model(x, y)
        loss.backward()
        # save model params, in both float32 and bfloat16
        write_model(model, "gpt2_124M.bin", dtype="float32")
        write_model(model, "gpt2_124M_bf16.bin", dtype="bfloat16")
        # save x, y, logits, loss, and parameter gradients, for debugging C
        # always store these in fp32 to have an accurate reference (?)
        write_state(model, x, y, logits, loss, "gpt2_124M_debug_state.bin")

    # -------------------------------------------------------------------------
    # STAGE 2: training loop to get timings

    # here we wrap model into DDP container
    if ddp:
        model = DDP(model, device_ids=[ddp_local_rank])
    raw_model = model.module if ddp else model # always contains the "raw" unwrapped model

    # init the optimizer
    adam_use_fused = device == "cuda" # only works on CUDA (?)
    optimizer = torch.optim.Adam(model.parameters(), lr=1e-4, fused=adam_use_fused)

    if device == "cuda":
        torch.cuda.reset_peak_memory_stats()
    timings = []
    for i in range(args.num_iterations):
        t0 = time.time()
        with ctx:
            logits, loss = model(x, y)
            del logits
        if not args.inference_only:
            optimizer.zero_grad(set_to_none=True)
            loss.backward()
            optimizer.step()
        # wait on the CPU for all device work to end so we get accurate per-iteration timings below
        if device == "mps":
            torch.mps.synchronize()
        elif device == "cuda":
            torch.cuda.synchronize()
        # time and print
        t1 = time.time()
        # the 0th iteration is often an outlier (much slower) => skip logging it
        tokens_per_second = ddp_world_size * B * T / (t1-t0)
        print0(f"iteration {i+1}, loss: {loss.item():.4f}, time: {(t1-t0)*1000:.3f}ms, tok/s: {tokens_per_second:.2f}")
        if i > 0 and i > args.num_iterations - 20:
            timings.append(t1-t0)

    # print the average of the last 20 timings, to get something smooth-ish
    timings = timings[-20:]
    print0(f"final {len(timings)} iters avg: {np.mean(timings)*1000:.3f}ms")
    #print0(f"peak memory consumption: {torch.cuda.max_memory_allocated() // 1024 // 1024} MiB")

    # -------------------------------------------------------------------------
    # STAGE 3: Few steps of inference
    if master_process:

        # before we end, let's also do one round of inference
        # we'll kick off the generation with "<|endoftext|>", which designates the start of a new sequence
        start = "<|endoftext|>"
        start_ids = encode(start)
        x = (torch.tensor(start_ids, dtype=torch.long, device=device)[None, ...])

        # run generation for 16 time steps (tokens)
        max_new_tokens = 16
        temperature = 1.0
        top_k = 40
        raw_model.eval()
        y = raw_model.generate(x, max_new_tokens, temperature=temperature, top_k=top_k)
        print0(decode(y[0].tolist()))
        print0('---------------')

    # -------------------------------------------------------------------------
    # clean up nice
    if ddp:
        destroy_process_group()