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# Copyright (c) 2023 Amphion.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
import os
import time
import random
from pathlib import Path
import re
import glob
import accelerate
import json
import numpy as np
import torch
from accelerate.utils import ProjectConfiguration
from torch.utils.data import DataLoader
from tqdm import tqdm
import torch
import torch.nn.functional as F
import torchaudio
from accelerate.logging import get_logger
from models.codec.facodec.facodec_dataset import FAcodecDataset, FAcodecCollator
from models.codec.codec_sampler import build_samplers
from models.codec.codec_trainer import CodecTrainer
from modules.dac.nn.loss import (
MultiScaleSTFTLoss,
MelSpectrogramLoss,
GANLoss,
L1Loss,
FocalLoss,
)
from audiotools import AudioSignal
from transformers import Wav2Vec2Processor, Wav2Vec2ForCTC
try:
import nemo.collections.asr as nemo_asr
except ImportError:
print(
"Unable to import nemo_asr, titanet outputs will be set to random values, you may only run debugging mode. DO NOT USE THIS FOR TRAINING"
)
nemo_asr = None
from models.codec.facodec.modules.commons import (
build_model,
load_checkpoint,
load_F0_models,
log_norm,
)
from models.codec.facodec.optimizer import build_optimizer
class FAcodecTrainer(CodecTrainer):
def __init__(self, args, cfg):
super().__init__()
self.args = args
self.cfg = cfg
cfg.exp_name = args.exp_name
# Init accelerator
self._init_accelerator()
self.accelerator.wait_for_everyone()
# Init logger
with self.accelerator.main_process_first():
self.logger = get_logger(args.exp_name, log_level=args.log_level)
self.logger.info("=" * 56)
self.logger.info("||\t\t" + "New training process started." + "\t\t||")
self.logger.info("=" * 56)
self.logger.info("\n")
self.logger.debug(f"Using {args.log_level.upper()} logging level.")
self.logger.info(f"Experiment name: {args.exp_name}")
self.logger.info(f"Experiment directory: {self.exp_dir}")
self.checkpoint_dir = os.path.join(self.exp_dir, "checkpoint")
if self.accelerator.is_main_process:
os.makedirs(self.checkpoint_dir, exist_ok=True)
self.logger.debug(f"Checkpoint directory: {self.checkpoint_dir}")
# Init training status
self.batch_count: int = 0
self.step: int = 0
self.epoch: int = 0
self.max_epoch = (
self.cfg.train.max_epoch if self.cfg.train.max_epoch > 0 else float("inf")
)
self.logger.info(
"Max epoch: {}".format(
self.max_epoch if self.max_epoch < float("inf") else "Unlimited"
)
)
# Check potential erorrs
if self.accelerator.is_main_process:
self._check_basic_configs()
self.save_checkpoint_stride = self.cfg.train.save_checkpoint_stride
self.checkpoints_path = [
[] for _ in range(len(self.save_checkpoint_stride))
]
self.run_eval = self.cfg.train.run_eval
# Set random seed
with self.accelerator.main_process_first():
start = time.monotonic_ns()
self._set_random_seed(self.cfg.train.random_seed)
end = time.monotonic_ns()
self.logger.debug(
f"Setting random seed done in {(end - start) / 1e6:.2f}ms"
)
self.logger.debug(f"Random seed: {self.cfg.train.random_seed}")
# Build dataloader
with self.accelerator.main_process_first():
self.logger.info("Building dataset...")
start = time.monotonic_ns()
self.train_dataloader, self.valid_dataloader = self._build_dataloader()
end = time.monotonic_ns()
self.logger.info(f"Building dataset done in {(end - start) / 1e6:.2f}ms")
# Build model
with self.accelerator.main_process_first():
self.logger.info("Building model...")
start = time.monotonic_ns()
self.model = self._build_model()
end = time.monotonic_ns()
for _, model in self.model.items():
self.logger.debug(model)
self.logger.info(f"Building model done in {(end - start) / 1e6:.2f}ms")
self.logger.info(f"Model parameters: {self._count_parameters()/1e6:.2f}M")
# Build optimizers and schedulers
with self.accelerator.main_process_first():
self.logger.info("Building optimizer and scheduler...")
start = time.monotonic_ns()
self.optimizer = self._build_optimizer()
end = time.monotonic_ns()
self.logger.info(
f"Building optimizer and scheduler done in {(end - start) / 1e6:.2f}ms"
)
# Build helper models
with self.accelerator.main_process_first():
self.logger.info("Building helper models...")
start = time.monotonic_ns()
self._built_helper_model()
end = time.monotonic_ns()
self.logger.info(
f"Building helper models done in {(end - start) / 1e6:.2f}ms"
)
# Accelerator preparing
self.logger.info("Initializing accelerate...")
start = time.monotonic_ns()
for k in self.model:
self.model[k] = self.accelerator.prepare(self.model[k])
for k, v in self.optimizer.optimizers.items():
self.optimizer.optimizers[k] = self.accelerator.prepare(
self.optimizer.optimizers[k]
)
self.optimizer.schedulers[k] = self.accelerator.prepare(
self.optimizer.schedulers[k]
)
end = time.monotonic_ns()
self.logger.info(f"Initializing accelerate done in {(end - start) / 1e6:.2f}ms")
# Build criterions
with self.accelerator.main_process_first():
self.logger.info("Building criterion...")
start = time.monotonic_ns()
self.criterions = self._build_criterion()
end = time.monotonic_ns()
self.logger.info(f"Building criterion done in {(end - start) / 1e6:.2f}ms")
# Resume checkpoints
with self.accelerator.main_process_first():
self.checkpoint_dir = os.path.join(self.exp_dir, "checkpoint")
if args.resume_type:
self.logger.info("Resuming from checkpoint...")
start = time.monotonic_ns()
ckpt_path = Path(args.checkpoint)
if self._is_valid_pattern(ckpt_path.parts[-1]):
ckpt_path = self._load_model(args.checkpoint, args.resume_type)
else:
ckpt_path = self._load_model(
args.checkpoint, resume_type=args.resume_type
)
end = time.monotonic_ns()
self.logger.info(
f"Resuming from checkpoint done in {(end - start) / 1e6:.2f}ms"
)
self.checkpoints_path = json.load(
open(os.path.join(ckpt_path, "ckpts.json"), "r")
)
if self.accelerator.is_main_process:
os.makedirs(self.checkpoint_dir, exist_ok=True)
self.logger.debug(f"Checkpoint directory: {self.checkpoint_dir}")
# Save config
self.config_save_path = os.path.join(self.exp_dir, "args.json")
def _build_dataset(self):
return FAcodecDataset, FAcodecCollator
def _build_criterion(self):
criterions = dict()
stft_criterion = MultiScaleSTFTLoss()
mel_criterion = MelSpectrogramLoss(
n_mels=[5, 10, 20, 40, 80, 160, 320],
window_lengths=[32, 64, 128, 256, 512, 1024, 2048],
mel_fmin=[0, 0, 0, 0, 0, 0, 0],
mel_fmax=[None, None, None, None, None, None, None],
pow=1.0,
mag_weight=0.0,
clamp_eps=1e-5,
)
content_criterion = FocalLoss(gamma=2)
l1_criterion = L1Loss()
criterions["stft"] = stft_criterion
criterions["mel"] = mel_criterion
criterions["l1"] = l1_criterion
criterions["content"] = content_criterion
return criterions
def _build_model(self):
model = build_model(self.cfg.model_params)
_ = [model[key].to(self.accelerator.device) for key in model]
return model
def _built_helper_model(self):
device = self.accelerator.device
self.pitch_extractor = load_F0_models(self.cfg.F0_path).to(device)
# load model and processor
self.w2v_processor = Wav2Vec2Processor.from_pretrained(
"facebook/wav2vec2-xlsr-53-espeak-cv-ft"
)
self.w2v_model = Wav2Vec2ForCTC.from_pretrained(
"facebook/wav2vec2-xlsr-53-espeak-cv-ft"
).to(device)
self.w2v_model.eval()
if nemo_asr is None:
self.speaker_model = None
else:
self.speaker_model = (
nemo_asr.models.EncDecSpeakerLabelModel.from_pretrained(
"nvidia/speakerverification_en_titanet_large"
)
)
self.speaker_model = self.speaker_model.to(device)
self.speaker_model.eval()
def _build_optimizer(self):
scheduler_params = {
"warmup_steps": self.cfg.loss_params.warmup_steps,
"base_lr": self.cfg.loss_params.base_lr,
}
optimizer = build_optimizer(
{key: self.model[key] for key in self.model},
scheduler_params_dict={key: scheduler_params.copy() for key in self.model},
lr=float(scheduler_params["base_lr"]),
)
return optimizer
def train_loop(self):
"""Training process"""
self.accelerator.wait_for_everyone()
# Dump config
if self.accelerator.is_main_process:
self._dump_cfg(self.config_save_path)
_ = [self.model[key].train() for key in self.model]
self.optimizer.zero_grad()
# Sync and start training
self.accelerator.wait_for_everyone()
while self.epoch < self.max_epoch:
self.logger.info("\n")
self.logger.info("-" * 32)
self.logger.info("Epoch {}: ".format(self.epoch))
# Train and Validate
train_total_loss, train_losses = self._train_epoch()
for key, loss in train_losses.items():
self.logger.info(" |- Train/{} Loss: {:.6f}".format(key, loss))
self.accelerator.log(
{"Epoch/Train {} Loss".format(key): loss},
step=self.epoch,
)
self.accelerator.log(
{
"Epoch/Train Total Loss": train_total_loss,
},
step=self.epoch,
)
# Update scheduler
self.accelerator.wait_for_everyone()
# Check save checkpoint interval
run_eval = False
if self.accelerator.is_main_process:
save_checkpoint = False
for i, num in enumerate(self.save_checkpoint_stride):
if self.epoch % num == 0:
save_checkpoint = True
run_eval |= self.run_eval[i]
# Save checkpoints
self.accelerator.wait_for_everyone()
if self.accelerator.is_main_process and save_checkpoint:
print("Saving..")
state = {
"net": {key: self.model[key].state_dict() for key in self.model},
"optimizer": self.optimizer.state_dict(),
"scheduler": self.optimizer.scheduler_state_dict(),
"iters": self.step,
"epoch": self.epoch,
}
save_path = os.path.join(
self.checkpoint_dir,
"FAcodec_epoch_%05d_step_%05d.pth" % (self.epoch, self.iters),
)
torch.save(state, save_path)
json.dump(
self.checkpoints_path,
open(os.path.join(self.checkpoint_dir, "ckpts.json"), "w"),
ensure_ascii=False,
indent=4,
)
self.accelerator.wait_for_everyone()
self.epoch += 1
# Finish training
self.accelerator.wait_for_everyone()
if self.accelerator.is_main_process:
path = os.path.join(
self.checkpoint_dir,
"epoch-{:04d}_step-{:07d}".format(
self.epoch,
self.step,
),
)
print("Saving..")
state = {
"net": {key: self.model[key].state_dict() for key in self.model},
"optimizer": self.optimizer.state_dict(),
"scheduler": self.optimizer.scheduler_state_dict(),
"iters": self.step,
"epoch": self.epoch,
}
save_path = os.path.join(
self.checkpoint_dir,
"FAcodec_epoch_%05d_step_%05d.pth" % (self.epoch, self.iters),
)
torch.save(state, save_path)
def _train_epoch(self):
"""Training epoch. Should return average loss of a batch (sample) over
one epoch. See ``train_loop`` for usage.
"""
_ = [self.model[key].train() for key in self.model]
epoch_losses: dict = {}
epoch_total_loss: int = 0
for batch in tqdm(
self.train_dataloader,
desc=f"Training Epoch {self.epoch}",
unit="batch",
colour="GREEN",
leave=False,
dynamic_ncols=True,
smoothing=0.04,
disable=not self.accelerator.is_main_process,
):
# Get losses
total_loss, losses = self._train_step(batch)
self.batch_count += 1
# Log info
if self.batch_count % self.cfg.train.gradient_accumulation_step == 0:
self.accelerator.log(
{
"Step/Learning Rate": (
self.optimizer.schedulers["encoder"].get_last_lr()[0]
if self.step != 0
else 0
)
},
step=self.step,
)
for key, _ in losses.items():
self.accelerator.log(
{
"Step/Train {} Loss".format(key): losses[key],
},
step=self.step,
)
if not epoch_losses:
epoch_losses = losses
else:
for key, value in losses.items():
epoch_losses[key] += value
epoch_total_loss += total_loss
self.step += 1
# Get and log total losses
self.accelerator.wait_for_everyone()
epoch_total_loss = (
epoch_total_loss
/ len(self.train_dataloader)
* self.cfg.train.gradient_accumulation_step
)
for key in epoch_losses.keys():
epoch_losses[key] = (
epoch_losses[key]
/ len(self.train_dataloader)
* self.cfg.train.gradient_accumulation_step
)
return epoch_total_loss, epoch_losses
def _train_step(self, data):
"""Training forward step. Should return average loss of a sample over
one batch. Provoke ``_forward_step`` is recommended except for special case.
See ``_train_epoch`` for usage.
"""
# Init losses
train_losses = {}
total_loss = 0
# Use input feature to get predictions
data = [b.to(self.accelerator.device, non_blocking=True) for b in data]
waves, mels, wave_lengths, mel_input_length = data
# extract semantic latent with w2v model
waves_16k = torchaudio.functional.resample(waves, 24000, 16000)
w2v_input = self.w2v_processor(
waves_16k, sampling_rate=16000, return_tensors="pt"
).input_values.to(self.accelerator.device)
with torch.no_grad():
w2v_outputs = self.w2v_model(w2v_input.squeeze(0)).logits
predicted_ids = torch.argmax(w2v_outputs, dim=-1)
phone_ids = (
F.interpolate(
predicted_ids.unsqueeze(0).float(), mels.size(-1), mode="nearest"
)
.long()
.squeeze(0)
)
# get clips
mel_seg_len = min(
[int(mel_input_length.min().item()), self.cfg.train.max_frame_len]
)
gt_mel_seg = []
wav_seg = []
w2v_seg = []
for bib in range(len(mel_input_length)):
mel_length = int(mel_input_length[bib].item())
random_start = (
np.random.randint(0, mel_length - mel_seg_len)
if mel_length != mel_seg_len
else 0
)
gt_mel_seg.append(mels[bib, :, random_start : random_start + mel_seg_len])
# w2v_seg.append(w2v_latent[bib, :, random_start:random_start + mel_seg_len])
w2v_seg.append(phone_ids[bib, random_start : random_start + mel_seg_len])
y = waves[bib][random_start * 300 : (random_start + mel_seg_len) * 300]
wav_seg.append(y.to(self.accelerator.device))
gt_mel_seg = torch.stack(gt_mel_seg).detach()
wav_seg = torch.stack(wav_seg).float().detach().unsqueeze(1)
w2v_seg = torch.stack(w2v_seg).float().detach()
with torch.no_grad():
real_norm = log_norm(gt_mel_seg.unsqueeze(1)).squeeze(1).detach()
F0_real, _, _ = self.pitch_extractor(gt_mel_seg.unsqueeze(1))
# normalize f0
# Remove unvoiced frames (replace with -1)
gt_glob_f0s = []
f0_targets = []
for bib in range(len(F0_real)):
voiced_indices = F0_real[bib] > 5.0
f0_voiced = F0_real[bib][voiced_indices]
if len(f0_voiced) != 0:
# Convert to log scale
log_f0 = f0_voiced.log2()
# Calculate mean and standard deviation
mean_f0 = log_f0.mean()
std_f0 = log_f0.std()
# Normalize the F0 sequence
normalized_f0 = (log_f0 - mean_f0) / std_f0
# Create the normalized F0 sequence with unvoiced frames
normalized_sequence = torch.zeros_like(F0_real[bib])
normalized_sequence[voiced_indices] = normalized_f0
normalized_sequence[~voiced_indices] = (
-10
) # Assign -10 to unvoiced frames
gt_glob_f0s.append(mean_f0)
else:
normalized_sequence = torch.zeros_like(F0_real[bib]) - 10.0
gt_glob_f0s.append(torch.tensor(0.0).to(self.accelerator.device))
# f0_targets.append(normalized_sequence[single_side_context // 200:-single_side_context // 200])
f0_targets.append(normalized_sequence)
f0_targets = torch.stack(f0_targets).to(self.accelerator.device)
# fill nan with -10
f0_targets[torch.isnan(f0_targets)] = -10.0
# fill inf with -10
f0_targets[torch.isinf(f0_targets)] = -10.0
# if frame_rate not equal to 80, interpolate f0 from frame rate of 80 to target frame rate
if self.cfg.preprocess_params.frame_rate != 80:
f0_targets = F.interpolate(
f0_targets.unsqueeze(1),
mel_seg_len // 80 * self.cfg.preprocess_params.frame_rate,
mode="nearest",
).squeeze(1)
w2v_seg = F.interpolate(
w2v_seg,
mel_seg_len // 80 * self.cfg.preprocess_params.frame_rate,
mode="nearest",
)
wav_seg_input = wav_seg
wav_seg_target = wav_seg
z = self.model.encoder(wav_seg_input)
z, quantized, commitment_loss, codebook_loss, timbre = self.model.quantizer(
z, wav_seg_input, n_c=2, full_waves=waves, wave_lens=wave_lengths
)
preds, rev_preds = self.model.fa_predictors(quantized, timbre)
pred_wave = self.model.decoder(z)
len_diff = wav_seg_target.size(-1) - pred_wave.size(-1)
if len_diff > 0:
wav_seg_target = wav_seg_target[..., len_diff // 2 : -len_diff // 2]
# discriminator loss
d_fake = self.model.discriminator(pred_wave.detach())
d_real = self.model.discriminator(wav_seg_target)
loss_d = 0
for x_fake, x_real in zip(d_fake, d_real):
loss_d += torch.mean(x_fake[-1] ** 2)
loss_d += torch.mean((1 - x_real[-1]) ** 2)
self.optimizer.zero_grad()
self.accelerator.backward(loss_d)
grad_norm_d = torch.nn.utils.clip_grad_norm_(
self.model.discriminator.parameters(), 10.0
)
self.optimizer.step("discriminator")
self.optimizer.scheduler(key="discriminator")
# generator loss
signal = AudioSignal(wav_seg_target, sample_rate=24000)
recons = AudioSignal(pred_wave, sample_rate=24000)
stft_loss = self.criterions["stft"](recons, signal)
mel_loss = self.criterions["mel"](recons, signal)
waveform_loss = self.criterions["l1"](recons, signal)
d_fake = self.model.discriminator(pred_wave)
d_real = self.model.discriminator(wav_seg_target)
loss_g = 0
for x_fake in d_fake:
loss_g += torch.mean((1 - x_fake[-1]) ** 2)
loss_feature = 0
for i in range(len(d_fake)):
for j in range(len(d_fake[i]) - 1):
loss_feature += F.l1_loss(d_fake[i][j], d_real[i][j].detach())
pred_f0, pred_uv = preds["f0"], preds["uv"]
rev_pred_f0, rev_pred_uv = rev_preds["rev_f0"], rev_preds["rev_uv"]
common_min_size = min(pred_f0.size(-2), f0_targets.size(-1))
f0_targets = f0_targets[..., :common_min_size]
real_norm = real_norm[..., :common_min_size]
f0_loss = F.smooth_l1_loss(
f0_targets, pred_f0.squeeze(-1)[..., :common_min_size]
)
uv_loss = F.smooth_l1_loss(
real_norm, pred_uv.squeeze(-1)[..., :common_min_size]
)
rev_f0_loss = (
F.smooth_l1_loss(f0_targets, rev_pred_f0.squeeze(-1)[..., :common_min_size])
if rev_pred_f0 is not None
else torch.FloatTensor([0]).to(self.accelerator.device)
)
rev_uv_loss = (
F.smooth_l1_loss(real_norm, rev_pred_uv.squeeze(-1)[..., :common_min_size])
if rev_pred_uv is not None
else torch.FloatTensor([0]).to(self.accelerator.device)
)
tot_f0_loss = f0_loss + rev_f0_loss
tot_uv_loss = uv_loss + rev_uv_loss
pred_content = preds["content"]
rev_pred_content = rev_preds["rev_content"]
target_content_latents = w2v_seg[..., :common_min_size]
content_loss = self.criterions["content"](
pred_content.transpose(1, 2)[..., :common_min_size],
target_content_latents.long(),
)
rev_content_loss = (
self.criterions["content"](
rev_pred_content.transpose(1, 2)[..., :common_min_size],
target_content_latents.long(),
)
if rev_pred_content is not None
else torch.FloatTensor([0]).to(self.accelerator.device)
)
tot_content_loss = content_loss + rev_content_loss
if self.speaker_model is not None:
spk_logits = torch.cat(
[
self.speaker_model.infer_segment(w16.cpu()[..., :wl])[1]
for w16, wl in zip(waves_16k, wave_lengths)
],
dim=0,
)
spk_labels = spk_logits.argmax(dim=-1)
else:
spk_labels = torch.zeros([len(waves_16k)], dtype=torch.long).to(
self.accelerator.device
)
spk_pred_logits = preds["timbre"]
spk_loss = F.cross_entropy(spk_pred_logits, spk_labels)
x_spk_pred_logits = rev_preds["x_timbre"]
x_spk_loss = (
F.cross_entropy(x_spk_pred_logits, spk_labels)
if x_spk_pred_logits is not None
else torch.FloatTensor([0]).to(self.accelerator.device)
)
tot_spk_loss = spk_loss + x_spk_loss
loss_gen_all = (
mel_loss * 15.0
+ loss_feature * 1.0
+ loss_g * 1.0
+ commitment_loss * 0.25
+ codebook_loss * 1.0
+ tot_f0_loss * 1.0
+ tot_uv_loss * 1.0
+ tot_content_loss * 5.0
+ tot_spk_loss * 5.0
)
self.optimizer.zero_grad()
self.accelerator.backward(loss_gen_all)
with torch.no_grad():
total_loss = loss_gen_all.item()
train_losses["stft"] = stft_loss.item()
train_losses["mel"] = mel_loss.item()
train_losses["l1"] = waveform_loss.item()
train_losses["f0"] = f0_loss.item()
train_losses["uv"] = uv_loss.item()
train_losses["content"] = content_loss.item()
train_losses["speaker"] = spk_loss.item()
train_losses["rev_f0"] = rev_f0_loss.item()
train_losses["rev_uv"] = rev_uv_loss.item()
train_losses["rev_content"] = rev_content_loss.item()
train_losses["rev_speaker"] = x_spk_loss.item()
train_losses["feature"] = loss_feature.item()
train_losses["generator"] = loss_g.item()
train_losses["commitment"] = commitment_loss.item()
train_losses["codebook"] = codebook_loss.item()
# discriminators
train_losses["discriminator"] = loss_d.item()
return total_loss, train_losses
def _inference(self, eval_wave):
"""Inference during training for test audios."""
z = self.model.encoder(
eval_wave[None, None, ...].to(self.accelerator.device).float()
)
z, quantized, commitment_loss, codebook_loss, timbre = self.model.quantizer(
z, eval_wave[None, None, ...], n_c=self.cfg.model_params.n_c_codebooks
)
full_pred_wave = self.model.decoder(z)
return full_pred_wave[0]
def _load_model(self, checkpoint_path=None, resume_type="resume"):
"""Load model from checkpoint. If checkpoint_path is None, it will
load the latest checkpoint in checkpoint_dir. If checkpoint_path is not
None, it will load the checkpoint specified by checkpoint_path. **Only use this
method after** ``accelerator.prepare()``.
"""
if resume_type == "resume":
if checkpoint_path is None:
available_checkpoints = glob.glob(
os.path.join(self.checkpoint_dir, "FAcodc_epoch_*_step_*.pth")
)
# find the checkpoint that has the highest step number
latest_checkpoint = max(
available_checkpoints,
key=lambda x: int(x.split("_")[-1].split(".")[0]),
)
earliest_checkpoint = min(
available_checkpoints,
key=lambda x: int(x.split("_")[-1].split(".")[0]),
)
# delete the earliest checkpoint
if (
earliest_checkpoint != latest_checkpoint
and self.accelerator.is_main_process
and len(available_checkpoints) > 4
):
os.remove(earliest_checkpoint)
print(f"Removed {earliest_checkpoint}")
else:
latest_checkpoint = checkpoint_path
self.model, self.optimizer, self.epoch, self.step = load_checkpoint(
self.model,
self.optimizer,
latest_checkpoint,
load_only_params=False,
ignore_modules=[],
is_distributed=self.accelerator.num_processes > 1,
)
else:
raise ValueError("Invalid resume type")
return checkpoint_path
def _count_parameters(self):
total_num = sum(
sum(p.numel() for p in self.model[key].parameters()) for key in self.model
)
# trainable_num = sum(p.numel() for p in self.model.parameters() if p.requires_grad)
return total_num