optimizer.py

# coding=utf-8
# Copyright (c) 2020, NVIDIA CORPORATION.  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.

"""Megatron optimizer."""

from abc import ABC
from abc import abstractmethod

import torch

from apex.multi_tensor_apply import multi_tensor_applier
import amp_C

from megatron import get_timers
from megatron import mpu
from megatron import print_rank_0

from .clip_grads import clip_grad_norm_fp32, count_zeros_fp32

# >>>
from lutil import pax, tp

DEBUG_ITERATION = 2 # 10
# <<<


def _zero_grad_group_helper(group, set_to_none):
    """Zero out the gradient for a group of parameters.
    Note: copied from torch.optim.optimizer."""
    for param in group:
        if param.grad is not None:
            if set_to_none:
                param.grad = None
            else:
                if param.grad.grad_fn is not None:
                    param.grad.detach_()
                else:
                    param.grad.requires_grad_(False)
                param.grad.zero_()


def _multi_tensor_copy_this_to_that(this, that, overflow_buf=None):
    """Use multi-tensor-applier to copy values from one list to another.
    We don't have a blfoat16 implementation so for now if the overflow_buf
    is not provided, we default back to simple loop copy to be compatible
    with bfloat16."""
    if overflow_buf:
        overflow_buf.fill_(0)
        # Scaling with factor `1.0` is equivalent to copy.
        multi_tensor_applier(amp_C.multi_tensor_scale,
                             overflow_buf,
                             [this, that],
                             1.0)
    else:
        for this_, that_ in zip(this, that):
            that_.copy_(this_)



class MegatronOptimizer(ABC):


    def __init__(self, optimizer, clip_grad,
                 log_num_zeros_in_grad,
                 params_have_main_grad,
                 use_contiguous_buffers_in_local_ddp):

        """Input optimizer is the base optimizer for example Adam."""
        self.optimizer = optimizer
        assert self.optimizer, 'no optimizer is provided.'
        # Set gradient clipping and logging params.
        self.clip_grad = clip_grad
        self.log_num_zeros_in_grad = log_num_zeros_in_grad
        self.params_have_main_grad = params_have_main_grad
        self.use_contiguous_buffers_in_local_ddp = use_contiguous_buffers_in_local_ddp

        if self.use_contiguous_buffers_in_local_ddp:
            assert self.params_have_main_grad, \
                "use of contiguous buffer requires that params have main grad"

    def get_parameters(self):
        params = []
        for param_group in self.optimizer.param_groups:
            for param in param_group['params']:
                params.append(param)
        return params


    def clip_grad_norm(self, clip_grad, ITERATION):
        params = self.get_parameters()
        return clip_grad_norm_fp32(params, clip_grad, ITERATION = ITERATION)


    def count_zeros(self):
        params = self.get_parameters()
        return count_zeros_fp32(params)


    @abstractmethod
    def zero_grad(self, set_to_none=True):
        pass


    @abstractmethod
    def get_loss_scale(self):
        """The output should be a cuda tensor of size 1."""
        pass


    def scale_loss(self, loss):
        """Simple scaling."""
        return self.get_loss_scale() * loss


    @abstractmethod
    def reload_model_params(self):
        """Refreshes any internal state from the current model parameters.
        Call whenever the parameters are changed outside of the optimizer.
        For example, when we load a model from a checkpoint  without loading
        the optimizer, the model parameters are updated but for fp16 optimizer
        with main parameters, the main parameters need to also be updated."""
        pass


    @abstractmethod
    def state_dict(self):
        pass


    @abstractmethod
    def load_state_dict(self, state_dict):
        pass


    # Promote state so it can be retrieved or set via
    # "optimizer_instance.state"
    def _get_state(self):
        return self.optimizer.state

    def _set_state(self, value):
        self.optimizer.state = value

    state = property(_get_state, _set_state)


    # Promote param_groups so it can be retrieved or set via
    # "optimizer_instance.param_groups"
    # (for example, to adjust the learning rate)
    def _get_param_groups(self):
        return self.optimizer.param_groups

    def _set_param_groups(self, value):
        self.optimizer.param_groups = value

    param_groups = property(_get_param_groups, _set_param_groups)


    @abstractmethod
    def step(self):
        pass

    def gather_params(self):
        pass

    def reduce_grads(self, model):

        # >>>
        from torch.nn.parallel.distributed import DistributedDataParallel as torchDDP

        from megatron import get_args
        from megatron import get_timers
        from megatron.model import DistributedDataParallel as LocalDDP
        from megatron.model import Float16Module
        from megatron.utils import unwrap_model

        args = get_args()
        timers = get_timers()
        # <<<

        # All-reduce if needed.
        if args.DDP_impl == 'local':
            timers('backward-params-all-reduce').start()
            for model_module in model:
                model_module.allreduce_gradients()
            timers('backward-params-all-reduce').stop()

        # All-reduce word_embeddings' grad across first and last stages to ensure
        # that word_embeddings parameters stay in sync.
        # This should only run for models that support pipelined model parallelism
        # (BERT and GPT-2).
        timers('backward-embedding-all-reduce').start()
        if mpu.is_rank_in_embedding_group(ignore_virtual=True) and \
                mpu.get_pipeline_model_parallel_world_size() > 1:
            # >>>
            # raise Exception("[main] ready for weight sync?")
            # <<<
            if mpu.is_pipeline_first_stage(ignore_virtual=True):
                unwrapped_model = model[0]
            elif mpu.is_pipeline_last_stage(ignore_virtual=True):
                unwrapped_model = model[-1]
            else:  # We do not support the interleaved schedule for T5 yet.
                unwrapped_model = model[0]
            unwrapped_model = unwrap_model(
                unwrapped_model, (torchDDP, LocalDDP, Float16Module))

            if unwrapped_model.share_word_embeddings:
                word_embeddings_weight = unwrapped_model.word_embeddings_weight()
                if args.DDP_impl == 'local':
                    grad = word_embeddings_weight.main_grad
                else:
                    grad = word_embeddings_weight.grad
                torch.distributed.all_reduce(grad, group=mpu.get_embedding_group())

        # All-reduce position_embeddings grad across first (encoder) and split (decoder) 
        # stages to ensure that position embeddings parameters stay in sync.
        # This should only run for T5 models with pipeline parallelism
        if mpu.is_rank_in_position_embedding_group() and \
                mpu.get_pipeline_model_parallel_world_size() > 1 and \
                args.pipeline_model_parallel_split_rank is not None:
            # >>>
            raise Exception("[main] ready for t5 sync?")
            # <<<
            unwrapped_model = model[0]
            unwrapped_model = unwrap_model(
                unwrapped_model, (torchDDP, LocalDDP, Float16Module))
            assert args.DDP_impl == 'local', \
                'T5 model is only supported with local DDP mode'
            grad = unwrapped_model.language_model.embedding.position_embeddings.weight.main_grad
            torch.distributed.all_reduce(grad, group=mpu.get_position_embedding_group())
        timers('backward-embedding-all-reduce').stop()

# class BaseFloat16Optimizer(MegatronOptimizer):
class MixedPrecisionOptimizer(MegatronOptimizer):

    def __init__(self, optimizer, clip_grad, log_num_zeros_in_grad,
                 params_have_main_grad, use_contiguous_buffers_in_local_ddp,
                 bf16, grad_scaler,
                 models):

        super().__init__(
            optimizer, clip_grad, log_num_zeros_in_grad,
            params_have_main_grad, use_contiguous_buffers_in_local_ddp)

        # >>>
        self.models = models
        # <<<
        self.bf16 = bf16
        self.grad_scaler = grad_scaler
        # None grad scaler is only supported for bf16.
        if self.grad_scaler is None:
            assert self.bf16, 'fp16 expects a grad scaler.'

        # Tensor used to determine if a nan/if has happend.
        # Any non-zero value indicates inf/nan.
        # Note that we keep this for the cases that grad scaler is none.
        # We still record nan/inf if we have a bfloat16 with a grad scaler.
        if self.grad_scaler:
            self.found_inf = torch.cuda.FloatTensor([0.0])

        # Dummy tensor needed for apex multi-apply tensor.
        # For bfloat, we don't have multi-tensor apply and for now
        # we set it to none so the multi-tensor apply gets ignored.
        if bf16:
            self._dummy_overflow_buf = None
        else:
            self._dummy_overflow_buf = torch.cuda.IntTensor([0])

        # In case grad scaler is not passed, define the unity scale.
        if self.grad_scaler is None:
            self._scale_one = torch.cuda.FloatTensor([1.0])


    @abstractmethod
    def get_model_parallel_group(self, state_dict):
        pass

    def get_loss_scale(self):
        if self.grad_scaler is None:
            return self._scale_one
        return self.grad_scaler.scale


    def reload_model_params(self):
        self._copy_model_params_to_main_params()


    def _unscale_main_grads_and_check_for_nan(self, group):

        # Collect main grads.
        main_grads = self._collect_main_grad_data_for_unscaling()
        # pax(1, {"main_grads": main_grads})

        # Reset found inf.
        self.found_inf.fill_(0.0)

        # Unscale and set found inf/nan
        torch._amp_foreach_non_finite_check_and_unscale_(
            main_grads, self.found_inf, self.grad_scaler.inv_scale)

        # Update across all model parallel instances.
        torch.distributed.all_reduce(self.found_inf,
                                     op=torch.distributed.ReduceOp.MAX,
                                     group=self.get_model_parallel_group())

        # Check for nan.
        found_inf_flag = (self.found_inf.item() > 0)

        return found_inf_flag

    # >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
    # @classmethod
    # def debug_base(cls, ITERATION, key, value):
    #     from megatron import get_args
    #     args = get_args()
    #     my_rank = torch.distributed.get_rank()
    #     if ITERATION != DEBUG_ITERATION:
    #         return
    #     for r in range(torch.distributed.get_world_size()):
    #         if my_rank == r:
    #             print("            + br/%s; [r%d, i%d]; %s, %.12e" % ("fix " if args.use_distributed_optimizer else "main", my_rank, ITERATION, key, value))
    #         torch.distributed.barrier()
    #     torch.distributed.barrier()
    #     # if my_rank == 0:
    #     #     raise Exception("debug.")
    #     # else:
    #     #     exit(0)
    #     exit(0)
    # def debug_model(self, ITERATION, key, use_grad):
    #     use_grad = bool(use_grad)
    #     tensors = [
    #         (p.main_grad.float() if use_grad else p.float())
    #         for m in self.models for p in m.parameters()
    #     ]
    #     count = sum(t.nelement() for t in tensors)
    #     return self.debug_base(
    #         ITERATION,
    #         "model/%s, %s [count %d]" % (
    #             "grad" if use_grad else "param",
    #             key,
    #             count,
    #         ),
    #         # sum(torch.sum(torch.abs(t)) for t in tensors).item() / count,
    #         sum(torch.sum(torch.abs(t)) for t in tensors),
    #     )
    # def debug_main(self, ITERATION, key, use_grad):
    #     use_grad = bool(use_grad)
    #     tensors = [
    #         p.grad if use_grad else p
    #         for g in self.optimizer.param_groups
    #         for p in g["params"]
    #     ]
    #     tensors = [ t.float() for t in tensors ]
    #     count = sum(t.nelement() for t in tensors)
    #     return self.debug_base(
    #         ITERATION,
    #         "main/%s, %s [count %d]" % (
    #             "grad" if use_grad else "param",
    #             key,
    #             count,
    #         ),
    #         sum(torch.sum(torch.abs(t)) for t in tensors),
    #     )
    # <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

    @torch.no_grad()
    def step(self, ITERATION):

        timers = get_timers()

        # >>>
        # self.debug_model(ITERATION, "before copy grad.", 0)
        # self.debug_main(ITERATION, "before copy grad.", 0)
        # <<<

        # Copy gradients from model params to main params.
        timers('optimizer-copy-to-main-grad').start()
        self._copy_model_grads_to_main_grads(ITERATION)
        timers('optimizer-copy-to-main-grad').stop()

        # Do unscale, check for inf, and update grad scaler only for
        # the case that grad scaler is provided.
        if self.grad_scaler:

            # Unscale and check for inf/nan.
            timers('optimizer-unscale-and-check-inf').start()
            found_inf_flag = self._unscale_main_grads_and_check_for_nan()
            timers('optimizer-unscale-and-check-inf').stop()

            # We are done with scaling gradients
            # so we can update the loss scale.
            self.grad_scaler.update(found_inf_flag)

            # If we found inf/nan, skip the update.
            if found_inf_flag:
                return False, None, None

        # Clip the main gradients.
        timers('optimizer-clip-main-grad').start()
        grad_norm = None
        if self.clip_grad > 0.0:
            grad_norm = self.clip_grad_norm(self.clip_grad, ITERATION)
        timers('optimizer-clip-main-grad').stop()

        # count the zeros in the grads
        num_zeros_in_grad = self.count_zeros() if \
                            self.log_num_zeros_in_grad else None

        # Step the optimizer.
        self.optimizer.step()

        # Update params from main params.
        timers('optimizer-copy-main-to-model-params').start()
        self._copy_main_params_to_model_params(ITERATION)
        timers('optimizer-copy-main-to-model-params').stop()

        # Successful update.
        return True, grad_norm, num_zeros_in_grad


# class Float16OptimizerWithFloat16Params(MegatronOptimizer):
# class Float16OptimizerWithFloat16Params(BaseFloat16Optimizer):
class Float16OptimizerWithFloat16Params(MixedPrecisionOptimizer):
    """Float16 optimizer for fp16 and bf16 data types.

    Arguments:
        optimizer: base optimizer such as Adam or SGD
        clip_grad: clip gradeints with this global L2 norm. Note
            that clipping is ignored if clip_grad == 0
        log_num_zeros_in_grad: return number of zeros in the gradients.
        params_have_main_grad: flag indicating if parameters have
            a `main_grad` field. If this is set, we are assuming
            that the model parameters are store in the `main_grad`
            field instead of the typical `grad` field. This happens
            for the DDP cases where there is a continuous buffer
            holding the gradients. For example for bfloat16, we want
            to do gradient accumulation and all-reduces in float32
            and as a result we store those gradients in the main_grad.
            Note that main grad is not necessarily in float32.
        bf16: if true, the model is running in bfloat16.
        grad_scaler: used for scaling gradients. Note that this can be
            None. This case happens when `bf16 = True` and we don't
            use any loss scale. Note that for `bf16 = True`, we can have
            a constnat gradient scaler. Also for `bf16 = False`, we
            always require a grad scaler.
    """

    def __init__(self, optimizer, clip_grad, log_num_zeros_in_grad,
                 params_have_main_grad, use_contiguous_buffers_in_local_ddp,
                 bf16, grad_scaler, models):

        super().__init__(
            optimizer, clip_grad, log_num_zeros_in_grad,
            params_have_main_grad, use_contiguous_buffers_in_local_ddp,
            bf16, grad_scaler, models)

        # ======================
        # main parameter stuff
        # ======================

        # Three groups of parameters:
        #   float16_groups: original float16 parameters
        #   fp32_from_float16_groups: fp32 copy of float16 parameters
        #   fp32_from_fp32_groups: original fp32 parameters
        self.float16_groups = []
        self.fp32_from_float16_groups = []
        self.fp32_from_fp32_groups = []

        # For all the groups in the original optimizer:
        for param_group in self.optimizer.param_groups:
            float16_params_this_group = []
            fp32_params_this_group = []
            fp32_from_float16_params_this_group = []
            # For all the parameters in this group:
            for i, param in enumerate(param_group['params']):
                if param.requires_grad:

                    # float16 params:
                    if param.type() in ['torch.cuda.HalfTensor',
                                        'torch.cuda.BFloat16Tensor']:
                        float16_params_this_group.append(param)
                        # Create a copy
                        main_param = param.detach().clone().float()
                        # Copy tensor model parallel attributes.
                        mpu.copy_tensor_model_parallel_attributes(main_param,
                                                                  param)
                        if hasattr(param, 'shared'):
                            main_param.shared = param.shared
                        # Replace the optimizer params with the new fp32 copy.
                        param_group['params'][i] = main_param

                        fp32_from_float16_params_this_group.append(main_param)
                        # Reset existing state dict key to the new main param.
                        if param in self.optimizer.state:
                            self.optimizer.state[main_param] \
                                = self.optimizer.state.pop(param)

                    # fp32 params.
                    elif param.type() == 'torch.cuda.FloatTensor':
                        fp32_params_this_group.append(param)
                        param_group['params'][i] = param

                    else:
                        raise TypeError('Wrapped parameters must be one of '
                                        'torch.cuda.FloatTensor,  '
                                        'torch.cuda.HalfTensor, or '
                                        'torch.cuda.BFloat16Tensor. '
                                        'Received {}'.format(param.type()))

            self.float16_groups.append(float16_params_this_group)
            self.fp32_from_float16_groups.append(
                fp32_from_float16_params_this_group)
            self.fp32_from_fp32_groups.append(fp32_params_this_group)

        # Leverage state_dict() and load_state_dict() to
        # recast preexisting per-param state tensors
        self.optimizer.load_state_dict(self.optimizer.state_dict())


    def get_model_parallel_group(self):
        return mpu.get_model_parallel_group()


    def zero_grad(self, set_to_none=True):
        """We only need to zero the model related parameters, i.e.,
        float16_groups & fp32_from_fp32_groups. We additionally zero
        fp32_from_float16_groups as a memory optimization to reduce
        fragmentation; in the case of set_to_none==True, the space
        used by this field can be safely deallocated at this point."""
        for group in self.float16_groups:
            _zero_grad_group_helper(group, set_to_none)
        for group in self.fp32_from_float16_groups:
            _zero_grad_group_helper(group, set_to_none)
        for group in self.fp32_from_fp32_groups:
            _zero_grad_group_helper(group, set_to_none)


    def _collect_main_grad_data_for_unscaling(self):

        main_grads = []

        # fp32 params from float16 ones.
        for main_group in self.fp32_from_float16_groups:
            for main_param in main_group:
                if main_param.grad is not None:
                    main_grads.append(main_param.grad.data)

        # Append fp32 parameters.
        for main_group in self.fp32_from_fp32_groups:
            for main_param in main_group:
                if main_param.grad is not None:
                    main_grads.append(main_param.grad.data)
        
        return main_grads


    def _get_model_and_main_params_data_float16(self):
        model_data = []
        main_data = []
        for model_group, main_group in zip(self.float16_groups,
                                           self.fp32_from_float16_groups):
            for model_param, main_param in zip(model_group, main_group):
                model_data.append(model_param.data)
                main_data.append(main_param.data)
        return model_data, main_data


    def _copy_model_grads_to_main_grads(self, ITERATION):
        # This only needs to be done for the float16 group.
        for model_group, main_group in zip(self.float16_groups,
                                           self.fp32_from_float16_groups):
            for model_param, main_param in zip(model_group, main_group):
                if self.params_have_main_grad and hasattr(model_param, 'main_grad'):
                    main_param.grad = model_param.main_grad.float()
                else:
                    if model_param.grad is not None:
                        main_param.grad = model_param.grad.float()

                # Safe to deallocate model's grad/main_grad after copying.
                # (If using contiguous buffers, main_grad's memory should
                # persist and therefore should not be deallocated.)
                model_param.grad = None
                if self.params_have_main_grad and \
                   not self.use_contiguous_buffers_in_local_ddp:
                    model_param.main_grad = None

        # For fp32 grads, we need to reset the grads to main grad.
        if self.params_have_main_grad:
            for model_group in self.fp32_from_fp32_groups:
                for model_param in model_group:
                    model_param.grad = model_param.main_grad

                    # Safe to de-reference model's main_grad after copying.
                    # (If using contiguous buffers, main_grad's memory should
                    # persist and therefore should not be deallocated.)
                    if not self.use_contiguous_buffers_in_local_ddp:
                        model_param.main_grad = None

        # >>>
        # if ITERATION == DEBUG_ITERATION:
        #     pax(0, {
        #         "** branch **" : "** main. **",
        #         "ITERATION" : ITERATION,
        #         "model grads" :
        #         [ p.main_grad for m in self.models for p in m.parameters() ],
        #     })
        # <<<


    def _copy_main_params_to_model_params(self, ITERATION):
        # Only needed for the float16 params.
        model_data, main_data = self._get_model_and_main_params_data_float16()
        _multi_tensor_copy_this_to_that(this=main_data, that=model_data,
                                        overflow_buf=self._dummy_overflow_buf)


    def _copy_model_params_to_main_params(self):
        # Only needed for the float16 params.
        model_data, main_data = self._get_model_and_main_params_data_float16()
        _multi_tensor_copy_this_to_that(this=model_data, that=main_data,
                                        overflow_buf=self._dummy_overflow_buf)


    def state_dict(self):
        state_dict = {}
        state_dict['optimizer'] = self.optimizer.state_dict()
        if self.grad_scaler:
            state_dict['grad_scaler'] = self.grad_scaler.state_dict()
        state_dict['fp32_from_fp16_params'] = self.fp32_from_float16_groups
        return state_dict


    def load_state_dict(self, state_dict):
        # Optimizer.
        optimizer_key = 'optimizer'
        if optimizer_key not in state_dict:
            optimizer_key = 'optimizer_state_dict'
            print_rank_0('***WARNING*** loading optimizer from '
                         'an old checkpoint ...')
        self.optimizer.load_state_dict(state_dict[optimizer_key])

        # Grad scaler.
        if 'grad_scaler' not in state_dict:
            print_rank_0('***WARNING*** found an old checkpoint, will not '
                         'load grad scaler ...')
        else:
            if self.grad_scaler:
                self.grad_scaler.load_state_dict(state_dict['grad_scaler'])
            else:
                print_rank_0('***WARNING*** fould the grad scaler in the '
                             'checkpoint but it is None in the class. '
                             'Skipping loading grad scaler ...')

        # Copy data for the main params.
        fp32_from_float16_params_key = 'fp32_from_fp16_params'
        if fp32_from_float16_params_key not in state_dict:
            fp32_from_float16_params_key = 'fp32_from_fp16'
        for current_group, saved_group in zip(
                self.fp32_from_float16_groups,
                state_dict[fp32_from_float16_params_key]):
            for current_param, saved_param in zip(current_group, saved_group):
                current_param.data.copy_(saved_param.data)


class FP32Optimizer(MegatronOptimizer):

    def __init__(self, optimizer, clip_grad,
                 log_num_zeros_in_grad,
                 params_have_main_grad,
                 use_contiguous_buffers_in_local_ddp):

        super(FP32Optimizer, self).__init__(
            optimizer, clip_grad, log_num_zeros_in_grad,
            params_have_main_grad, use_contiguous_buffers_in_local_ddp)

        self._scale = torch.cuda.FloatTensor([1.0])


    def zero_grad(self, set_to_none=True):
        """Copied from torch.optim.optimizer"""
        for group in self.optimizer.param_groups:
            _zero_grad_group_helper(group['params'], set_to_none)


    def get_loss_scale(self):
        """FP32 optimizer does not do any scaling."""
        return self._scale


    @torch.no_grad()
    def step(self):
        """Clip gradients (if needed) and step the base optimizer.
        Always return successful since there is no overflow."""

        # Copy main_grads to grads.
        if self.params_have_main_grad:
            for param_group in self.optimizer.param_groups:
                for param in param_group['params']:
                    param.grad = param.main_grad

                    # Safe to de-reference model's main_grad after copying.
                    # (If using contiguous buffers, main_grad's memory should
                    # persist and therefore should not be deallocated.)
                    if not self.use_contiguous_buffers_in_local_ddp:
                        param.main_grad = None

        # Clip gradients.
        grad_norm = None
        if self.clip_grad > 0.0:
            grad_norm = self.clip_grad_norm(self.clip_grad)

        # count the zeros in the grads
        num_zeros_in_grad = self.count_zeros() if \
                            self.log_num_zeros_in_grad else None

        # Update parameters.
        self.optimizer.step()

        # No overflow for FP32 optimizer.
        return True, grad_norm, num_zeros_in_grad


    def reload_model_params(self):
        pass


    def state_dict(self):
        return self.optimizer.state_dict()


    def load_state_dict(self, state_dict):
        self.optimizer.load_state_dict(state_dict)