pytorch/torch/ao/quantization/fx/_equalize.py

# mypy: allow-untyped-defs
import warnings

from collections import namedtuple
from typing import Any, Dict, List, Optional, Tuple

import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.ao.nn.intrinsic as nni
from torch.fx import GraphModule
from torch.fx.graph import Node
from torch.ao.quantization.fx.graph_module import _get_observed_graph_module_attr

from ..observer import _with_args, ObserverBase, PerChannelMinMaxObserver
from ..utils import _parent_name, check_min_max_valid

from .utils import (
    get_new_attr_name_with_prefix,
    maybe_get_next_module,
    node_arg_is_weight,
)
import operator

CUSTOM_MODULE_SUPP_LIST: List[Any] = []

def reshape_scale(scale: torch.Tensor, axis: int, input: torch.Tensor) -> torch.Tensor:
    """Reshapes the scale so that we can multiply it to the input by the given axis.
    """
    new_shape = [1] * input.ndim
    new_shape[axis] = input.size(axis)
    return scale.view(new_shape)

qsheme_mapping_per_tensor_to_per_channel = {
    torch.per_tensor_affine: torch.per_channel_affine,
    torch.per_tensor_symmetric: torch.per_channel_symmetric,
}


class _InputEqualizationObserver(nn.Module):
    r"""Observer for tracking the running min/max values of input columns, and
    computing the quantization parameters for the overall min/max input values.

    Args:
        dtype: Quantized data type
        qscheme: Quantization scheme
        quant_min: Minimum quantization value. If unspecified, it will
            follow the 8-bit setup.
        quant_max: Maximum quantization value. If unspecified, it will
            follow the 8-bit setup.

    The running minimum/maximum :math:`x_\text{min/max}` are computed in the
    same way as :class:`~torch.ao.quantization.observer.PerChannelMinMaxObserver`,
    with the difference that the running min/max values are stored per column.
    This observer is intended to be used along with a WeightEqualizationObserver
    to calculate the equalization scale.
    """

    def __init__(self, dtype=torch.quint8, qscheme=torch.per_tensor_affine,
                 quant_min=None, quant_max=None, factory_kwargs=None) -> None:
        super().__init__()

        if qscheme not in {torch.per_tensor_affine, torch.per_tensor_symmetric}:
            raise TypeError("Input qscheme must be per-tensor")

        self.dtype = dtype
        self.qscheme = qscheme

        per_channel_qscheme = qsheme_mapping_per_tensor_to_per_channel[qscheme]
        self.input_obs = PerChannelMinMaxObserver(ch_axis=1, dtype=dtype,
                                                  qscheme=per_channel_qscheme,
                                                  quant_min=quant_min,
                                                  quant_max=quant_max,
                                                  factory_kwargs=factory_kwargs)

        self.equalization_scale = torch.tensor(1)
        self.equalization_shape: List[int] = []

    def forward(self, x_orig):
        if not (x_orig.ndim >= 2 and x_orig.ndim <= 5):
            raise ValueError("InputEqualizationObserver only supports Linear and Conv layers")

        # Calculate the shape needed to reshape the equalization scale later (needed for Conv layers)
        self.equalization_shape = [1] * x_orig.ndim
        self.equalization_shape[1] = x_orig.size(1)

        return self.input_obs(x_orig)

    def get_input_minmax(self):
        return (self.input_obs.min_val, self.input_obs.max_val)

    def set_equalization_scale(self, equalization_scale):
        # Reshape the equalization scale along axis=1 so that it can be
        # multiplied with the input along axis=1
        if equalization_scale.nelement() == 1 and equalization_scale == torch.tensor(1):
            return
        self.equalization_scale = torch.reshape(equalization_scale, self.equalization_shape)

    def calculate_scaled_minmax(self):
        r""" Returns the scaled min/max inputs
        """
        if self.equalization_scale.nelement() == 1 and self.equalization_scale == torch.tensor(1):
            warnings.warn(
                "Must call calculate_equalization_scale before calling calculate_scaled_minmax. " +
                "Will not scale the next quantization observer."
            )
            return None, None

        # Calculate qparams for the scaled min/max inputs
        # Scale the input by the equalization scale located at the same column
        # index
        (min_inputs, max_inputs) = self.get_input_minmax()
        equalization_scale_reshaped = reshape_scale(self.equalization_scale, 0, min_inputs)
        min_input_scaled = torch.min(torch.mul(min_inputs, equalization_scale_reshaped))
        max_input_scaled = torch.max(torch.mul(max_inputs, equalization_scale_reshaped))

        return min_input_scaled, max_input_scaled

    with_args = classmethod(_with_args)


class _WeightEqualizationObserver(nn.Module):
    r"""Observer for tracking the running min/max values of weight columns and
    rows, and computing the quantization parameters for the weight rows.

    Args:
        dtype: Quantized data type
        qscheme: Quantization scheme
        quant_min: Minimum quantization value. If unspecified, it will
            follow the 8-bit setup.
        quant_max: Maximum quantization value. If unspecified, it will
            follow the 8-bit setup.

    This observer is made up of 1 PerChannelMinMaxObserver `weight_col_obs` used
    to record the running minimum and maximum of columns of incoming weight
    tensors. This observer is intended to be used along with an
    InputEqualizationObserver to calculate the equalization scale.

    The running minimum/maximum :math:`w_\text{min/max}` are computed in the
    same way as :class:`~torch.ao.quantization.observer.PerChannelMinMaxObserver`.
    """

    def __init__(self, dtype=torch.qint8, qscheme=torch.per_tensor_affine, quant_min=None,
                 quant_max=None, factory_kwargs=None) -> None:
        super().__init__()

        self.dtype = dtype
        self.qscheme = qscheme
        self.ch_axis = 1

        per_channel_qscheme = qscheme
        if qscheme in {torch.per_tensor_affine, torch.per_tensor_symmetric}:
            per_channel_qscheme = qsheme_mapping_per_tensor_to_per_channel[qscheme]
        self.weight_col_obs = PerChannelMinMaxObserver(ch_axis=1, dtype=dtype,
                                                       qscheme=per_channel_qscheme,
                                                       quant_min=quant_min,
                                                       quant_max=quant_max,
                                                       factory_kwargs=factory_kwargs)

        self.equalization_scale = torch.tensor(1)

    def forward(self, w_orig):
        if not (w_orig.ndim >= 2 and w_orig.ndim <= 5):
            raise ValueError("InputEqualizationObserver only supports Linear and Conv layers")

        return self.weight_col_obs(w_orig)

    def get_weight_col_minmax(self):
        return (self.weight_col_obs.min_val, self.weight_col_obs.max_val)

    def set_equalization_scale(self, equalization_scale):
        self.equalization_scale = equalization_scale

    with_args = classmethod(_with_args)


def calculate_equalization_scale(input_obs: _InputEqualizationObserver,
                                 weight_obs: _WeightEqualizationObserver) -> torch.Tensor:
    r""" Calculates the equalization scale and sets the equalization_scale value
    in the observers.

    Args:
        input_obs: Observer that tracks the ranges for the input columns
        weight_obs: Observer that tracks the ranges for the weight columns
    """

    (min_inputs, max_inputs) = input_obs.get_input_minmax()
    (min_weights, max_weights) = weight_obs.get_weight_col_minmax()

    if not (check_min_max_valid(min_inputs, max_inputs) and check_min_max_valid(min_weights, max_weights)):
        warnings.warn(
            "Must run observer before calling calculate_equalization_scale. " +
            "Returning default equalization scale torch.tensor(1)."
        )
        return torch.tensor(1)

    if not (min_inputs.shape == min_weights.shape):
        raise ValueError(
            "Input and Weight must have the same column dimension. " +
            f"Found {min_inputs.shape} and {min_weights.shape} shapes instead."
        )

    equalization_scale = torch.sqrt((max_weights - min_weights) / (max_inputs - min_inputs))
    # Replace all 'inf', 'nan', 0's with 1s to prevent errors
    equalization_scale[equalization_scale == 0.] = 1
    equalization_scale = torch.nan_to_num(equalization_scale, nan=1, posinf=1, neginf=1)
    return equalization_scale


class EqualizationQConfig(namedtuple('EqualizationQConfig', ['input_activation', 'weight'])):
    """
    Describes how to quantize a layer or a part of the network specifically for
    input-weight equalization by providing settings (observer classes) for
    inputs, outputs, and weights.

    Note that EqualizationQConfig needs to contain observer **classes** (like
    MinMaxObserver) or a callable that returns instances on invocation, not the
    concrete observer instances themselves.
    Quantization function will instantiate observers multiple times for each of
    the layers.

    Observer classes have usually reasonable default arguments, but they can be
    overwritten with `with_args` method (that behaves like functools.partial):

    my_qconfig = EqualizationQConfig(input_activation=_InputEqualizationObserver.with_args(dtype=torch.qint8),
                                    weight=_WeightEqualizationObserver.with_args(dtype=torch.qint8))
    """
    def __new__(cls, input_activation=torch.nn.Identity, weight=torch.nn.Identity):
        if isinstance(input_activation, nn.Module) or isinstance(weight, nn.Module):
            raise ValueError("EqualizationQConfig received observer instance, please pass observer class instead. " +
                             "Use MyObserver.with_args(x=1) to override arguments to constructor if needed")
        self = super().__new__(cls, input_activation, weight)
        return self


input_equalization_observer = _InputEqualizationObserver.with_args(
    dtype=torch.quint8, qscheme=torch.per_tensor_symmetric)
weight_equalization_observer = _WeightEqualizationObserver.with_args(
    dtype=torch.qint8, qscheme=torch.per_channel_symmetric)
default_equalization_qconfig = EqualizationQConfig(input_activation=input_equalization_observer,
                                                   weight=weight_equalization_observer)


def fused_module_supports_equalization(module) -> bool:
    """ Checks if the fused node supports equalization. """
    return type(module) in [nni.LinearReLU, nni.ConvReLU1d, nni.ConvReLU2d, nni.ConvReLU3d]

def nn_module_supports_equalization(module) -> bool:
    """ Checks if the torch.nn node supports equalization. """
    return type(module) in [nn.Linear, nn.Conv1d, nn.Conv2d, nn.Conv3d]

def custom_module_supports_equalization(module) -> bool:
    """ Checks if the custom node supports equalization. """
    return type(module) in CUSTOM_MODULE_SUPP_LIST


def node_supports_equalization(node: Node, modules) -> bool:
    """ Checks if the current node supports equalization
    Currently we only support nn.Linear/F.Linear and nn.Conv/F.conv layers
    """
    if node.op == 'call_module':
        return nn_module_supports_equalization(modules[str(node.target)]) or \
            fused_module_supports_equalization(modules[str(node.target)]) or \
            custom_module_supports_equalization(modules[str(node.target)])
    elif node.op == 'call_function':
        return node.target in [F.linear, F.conv1d, F.conv2d, F.conv3d]
    return False

def is_equalization_observer(observer: nn.Module) -> bool:
    return (isinstance(observer, (_InputEqualizationObserver, _WeightEqualizationObserver)))


###############################################################################
# Functions for equalization during convert                                   #
###############################################################################

def get_op_node_and_weight_eq_obs(
    input_eq_obs_node: Node,
    model: GraphModule,
    modules: Dict[str, nn.Module]
) -> Tuple[Optional[Node], Optional[_WeightEqualizationObserver]]:
    """ Gets the following weight equalization observer. There should always
    exist a weight equalization observer after an input equalization observer.

    Returns the operation node that follows the input equalization observer node
    and the weight equalization observer
    """

    # Find the op node that comes directly after the input equalization observer
    op_node = None
    for user in input_eq_obs_node.users.keys():
        if node_supports_equalization(user, modules):
            op_node = user
            break

    assert op_node is not None
    if op_node.op == 'call_module':
        # If the op_node is a nn.Linear layer, then it must have a
        # WeightEqualizationObserver configuration
        maybe_equalization_node_name_to_config = _get_observed_graph_module_attr(model, "equalization_node_name_to_qconfig")
        assert maybe_equalization_node_name_to_config is not None
        equalization_node_name_to_qconfig: Dict[str, Any] = maybe_equalization_node_name_to_config  # type: ignore[assignment]
        assert equalization_node_name_to_qconfig.get(op_node.name, None) is not None
        weight_eq_obs = equalization_node_name_to_qconfig.get(op_node.name, None).weight()

        assert isinstance(weight_eq_obs, _WeightEqualizationObserver)
        return op_node, weight_eq_obs

    elif op_node.op == 'call_function':
        weight_node = maybe_get_weight_eq_obs_node(op_node, modules)
        if weight_node is not None:
            weight_eq_obs = modules[str(weight_node.target)]
            assert isinstance(weight_eq_obs, _WeightEqualizationObserver)
            return op_node, weight_eq_obs

    return None, None

def maybe_get_weight_eq_obs_node(op_node: Node, modules: Dict[str, nn.Module]) -> Optional[Node]:
    """ Gets the weight equalization observer node if it exists.
    """
    assert op_node.op == 'call_function'
    for node_arg in op_node.args:
        if node_arg_is_weight(op_node, node_arg):
            assert (isinstance(node_arg, Node) and node_arg.op == 'call_module' and
                   isinstance(modules[str(node_arg.target)], _WeightEqualizationObserver))
            return node_arg
    return None

def maybe_get_next_input_eq_obs(node: Node, modules: Dict[str, nn.Module]) -> Optional[_InputEqualizationObserver]:
    """ Gets the following input equalization observer if it exists.

    For example, in the case of connecting linear layers:
        x -> inp_obs1 -> eq_obs1 -> linear1 -> out_obs1 -> eq_obs2 -> linear2 -> out_obs2
    If the node being passed in is the linear1 node, then we want to return eq_obs2,
    the following equalization observer for linear2.

    However, if there are no connecting layers:
        x -> inp_obs1 -> eq_obs1 -> linear1 -> out_obs1 -> add
    Then we want to return None.

    In the case of an unfused linear-relu layer with a connecting linear layer:
        linear1 -> relu -> out_obs1 -> eq_obs2 -> linear2 -> out_obs2
    Since it is unfused, we want to skip over the relu layer and return eq_obs2,
    the following equalization observer for linear2.
    """

    assert node_supports_equalization(node, modules)

    # Locate the following nn.ReLU or F.relu node if it exists
    maybe_relu_node = maybe_get_next_module(node, modules, nn.ReLU)
    if maybe_relu_node is None:
        maybe_relu_node = maybe_get_next_module(node, modules, target_functional_type=F.relu)

    # Locate the following output observer if it exists.
    # We will skip the relu node if it exists.
    maybe_obs_node = (
        maybe_get_next_module(node, modules, ObserverBase)
        if maybe_relu_node is None
        else maybe_get_next_module(maybe_relu_node, modules, ObserverBase)
    )
    if maybe_obs_node is None:
        return None

    maybe_eq_obs_node = maybe_get_next_module(maybe_obs_node, modules, _InputEqualizationObserver)
    if maybe_eq_obs_node is None:
        return None

    maybe_eq_obs = modules[str(maybe_eq_obs_node)]
    assert isinstance(maybe_eq_obs, _InputEqualizationObserver)
    return maybe_eq_obs

def maybe_get_next_equalization_scale(node: Node, modules: Dict[str, nn.Module]) -> Optional[torch.Tensor]:
    """ If the next next node is an InputEqualizationObserver then we want to
    return its equalization scale, else we return 1

    This is used in the case where there are two connecting linear layers:
        linear1 -> LinearOutObs -> InputEqObs -> linear2
    In this case, the node given is linear1 and we want to locate the InputEqObs.
    """
    next_inp_eq_obs = maybe_get_next_input_eq_obs(node, modules)
    if next_inp_eq_obs:
        if next_inp_eq_obs.equalization_scale.nelement() == 1 and \
           next_inp_eq_obs.equalization_scale == torch.tensor(1):
            return None
        return next_inp_eq_obs.equalization_scale
    return None

def scale_input_observer(node: Node, modules: Dict[str, nn.Module]) -> None:
    """ Scales the following input quantization observer's min/max values by
    updating the values with the scaled min/max values calculated by the input
    equalization observer
    """
    input_eq_obs = modules[str(node.target)]
    assert isinstance(input_eq_obs, _InputEqualizationObserver)

    input_quant_obs_node = node.args[0]
    assert isinstance(input_quant_obs_node, Node)

    input_quant_obs = modules[str(input_quant_obs_node.target)]
    if not isinstance(input_quant_obs, ObserverBase):
        return

    min_input_scaled, max_input_scaled = input_eq_obs.calculate_scaled_minmax()
    if min_input_scaled is None and max_input_scaled is None:
        return
    input_quant_obs.min_val = min_input_scaled
    input_quant_obs.max_val = max_input_scaled

def scale_weight_node(
    node: Node,
    modules: Dict[str, nn.Module],
    equalization_scale: torch.Tensor,
    next_equalization_scale: Optional[torch.Tensor],
) -> None:
    """ Scale the weights for input-weight equalization by multiplying the
    weight by 1/equalization_scale and next_equalization_scale

    Args:
        node: Current node whose weights we want to scale
        equalization_scale: Current node's calculated equalization scale
        next_equalization_scale: Next node's calculated equalization scale if
           the following node needs to be equalized, 1 otherwise
    """
    if equalization_scale is None:
        return

    if fused_module_supports_equalization(modules[str(node.target)]):
        op_module = modules[str(node.target)][0]    # type: ignore[index]
    else:
        op_module = modules[str(node.target)]
    assert nn_module_supports_equalization(op_module) or custom_module_supports_equalization(op_module)

    # Scale the weights for input-weight equalization
    # If the following layer needs to be equalized then we will multiply its scale
    weight = op_module.weight
    assert isinstance(weight, torch.Tensor)

    # Scale the weights by the reciprocal of the equalization scale
    # Reshape the equalization scale so that we can multiply it to the weight along axis=1
    equalization_scale_reshaped = reshape_scale(equalization_scale, 1, weight)
    scaled_weight = torch.mul(weight, torch.reciprocal(equalization_scale_reshaped))

    if next_equalization_scale is None:
        op_module.weight = nn.Parameter(scaled_weight)
        return

    # Multiply the weights row wise by the next equalization scale
    # Reshape the equalization scale so that we can multiply it to the weight along axis=0
    next_equalization_scale_reshaped = reshape_scale(next_equalization_scale, 0, weight)
    scaled_weight = torch.mul(scaled_weight, next_equalization_scale_reshaped)

    op_module.weight = nn.Parameter(scaled_weight)

    # Multiply the bias element wise by the next equalization scale
    bias = op_module.bias
    if bias is None:
        return
    assert isinstance(bias, torch.Tensor)

    # Reshape the equalization scale so that we can multiply it element-wise to the bias
    next_equalization_scale_reshaped = reshape_scale(next_equalization_scale, 0, bias)
    scaled_bias = torch.mul(bias, next_equalization_scale_reshaped)
    op_module.bias = nn.Parameter(scaled_bias)

def scale_weight_functional(
    op_node: Node,
    model: GraphModule,
    modules: Dict[str, nn.Module],
    equalization_scale: torch.Tensor,
    next_equalization_scale: Optional[torch.Tensor],
) -> None:
    """ Scales the weight value for functional layers
    """
    if equalization_scale is None:
        return

    # From the given op_node, the path looks like:
    #   get_attr(weight) -> weight_quant_obs -> weight_eq_obs -> op_node
    # So we want to trace back from the op_node to get the equalization observer
    # node, then the quantization observer node, and then finally the weight
    # node which contains the weight values.

    # Get the equalization observer node
    weight_eq_obs_node = maybe_get_weight_eq_obs_node(op_node, modules)
    if weight_eq_obs_node is None:
        return

    # Get the quantization observer node
    weight_quant_obs_node = weight_eq_obs_node.args[0]
    if weight_quant_obs_node is None:
        return
    assert (isinstance(weight_quant_obs_node, Node) and
           isinstance(modules[str(weight_quant_obs_node.target)], ObserverBase))

    # Get the get_attr(weight) node
    weight_node = weight_quant_obs_node.args[0]
    if weight_node is None:
        return
    assert isinstance(weight_node, Node) and weight_node.op == 'get_attr'

    weight_parent_name, weight_name = _parent_name(weight_node.target)
    weight = getattr(modules[weight_parent_name], weight_name)

    # Scale the weights for input-weight equalization
    # If the following layer needs to be equalized then we will multiply its scale
    # Reshape the equalization scale so that we can multiply it to the weight along axis=1
    equalization_scale_reshaped = reshape_scale(equalization_scale, 1, weight)
    scaled_weight = torch.mul(weight, torch.reciprocal(equalization_scale_reshaped))

    if next_equalization_scale is None:
        setattr(modules[weight_parent_name], weight_name, scaled_weight)
        return

    # Multiply the weights row wise by the next equalization scale
    # Reshape the equalization scale so that we can multiply it to the weight along axis=1
    next_equalization_scale_reshaped = reshape_scale(next_equalization_scale, 0, scaled_weight)
    scaled_weight = torch.mul(scaled_weight, next_equalization_scale_reshaped)

    setattr(modules[weight_parent_name], weight_name, scaled_weight)
    assert torch.allclose(model.get_buffer(str(weight_node.target)), scaled_weight)

    # Multiply the bias element wise by the next equalization scale
    bias_node = None
    for node in op_node.args:
        # Find the node containing the weight values
        if isinstance(node, Node) and node.op == 'get_attr' and 'bias' in node.name:
            bias_node = node
            break
    if bias_node is None:
        return

    bias_parent_name, bias_name = _parent_name(bias_node.target)
    bias = getattr(modules[bias_parent_name], bias_name)

    # Reshape the equalization scale so that we can multiply it element-wise to the bias
    next_equalization_scale_reshaped = reshape_scale(next_equalization_scale, 0, bias)
    scaled_bias = torch.mul(bias, next_equalization_scale_reshaped)
    setattr(modules[bias_parent_name], bias_name, scaled_bias)

def clear_weight_quant_obs_node(op_node: Node, modules: Dict[str, nn.Module]) -> None:
    """ Given the operation node, we want find the corresponding quantization
    observer and reset its min/max values
    """
    weight_eq_obs_node = maybe_get_weight_eq_obs_node(op_node, modules)
    if weight_eq_obs_node is None:
        return

    weight_quant_obs_node = weight_eq_obs_node.args[0]
    if weight_quant_obs_node is None:
        return
    assert isinstance(weight_quant_obs_node, Node)

    weight_quant_obs = modules[str(weight_quant_obs_node.target)]
    assert isinstance(modules[str(weight_quant_obs_node.target)], ObserverBase)
    weight_quant_obs.reset_min_max_vals()   # type: ignore[operator]

def remove_node(model: GraphModule, node: Node, prev_node: Node):
    """ Removes the given node from the model by replacing all of its users with
    the given previous node
    """
    # For all of the current node's users, replace the current node with
    # the input quantization observer node
    orig_users = list(node.users.keys())
    for user_node in orig_users:
        user_node.replace_input_with(node, prev_node)

    # Erase the InputEqualizationObserver node
    model.graph.erase_node(node)

def update_obs_for_equalization(model: GraphModule, modules: Dict[str, nn.Module]) -> Dict[str, _WeightEqualizationObserver]:
    """ Update all of the observer's equalization scale. For each
    InputEqualizationObserver, we will find the location of the next
    WeightEqualizationObserver, create it, and calculate the equalization scale
    based on the two observers.

    We will then return a dictionary mapping operation node names to
    the corresponding WeightEqualizationObservers for that operation.
    """
    weight_eq_obs_dict = {}
    for node in model.graph.nodes:
        if node.op == 'call_module' and isinstance(modules[node.target], _InputEqualizationObserver):
            input_eq_obs = modules[node.target]
            assert isinstance(input_eq_obs, _InputEqualizationObserver)
            op_node, weight_eq_obs = get_op_node_and_weight_eq_obs(node, model, modules)

            if op_node is None or weight_eq_obs is None:
                continue

            if op_node.op == 'call_module':
                # Calibrate the weight equalization observer since it has just
                # been created
                if fused_module_supports_equalization(modules[str(op_node.target)]):
                    module = modules[str(op_node.target)][0]   # type: ignore[index]
                    assert nn_module_supports_equalization(module)
                    weight_eq_obs(module.weight)
                else:
                    weight_eq_obs(modules[str(op_node.target)].weight)

            # Calculate and set the equalization scale values
            equalization_scale = calculate_equalization_scale(input_eq_obs, weight_eq_obs)
            input_eq_obs.set_equalization_scale(equalization_scale)
            weight_eq_obs.set_equalization_scale(equalization_scale)

            weight_eq_obs_dict[op_node.name] = weight_eq_obs

    return weight_eq_obs_dict

def convert_eq_obs(
    model: GraphModule,
    modules: Dict[str, nn.Module],
    weight_eq_obs_dict: Dict[str, _WeightEqualizationObserver],
) -> None:
    """ Converts the equalization operations and updates the other nodes in the
    following way:
        - Removes the input equalization observers and inserts a mul operator
          along with an equalization scale node wherever applicable (we do not
          want to insert a mul operator between connecting linear layers).
        - Updates the input quantization observers with the scaled input min/max
          values.
        - Scales the weights by the current and next equalization scales.
        - Removes the weight equalization observer node if it exists.

    Before (after prepare):
                                    weight values
                                          |
                                    WeightQuantObs
                                          |
                                      WeightEqObs
                                          |
        x -> InpQuantObs -> InpEqObs -> linear -> OutQuantObs

    After this function:
                                              scaled weight values
                                                      |
       equalization scale                       WeightQuantObs
              |                                       |
        x -> mul -> InpQuantObs (scaled min/max) -> linear -> OutQuantObs

    After convert:
       equalization scale                 scaled weight values
              |                                    |
        x -> mul -> quantize_per_tensor -> quantized::linear

    Note that although the equalization observer appeared after the quantization
    observer after prepare_fx, the mul node appears before the quantization node
    after convert_fx. This is because placing the equalization observer after
    the quantization observer in prepare_fx would allow us to keep the invariant
    that the graph before the current node inserts its observers is not
    modified.

    Having the equalization observer before the quantization observer would also
    cause some inconsistences between the ordering of the quantization and
    equalization observers.
    For example, a single linear layer would look like:
        x -> InpEqObs1 -> InpQuantObs1 -> linear1 -> OutQuantObs1
    But between two connected linear layers, it would look like:
        linear1 -> OutQuantObs1 -> InpEqObs2 -> linear2 -> OutQuantObs2
    """
    for node in model.graph.nodes:
        if node.op == 'call_module' and isinstance(modules[node.target], _InputEqualizationObserver):
            inp_quant_obs_node = node.args[0]
            prev_node = inp_quant_obs_node.args[0]

            # If the previous node is a layer that needs to be equalized, then
            # we will remove the current node because we do not need to add any
            # equalization nodes between two layers that need to be equalized

            # Before: linear1/relu (prev_node) -> output_quant_obs1 (inp_quant_obs_node) -> input_eq_obs2 (node) -> linear2
            # After: linear1/relu (prev_node) -> output_quant_obs1 (inp_quant_obs_node) -> linear2
            if node_supports_equalization(prev_node, modules) or "relu" in prev_node.name:
                remove_node(model, node, inp_quant_obs_node)
                continue

            # Update the following input quantization observer's min/max values
            scale_input_observer(node, modules)

            # Remove the InputEqualization node and add a mul operator before
            # the quantization observer node that appears before the equalization node
            # Before: x -> input_quant_obs -> input_eq_obs -> linear
            # After: x -> mul -> input_quant_obs -> linear

            # Create a node containing the equalization scale
            with model.graph.inserting_before(inp_quant_obs_node):
                get_new_eq_scale_name = get_new_attr_name_with_prefix(prev_node.name + '_equalization_scale')
                name = get_new_eq_scale_name(modules)
                setattr(model, name, modules[node.target].equalization_scale)
                eq_scale_node = model.graph.create_node('get_attr', name)

            # Create a node multiplying the input with the equalization scale
            with model.graph.inserting_after(eq_scale_node):
                inputs = (prev_node, eq_scale_node)
                mul_node = model.graph.create_node("call_function", torch.mul, inputs)

            # Set the mul nod to be the input_quant_obs_node's input instead of
            # the previous node
            inp_quant_obs_node.replace_input_with(prev_node, mul_node)
            remove_node(model, node, inp_quant_obs_node)

        elif weight_eq_obs_dict.get(node.name, None) is not None:
            weight_eq_obs = weight_eq_obs_dict.get(node.name)
            assert isinstance(weight_eq_obs, _WeightEqualizationObserver)
            equalization_scale = weight_eq_obs.equalization_scale

            if equalization_scale.nelement() == 1 and equalization_scale == torch.tensor(1):
                equalization_scale = None  # type: ignore[assignment]
            maybe_next_equalization_scale = maybe_get_next_equalization_scale(node, modules)

            # Scale the weight nodes
            if node.op == 'call_module':
                scale_weight_node(node, modules, equalization_scale, maybe_next_equalization_scale)
            elif node.op == 'call_function':
                scale_weight_functional(node, model, modules, equalization_scale, maybe_next_equalization_scale)

                weight_eq_obs_node = maybe_get_weight_eq_obs_node(node, modules)
                if weight_eq_obs_node is None:
                    return
                assert isinstance(modules[str(weight_eq_obs_node.target)], _WeightEqualizationObserver)

                # Clear the quantization observer's min/max values so that they
                # can get updated later based on the new scale values
                clear_weight_quant_obs_node(node, modules)

                # Erase the weight equalization observer node
                prev_node = weight_eq_obs_node.args[0]
                remove_node(model, weight_eq_obs_node, prev_node)
            else:
                raise ValueError("Expected operation node to be 'call_module' or 'call_function" +
                                 f"Instead got node {node.name} as '{node.op}'.")

def _convert_equalization_ref(model: GraphModule):
    """ Reference function which applies changes needed for equalization, but
    does not quantize the nodes
    """
    modules = dict(model.named_modules(remove_duplicate=False))

    # Calculate the equalization scale, update the observers with the scaled
    # inputs, and scale the weight
    weight_eq_obs_dict = update_obs_for_equalization(model, modules)
    convert_eq_obs(model, modules, weight_eq_obs_dict)

    return GraphModule(model, model.graph)


###############################################################################
# Functions for running the equalized model on the Numeric Suite              #
###############################################################################

def get_layer_sqnr_dict(model_a: nn.Module, model_b: nn.Module, x: torch.Tensor) -> Dict[str, float]:
    """ Runs the Numeric Suite on model_a and model_b and returns a dictionary
    containing the SQNR between layers in model_a and model_b.

    Note: In order to support equalized models, this function has a hacky fix in
    which we do not match any torch.mul operators. This is because equalized
    models contain extra mul operators to scale the input by the equalization
    scale, but this edge case has not been resolved yet within the numeric suite code.

    Args:
        model_a: A float model
        model_b: A quantized model
        x: Inputs to use during calibration
    """
    import torch.ao.ns._numeric_suite_fx as ns
    from torch.ao.ns.fx.mappings import get_unmatchable_types_map

    unmatchable_types_map = get_unmatchable_types_map()
    unmatchable_types_map["funs_unmatchable"].add(torch.mul)

    model_a_ns, model_b_ns = ns.add_loggers(
        'fp32', model_a,
        'int8', model_b,
        ns.OutputLogger,
        unmatchable_types_map=unmatchable_types_map
    )

    model_a_ns(x)
    model_b_ns(x)

    activation_comparison_dict = ns.extract_logger_info(
        model_a_ns,
        model_b_ns,
        ns.OutputLogger,
        'int8')
    ns.extend_logger_results_with_comparison(
        activation_comparison_dict,
        'fp32', 'int8',
        torch.ao.ns.fx.utils.compute_sqnr, 'sqnr'
    )

    # Construct a dictionary mapping layer names to the SQNR values
    layer_sqnr_dict = {}
    for key in activation_comparison_dict:
        layer = activation_comparison_dict[key]['node_output']['int8'][0]['fqn']
        sqnr = activation_comparison_dict[key]['node_output']['int8'][0]['sqnr'][0]
        layer_sqnr_dict[layer] = sqnr

    return layer_sqnr_dict

def get_equalization_qconfig_dict(
    layer_sqnr_dict: Dict[str, float],
    num_layers_to_equalize: int
) -> Any:
    """ Given the layer to SQNR dictionary, find the layers with the highest
    quantization errors, and return an equalization_qconfig_dict
    specifying to only equalize those top layers.

    Args:
        layer_sqnr_dict: Dictionary mapping layer names to SQNR values (found
            when comparing an equalized model against a float model)
        num_layers_to_equalize: Number of layers with the highest quantization
           errors to equalize
    """

    # Sort the layer_sqnr_dictionary values and get the layers with the lowest
    # SQNR values (aka highest quantization errors)
    layer_sqnr_sorted = sorted(layer_sqnr_dict.items(), key=operator.itemgetter(1))
    layers_to_equalize = layer_sqnr_sorted[:num_layers_to_equalize]

    # Constructs an equalization_qconfig_dict that specifies to only equalize
    # the layers with the highest quantization errors
    module_to_qconfig_list = [(item[0], default_equalization_qconfig) for item in layers_to_equalize]
    equalization_qconfig_dict = {"module_name": module_to_qconfig_list}
    return equalization_qconfig_dict