| from typing import Any, List, Optional, Dict |
|
|
| from einops import EinopsError |
| from einops.parsing import ParsedExpression |
| import warnings |
| import string |
| from ..einops import _product |
|
|
|
|
| def _report_axes(axes: set, report_message: str): |
| if len(axes) > 0: |
| raise EinopsError(report_message.format(axes)) |
|
|
|
|
| class _EinmixMixin: |
| def __init__(self, pattern: str, weight_shape: str, bias_shape: Optional[str]=None, **axes_lengths: Any): |
| """ |
| EinMix - Einstein summation with automated tensor management and axis packing/unpacking. |
| |
| EinMix is an advanced tool, helpful tutorial: |
| https://github.com/arogozhnikov/einops/blob/master/docs/3-einmix-layer.ipynb |
| |
| Imagine taking einsum with two arguments, one of each input, and one - tensor with weights |
| >>> einsum('time batch channel_in, channel_in channel_out -> time batch channel_out', input, weight) |
| |
| This layer manages weights for you, syntax highlights separate role of weight matrix |
| >>> EinMix('time batch channel_in -> time batch channel_out', weight_shape='channel_in channel_out') |
| But otherwise it is the same einsum under the hood. |
| |
| Simple linear layer with bias term (you have one like that in your framework) |
| >>> EinMix('t b cin -> t b cout', weight_shape='cin cout', bias_shape='cout', cin=10, cout=20) |
| There is no restriction to mix the last axis. Let's mix along height |
| >>> EinMix('h w c-> hout w c', weight_shape='h hout', bias_shape='hout', h=32, hout=32) |
| Channel-wise multiplication (like one used in normalizations) |
| >>> EinMix('t b c -> t b c', weight_shape='c', c=128) |
| Multi-head linear layer (each head is own linear layer): |
| >>> EinMix('t b (head cin) -> t b (head cout)', weight_shape='head cin cout', ...) |
| |
| ... ah yes, you need to specify all dimensions of weight shape/bias shape in parameters. |
| |
| Use cases: |
| - when channel dimension is not last, use EinMix, not transposition |
| - patch/segment embeddings |
| - when need only within-group connections to reduce number of weights and computations |
| - perfect as a part of sequential models |
| - next-gen MLPs (follow tutorial to learn more) |
| |
| Uniform He initialization is applied to weight tensor and encounters for number of elements mixed. |
| |
| Parameters |
| :param pattern: transformation pattern, left side - dimensions of input, right side - dimensions of output |
| :param weight_shape: axes of weight. A tensor of this shape is created, stored, and optimized in a layer |
| :param bias_shape: axes of bias added to output. Weights of this shape are created and stored. If `None` (the default), no bias is added. |
| :param axes_lengths: dimensions of weight tensor |
| """ |
| super().__init__() |
| self.pattern = pattern |
| self.weight_shape = weight_shape |
| self.bias_shape = bias_shape |
| self.axes_lengths = axes_lengths |
| self.initialize_einmix(pattern=pattern, weight_shape=weight_shape, bias_shape=bias_shape, axes_lengths=axes_lengths) |
|
|
| def initialize_einmix(self, pattern: str, weight_shape: str, bias_shape: Optional[str], axes_lengths: dict): |
| left_pattern, right_pattern = pattern.split('->') |
| left = ParsedExpression(left_pattern) |
| right = ParsedExpression(right_pattern) |
| weight = ParsedExpression(weight_shape) |
| _report_axes( |
| set.difference(right.identifiers, {*left.identifiers, *weight.identifiers}), |
| 'Unrecognized identifiers on the right side of EinMix {}' |
| ) |
|
|
| if left.has_ellipsis or right.has_ellipsis or weight.has_ellipsis: |
| raise EinopsError('Ellipsis is not supported in EinMix (right now)') |
| if any(x.has_non_unitary_anonymous_axes for x in [left, right, weight]): |
| raise EinopsError('Anonymous axes (numbers) are not allowed in EinMix') |
| if '(' in weight_shape or ')' in weight_shape: |
| raise EinopsError(f'Parenthesis is not allowed in weight shape: {weight_shape}') |
|
|
| pre_reshape_pattern = None |
| pre_reshape_lengths = None |
| post_reshape_pattern = None |
| if any(len(group) != 1 for group in left.composition): |
| names: List[str] = [] |
| for group in left.composition: |
| names += group |
| composition = ' '.join(names) |
| pre_reshape_pattern = f'{left_pattern}->{composition}' |
| pre_reshape_lengths = {name: length for name, length in axes_lengths.items() if name in names} |
|
|
| if any(len(group) != 1 for group in right.composition): |
| names = [] |
| for group in right.composition: |
| names += group |
| composition = ' '.join(names) |
| post_reshape_pattern = f'{composition}->{right_pattern}' |
|
|
| self._create_rearrange_layers(pre_reshape_pattern, pre_reshape_lengths, post_reshape_pattern, {}) |
|
|
| for axis in weight.identifiers: |
| if axis not in axes_lengths: |
| raise EinopsError('Dimension {} of weight should be specified'.format(axis)) |
| _report_axes( |
| set.difference(set(axes_lengths), {*left.identifiers, *weight.identifiers}), |
| 'Axes {} are not used in pattern', |
| ) |
| _report_axes( |
| set.difference(weight.identifiers, {*left.identifiers, *right.identifiers}), |
| 'Weight axes {} are redundant' |
| ) |
| if len(weight.identifiers) == 0: |
| warnings.warn('EinMix: weight has no dimensions (means multiplication by a number)') |
|
|
| _weight_shape = [axes_lengths[axis] for axis, in weight.composition] |
| |
| _fan_in = _product([axes_lengths[axis] for axis, in weight.composition if axis not in right.identifiers]) |
| if bias_shape is not None: |
| if not isinstance(bias_shape, str): |
| raise EinopsError('bias shape should be string specifying which axes bias depends on') |
| bias = ParsedExpression(bias_shape) |
| _report_axes( |
| set.difference(bias.identifiers, right.identifiers), |
| 'Bias axes {} not present in output' |
| ) |
| _report_axes( |
| set.difference(bias.identifiers, set(axes_lengths)), |
| 'Sizes not provided for bias axes {}', |
| ) |
|
|
| _bias_shape = [] |
| for axes in right.composition: |
| for axis in axes: |
| if axis in bias.identifiers: |
| _bias_shape.append(axes_lengths[axis]) |
| else: |
| _bias_shape.append(1) |
| else: |
| _bias_shape = None |
|
|
| weight_bound = (3 / _fan_in) ** 0.5 |
| bias_bound = (1 / _fan_in) ** 0.5 |
| self._create_parameters(_weight_shape, weight_bound, _bias_shape, bias_bound) |
|
|
| |
| |
| mapped_identifiers = {*left.identifiers, *right.identifiers, *weight.identifiers} |
| mapping2letters = {k: letter for letter, k in zip(string.ascii_lowercase, mapped_identifiers)} |
|
|
| def write_flat(axes: list): |
| return ''.join(mapping2letters[axis] for axis in axes) |
|
|
| self.einsum_pattern: str = '{},{}->{}'.format( |
| write_flat(left.flat_axes_order()), |
| write_flat(weight.flat_axes_order()), |
| write_flat(right.flat_axes_order()), |
| ) |
|
|
| def _create_rearrange_layers(self, |
| pre_reshape_pattern: Optional[str], |
| pre_reshape_lengths: Optional[Dict], |
| post_reshape_pattern: Optional[str], |
| post_reshape_lengths: Optional[Dict]): |
| raise NotImplementedError('Should be defined in framework implementations') |
|
|
| def _create_parameters(self, weight_shape, weight_bound, bias_shape, bias_bound): |
| """ Shape and implementations """ |
| raise NotImplementedError('Should be defined in framework implementations') |
|
|
| def __repr__(self): |
| params = repr(self.pattern) |
| params += f", '{self.weight_shape}'" |
| if self.bias_shape is not None: |
| params += f", '{self.bias_shape}'" |
| for axis, length in self.axes_lengths.items(): |
| params += ', {}={}'.format(axis, length) |
| return '{}({})'.format(self.__class__.__name__, params) |
|
|
