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 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) Separate dense layer within each head, no connection between different heads >>> 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] # single output element is a combination of fan_in input elements _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) # rewrite einsum expression with single-letter latin identifiers so that # expression will be understood by any framework 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)