MaskNet 这个模型是微博21年提出的，23年twitter(X)开源的推荐系统排序模块使用的backbone结构。
核心思想是认为DNN为主的特征交叉是addictive，交叉效率不高；所以设计了一种multiplicatvie的特征交叉
如何设计muliplicative特征交叉呢？
1）首先设计了一个instance-guide-mask，下图是instance-guide-mask的设计，其实就是两层feed-forward-layer，第一层把原始输入维度扩增，第二层再还原回去，总结而言，就是这个公式：
$$V_{mask}=W_{d2}(Relu(W_{d1}{V}_{emb}+{\beta }_{d1}))+{\beta }_{d2}$$

$V_{emb}\in R^{m=f\times k}$ 输入的embedding结果, f是输入特征的数量，k是特征embedding维度。
最终输出的是一个处理后的embedding向量，后面简称为mask
2） 这个embedding得到后，怎么使用呢，这个就是MaskBlock干的事情。
主要有两种使用，一个是对embedding进行处理，图里LN-EMB里的LN指的是Layer Normalization
$V_{maskedEMB}=V_{mask}\odot LN\_EMB(V_{emb})$, 把mask的结果和LN-EMB 进行element-wide product, 然后在接一个linear，LN后应用在Relu做下非线性激活，这个就是MaskBLock的全部了, 总结成一个公式：
$$V_{output}=LN\_HID(W_i{V}_{maskedEMB})=ReLU(LN(W_i(V_{mask}\odot LN\_EMB(V_{emb})))$$
除了对Embedding进行element-wide-product，还可以对神经网络的输出再和mask做一次处理，这个就是另一种mask的应用方式：
$$V_{output}=LN\_HID(W_i{V}_{maskdHID})=ReLU(LN(W_i(V_{mask}\odot V_{output}^p)))$$

1) 2) 结束之后，文章的核心内容也基本结束，后面3)是MaskBlock的应用
3）MaskNet
所有特征都和Instance-guide-mask进行运算，可以是串行的也可以是并行的。
串行的第一个是一个MaskBlock on feature embedding，后面接的都是MaskBlock on MaskBlock；
并行的比较简单，每一个都是一个MaskBlock on feature embedding，然后concat到一起

二 Implementation
1）torch 代码实现，摘录自twitter开源代码：

def _init_weights(module):if isinstance(module, torch.nn.Linear):torch.nn.init.xavier_uniform_(module.weight)torch.nn.init.constant_(module.bias, 0)class MaskBlock(torch.nn.Module):def __init__(self, mask_block_config: config.MaskBlockConfig, input_dim: int, mask_input_dim: int) -> None:super(MaskBlock, self).__init__()self.mask_block_config = mask_block_configoutput_size = mask_block_config.output_sizeif mask_block_config.input_layer_norm: # twitter实现的这里layer normalization做了可配置的self._input_layer_norm = torch.nn.LayerNorm(input_dim)else:self._input_layer_norm = None# instace-guide-mask第一层aggregation的神经元数量配置# 如果指定了压缩量，就是input * 压缩量；如果没有，那么也可以手动指定大小if mask_block_config.reduction_factor:aggregation_size = int(mask_input_dim * mask_block_config.reduction_factor)elif mask_block_config.aggregation_size is not None:aggregation_size = mask_block_config.aggregation_sizeelse:raise ValueError("Need one of reduction factor or aggregation size.")# instance-guide-mask is here# 两层Linearself._mask_layer = torch.nn.Sequential(torch.nn.Linear(mask_input_dim, aggregation_size),torch.nn.ReLU(),torch.nn.Linear(aggregation_size, input_dim),)# 参数初始化self._mask_layer.apply(_init_weights)self._hidden_layer = torch.nn.Linear(input_dim, output_size)self._hidden_layer.apply(_init_weights)self._layer_norm = torch.nn.LayerNorm(output_size)def forward(self, net: torch.Tensor, mask_input: torch.Tensor):# LNif self._input_layer_norm:net = self._input_layer_norm(net)# self._mask_layer(mask_input)-- V_mask# net * V_maskhidden_layer_output = self._hidden_layer(net * self._mask_layer(mask_input))return self._layer_norm(hidden_layer_output)class MaskNet(torch.nn.Module):def __init__(self, mask_net_config: config.MaskNetConfig, in_features: int):super().__init__()self.mask_net_config = mask_net_configmask_blocks = []if mask_net_config.use_parallel:total_output_mask_blocks = 0# 从local_prod参数看，用了4个blockfor mask_block_config in mask_net_config.mask_blocks:mask_blocks.append(MaskBlock(mask_block_config, in_features, in_features))total_output_mask_blocks += mask_block_config.output_sizeself._mask_blocks = torch.nn.ModuleList(mask_blocks)else:input_size = in_featuresfor mask_block_config in mask_net_config.mask_blocks:mask_blocks.append(MaskBlock(mask_block_config, input_size, in_features))input_size = mask_block_config.output_sizeself._mask_blocks = torch.nn.ModuleList(mask_blocks)total_output_mask_blocks = mask_block_config.output_sizeif mask_net_config.mlp:self._dense_layers = mlp.Mlp(total_output_mask_blocks, mask_net_config.mlp)self.out_features = mask_net_config.mlp.layer_sizes[-1]else:self.out_features = total_output_mask_blocksself.shared_size = total_output_mask_blocksdef forward(self, inputs: torch.Tensor):if self.mask_net_config.use_parallel:# 并行化的网络结构实现mask_outputs = []# 对于多个Block，每一个block输入都是一样，只是其中学习到的参数有所不同for mask_layer in self._mask_blocks:# mask_input,net 都是inputsmask_outputs.append(mask_layer(mask_input=inputs, net=inputs)) # Share the outputs of the MaskBlocks.all_mask_outputs = torch.cat(mask_outputs, dim=1)# 最终输出处理output = (all_mask_outputsif self.mask_net_config.mlp is Noneelse self._dense_layers(all_mask_outputs)["output"])return {"output": output, "shared_layer": all_mask_outputs}else:# 串行net = inputsfor mask_layer in self._mask_blocks:# mask_input 是inputs，net输入是上一层的输出net = mask_layer(net=net, mask_input=inputs)# Share the output of the stacked MaskBlocks.output = net if self.mask_net_config.mlp is None else self._dense_layers[net]["output"]return {"output": output, "shared_layer": net}

2）tensorflow实现
摘录自EasyRec(阿里开源推荐工具)

# Copyright (c) Alibaba, Inc. and its affiliates.
import tensorflow as tf
from tensorflow.python.keras.layers import Activation
from tensorflow.python.keras.layers import Dense
from tensorflow.python.keras.layers import Layer
from easy_rec.python.layers.keras.blocks import MLP
from easy_rec.python.layers.keras.layer_norm import LayerNormalization
from easy_rec.python.layers.utils import Parameterclass MaskBlock(Layer):"""MaskBlock use in MaskNet.Args:projection_dim: project dimension to reduce the computational cost.Default is `None` such that a full (`input_dim` by `aggregation_size`) matrixW is used. If enabled, a low-rank matrix W = U*V will be used, where Uis of size `input_dim` by `projection_dim` and V is of size`projection_dim` by `aggregation_size`. `projection_dim` need to be smallerthan `aggregation_size`/2 to improve the model efficiency. In practice, we'veobserved that `projection_dim` = d/4 consistently preserved theaccuracy of a full-rank version."""def __init__(self, params, name='mask_block', reuse=None, **kwargs):super(MaskBlock, self).__init__(name=name, **kwargs)self.config = params.get_pb_config()self.l2_reg = params.l2_regularizerself._projection_dim = params.get_or_default('projection_dim', None)self.reuse = reuseself.final_relu = Activation('relu', name='relu')def build(self, input_shape):if type(input_shape) in (tuple, list):assert len(input_shape) >= 2, 'MaskBlock must has at least two inputs'input_dim = int(input_shape[0][-1])mask_input_dim = int(input_shape[1][-1])else:input_dim, mask_input_dim = input_shape[-1], input_shape[-1]# 这里实现和pytorch一样if self.config.HasField('reduction_factor'):aggregation_size = int(mask_input_dim * self.config.reduction_factor)elif self.config.HasField('aggregation_size') is not None:aggregation_size = self.config.aggregation_sizeelse:raise ValueError('Need one of reduction factor or aggregation size for MaskBlock.')# instance-guide-mask第一层      self.aggr_layer = Dense(aggregation_size,activation='relu',kernel_initializer='he_uniform',kernel_regularizer=self.l2_reg,name='aggregation')# instance-guide-mask第二层self.weight_layer = Dense(input_dim, name='weights')# 对比pytorch实现，增加了projection_dim, 低秩矩阵（详见DCN）if self._projection_dim is not None:logging.info('%s project dim is %d', self.name, self._projection_dim)self.project_layer = Dense(self._projection_dim,kernel_regularizer=self.l2_reg,use_bias=False,name='project')if self.config.input_layer_norm:# 推荐在调用MaskBlock之前做好 layer norm，否则每一次调用都需要对input做lnif tf.__version__ >= '2.0':self.input_layer_norm = tf.keras.layers.LayerNormalization(name='input_ln')else:self.input_layer_norm = LayerNormalization(name='input_ln')if self.config.HasField('output_size'):self.output_layer = Dense(self.config.output_size, use_bias=False, name='output')# tensorflow遗留问题，兼容1/2if tf.__version__ >= '2.0':self.output_layer_norm = tf.keras.layers.LayerNormalization(name='output_ln')else:self.output_layer_norm = LayerNormalization(name='output_ln')super(MaskBlock, self).build(input_shape)def call(self, inputs, training=None, **kwargs):if type(inputs) in (tuple, list):net, mask_input = inputs[:2]else:net, mask_input = inputs, inputs# LNif self.config.input_layer_norm:net = self.input_layer_norm(net)# tensorflow实现aggregate层和projection层是分开的，上面pytorch是用一个sequenceif self._projection_dim is None:aggr = self.aggr_layer(mask_input)else:u = self.project_layer(mask_input)aggr = self.aggr_layer(u)# 得到mask结果weights = self.weight_layer(aggr)# elemnet-wide productmasked_net = net * weightsif not self.config.HasField('output_size'):return masked_net# 最终处理，一个Liner+layer norm层hidden = self.output_layer(masked_net)ln_hidden = self.output_layer_norm(hidden)return self.final_relu(ln_hidden)class MaskNet(Layer):def __init__(self, params, name='mask_net', reuse=None, **kwargs):super(MaskNet, self).__init__(name=name, **kwargs)self.reuse = reuseself.params = paramsself.config = params.get_pb_config()if self.config.HasField('mlp'):p = Parameter.make_from_pb(self.config.mlp)p.l2_regularizer = params.l2_regularizerself.mlp = MLP(p, name='mlp', reuse=reuse)else:self.mlp = Noneself.mask_layers = []for i, block_conf in enumerate(self.config.mask_blocks):params = Parameter.make_from_pb(block_conf)params.l2_regularizer = self.params.l2_regularizermask_layer = MaskBlock(params, name='block_%d' % i, reuse=self.reuse)self.mask_layers.append(mask_layer)if self.config.input_layer_norm:if tf.__version__ >= '2.0':self.input_layer_norm = tf.keras.layers.LayerNormalization(name='input_ln')else:self.input_layer_norm = LayerNormalization(name='input_ln')def call(self, inputs, training=None, **kwargs):# 与pytorch版本对比，对输入也进行了一次layer normif self.config.input_layer_norm:inputs = self.input_layer_norm(inputs)# 下面的并行/串行实现逻辑无差if self.config.use_parallel:mask_outputs = [mask_layer((inputs, inputs)) for mask_layer in self.mask_layers]all_mask_outputs = tf.concat(mask_outputs, axis=1)if self.mlp is not None:output = self.mlp(all_mask_outputs, training=training)else:output = all_mask_outputsreturn outputelse:net = inputsfor i, _ in enumerate(self.config.mask_blocks):mask_layer = self.mask_layers[i]net = mask_layer((net, inputs))if self.mlp is not None:output = self.mlp(net, training=training)else:output = netreturn output

Reference:
MaskNet: Introducing Feature-Wise Multiplication to CTR Ranking Models by Instance-Guided Mask
tesorflow实现
twitter-alg-ml