question about concurrently stacking the activation function

[pupupubb]

Hi, thanks for the great work.

Can I understand the class 'activation(nn.ReLU)' as a combination of ReLU->depth Conv-> BN?

I don't seem to see concurrently stacking activation functions in the code?Is 'concurrently ' mean Multi-branch activation functions?

Thank you very much!

[HantingChen]

Thanks for the attention. We use the depth conv as an efficient implementation of our activation function, which is same as Eq. (6) in our paper. Each element of the output of this activation is related to various non-linear inputs, which can be regarded as concurrently stacking.

[pupupubb]

Thank you for your reply!

The learnable parameters game and beta of BN in the activation function are a and b in Eq.(6)?

[HantingChen]

Not really. In fact, the BN can be merged into the conv in the activation. Then, the weight and bias of the merged conv are a and b in Eq.(6).

[pupupubb]

Excellent idea!
Thanks!

[cheezi]

Not really. In fact, the BN can be merged into the conv in the activation. Then, the weight and bias of the merged conv are a and b in Eq.(6).

Is this actually true?
So the equation states aA(x+b), but with the conv you basically implement wA(x)+b. So mathematically you cannot just pull out the b with non linear activations. E.g. assuming x=-2, b=2, w=1 assuming ReLU with the equation you get 1ReLU(-2+2)=0 and with the implementation you get 1ReLU(-2)+2=2...
Also this way isn't it just a simple DepthwiseSeparable Conv once you stack multiple Blocks:
Conv1x1->ReLu->ConvDW3x3->Conv1x1->ReLU->...
And last but not least why is the KernelSize actually "doubled", if you state in the paper you use n=3 for the activation series?

[mikljohansson]

Not really. In fact, the BN can be merged into the conv in the activation. Then, the weight and bias of the merged conv are a and b in Eq.(6).

Is this actually true? So the equation states a_A(x+b), but with the conv you basically implement w_A(x)+b. So mathematically you cannot just pull out the b with non linear activations. E.g. assuming x=-2, b=2, w=1 assuming ReLU with the equation you get 1_ReLU(-2+2)=0 and with the implementation you get 1_ReLU(-2)+2=2... Also this way isn't it just a simple DepthwiseSeparable Conv once you stack multiple Blocks: Conv1x1->ReLu->ConvDW3x3->Conv1x1->ReLU->... And last but not least why is the KernelSize actually "doubled", if you state in the paper you use n=3 for the activation series?

I wonder the same thing. Afaikt from reading the code the sequence of layers is as below

At training time:

• Conv1x1
• BatchNorm
• LeakyReLU
• Conv1x1
• BatchNorm
• Optional Max/AvgPool (downsampling)
• ReLU
• DepthwiseConv7x7 (kernel_size=7, groups=in_channels). The "activation sequence number" is the kernel size (kernel_size=n*2+1)
• BatchNorm

At inference time (the LeakyReLU is gradually removed during training and the two 1x1 convs are fused, the BatchNorm's are fused into the preceeding convs):

• Conv1x1
• Optional Max/AvgPool (downsampling)
• ReLU
• DepthwiseConv7x7 (kernel_size=7, groups=in_channels)

When considering that there's several of these blocks stacked after each other this seems kind of like an inverted MobileNet block (7x7 depthwise -> 1x1 conv -> downsample -> ReLU), but I don't understand the activation sequence. Afaikt it's just one activation and a regular depthwise convolution, perhaps I'm missing something?

There's ablation test in the paper (Table 1) showing a performance increase from 60% to 74% when comparing plain ReLU with your "activation" function, is this then comparing "1x1 convs -> ReLU" with "1x1 convs -> ReLU -> 3x3 depthwise (n=1)"? If so I can imagine that you'd get a big jump in performance when just comparing 1x1 convs against 1x1+3x3 convs, since with just 1x1 convs and no depthwise convs the receptive field of the network would be a lot worse.

[HantingChen]

Not really. In fact, the BN can be merged into the conv in the activation. Then, the weight and bias of the merged conv are a and b in Eq.(6).

Is this actually true? So the equation states a_A(x+b), but with the conv you basically implement w_A(x)+b. So mathematically you cannot just pull out the b with non linear activations. E.g. assuming x=-2, b=2, w=1 assuming ReLU with the equation you get 1_ReLU(-2+2)=0 and with the implementation you get 1_ReLU(-2)+2=2... Also this way isn't it just a simple DepthwiseSeparable Conv once you stack multiple Blocks: Conv1x1->ReLu->ConvDW3x3->Conv1x1->ReLU->... And last but not least why is the KernelSize actually "doubled", if you state in the paper you use n=3 for the activation series?

1. Sorry for the mistake, the b in A(x+b) is derived from the former conv.
2. The activation function is in fact implemented by DepthwiseSeparable Conv.
3. In Equ. (6), the i and j is counted from -n to n. Therefore, n=3 denotes the conv with kernel size 7.

[HantingChen]

Not really. In fact, the BN can be merged into the conv in the activation. Then, the weight and bias of the merged conv are a and b in Eq.(6).

Is this actually true? So the equation states a_A(x+b), but with the conv you basically implement w_A(x)+b. So mathematically you cannot just pull out the b with non linear activations. E.g. assuming x=-2, b=2, w=1 assuming ReLU with the equation you get 1_ReLU(-2+2)=0 and with the implementation you get 1_ReLU(-2)+2=2... Also this way isn't it just a simple DepthwiseSeparable Conv once you stack multiple Blocks: Conv1x1->ReLu->ConvDW3x3->Conv1x1->ReLU->... And last but not least why is the KernelSize actually "doubled", if you state in the paper you use n=3 for the activation series?

I wonder the same thing. Afaikt from reading the code the sequence of layers is as below

At training time:

• Conv1x1
• BatchNorm
• LeakyReLU
• Conv1x1
• BatchNorm
• Optional Max/AvgPool (downsampling)
• ReLU
• DepthwiseConv7x7 (kernel_size=7, groups=in_channels). The "activation sequence number" is the kernel size (kernel_size=n*2+1)
• BatchNorm

At inference time (the LeakyReLU is gradually removed during training and the two 1x1 convs are fused, the BatchNorm's are fused into the preceeding convs):

• Conv1x1
• Optional Max/AvgPool (downsampling)
• ReLU
• DepthwiseConv7x7 (kernel_size=7, groups=in_channels)

When considering that there's several of these blocks stacked after each other this seems kind of like an inverted MobileNet block (7x7 depthwise -> 1x1 conv -> downsample -> ReLU), but I don't understand the activation sequence. Afaikt it's just one activation and a regular depthwise convolution, perhaps I'm missing something?

There's ablation test in the paper (Table 1) showing a performance increase from 60% to 74% when comparing plain ReLU with your "activation" function, is this then comparing "1x1 convs -> ReLU" with "1x1 convs -> ReLU -> 3x3 depthwise (n=1)"? If so I can imagine that you'd get a big jump in performance when just comparing 1x1 convs against 1x1+3x3 convs, since with just 1x1 convs and no depthwise convs the receptive field of the network would be a lot worse.

Your understanding is correct, we currently use depthwise conv to implement the activation function we proposed, which is for latency friendliness.

[Haus226]

Hi, thank you for the innovative work. Would you mind to explain why the fusion of bias (b in Eq.6) are zeros? Why we dont let the bias becomes a learnable parameter like the normal convolution since they actually let it be a learnable parameters in BNET. And I think in both case of deploy variable, self.bias can be initialized as None for cleaner code since None and zeros for bias are actually same in convolution.

Code before changes

class activation(nn.ReLU):
    def __init__(self, dim, act_num=3, deploy=False):
        super(activation, self).__init__()
        self.act_num = act_num
        self.deploy = deploy
        self.dim = dim
        self.weight = torch.nn.Parameter(torch.randn(dim, 1, act_num*2 + 1, act_num*2 + 1))
        if deploy:
            self.bias = torch.nn.Parameter(torch.zeros(dim))
        else:
            self.bias = None
            self.bn = nn.BatchNorm2d(dim, eps=1e-6)
        weight_init.trunc_normal_(self.weight, std=.02)

    def forward(self, x):
        if self.deploy:
            return torch.nn.functional.conv2d(
                super(activation, self).forward(x), 
                self.weight, self.bias, padding=self.act_num, groups=self.dim)
        else:
            return self.bn(torch.nn.functional.conv2d(
                super(activation, self).forward(x),
                self.weight, padding=self.act_num, groups=self.dim))

    def _fuse_bn_tensor(self, weight, bn):
        kernel = weight
        running_mean = bn.running_mean
        running_var = bn.running_var
        gamma = bn.weight
        beta = bn.bias
        eps = bn.eps
        std = (running_var + eps).sqrt()
        t = (gamma / std).reshape(-1, 1, 1, 1)
        return kernel * t, beta + (0 - running_mean) * gamma / std

Code after changes

class activation(nn.ReLU):
    def __init__(self, dim, act_num=3, deploy=False):
        super(activation, self).__init__()
        self.act_num = act_num
        self.deploy = deploy
        self.dim = dim
        self.weight = torch.nn.Parameter(torch.randn(dim, 1, act_num*2 + 1, act_num*2 + 1))
        self.bias = None
        if not deploy:
            self.bn = nn.BatchNorm2d(dim, eps=1e-6)
        weight_init.trunc_normal_(self.weight, std=.02)

    def forward(self, x):
        if self.deploy:
            return torch.nn.functional.conv2d(
                super(activation, self).forward(x), 
                self.weight, self.bias, padding=self.act_num, groups=self.dim)
        else:
            return self.bn(torch.nn.functional.conv2d(
                super(activation, self).forward(x),
                self.weight, padding=self.act_num, groups=self.dim))

    def _fuse_bn_tensor(self, weight, bn):
        kernel = weight
        running_mean = bn.running_mean
        running_var = bn.running_var
        gamma = bn.weight
        beta = bn.bias
        eps = bn.eps
        std = (running_var + eps).sqrt()
        t = (gamma / std).reshape(-1, 1, 1, 1)
        return kernel * t, beta + (0 - running_mean) * gamma / std