Propagation Pattern
=======================================
Authors: `fangwei123456 <https://github.com/fangwei123456>`_

Single-Step and Multi-Step
------------------------------------
Most modules in SpikingJelly (except for :class:`spikingjelly.activation_based.rnn`), e.g., :class:`spikingjelly.activation_based.layer.Dropout`, don't have a ``MultiStep`` prefix. These modules' ``forward`` functions define a single-step forward:

    Input :math:`X_{t}`, output :math:`Y_{t}`

If a module has a ``MultiStep`` prefix, e.g., :class:`spikingjelly.activation_based.layer.MultiStepDropout`, then this module's ``forward`` function defines the multi-step forward:

    Input :math:`X_{t}, t=0,1,...,T-1`, output :math:`Y_{t}, t=0,1,...,T-1`

A single-step module can be easily packaged as a multi-step module. For example, we can use :class:`spikingjelly.activation_based.layer.MultiStepContainer`, which contains the origin module as a sub-module and implements the loop in time-steps in its ``forward`` function:

.. code-block:: python

    class MultiStepContainer(nn.Sequential):
        def __init__(self, *args):
            super().__init__(*args)

        def forward(self, x_seq: torch.Tensor):
            """
            :param x_seq: shape=[T, batch_size, ...]
            :type x_seq: torch.Tensor
            :return: y_seq, shape=[T, batch_size, ...]
            :rtype: torch.Tensor
            """
            y_seq = []
            for t in range(x_seq.shape[0]):
                y_seq.append(super().forward(x_seq[t]))

            for t in range(y_seq.__len__()):
                y_seq[t] = y_seq[t].unsqueeze(0)
            return torch.cat(y_seq, 0)

Let us use :class:`spikingjelly.activation_based.layer.MultiStepContainer` to implement a multi-step IF neuron:

.. code-block:: python

    from spikingjelly.activation_based import neuron, layer, functional
    import torch

    neuron_num = 4
    T = 8
    if_node = neuron.IFNode()
    x = torch.rand([T, neuron_num]) * 2
    for t in range(T):
        print(f'if_node output spikes at t={t}', if_node(x[t]))
    functional.reset_net(if_node)

    ms_if_node = layer.MultiStepContainer(if_node)
    print("multi step if_node output spikes\n", ms_if_node(x))
    functional.reset_net(ms_if_node)

The outputs are:

.. code-block:: shell

    if_node output spikes at t=0 tensor([1., 1., 1., 0.])
    if_node output spikes at t=1 tensor([0., 0., 0., 1.])
    if_node output spikes at t=2 tensor([1., 1., 1., 1.])
    if_node output spikes at t=3 tensor([0., 0., 1., 0.])
    if_node output spikes at t=4 tensor([1., 1., 1., 1.])
    if_node output spikes at t=5 tensor([1., 0., 0., 0.])
    if_node output spikes at t=6 tensor([1., 0., 1., 1.])
    if_node output spikes at t=7 tensor([1., 1., 1., 0.])
    multi step if_node output spikes
     tensor([[1., 1., 1., 0.],
            [0., 0., 0., 1.],
            [1., 1., 1., 1.],
            [0., 0., 1., 0.],
            [1., 1., 1., 1.],
            [1., 0., 0., 0.],
            [1., 0., 1., 1.],
            [1., 1., 1., 0.]])

We can find that the single-step module and the multi-step module have the identical outputs.

Step-by-step and Layer-by-Layer
--------------------------------------

In the previous tutorials and examples, we run the SNNs `step-by-step`, e.g.,:

.. code-block:: python

    if_node = neuron.IFNode()
    x = torch.rand([T, neuron_num]) * 2
    for t in range(T):
        print(f'if_node output spikes at t={t}', if_node(x[t]))


`step-by-step` means that during the forward propagation, we firstly calculate the SNN's outputs :math:`Y_{0}` at :math:`t=0`, then we calculate the SNN's outputs :math:`Y_{1}` at :math:`t=1`,..., and we can get the outputs at all time-steps :math:`Y_{t}, t=0,1,...,T-1`. The followed code is a `step-by-step` example (we suppose ``M0, M1, M2`` are single-step modules):

.. code-block:: python

   net = nn.Sequential(M0, M1, M2)

   for t in range(T):
       Y[t] = net(X[t])

The computation graph of forward propagation is built as followed:

.. image:: ../_static/tutorials/activation_based/10_propagation_pattern/step-by-step.png
    :width: 100%

The forward propagation of SNN and RNN is along both spatial domain and temporal domain. `step-by-step` calculates states of the whole network step by step. We can also use an another order, which is `layer-by-layer`. `layer-by-layer` calculates states layer-by-layer. The followed code is a `layer-by-layer` example (we suppose ``M0, M1, M2`` are multi-step modules):

.. code-block:: python

   net = nn.Sequential(M0, M1, M2)

   Y = net(X)

The computation graph of forward propagation is built as followed:

.. image:: ../_static/tutorials/activation_based/10_propagation_pattern/layer-by-layer.png
    :width: 100%

The `layer-by-layer` method is widely used in RNN and SNN, e.g., `Low-activity supervised convolutional spiking neural networks applied to speech commands recognition <https://arxiv.org/abs/2011.06846>`_ calculates outputs of each layer to implement a temporal convolution. Their codes are availble at https://github.com/romainzimmer/s2net.

The difference between `step-by-step` and `layer-by-layer` is the order of traverse the computation graph. The computed results of both methods are exactly same. However, `step-by-step` has more degree of parallelism. When a layer is stateless, e.g., :class:`torch.nn.Linear`, the `step-by-step` method may calculate as:

.. code-block:: python

    for t in range(T):
        y[t] = fc(x[t])  # x.shape=[T, batch_size, in_features]

The `layer-by-layer` method can calculate parallelly:

.. code-block:: python

    y = fc(x)  # x.shape=[T, batch_size, in_features]

For a stateless layer, we can concatenate inputs ``shape=[T, batch_size, ...]`` at time dimension as ``shape=[T * batch_size, ...]`` to avoid loop in time-steps. :class:`spikingjelly.activation_based.layer.SeqToANNContainer` has provided such a function in its ``forward``. We can directly use this module:

.. code-block:: python

    with torch.no_grad():
        T = 16
        batch_size = 8
        x = torch.rand([T, batch_size, 4])
        fc = SeqToANNContainer(nn.Linear(4, 2), nn.Linear(2, 3))
        print(fc(x).shape)

The outputs are

.. code-block:: shell

    torch.Size([16, 8, 3])

The outputs have ``shape=[T, batch_size, ...]`` and can be directly fed to the next layer.

Wrap Forward Propagation
-------------------------------
After we use ``SeqToANNContainer`` to wrap stateless ANN's layers, the ``.keys()`` of network's ``state_dict`` will change
because we introduce an external wrapper. Here is an example:

.. code-block:: python

    net_step_by_step = nn.Sequential(
        nn.Conv2d(3, 16, kernel_size=3, padding=1, bias=False),
        nn.BatchNorm2d(16),
        neuron.IFNode()
    )

    net_layer_by_layer = nn.Sequential(
        layer.SeqToANNContainer(
            nn.Conv2d(3, 16, kernel_size=3, padding=1, bias=False),
            nn.BatchNorm2d(16),
        ),
        neuron.MultiStepIFNode()
    )

    print('net_step_by_step.state_dict:', net_step_by_step.state_dict().keys())
    print('net_layer_by_layer.state_dict:', net_layer_by_layer.state_dict().keys())

The outputs are:

.. code-block:: shell

    net_step_by_step.state_dict: odict_keys(['0.weight', '1.weight', '1.bias', '1.running_mean', '1.running_var', '1.num_batches_tracked'])
    net_layer_by_layer.state_dict: odict_keys(['0.0.weight', '0.1.weight', '0.1.bias', '0.1.running_mean', '0.1.running_var', '0.1.num_batches_tracked'])

We can find that keys have been changed, which causes some trouble to load model's weights. For example, if we want to build
a multi-step Spiking ResNet-18 (:class:`spikingjelly.activation_based.model.spiking_resnet.spiking_resnet18`), and we want to
load the pre-train model's weights from ANN. If the network is built by ``SeqToANNContainer``, it wil be not able to load
weights from ANN because keys of ``state_dict`` are different. To avoid such problems, we can wrap forward propagation,
rather than wrap layers. Here is an example:

.. code-block:: python

    class NetStepByStep(nn.Module):
        def __init__(self):
            super().__init__()
            self.conv = nn.Conv2d(3, 16, kernel_size=3, padding=1, bias=False)
            self.bn = nn.BatchNorm2d(16)
            self.sn = neuron.IFNode()

        def forward(self, x):
            # x.shape = [N, C, H, W]
            x = self.conv(x)
            x = self.bn(x)
            x = self.sn(x)
            return x


    class NetLayerByLayer1(NetStepByStep):

        def forward(self, x_seq):
            # x_seq.shape = [T, N, C, H, W]
            x_seq = functional.seq_to_ann_forward(x_seq, [self.conv, self.bn])
            x_seq = functional.multi_step_forward(x_seq, self.sn)
            return x_seq


    class NetLayerByLayer2(NetStepByStep):
        def __init__(self):
            super().__init__()

            # replace single-step neuron to multi-step neuron
            del self.sn
            self.sn = neuron.MultiStepIFNode()

        def forward(self, x_seq):
            # x_seq.shape = [T, N, C, H, W]
            x_seq = functional.seq_to_ann_forward(x_seq, [self.conv, self.bn])
            x_seq = self.sn(x_seq)
            return x_seq

``state_dict.keys()`` of ``NetStepByStep, NetLayerByLayer1, NetLayerByLayer2`` are identical, and they can load model weights
from each others.