BindsNET学习系列——Encoding

相关源码：bindsnet/bindsnet/encoding/encodings.py；

1、bernoulli

def bernoulli(
    datum: torch.Tensor,
    time: Optional[int] = None,
    dt: float = 1.0,
    device="cpu",
    **kwargs
) -> torch.Tensor:
    # language=rst
    """
    Generates Bernoulli-distributed spike trains based on input intensity. Inputs must
    be non-negative. Spikes correspond to successful Bernoulli trials, with success
    probability equal to (normalized in [0, 1]) input value.

    :param datum: Tensor of shape ``[n_1, ..., n_k]``.
    :param time: Length of Bernoulli spike train per input variable.
    :param dt: Simulation time step.
    :return: Tensor of shape ``[time, n_1, ..., n_k]`` of Bernoulli-distributed spikes.

    Keyword arguments:

    :param float max_prob: Maximum probability of spike per Bernoulli trial.
    """
    # Setting kwargs.
    max_prob = kwargs.get("max_prob", 1.0)

    assert 0 <= max_prob <= 1, "Maximum firing probability must be in range [0, 1]"
    assert (datum >= 0).all(), "Inputs must be non-negative"

    shape, size = datum.shape, datum.numel()
    datum = datum.flatten()

    if time is not None: 
        time = int(time / dt) # 100

    # Normalize inputs and rescale (spike probability proportional to input intensity).
    if datum.max() > 1.0:
        datum /= datum.max()

    # Make spike data from Bernoulli sampling.
    if time is None: # pass
        spikes = torch.bernoulli(max_prob * datum).to(device)
        spikes = spikes.view(*shape)
    else: 
        spikes = torch.bernoulli(max_prob * datum.repeat([time, 1]))
        spikes = spikes.view(time, *shape)

    return spikes.byte()

Bernoulli编码：基于输入强度生成Bernoulli分布脉冲序列。输入必须为非负。脉冲对应于成功的Bernoulli试验，成功概率等于(标准化为[0, 1])输入值。

2、poisson

def poisson(
    datum: torch.Tensor,
    time: int,
    dt: float = 1.0,
    device="cpu",
    approx=False,
    **kwargs
) -> torch.Tensor:
    # language=rst
    """
    Generates Poisson-distributed spike trains based on input intensity. Inputs must be
    non-negative, and give the firing rate in Hz. Inter-spike intervals (ISIs) for
    non-negative data incremented by one to avoid zero intervals while maintaining ISI
    distributions.

    :param datum: Tensor of shape ``[n_1, ..., n_k]``.
    :param time: Length of Poisson spike train per input variable.
    :param dt: Simulation time step.
    :param device: target destination of poisson spikes.
    :param approx: Bool: use alternate faster, less accurate computation.
    :return: Tensor of shape ``[time, n_1, ..., n_k]`` of Poisson-distributed spikes.
    """
    assert (datum >= 0).all(), "Inputs must be non-negative"

    # Get shape and size of data.
    shape, size = datum.shape, datum.numel()
    datum = datum.flatten()
    time = int(time / dt)

    if approx:
        # random normal power awful approximation
        x = torch.randn((time, size), device=device).abs()
        x = torch.pow(x, (datum * 0.11 + 5) / 50)
        y = torch.tensor(x < 0.6, dtype=torch.bool, device=device)

        return y.view(time, *shape).byte()
    else:
        # Compute firing rates in seconds as function of data intensity,
        # accounting for simulation time step.
        rate = torch.zeros(size, device=device)
        rate[datum != 0] = 1 / datum[datum != 0] * (1000 / dt)

        # Create Poisson distribution and sample inter-spike intervals
        # (incrementing by 1 to avoid zero intervals).
        dist = torch.distributions.Poisson(rate=rate, validate_args=False)
        intervals = dist.sample(sample_shape=torch.Size([time + 1]))
        intervals[:, datum != 0] += (intervals[:, datum != 0] == 0).float()

        # Calculate spike times by cumulatively summing over time dimension.
        times = torch.cumsum(intervals, dim=0).long()
        times[times >= time + 1] = 0

        # Create tensor of spikes.
        spikes = torch.zeros(time + 1, size, device=device).byte()
        spikes[times, torch.arange(size)] = 1
        spikes = spikes[1:]

        return spikes.view(time, *shape)

Poisson编码：根据输入强度生成泊松分布的脉冲序列。输入必须是非负的，并给出以赫兹为单位的发放率。非负数据的脉冲间隔(ISI)通过增加1以避免间隔为零，同时保持ISI分布。通过在时间维度上对ISI序列累计求和来计算脉冲时间，并基于此创建脉冲张量。

3、rank_order

def rank_order(
    datum: torch.Tensor, time: int, dt: float = 1.0, **kwargs
) -> torch.Tensor:
    # language=rst
    """
    Encodes data via a rank order coding-like representation. One spike per neuron,
    temporally ordered by decreasing intensity. Inputs must be non-negative.

    :param datum: Tensor of shape ``[n_samples, n_1, ..., n_k]``.
    :param time: Length of rank order-encoded spike train per input variable.
    :param dt: Simulation time step.
    :return: Tensor of shape ``[time, n_1, ..., n_k]`` of rank order-encoded spikes.
    """
    assert (datum >= 0).all(), "Inputs must be non-negative"

    shape, size = datum.shape, datum.numel()
    datum = datum.flatten()
    time = int(time / dt)

    # Create spike times in order of decreasing intensity.
    datum /= datum.max()
    times = torch.zeros(size)
    times[datum != 0] = 1 / datum[datum != 0]
    times *= time / times.max()  # Extended through simulation time.
    times = torch.ceil(times).long()

    # Create spike times tensor.
    spikes = torch.zeros(time, size).byte()
    for i in range(size):
        if 0 < times[i] < time:
            spikes[times[i] - 1, i] = 1

    return spikes.reshape(time, *shape)

通过类似于秩的编码表征对数据进行编码。每个神经元一个脉冲，按强度递减的时序排列。输入必须为非负。