Keras输入/输出dims和横向节点连接中的自定义Hebbian层实现

Question

我尝试在Keras中使用Hebbian更新实现一个无监督的ANN。我在这里发现了丹·桑德斯做的一个定制的赫比亚图层-https://github.com/djsaunde/rinns_python/blob/master/hebbian/hebbian.py （我希望在这里询问其他人的代码不会太差）

在我发现的在repo中使用这个层的例子中，这个层被用作稠密层/Conv层之间的中间层，但是我希望只使用Hebbian层来构建一个网络。在

在这一实施过程中，有两件关键的事情让我困惑不解：

1. 似乎输入尺寸和输出尺寸必须相同才能使这一层工作。为什么会出现这种情况？我能做些什么使它们变得不同？

2. 为什么权重矩阵的对角线设置为零？它说这是为了“确保没有神经元横向连接到自身”，但我认为连接权重是在前一层和当前层之间，而不是当前层和自身之间。

以下是Hebbian层实现的代码：

    from keras import backend as K
    from keras.engine.topology import Layer

    import numpy as np
    import tensorflow as tf

    np.set_printoptions(threshold=np.nan)

    sess = tf.Session()


    class Hebbian(Layer):


    def __init__(self, output_dim, lmbda=1.0, eta=0.0005, connectivity='random', connectivity_prob=0.25, **kwargs):
    '''
    Constructor for the Hebbian learning layer.

    args:
        output_dim - The shape of the output / activations computed by the layer.
        lambda - A floating-point valued parameter governing the strength of the Hebbian learning activation.
        eta - A floating-point valued parameter governing the Hebbian learning rate.
        connectivity - A string which determines the way in which the neurons in this layer are connected to
            the neurons in the previous layer.
    '''
    self.output_dim = output_dim
    self.lmbda = lmbda
    self.eta = eta
    self.connectivity = connectivity
    self.connectivity_prob = connectivity_prob

    if self.connectivity == 'random':
        self.B = np.random.random(self.output_dim) < self.connectivity_prob
    elif self.connectivity == 'zero':
        self.B = np.zeros(self.output_dim)

    super(Hebbian, self).__init__(**kwargs)


    def random_conn_init(self, shape, dtype=None):
    A = np.random.normal(0, 1, shape)
    A[self.B] = 0
    return tf.constant(A, dtype=tf.float32)


    def zero_init(self, shape, dtype=None):
    return np.zeros(shape)


    def build(self, input_shape):
    # create weight variable for this layer according to user-specified initialization
    if self.connectivity == 'all':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                            np.prod(self.output_dim)), initializer='uniform', trainable=False)
    elif self.connectivity == 'random':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                            np.prod(self.output_dim)), initializer=self.random_conn_init, trainable=False)
    elif self.connectivity == 'zero':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                            np.prod(self.output_dim)), initializer=self.zero_init, trainable=False)
    else:
        raise NotImplementedError

    # ensure that no neuron is laterally connected to itself
    self.kernel = self.kernel * tf.diag(tf.zeros(self.output_dim))

    # call superclass "build" function
    super(Hebbian, self).build(input_shape)


    def call(self, x):
    x_shape = tf.shape(x)
    batch_size = tf.shape(x)[0]

    # reshape to (batch_size, product of other dimensions) shape
    x = tf.reshape(x, (tf.reduce_prod(x_shape[1:]), batch_size))

    # compute activations using Hebbian-like update rule
    activations = x + self.lmbda * tf.matmul(self.kernel, x)

    # compute outer product of activations matrix with itself
    outer_product = tf.matmul(tf.expand_dims(x, 1), tf.expand_dims(x, 0))

    # update the weight matrix of this layer
    self.kernel = self.kernel + tf.multiply(self.eta, tf.reduce_mean(outer_product, axis=2))
    self.kernel = tf.multiply(self.kernel, self.B)
    self.kernel = self.kernel * tf.diag(tf.zeros(self.output_dim))

    return K.reshape(activations, x_shape)

在第一次检查时，我希望这个层能够从前一层获取输入，执行一个简单的激活计算（input*weight），根据Hebbian更新更新更新权重（类似于-如果激活是高b/t节点，则增加权重），然后将激活传递到下一层。在

我还希望它能够处理从一层到下一层的节点数量的减少/增加。在

相反，我似乎不明白为什么输入和输出的尺寸必须相同，以及为什么权重矩阵的对角线设置为零。在

代码中（隐式或显式）的哪一个规范要求图层必须是相同的尺寸？在

代码中（隐式或显式）的哪一个规范说明此层的权重矩阵将当前层连接到自身？在

很抱歉，如果这个Q应该被分成2，但看起来它们可能与e/o有关，所以我将它们保留为1。在

如有需要，乐意提供更多细节。在

编辑：意识到当我试图创建一个输出尺寸与输入尺寸不同的图层时，我忘记添加错误消息：

^{pr2}$

这将编译不带错误^

model = Sequential()
model.add(Hebbian(input_shape = (256,1), output_dim = 24))

此^将引发错误： 索引器错误：布尔索引与沿维度0的索引数组不匹配；维度为256，但相应的布尔维度为24

Answer 1

好吧，我想我可能已经想好了。有很多小问题，但最大的问题是我需要添加compute_output_shape函数，该函数使层能够修改其输入的形状，如下所述： https://keras.io/layers/writing-your-own-keras-layers/

这里是我所做的所有更改的代码。它可以编译和修改输入形状。请注意，这个层计算层本身内部的权重变化，如果您尝试实际使用层，可能会有一些问题（我仍在熨平这些），但这是一个单独的问题。在

class Hebbian(Layer):


def __init__(self, output_dim, lmbda=1.0, eta=0.0005, connectivity='random', connectivity_prob=0.25, **kwargs):
    '''
    Constructor for the Hebbian learning layer.

    args:
        output_dim - The shape of the output / activations computed by the layer.
        lambda - A floating-point valued parameter governing the strength of the Hebbian learning activation.
        eta - A floating-point valued parameter governing the Hebbian learning rate.
        connectivity - A string which determines the way in which the neurons in this layer are connected to
            the neurons in the previous layer.
    '''
    self.output_dim = output_dim
    self.lmbda = lmbda
    self.eta = eta
    self.connectivity = connectivity
    self.connectivity_prob = connectivity_prob

    super(Hebbian, self).__init__(**kwargs)



def random_conn_init(self, shape, dtype=None):
    A = np.random.normal(0, 1, shape)
    A[self.B] = 0
    return tf.constant(A, dtype=tf.float32)


def zero_init(self, shape, dtype=None):
    return np.zeros(shape)


def build(self, input_shape):
    # create weight variable for this layer according to user-specified initialization
    if self.connectivity == 'random':
        self.B = np.random.random(input_shape[0]) < self.connectivity_prob
    elif self.connectivity == 'zero':
        self.B = np.zeros(self.output_dim)

    if self.connectivity == 'all':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                    np.prod(self.output_dim)), initializer='uniform', trainable=False)
    elif self.connectivity == 'random':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                    np.prod(self.output_dim)), initializer=self.random_conn_init, trainable=False)
    elif self.connectivity == 'zero':
        self.kernel = self.add_weight(name='kernel', shape=(np.prod(input_shape[1:]), \
                    np.prod(self.output_dim)), initializer=self.zero_init, trainable=False)
    else:
        raise NotImplementedError


    # call superclass "build" function
    super(Hebbian, self).build(input_shape)


def call(self, x):  # x is the input to the network
    x_shape = tf.shape(x)
    batch_size = tf.shape(x)[0]

    # reshape to (batch_size, product of other dimensions) shape
    x = tf.reshape(x, (tf.reduce_prod(x_shape[1:]), batch_size))

    # compute activations using Hebbian-like update rule
    activations = x + self.lmbda * tf.matmul(self.kernel, x)  


    # compute outer product of activations matrix with itself
    outer_product = tf.matmul(tf.expand_dims(x, 1), tf.expand_dims(x, 0)) 

    # update the weight matrix of this layer
    self.kernel = self.kernel + tf.multiply(self.eta, tf.reduce_mean(outer_product, axis=2)) 
    self.kernel = tf.multiply(self.kernel, self.B)
    return K.reshape(activations, x_shape)

def compute_output_shape(self, input_shape):
    return (input_shape[0], self.output_dim)