Assume we have two TensorFlow tensors:
input and weights.
input is a tensor of n images, say. So its shape is [n, H, W, C].
weights is a simple list of n scalar weights: [w1 w2 ... wn]
The aim is to scalar-multiply each image by its corresponding weight.
How would one do that?
I tried to use tf.nn.conv2D with 1x1 kernels but I do not know how to reshape our rank 1 weight tensor into the required rank 4 kernel tensor.
Any help would be appreciated.
Thanks to user zihaozhihao:
The answer is to change the shape of weights to (-1, 1, 1, 1) and then multiply it with input.
weights = tf.reshape(weights, (-1, 1, 1, 1))
weighted_input = input * weights
Related
I'm creating a SSL neural network and my input tensor is a NxM tensor where N is the length of the sound wave and M is the number of microphones. The actual size is roughly 14000x4
I need to pool, but I only want to pool the rows for each column (not the columns together). For example:
Pool(2)(tensor) --> tensor of size (N/2)xM
Is this possible without splitting the tensor into 4 tensors, preforming 4 separate Pool1D, then concatenating?
Pool1D gives dimensionality error
Pool2D reduces the number of rows and columns
Set the stride to 1 for the columns,
tf.keras.layers.MaxPooling2D(pool_size=(2, 2),strides=(2, 1), padding='same')
Example,
inputs = tf.random.normal(shape=(14000,4))
inputs = inputs[None,...,None]
max_pool_2d = tf.keras.layers.MaxPooling2D(pool_size=(2, 2),strides=(2, 1), padding='same')
max_pool_2d(inputs).shape
#[1, 7000, 4, 1]
I have an idea for a tensor operation that would not be difficult to implement via iteration, with batch size one. However I would like to parallelize it as much as possible.
I have two tensors with shape (n, 5) called X and Y. X is actually supposed to represent 5 one-dimensional tensors with shape (n, 1): (x_1, ..., x_n). Ditto for Y.
I would like to compute a tensor with shape (n, 25) where each column represents the output of the tensor operation f(x_i, y_j), where f is fixed for all 1 <= i, j <= 5. The operation f has output shape (n, 1), just like x_i and y_i.
I feel it is important to clarify that f is essentially a fully-connected layer from the concatenated [...x_i, ...y_i] tensor with shape (1, 10), to an output layer with shape (1,5).
Again, it is easy to see how to do this manually with iteration and slicing. However this is probably very slow. Performing this operation in batches, where the tensors X, Y now have shape (n, 5, batch_size) is also desirable, particularly for mini-batch gradient descent.
It is difficult to really articulate here why I desire to create this network; I feel it is suited for my domain of 'itemized tabular data' and cuts down significantly on the number of weights per operation, compared to a fully connected network.
Is this possible using tensorflow? Certainly not using just keras.
Below is an example in numpy per AloneTogether's request
import numpy as np
features = 16
batch_size = 256
X_batch = np.random.random((features, 5, batch_size))
Y_batch = np.random.random((features, 5, batch_size))
# one tensor operation to reduce weights in this custom 'layer'
f = np.random.random((features, 2 * features))
for b in range(batch_size):
X = X_batch[:, :, b]
Y = Y_batch[:, :, b]
for i in range(5):
x_i = X[:, i:i+1]
for j in range(5):
y_j = Y[:, j:j+1]
x_i_y_j = np.concatenate([x_i, y_j], axis=0)
# f(x_i, y_j)
# implemented by a fully-connected layer
f_i_j = np.matmul(f, x_i_y_j)
All operations you need (concatenation and matrix multiplication) can be batched.
Difficult part here is, that you want to concatenate features of all items in X with features of all items in Y (all combinations).
My recommended solution is to expand the dimensions of X to [batch, features, 5, 1], expand dimensions of Y to [batch, features, 1, 5]
Than tf.repeat() both tensors so their shapes become [batch, features, 5, 5].
Now you can concatenate X and Y. You will have a tensor of shape [batch, 2*features, 5, 5]. Observe that this way all combinations are built.
Next step is matrix multiplication. tf.matmul() can also do batch matrix multiplication, but I use here tf.einsum() because I want more control over which dimensions are considered as batch.
Full code:
import tensorflow as tf
import numpy as np
batch_size=3
features=6
items=5
x = np.random.uniform(size=[batch_size,features,items])
y = np.random.uniform(size=[batch_size,features,items])
f = np.random.uniform(size=[2*features,features])
x_reps= tf.repeat(x[:,:,:,tf.newaxis], items, axis=3)
y_reps= tf.repeat(y[:,:,tf.newaxis,:], items, axis=2)
xy_conc = tf.concat([x_reps,y_reps], axis=1)
f_i_j = tf.einsum("bfij, fg->bgij", xy_conc,f)
f_i_j = tf.reshape(f_i_j , [batch_size,features,items*items])
I have a tensor T of shape Batch_Size x Num_Items x Item_Dimension and another tensor P of shape Batch_Size x Num_Items, where the Num_Items values in each batch of P sum to 1 (a probability distribution of items for each batch). I want to sample without replacement N items from T according to probability distribution P. The resulting tensor should be of shape Batch_Size x N x Item_Dimension. How would I do this?
Take a look at
https://github.com/tensorflow/tensorflow/issues/9260
Though note I believe you need logits instead of probs for Gumbel max sampling.
I would like to multiply a sparse tensor by a dense tensor but do so within a batch.
For example I have a sparse tensor with the corresponding dense shape of (20,65536,65536) where 20 is the batch size. I would like to multiply each (65536,65536) in the batch with the corresponding (65536x1) from a tensor shape (20,65536) which has a dense representation. tf.sparse_tensor_dense_matmul only accepts a rank 2 sparse tensor. Is there a way to perform this over a batch?
I would like to avoid converting the sparse matrix to a dense matrix if possible due to memory constraints.
Assuming that a is a sparse tensor with shape (20, 65536, 65536) and b a dense tensor with shape (20, 65536), you could perform the batch sparse-dense matrix multiplication as follows:
y_sparse = tf.sparse.reduce_sum_sparse(a * b[:, None, :], axis=-1)
This solution expands the second dimension of tensor b to enable implicit broadcasting. Then, the batch matrix multiplication takes place by performing a sparse-dense multiplication and a sparse sum along the last axis.
If b has got a third dimension so it is a batch of matrices, you can multiply their columns individually and concatenate them later:
multiplied_dims = []
for i in range (b.shape[-1]):
multiplied_dims.append(tf.expand_dims(tf.sparse.reduce_sum(a * b[:, :, i][:, None, :], axis=-1), -1))
result = tf.concat(multiplied_dims, -1)
The answer is simple - you reshape the sparse tensor first and then multiply it by the dense matrix. Something like this would work:
sparse_tensor_rank2 = tf.sparse_reshape(sparse_tensor, [-1, 65536])
Keras Dense layer needs an input_dim or input_shape to be specified. What value do I put in there?
My input is a matrix of 1,000,000 rows and only 3 columns. My output is 1,600 classes.
What do I put there?
dimensionality of the inputs (1000000, 1600)
2 because it's a 2D matrix
input_dim is the number of dimensions of the features, in your case that is just 3. The equivalent notation for input_shape, which is an actual dimensional shape, is (3,)
In your case
lets assume x and y=target variable and are look like as follows after feature engineering
x.shape
(1000000, 3)
y.shape
((1000000, 1600)
# as first layer in a sequential model:
model = Sequential()
model.add(Dense(32, input_shape=x.shape[1])) # Input layer
# now the model will take as input arrays of shape (*, 3)
# and output arrays of shape (*, 32)
...
...
model.add(Dense(y.shape[1],activation='softmax')) # Output layer
y.shape[1]= 1600, the number of output which is the number of classes you have, since you are dealing with Classification.
X = dataset.iloc[:, 3:13]
meaning the X parameter having all the rows and 3rd column till 12th column inclusive and 13th column exclusive.
We will also have a X0 parameter to be given to the neural network, so total
input layers becomes 10+1 = 11.
Dense(input_dim = 11, activation = 'relu', kernel_initializer = 'he_uniform')