RNN LSTM network for inputting a sequence of numbers - tensorflow

Question

I'm trying to use LSTM networks to input a simple dataset that has multiple different sequences of numbers that represent musical data. The data is just a bunch of numpy arrays of floating point numbers with each song being one array. The data looks like this:
Song 1: [0.00013487907, 0.0002517006, 0.00021654845, ...]
Song 2: [-0.007279772, -0.011207076, -0.010082608, ...]
Song 3: [-0.00060827745, -0.00082834775, -0.0006534484, ...]
..and so on
I have done this before for MIDI files before, but those require embeddings of the different characters, however this is more continuous data as opposed to discrete data, so I'm not sure what the input model will look like, and how the data can be loaded for this particular task. For example, for the MIDI file project the input had an embedding layer to the model:
batch_size = 16
seq_length = 64
num_epochs = 100
optimizer_ = tf.keras.optimizers.Adam()
model = Sequential()
model.add(Embedding(input_dim = num_unique_chars, output_dim = 512, batch_input_shape = (batch_size, seq_length)))
model.add(LSTM(256, return_sequences = True, stateful = True))
model.add(Dropout(0.2))
model.add(LSTM(256, return_sequences = True, stateful = True))
model.add(Dropout(0.2))
model.add(LSTM(256, return_sequences = True, stateful = True))
model.add(Dropout(0.2))
model.add(TimeDistributed(Dense(num_unique_chars)))
model.add(Activation("softmax"))
model.compile(loss = "categorical_crossentropy", optimizer = optimizer_, metrics = ["accuracy"])
I wanna know how to do the same without tokenization/embedding, and feed each song into the model separately, and then further be able to generate samples from it.
I've tried looking for examples of this but everything related to LSTM networks seems to be text-based. Would appreciate any help/guidance with this!
Thanks

Answer 1

If you already have continuous values, you will not need an Embedding-layer. Either you directly pass the data into the LSTMs or you can use a Dense layer in-between. Additionally, you can also add a Masking-layer (depending on your data).
Also you have to adjust the shape of your data to (batch_size, seq_len, 1) as you only have one feature, but the time-series has to be "recognizable".
Here is a minimum working example with a Dense-layer instead the non-functioning Embedding-layer:
import tensorflow as tf
from tensorflow.keras import layers
from tensorflow.keras import Sequential
batch_size = 16
seq_length = 64
num_epochs = 100
num_unique_chars = 55 # I just picked any number
optimizer_ = tf.keras.optimizers.Adam()
model = Sequential()
model.add(layers.Dense(256, use_bias=False))
model.add(layers.LSTM(256, return_sequences = True, stateful = True))
model.add(layers.Dropout(0.2))
model.add(layers.LSTM(256, return_sequences = True, stateful = True))
model.add(layers.Dropout(0.2))
model.add(layers.LSTM(256, return_sequences = True, stateful = True))
model.add(layers.Dropout(0.2))
model.add(layers.TimeDistributed(layers.Dense(num_unique_chars)))
model.add(layers.Activation("softmax"))
model.compile(loss = "categorical_crossentropy", optimizer = optimizer_, metrics = ["accuracy"])
test_data = tf.random.normal(shape=(batch_size, seq_length, 1))
test_out = model(test_data)
print(test_out.shape)
Output: (16, 64, 55)
P. S.: With Dense layers the TimeDistributed-layer is optional. The Dense layer will just manipulate the last dimension of its input tensor.
P. P. S.: I think for your limited amount of features, three LSTM-layers with a dimension of 256 might easily result in over-fitting or some other unpleasant effects. So it might be useful to reduce the number of layers and their dimension. (Of course, this does not target your initial question)