We use "channels" or C to refer to the feature dimension - in the case of LSTM, BiLSTM, GRU I think of the operation as a loop over a sequence of vector inputs - each vector has size C. In practice we have a multi-dimensional array with size CxBxT - the operation loops over the sequence T dimension, vectorizes over the batch B dimension, and uses the C dimension in the computation.
Perhaps the confusion is that often LSTM-s have their output feedback as their input, but this is not necessary, so you can have an LSTM with inputs as vectors of size C1 and outputs of size C2. You can find a description of the algorithm in the "Algorithms" section of the doc page: https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layer.lstmlayer.html or you can see that the input state dimension and output/hidden state dimensions can be different in the algorithm described here https://en.wikipedia.org/wiki/Long_short-term_memory
Could you clarify what an SE attention module is?
We can implement attention mechanisms that require batch-matrix multiplies by using pagemtimes: https://www.mathworks.com/help/matlab/ref/pagemtimes.html - this is supported as a dlarray method, so it can be used in autodiff workflows such as custom training loops, and implementing custom layers. Alternatively if you need standard self attention you can use selfAttentionLayer: https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layer.selfattentionlayer.html
