.. _model-geometry:

Model Geometry
==============

This document explains several constants related to the geometry of an STT model.

n_input
-------
Each of the at maximum ``n_steps`` vectors is a vector of MFCC features of a
time-slice of the speech sample. We will make the number of MFCC features
dependent upon the sample rate of the data set. Generically, if the sample rate
is 8kHz we use 13 features. If the sample rate is 16kHz we use 26 features...
We capture the dimension of these vectors, equivalently the number of MFCC
features, in the variable ``n_input``. By default ``n_input`` is 26.

n_context
---------
As previously mentioned, the RNN is not simply fed the MFCC features of a given
time-slice. It is fed, in addition, a context of :math:`C` frames on
either side of the frame in question. The number of frames in this context is
captured in the variable ``n_context``. By default ``n_context`` is 9.

Next we will introduce constants that specify the geometry of some of the
non-recurrent layers of the network. We do this by simply specifying the number
of units in each of the layers.

n_hidden_1, n_hidden_2, n_hidden_5
----------------------------------
``n_hidden_1`` is the number of units in the first layer, ``n_hidden_2`` the number
of units in the second, and  ``n_hidden_5`` the number in the fifth. We haven't
forgotten about the third or sixth layer. We will define their unit count below.

The RNN consists of an LSTM RNN that works "forward in time":

.. image:: ../images/LSTM3-chain.png
    :alt: Image shows a diagram of a recurrent neural network with LSTM cells, with arrows depicting the flow of data from earlier time steps to later timesteps within the RNN.

The dimension of the cell state, the upper line connecting subsequent LSTM units,
is independent of the input dimension.

n_cell_dim
----------
Hence, we are free to choose the dimension of this cell state independent of the
input dimension. We capture the cell state dimension in the variable ``n_cell_dim``.

n_hidden_3
----------
The number of units in the third layer, which feeds in to the LSTM, is
determined by ``n_cell_dim`` as follows

.. code:: python

    n_hidden_3 = n_cell_dim

n_hidden_6
-----------
The variable ``n_hidden_6`` will hold the number of characters in the target
language plus one, for the :math:`blank`.
For English it is the cardinality of the set

.. math::
    \{a,b,c, . . . , z, space, apostrophe, blank\}

we referred to earlier.
