Dynamic Boltzmann Machine for Lattice Chemical Kinetics

Installation

Dependencies

Dependencies are automatically handled using the CPM.cmake package manager. There is no need to install anything extra, simply building the library through CMake will install the needed dependencies.

For the record, the dependencies installed are:

• The armadillo library.
• The q3c1 library for the Q3 C1 finite elements.

Building

Use cmake:

mkdir build
cd build
cmake ..
make

Two libraries will be made: dblz (for learning dynamics) and bmla (for learning initial conditions).

make install

The default install locations are /usr/local/include and /usr/local/lib.

If not installing, make sure to move the library to somewhere it will be found, or at worst

export DYLD_LIBRARY_PATH=$DYLD_LIBRARY_PATH:/absolute/path/to/lib

In this case, you will also need to specify using -L the location of the library at linking time (-L is needed for finding the library at linking time; DYLD_LIBRARY_PATH is at runtime).

Including

To access the headers, simply use: include <dblz> or `include .

Linking

Link your program using:

g++ -std=c++14 -O3 -ldblz -lq3c1 myprogram.cpp -o myprogram.o
g++ -std=c++14 -O3 -lbmla myprogram.cpp -o myprogram.o

(this assumes you have install -lq3c1).

Namespace

The namespace is dblz ("DynamicBoltzmann").

Usage

More documentation TBD!

Simulations

Simulations can be generated using the lattgillespie library located here.

Creating directory structure

To create the directory structure, use the included Python script create_data_dirs.py.

This takes 1 argument: the path of the directory (relative to local directory where you run create_data_dirs.py) that you want to create and create the substructure in.

For example, running:

python create_data_dirs.py data

creates in the working directory the following directories:

data
data/moments
data/ixn_params
data/diff_eq_rhs

Technical notes

Binary vs probabilistic units

The guidelines for RBMs in Geoffrey Hintons guide "A Practical Guide to Training Restricted Boltzmann Machines" state:

• "When the hidden units are being driven by data, always use stochastic binary states. When they are being driven by reconstructions, always use probabilities without sampling."

• "Assuming the visible units use the logistic function, use real-valued probabilities for both the data and the reconstructions."

• "When collecting the pairwise statistics for learning weights or the individual statistics for learning biases, use the probabilities, not the binary states, and make sure the weights have random initial values to break symmetry."

These rules lead to problems here - particularly the first rule: "When they are being driven by reconstructions, always use probabilities without sampling." Consider the following:

1. The stochastic simulations are binary by nature.
2. Assume we activate the hidden layer from these by also using binary units. Hence, when evaluating the awake phase moment <v * h> between visible and hidden units will have many terms of the form 0*1 or 1*0 or 0*0, leading to many null contributions to sum_i <v_i * h_i>.
3. Now we switch do using probabilistic units for doing the sampling for the asleep phase moment. In this case, in the contributions from before, we replace 0 by some small #. The upshot is that where contributions were null before, here they are greater than zero.

Therefore, the asleep moment will always be larger than the awake phase moment. This drives the weights W to -infinity!

Instead, we simply use binary units everywhere, i.e.:

1. The stochastic simulations are binary by nature.
2. Use binary units for the hidden units for the first round of sampling (driven by data). We then compute the awake phase moment.
3. Use binary units for other rounds of sampling both hidden and visible units, and to evaluate the asleep phase moments.

This avoids the infinity problem.