def show_fixed_points(self, ff):
NOISE_SCALE = 0.5 # Standard deviation of noise added to initial states
N_INITS = 2048 # The number of initial states to provide
n_bits = ff.hps.data_hps['n_bits']
is_lstm = ff.hps.rnn_type == 'lstm'
'''Fixed point finder hyperparameters. See FixedPointFinder.py for detailed
descriptions of available hyperparameters.'''
fpf_hps = {}
# Setup the fixed point finder
fpf = FixedPointFinder(ff.rnn_cell, ff.session, **fpf_hps)
# Study the system in the absence of input pulses (e.g., all inputs are 0)
inputs = np.zeros([1, n_bits])
example_trials = ff.generate_SineWave_trials()
'''Draw random, noise corrupted samples of those state trajectories
to use as initial states for the fixed point optimizations.'''
example_predictions = ff.predict(example_trials,
do_predict_full_LSTM_state=is_lstm)
initial_states = fpf.sample_states(example_predictions['state'],
n_inits=N_INITS,
noise_scale=NOISE_SCALE)
# Run the fixed point finder
unique_fps, all_fps = fpf.find_fixed_points(initial_states, inputs)
# Visualize identified fixed points with overlaid RNN state trajectories
# All visualized in the 3D PCA space fit the the example RNN states.
plot_fps(unique_fps,
example_predictions['state'],
plot_batch_idx=range(30),
plot_start_time=10)
print(
'Entering debug mode to allow interaction with objects and figures.'
)
pdb.set_trace()
def find_fixed_points(model, valid_predictions):
''' Find, analyze, and visualize the fixed points of the trained RNN.
Args:
model: FlipFlop object.
Trained RNN model, as returned by train_FlipFlop().
valid_predictions: dict.
Model predictions on validation trials, as returned by
train_FlipFlop().
Returns:
None.
'''
'''Initial states are sampled from states observed during realistic
behavior of the network. Because a well-trained network transitions
instantaneously from one stable state to another, observed networks states
spend little if any time near the unstable fixed points. In order to
identify ALL fixed points, noise must be added to the initial states
before handing them to the fixed point finder. In this example, the noise
needed is rather large, which can lead to identifying fixed points well
outside of the domain of states observed in realistic behavior of the
network--such fixed points can be safely ignored when interpreting the
dynamical landscape (but can throw visualizations).'''
NOISE_SCALE = 0.5 # Standard deviation of noise added to initial states
N_INITS = 1024 # The number of initial states to provide
n_bits = model.hps.data_hps['n_bits']
is_lstm = model.hps.rnn_type == 'lstm'
'''Fixed point finder hyperparameters. See FixedPointFinder.py for detailed
descriptions of available hyperparameters.'''
fpf_hps = {}
# Setup the fixed point finder
fpf = FixedPointFinder(model.rnn_cell, model.session, **fpf_hps)
# Study the system in the absence of input pulses (e.g., all inputs are 0)
inputs = np.zeros([1,n_bits])
'''Draw random, noise corrupted samples of those state trajectories
to use as initial states for the fixed point optimizations.'''
initial_states = fpf.sample_states(valid_predictions['state'],
n_inits=N_INITS,
noise_scale=NOISE_SCALE)
# Run the fixed point finder
unique_fps, all_fps = fpf.find_fixed_points(initial_states, inputs)
# Visualize identified fixed points with overlaid RNN state trajectories
# All visualized in the 3D PCA space fit the the example RNN states.
plot_fps(unique_fps, valid_predictions['state'],
plot_batch_idx=list(range(30)),
plot_start_time=10)
print('Entering debug mode to allow interaction with objects and figures.')
print('You should see a figure with:')
print('\tMany blue lines approximately outlining a cube')
print('\tStable fixed points (black dots) at corners of the cube')
print('\tUnstable fixed points (red lines or crosses) '
'on edges, surfaces and center of the cube')
print('Enter q to quit.\n')
pdb.set_trace()
'''Fixed point finder hyperparameters. See FixedPointFinder.py for detailed
descriptions of available hyperparameters.'''
fpf_hps = {}
# Setup the fixed point finder
fpf = FixedPointFinder(ff.rnn_cell,
ff.session,
**fpf_hps)
# Study the system in the absence of input pulses (e.g., all inputs are 0)
inputs = np.zeros([1,n_bits])
'''Draw random, noise corrupted samples of those state trajectories
to use as initial states for the fixed point optimizations.'''
example_predictions, example_summary = ff.predict(example_trials)
initial_states = fpf.sample_states(example_predictions['state'],
n_inits=N_INITS,
noise_scale=NOISE_SCALE)
# Run the fixed point finder
unique_fps, all_fps = fpf.find_fixed_points(initial_states, inputs)
# Visualize identified fixed points with overlaid RNN state trajectories
# All visualized in the 3D PCA space fit the the example RNN states.
plot_fps(unique_fps, example_predictions['state'],
plot_batch_idx=range(30),
plot_start_time=10)
print('Entering debug mode to allow interaction with objects and figures.')
pdb.set_trace()