sorn 0.5.3

Self-Organizing Recurrent Neural Networks

Self-Organizing Recurrent Neural Networks

SORN is a class of neuro-inspired artificial network build based on plasticity mechanisms in biological brain and mimic neocortical circuits ability of learning and adaptation through neuroplasticity mechanisms.

The network is developed as part of my Master thesis at Universität Osnabrück, Germany. For the ease of maintainance, the notebooks and the use cases are moved to SORN-Notebook

SORN Reservoir and the evolution of synaptic efficacies

Contents

• Self-Organizing Recurrent Neural Networks
• Getting Started
  • Installation
  • Dependencies
• Simulate and Train
  • Update Network configurations
  • Plasticity Phase
  • Training phase
  • Network Output Descriptions
  • Colaboratory Notebook
• Integrate with OpenAI gym
  • Cartpole balance problem
• Plotting functions
• Statistics and Analysis functions
• Citation
  • Package
  • Thesis
• Contributions

Installation

pip install sorn

The library is still in alpha stage, so you may also want to install the latest version from the development branch:

pip install git+https://github.com/Saran-nns/sorn

Dependencies

SORN supports Python 3.5+ ONLY. For older Python versions please use the official Python client. To install all optional dependencies,

  pip install 'sorn[all]'

For detailed documentation about usage and development, please visit SORN-Documentation

Usage

Plasticity Phase

import sorn
from sorn import Simulator
import numpy as np

# Sample input
num_features = 10
time_steps = 200
inputs = np.random.rand(num_features,time_steps)

# Simulate the network with default hyperparameters under gaussian white noise
state_dict, E, I, R, C = Simulator.simulate_sorn(inputs = inputs, phase='plasticity',
                                                matrices=None, noise = True,
                                                time_steps=time_steps)

The default values of the network hyperparameters are,

Keyword argument	Value	Description
ne	200	Number of Encitatory neurons in the reservoir
nu	10	Number of Input neurons in the reservoir
network_type_ee	"Sparse"	Sparse or Dense connectivity between Excitatory neurons
network_type_ie	"Dense"	Sparse or Dense connectivity from Excitatory to Inhibitory neurons
network_type_ei	"Sparse"	Sparse or Dense connectivity from Inhibitory to Excitatory neurons
lambda_ee	20	% of connections between neurons in Excitatory pool
lambda_ei	40	% of connections from Inhibitory to Excitatory neurons
lambda_ie	100	% of connections from Excitatory to Inhibitory neurons
eta_stdp	0.004	Hebbian Learning rate for connections between excitatory neurons
eta_inhib	0.001	Hebbian Learning rate for connections from Inhibitory to Excitatory neurons
eta_ip	0.01	Intrinsic plasticity learning rate
te_max	1.0	Maximum excitatory neuron threshold value
ti_max	0.5	Maximum inhibitory neuron threshold value
ti_min	0.0	Minimum inhibitory neuron threshold value
te_min	0.0	Minimum excitatory neuron threshold value
mu_ip	0.1	Target mean firing rate of excitatory neuron
sigma_ip	0.0	Standard deviation of firing rate of excitatory neuron

To override the default hyperparameters, use the kwargs as shown below,

state_dict, E, I, R, C = Simulator.simulate_sorn(inputs = inputs, phase='plasticity',
                                                matrices=None, noise= True,
                                                time_steps=time_steps,
                                                ne = 200, nu=num_features)

Training phase

from sorn import Trainer
# NOTE: During training phase, input to `sorn` should have second (time) dimension set to 1. ie., input shape should be (input_features,1).

inputs = np.random.rand(num_features,1)

# SORN network is frozen during training phase
state_dict, E, I, R, C = Trainer.train_sorn(inputs = inputs, phase='training',
                                            matrices=state_dict,
                                            nu=num_features, time_steps=1)

Freeze plasticity

To turn off any plasticity mechanisms during simulation or training phase, use freeze argument. For example to stop intrinsic plasticity during simulation phase,

# Sample input
num_features = 10
time_steps = 200
inputs = np.random.rand(num_features,time_steps)

state_dict, E, I, R, C = Simulator.simulate_sorn(inputs = inputs, phase='plasticity',
                                                matrices=None, noise = True,
                                                time_steps=time_steps, ne = 200,
                                                nu=num_features, freeze=['ip'])

The other options are,

stdp - Spike Timing Dependent Plasticity

ss - Synaptic Scaling

sp - Structural Plasticity

istdp - Inhibitory Spike Timing Dependent Plasticity

Note: If you pass all above options to freeze, then the network will behave as Liquid State Machine(LSM)

Network Output Descriptions

state_dict - Dictionary of connection weights (Wee,Wei,Wie) , Excitatory network activity (X), Inhibitory network activities(Y), Threshold values (Te,Ti)

E - Collection of Excitatory network activity of entire simulation period

I - Collection of Inhibitory network activity of entire simulation period

R - Collection of Recurrent network activity of entire simulation period

C - List of number of active connections in the Excitatory pool at each time step

Colaboratory Notebook

Sample simulation and training runs with few plotting functions are found at

Usage with OpenAI gym

Cartpole balance problem

from sorn import Simulator, Trainer
import gym

# Hyperparameters
NUM_EPISODES = int(2e6)
NUM_PLASTICITY_EPISODES = 20

LEARNING_RATE = 0.0001 # Gradient ascent learning rate
GAMMA = 0.99 # Discounting factor for the Rewards

# Open AI gym; Cartpole Environment
env = gym.make('CartPole-v0')
action_space = env.action_space.n

# SORN network parameters
ne = 50
nu = 4
# Init SORN using Simulator under random input;
state_dict, E, I, R, C = Simulator.simulate_sorn(inputs = np.random.randn(4,1),
                                                 phase ='plasticity',
                                                 time_steps = 1,
                                                 noise=False,
                                                 ne = ne, nu=nu)

w = np.random.rand(ne, 2) # Output layer weights

# Policy
def policy(state,w):
    "Implementation of softmax policy"
    z = state.dot(w)
    exp = np.exp(z)
    return exp/np.sum(exp)

# Vectorized softmax Jacobian
def softmax_grad(softmax):
    s = softmax.reshape(-1,1)
    return np.diagflat(s) - np.dot(s, s.T)

for EPISODE in range(NUM_EPISODES):

    # Environment observation;
    # NOTE: Input to sorn should have time dimension. ie., input shape should be (input_features,time_steps)
    state = env.reset()[:, None] # (4,) --> (4,1)

    grads = [] # Episode log policy gradients
    rewards = [] # Episode rewards

    # Keep track of total score
    score = 0

    # Play the episode
    while True:

      # env.render() # Uncomment to see your model train in real time (slow down training progress)
      if EPISODE < NUM_PLASTICITY_EPISODES:

        # Plasticity phase
        state_dict, E, I, R, C = Simulator.simulate_sorn(inputs = state, phase ='plasticity',
                                                        matrices = state_dict, time_steps = 1,
                                                        ne = ne, nu=nu,
                                                        noise=False)

      else:
        # Training phase with frozen reservoir connectivity
        state_dict, E, I, R, C = Trainer.train_sorn(inputs = state, phase = 'training',
                                                matrices = state_dict, time_steps = 1,
                                                ne = ne, nu=nu,
                                                noise= False)

      # Feed E as input states to your RL algorithm, below goes for simple policy gradient algorithm
      # Sample policy w.r.t excitatory states and take action in the environment
      probs = policy(np.asarray(E),w)
      action = np.random.choice(action_space,p=probs[0])
      state,reward,done,_ = env.step(action)
      state = state[:,None]

      # COMPUTE GRADIENTS BASED ON YOUR OBJECTIVE FUNCTION;
      # Sample computation of policy gradient objective function
      dsoftmax = softmax_grad(probs)[action,:]
      dlog = dsoftmax / probs[0,action]
      grad = np.asarray(E).T.dot(dlog[None,:])
      grads.append(grad)
      rewards.append(reward)
      score+=reward

      if done:
          break

    # OPTIMIZE OUTPUT LAYER WEIGHTS `w` BASED ON YOUR OPTIMIZATION METHOD;
    # Below is a sample of weight update based on gradient ascent(maximize cumulative reward) method for temporal difference learning
    for i in range(len(grads)):

        # Loop through everything that happened in the episode and update towards the log policy gradient times future reward
        w += LEARNING_RATE * grads[i] * sum([ r * (GAMMA ** r) for t,r in enumerate(rewards[i:])])
    print('Episode %s  Score %s' %(str(EPISODE),str(score)))

There are several neural data analysis and visualization methods inbuilt with sorn package. Sample call for few plotting and statistical methods are shown below;

Plotting functions

from sorn import Plotter
# Plot weight distribution in the network
Wee = np.random.randn(200,200) # For example, the network has 200 neurons in the excitatory pool. Note that generally Wee is sparse
Wee=Wee/Wee.max() # state_dict['Wee'] returned by the SORN is already normalized
Plotter.weight_distribution(weights= Wee, bin_size = 5, savefig = True)

# Plot Spike train of all neurons in the network
E = np.random.randint(2, size=(200,1000)) # For example, activity of 200 excitatory neurons in 1000 time steps
Plotter.scatter_plot(spike_train = E, savefig=True)

# Raster plot of activity of only first 10 neurons in the excitatory pool
Plotter.raster_plot(spike_train = E[:,0:10], savefig=True)

# Histogram of number of presynaptic connections per neuron in the excitatory pool
Plotter.hist_incoming_conn(weights=state_dict['Wee], bin_size=10, histtype='bar', savefig=True)

# Distribution of firing rate of the network
Plotter.hist_firing_rate_network(E, bin_size=10, savefig=True)

# Plot pearson correlation between neurons
from sorn import Statistics
avg_corr_coeff,_ = Statistics.avg_corr_coeff(E)
Plotter.correlation(avg_corr_coeff,savefig=True)

# Inter spike intervals with exponential curve fit for neuron 1 in the Excitatory pool
Plotter.isi_exponential_fit(E,neuron=1,bin_size=10, savefig=True)

# Distribution of connection weights in linear and lognormal scale
Plotter.linear_lognormal_fit(weights=Wee,num_points=100, savefig=True)

# Draw network connectivity using the pearson correlation function between neurons in the excitatory pool
Plotter.plot_network(avg_corr_coeff,corr_thres=0.01,fig_name='network.png')

Statistics and Analysis functions

from sorn import Statistics
#t-lagged auto correlation between neural activity
pearson_corr_matrix = Statistics.autocorr(firing_rates = [1,1,5,6,3,7], t= 2)

# Fano factor: To verify poissonian process in spike generation of neuron 10
mean_firing_rate, variance_firing_rate, fano_factor = Statistics.fanofactor(spike_train= E,
                                                                            neuron = 10,
                                                                            window_size = 10)

# Spike Source Entropy: To measure the uncertainty about the origin of spike from the network using entropy
sse = Statistics.spike_source_entropy(spike_train= E, num_neurons=200)

Citation

Package

@software{saranraj_nambusubramaniyan_2020_4184103,
  author       = {Saranraj Nambusubramaniyan},
  title        = {Saran-nns/sorn: Stable alpha release},
  month        = nov,
  year         = 2020,
  publisher    = {Zenodo},
  version      = {v0.3.1},
  doi          = {10.5281/zenodo.4184103},
  url          = {https://doi.org/10.5281/zenodo.4184103}
}

Thesis

Saranraj Nambusubramaniyan(2019): Prospects of Biologically Plausible Artificial Brain Circuits Solving General Intelligence Tasks at the Imminence of Chaos DOI: 10.13140/RG.2.2.25393.81762

Contributions

I am welcoming contributions. If you wish to contribute, please create a branch with a pull request and the changes can be discussed there. If you find a bug in the code or errors in the documentation, please open a new issue in the Github repository and report the bug or the error. Please provide sufficient information for the bug to be reproduced.