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Kernel: Python 3
%matplotlib inline
%run ../gsc2
%run ../grammar

##Example 2: Spoken word recognition

# Grammar 2 (spoken word recognition)
# W[1] -> A B  (beaker)
# W[2] -> A C  (beetle)
# W[3] -> D B  (speaker)
# W[4] -> E F  (carousal)
# To make the model minimal, we ignore the root symbol and the null filler symbol.

role_names2 = ['R[0,1,2]', 'R[0,1]', 'R[1,2]']
filler_names2 = ['W[1]', 'W[2]', 'W[3]', 'W[4]', 'A', 'B', 'C', 'D', 'E', 'F']
#filler_names2 = ['W[1]', 'W[2]', 'W[3]', 'W[4]', 'A', 'B', 'C', 'D']
sentence_types2 = [['W[1]/R[0,1,2]', 'A/R[0,1]', 'B/R[1,2]'], 
                   ['W[2]/R[0,1,2]', 'A/R[0,1]', 'C/R[1,2]'],
                   ['W[3]/R[0,1,2]', 'D/R[0,1]', 'B/R[1,2]'],
                   ['W[4]/R[0,1,2]', 'E/R[0,1]', 'F/R[1,2]']]
#                   ['W[4]/R[0,1,2]', 'D/R[0,1]', 'C/R[1,2]']]  # for balance

net2 = GscNet(filler_names=filler_names2, role_names=role_names2, reptype_f='dist', reptype_r='dist',
             T_init=0.01, T_decay_rate=0, q_init=0, q_max=200, q_rate=0.01, q_fun='plinear', 
             beta=10, grid_points=sentence_types2)

net2.set_weight('W[1]/R[0,1,2]', ['A/R[0,1]', 'B/R[1,2]'], 2.0) # W1/012 -> A/01 B/12
net2.set_weight('W[2]/R[0,1,2]', ['A/R[0,1]', 'C/R[1,2]'], 2.0) # W2/012 -> A/01 C/12
net2.set_weight('W[3]/R[0,1,2]', ['D/R[0,1]', 'B/R[1,2]'], 2.0) # W3/012 -> D/01 B/12
net2.set_weight('W[4]/R[0,1,2]', ['E/R[0,1]', 'F/R[1,2]'], 2.0) # W4/012 -> E/01 F/12
#net2.set_weight('W[4]/R[0,1,2]', ['D/R[0,1]', 'C/R[1,2]'], 2.0) # W4/012 -> E/01 F/12
net2.set_filler_bias(['W[1]', 'W[2]', 'W[3]', 'W[4]'], -2.0)    # W1~W4: need two daughters
net2.set_filler_bias(['A', 'B', 'C', 'D', 'E', 'F'], -1.0)      # A~F: need a mother
#net2.set_filler_bias(['A', 'B', 'C', 'D'], -1.0)      # A~F: need a mother
net2.check_beta(disp=True)
Recommended beta min = 5.391 
init_state = copy.deepcopy(net2.zeta)   # The bowl center in neural coordinates
#net2.reset()
#net2.T = 0.
#net2.run(10000, plot=True, update_T=False, update_q=False) # In this way, 
#net2.read_state()
#init_state = copy.deepcopy(net2.act)

params2 = {'testvar': 'ema_speed',
           'norm_ord': np.inf,
           'convergence_check': True,
           'dist_space': 'S',
           'tol': 1e-3,
           'ema_factor': 0.1, 
           'grid_points': sentence_types2, 
           'input_method': 'ext',
           'cumulative_input': False,
           'input_inhib': False,
           'update_T': True, 
           'update_q': True, 
           'maxstep': np.array([2000, 3000]), 
           'nrep': 1,
           'q_fun': 'plinear', 
           'ext_overlap': True,
           'ext_overlap_steps': 500, 
           'init_state': init_state}

net2.reset()
net2.T_init = 0.001
net2.T_decay_rate = 0.0

input_list = ['A/R[0,1]', 'B/R[1,2]']
net2.reset()
sim2 = sim(net2, params2)
input_vals = [1.0, 1.0]
# input_vals = [1.0, 4.0]     # CHECK
sim2.input_list = input_list
sim2.input_vals = input_vals

sim2.simulate()
rep_num = 1
sim2.plot_act_trace(rep_num)
sim2.read_state(rep_num, 1)
sim2.read_grid_point(rep_num, 1)
sim2.read_state(rep_num, 2)
sim2.read_grid_point(rep_num, 2)
sim2.rt
sim2.plot_trace('dist', rep_num)
Image in a Jupyter notebook
R[0,1,2] R[0,1] R[1,2] W[1] 0.680110 0.132822 0.138200 W[2] 0.433897 0.131864 0.130456 W[3] 0.325543 0.135792 0.129669 W[4] 0.210912 0.127382 0.146636 A 0.193579 0.816680 0.205851 B 0.199245 0.207040 0.757427 C 0.184637 0.197060 0.377702 D 0.191011 0.294651 0.221406 E 0.189172 0.263287 0.206670 F 0.202317 0.209870 0.279746 ['W[1]/R[0,1,2]', 'A/R[0,1]', 'B/R[1,2]'] R[0,1,2] R[0,1] R[1,2] W[1] 0.958052 0.061416 0.058309 W[2] 0.119934 0.063364 0.065626 W[3] 0.121456 0.049999 0.053922 W[4] 0.061953 0.063937 0.054879 A 0.084248 0.962637 0.089404 B 0.080594 0.078881 0.966036 C 0.083815 0.084522 0.100514 D 0.084277 0.100529 0.096263 E 0.081234 0.092193 0.089884 F 0.090120 0.086231 0.089789 ['W[1]/R[0,1,2]', 'A/R[0,1]', 'B/R[1,2]']
Image in a Jupyter notebook
# There is no single word unit in this model.
# We will use a dot product as a structure's activation value.
# sim.act_trace[rep_ind, word_ind, timestep, unit_ind]   # from 0 
trace1 = sim2.act_trace[0, 0, :sim2.rt[0][0], :]   # activation trace given word 1 input
trace2 = sim2.act_trace[0, 1, 1:sim2.rt[0][1], :]  # activation trace given word 2 input
act_trace = np.vstack((trace1, trace2))

# compute similarity (dot product) of a state with each of four grid points at every time step.
dp_trace = np.zeros((act_trace.shape[0], len(sentence_types2)))
for ii, sent in enumerate(sentence_types2):
    net2.set_state(sent)
    dp_trace[:, ii] = act_trace.dot(net2.act)

C = 2
times = np.arange(act_trace.shape[0]) * net2.dt
k_trace = np.zeros(act_trace.shape[0])
k_trace = C * 1/(1+np.exp(-times))
k_trace_mat = np.tile(k_trace, (len(sentence_types2), 1)).T

# Response strength: Luce's choice rule
#k = 2
#S_trace = np.exp(k * dp_trace)
S_trace = np.exp(k_trace_mat * dp_trace)
L_trace = S_trace / np.tile(np.sum(S_trace, axis=1), (len(sentence_types2), 1)).T
delta_trace = np.max(dp_trace, axis=1) / np.max(dp_trace)
P_trace = np.tile(delta_trace, (len(sentence_types2), 1)).T * L_trace

plt.plot(P_trace)
plt.show()
Image in a Jupyter notebook

##Example 3: Garden Path

# Harmony difference
hdiff = 0.5    # S1 is preferred to S2.
#hdiff = 0.     # S1 and S2 are equally preferred.

# Grammar 3 (Garden path)
role_names3 = ['R[0,1,2]', 'R[0,1]', 'R[1,2]']
filler_names3 = ['S[1]', 'S[2]', 'A', 'B', 'C']
sentence_types3 = [['S[1]/R[0,1,2]', 'A/R[0,1]', 'B/R[1,2]'], 
                   ['S[2]/R[0,1,2]', 'A/R[0,1]', 'C/R[1,2]']]

net3 = GscNet(filler_names=filler_names3, role_names=role_names3, reptype_f='dist', reptype_r='dist',
             T_init=0.01, T_decay_rate=0, q_init=0, q_max=200, q_rate=0.01, q_fun='plinear', 
             beta=10, grid_points=sentence_types3)

net3.set_weight('S[1]/R[0,1,2]', ['A/R[0,1]', 'B/R[1,2]'], 2.0)
net3.set_weight('S[2]/R[0,1,2]', ['A/R[0,1]', 'C/R[1,2]'], 2.0)
net3.set_filler_bias('S[2]', -2.0)
net3.set_filler_bias('S[1]', -2.0 + hdiff)
net3.set_filler_bias(['A', 'B', 'C'], -1.0)
net3.check_beta(disp=True)
Recommended beta min = 4.928 
params3 = {'testvar': 'ema_speed',
           'norm_ord': np.inf,
           'convergence_check': True,
           'dist_space': 'S',
           'tol': 1e-3,
           'ema_factor': 0.1, 
           'grid_points': sentence_types3, 
           'input_method': 'ext',
           'cumulative_input': False,
           'input_inhib': False,
           'update_T': True, 
           'update_q': True, 
           'maxstep': np.array([2000, 3000]), 
           'nrep': 1,
           'q_fun': 'plinear', 
           'ext_overlap': True,
           'ext_overlap_steps': 500}

net3.reset()
net3.T_init = 0.005
net3.T_decay_rate = 0.0
net3.q_rate = 0.04
#net3.q_rate = 0.01        # To avoid parsing failure, q_rate should be set to a small number.

input_list = ['A/R[0,1]', 'C/R[1,2]']
net3.reset()
sim3 = sim(net3, params3)
input_vals = [1.0, 1.0]       # implement as the weighted average of external input
sim3.input_list = input_list
sim3.input_vals = input_vals

sim3.simulate()
rep_num = 1
sim3.plot_act_trace(rep_num)
sim3.read_state(rep_num, 1)
sim3.read_grid_point(rep_num, 1)
sim3.read_state(rep_num, 2)
sim3.read_grid_point(rep_num, 2)
sim3.rt
sim3.plot_trace('dist', rep_num)
Image in a Jupyter notebook
R[0,1,2] R[0,1] R[1,2] S[1] 0.766261 0.039014 0.043890 S[2] 0.683266 0.041443 0.033571 A 0.055800 0.989534 0.050274 B 0.049275 0.067513 0.707973 C 0.052004 0.056459 0.734532 ['S[1]/R[0,1,2]', 'A/R[0,1]', 'C/R[1,2]'] R[0,1,2] R[0,1] R[1,2] S[1] 0.032740 0.013211 0.013763 S[2] 0.991915 0.012883 0.005620 A 0.020981 0.992261 0.019592 B 0.012590 0.020289 0.015859 C 0.023807 0.009301 0.993357 ['S[2]/R[0,1,2]', 'A/R[0,1]', 'C/R[1,2]']
Image in a Jupyter notebook

##Example 4: Local Coherence