11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256 | def task_switching(
name="Task Switching",
resolution=50,
priming_default=0.3,
temperature=0.2,
minimum_task_control=0.15,
constant=1.5,
):
"""
Task Switchng
Args:
name: name of the experiment
resolution: number of allowed values for stimulus
priming_default: default for task priming
temperature: temperature for softmax when computing performance of current task
constant: constant for task activation
minimum_task_control: minimum task control
"""
params = dict(
name=name,
resolution=resolution,
priming_default=priming_default,
temperature=temperature,
minimum_task_control=minimum_task_control,
constant=constant,
)
current_task_strength = IV(
name="cur_task_strength",
allowed_values=np.linspace(1 / resolution, 1, resolution), #
value_range=(0, 1),
units="intensity",
variable_label="Strength of Current Task",
type=ValueType.REAL,
)
alt_task_strength = IV(
name="alt_task_strength",
allowed_values=np.linspace(1 / resolution, 1, resolution),
value_range=(0, 1),
units="intensity",
variable_label="Strength of Alternative Task",
type=ValueType.REAL,
)
is_switch = IV(
name="is_switch",
allowed_values=[0, 1],
value_range=(0, 1),
units="indicator",
variable_label="Is Switch",
type=ValueType.PROBABILITY_SAMPLE,
)
cur_task_performance = DV(
name="cur_task_performance",
value_range=(0, 1),
units="performance",
variable_label="Accuray of Current Task",
type=ValueType.PROBABILITY,
)
variables = VariableCollection(
independent_variables=[current_task_strength, alt_task_strength, is_switch],
dependent_variables=[cur_task_performance],
)
def inverse(x, A, B):
y = 1 / (A * x + B)
return y
def run(
conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
added_noise: float = 0.01,
random_state: Optional[int] = None,
):
rng = np.random.default_rng(random_state)
X = np.array(conditions)
Y = np.zeros((X.shape[0], 1))
for idx, x in enumerate(X):
cur_task_strength = x[0]
alt_task_strength = x[1]
is_switch = x[2]
# determine current task control
input_ratio = (cur_task_strength + priming_default * (1 - is_switch)) / (
alt_task_strength + priming_default * (is_switch)
)
cur_task_control = inverse(input_ratio, 2.61541389, 0.7042097)
cur_task_control = np.max([cur_task_control, minimum_task_control])
cur_task_input = (
cur_task_strength
+ priming_default * (1 - is_switch)
+ cur_task_control
+ rng.random.normal(0, added_noise)
)
alt_task_input = (
alt_task_strength
+ priming_default * (is_switch)
+ rng.random.normal(0, added_noise)
)
cur_task_activation = 1 - np.exp(-constant * cur_task_input)
alt_task_activation = 1 - np.exp(-constant * alt_task_input)
cur_task_performance = np.exp(cur_task_activation * 1 / temperature) / (
np.exp(cur_task_activation * 1 / temperature)
+ np.exp(alt_task_activation * 1 / temperature)
)
Y[idx] = cur_task_performance
return Y
ground_truth = partial(run, added_noise=0.0)
def domain():
s1_values = variables.independent_variables[0].allowed_values
s2_values = variables.independent_variables[1].allowed_values
X = np.array(np.meshgrid(s1_values, s2_values)).T.reshape(-1, 2)
# remove all combinations where s1 > s2
X = X[X[:, 0] <= X[:, 1]]
return X
def plotter(
model=None,
):
X = np.zeros((4, 3))
# Values taken from Table 4 in Yeung & Monsell (2003)
# word switch
X[0, 0] = 0.5 # current task strength
X[0, 1] = 0.1 # alternative task strength
# X[0, 2] = 0.2 # current task control
X[0, 2] = 1 # is switch
# word repetition
X[1, 0] = 0.5 # current task strength
X[1, 1] = 0.1 # alternative task strength
# X[1, 2] = 0.15 # current task control
X[1, 2] = 0 # is switch
# color switch
X[2, 0] = 0.1 # current task strength
X[2, 1] = 0.5 # alternative task strength
# X[2, 2] = 0.97 # current task control
X[2, 2] = 1 # is switch
# color repetition
X[3, 0] = 0.1 # current task strength
X[3, 1] = 0.5 # alternative task strength
# X[3, 2] = 0.38 # current task control
X[3, 2] = 0 # is switch
y = ground_truth(X, priming_constant=0.3, std=0)
word_switch_performance = y[0, 0]
word_repetition_performance = y[1, 0]
color_switch_performance = y[2, 0]
color_repetition_performance = y[3, 0]
x_data = [1, 2]
word_performance = (
1 - np.array([word_repetition_performance, word_switch_performance])
) * 100
color_performance = (
1 - np.array([color_repetition_performance, color_switch_performance])
) * 100
if model is not None:
y_pred = model.predict(X)
word_switch_performance_pred = y_pred[0][0]
word_repetition_performance_pred = y_pred[1][0]
color_switch_performance_pred = y_pred[2][0]
color_repetition_performance_pred = y_pred[3][0]
word_performance_recovered = (
1
- np.array(
[word_repetition_performance_pred, word_switch_performance_pred]
)
) * 100
color_performance_recovered = (
1
- np.array(
[color_repetition_performance_pred, color_switch_performance_pred]
)
) * 100
legend = (
"Word Task (Original)",
"Color Task (Original)",
"Word Task (Recovered)",
"Color Task (Recovered)",
)
# plot
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
colors = mcolors.TABLEAU_COLORS
col_keys = list(colors.keys())
plt.plot(x_data, word_performance, label=legend[0], c=colors[col_keys[0]])
plt.plot(x_data, color_performance, label=legend[1], c=colors[col_keys[1]])
if model is not None:
plt.plot(
x_data,
word_performance_recovered,
"--",
label=legend[2],
c=colors[col_keys[0]],
)
plt.plot(
x_data,
color_performance_recovered,
"--",
label=legend[3],
c=colors[col_keys[1]],
)
plt.xlim([0.5, 2.5])
plt.ylim([0, 50])
plt.ylabel("Error Rate (%)", fontsize="large")
plt.legend(loc=2, fontsize="large")
plt.title("Task Switching", fontsize="large")
plt.xticks(x_data, ["Repetition", "Switch"], rotation="horizontal")
plt.show()
collection = SyntheticExperimentCollection(
name=name,
description=task_switching.__doc__,
variables=variables,
run=run,
ground_truth=ground_truth,
domain=domain,
plotter=plotter,
params=params,
factory_function=task_switching,
)
return collection
|