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# ACT-R tutorial unit8 categorization experiment.
# This task sequentially presents the model with
# features which the model must classify as
# being small, medium, or large given a numeric
# description, and then after those features have
# been encoded it must make a choice as to which
# category of items it belongs based on the
# examples that it has pre-encoded in declarative
# memory. It is an abstraction and simplification
# of a face categorizing task:
#
# Nosofsky, R. M. (1991). Tests of an exemplar model for relating
# perceptual classification and recognition memory. Journal of Experimental
# Psychology: Human Perception and Performance. 17, 3-27.
# Import the actr module for tutorial tasks, the math
# module for sqrt, pi, and exp, and the numbers module
# for the Number class.
import actr
import math
import numbers
# These are the feature sets for the categories (based on
# the general values).
cat1 = [["small","large","medium","small"],
["medium","small","large","medium"],
["small","medium","medium","medium"],
["small","medium","large","medium"],
["small","medium","large","large"]]
cat2 = [["large","small","small","small"],
["medium","medium","small","large"],
["large","small","large","small"],
["large","small","large","large"],
["large","small","small","large"]]
# This is the data indicating the category 1 choice proportions
# for the set of stims below (represented by their underlying
# normalized numeric values)
cat_data = [0.975, 0.85, 0.987, 1.0, 0.963, 0.075, 0.138, 0.087, 0.05, 0.025, 0.937, 0.544, 0.988, 0.087]
stims = [[-1.025, 0.493, 0.048, -0.666],
[-0.172, -0.557, 0.337, 0.163],
[-0.98, 0.275, -0.005, -0.067],
[-0.951, 0.259, 0.399, 0.093],
[-0.96, 0.198, 0.38, 0.527],
[0.665, -0.441, -0.508, -0.396],
[-0.059, 0.243, -0.602, 0.624],
[0.586, -0.511, 0.381, -0.507],
[0.823, -0.539, 0.332, 0.633],
[0.823, -0.504, -0.487, 0.776],
[-1.114, -0.52, 0.636, -0.028],
[-0.154, -0.562, -0.043, 0.057],
[-0.856, 0.197, 0.241, 0.007],
[0.704, -0.287, -0.164, 0.178]]
# Global values for the similarity distribution, the mapping of
# sizes to an anchor point, the default slot names, and the
# offset to use for the presented stimulus values.
sigma2 = .15
size_mappings = {"small":-.9, "medium":0, "large":.9}
slots = ["eh", "es", "nl", "mh"]
offset = 0
# Functions for computing the similarity values using a
# normal distribution around the anchor point for a value
# and then scaling them from -1 to 0.
def scale_sim(x, max):
return( (x / max) - 1.0)
def normal(x,sigma2,m):
return ( ( 1 / math.sqrt(2 * math.pi * sigma2)) * math.exp(- (((x - m) * (x - m)) / (2 * sigma2))))
max_norm = normal(0,sigma2,0)
def size_similarities(a, b):
if isinstance(b,numbers.Number) and a.lower() in size_mappings:
return(scale_sim(normal((b - offset),sigma2,size_mappings[a.lower()]),max_norm))
else:
return False
actr.add_command("size-similarities", size_similarities,"Categorize model's similarity hook function.")
# categorize-stimulus resets the model and then presents the four
# feature values provided (which should be numbers from -2 to 2) to
# the model with the default slot names for features and then
# creates a goal chunk with state categorize for the model to
# determine a category for the features it encoded. If the
# model provides a category of 1 or 2 (by setting the category slot
# of the chunk in the imaginal buffer) then that value is
# returned, otherwise it returns nil.
def stimulus(a,b,c,d):
global offset,slots
offset = 0
slots = ["eh", "es", "nl", "mh"]
result,response = trial(a,b,c,d)
if response:
return (result)
else:
return (False)
# categorize-attribute takes two values which represent the
# name and value for an attribute in the task. it presents
# the attribute to the model by setting slots of the chunk in
# the goal buffer and then running the model. The state slot
# is set to add-attribute, the name slot is set to the name
# provided, and the value slot is set to the value provided.
# The model should encode that value into a general description
# (small, medium, or large) and store that into a slot of the
# chunk in the imaginal buffer with the provided name.
# It does not reset the model.
def attribute(name,value):
actr.schedule_set_buffer_chunk("goal",["state","add-attribute","name",name,"value", (value + offset)], 0)
actr.run(20)
# categorize-experiment takes one required value which
# is how many times to run the whole experiment (one presentation
# of each of the 14 testing stims). It has one optional parameter
# which indicates an offset to add to the values that are presented
# if it is provided, and accepts 4 additional parameters which
# specify the names of the attributes to present to the model (the
# default names will be used if none are provided). It runs the
# experiments, determines the proportion of category choices for
# each item, reports the fit to the experimental data, and prints
# out the proportion of choices for category 1.
def experiment(n,new_offset=0,s1="eh",s2="es",s3="nl",s4="mh"):
global offset,slots
if all(list(map(lambda x: isinstance(x,str),[s1,s2,s3,s4]))):
s1 = s1.lower()
s2 = s2.lower()
s3 = s3.lower()
s4 = s4.lower()
if s1 in [s2,s3,s4] or s2 in [s1,s3,s4] or s3 in [s1,s2,s4] or s4 in [s1, s2, s3]:
actr.print_warning("Duplicate slot names provided. Using default slots.")
slots = ["eh", "es", "nl", "mh"]
elif 'category' in [s1,s2,s3,s4]:
actr.print_warning("Slot named category cannot be used. Using default slots.")
slots = ["eh", "es", "nl", "mh"]
else:
slots=[s1,s2,s3,s4]
else:
actr.print_warning("Not all slot names provided are strings. Using default slots.")
slots = ["eh", "es", "nl", "mh"]
if isinstance(new_offset,numbers.Number):
offset = new_offset
else:
offset = 0
trials = len(cat_data)
results = [0] * trials
counts = [0] * trials
for i in range(n):
answers,responses = do_experiment()
results = list(map(lambda x,y: x + y,results,answers))
counts = list(map(lambda x,y: x + y,counts,responses))
results=list(map(lambda x: x/n,results))
offset = 0
actr.correlation(results,cat_data)
actr.mean_deviation(results,cat_data)
print("P(C=1)")
print(" ",end="")
for i in range(trials):
print("(%4d) " % counts[i],end="")
print()
print("data ",end="")
for i in range(trials):
print("%7.3f" % cat_data[i],end="")
print()
print("model ",end="")
for i in range(trials):
print("%7.3f" % results[i],end="")
print()
def do_experiment():
category_one = []
answered = []
for s in stims:
category,response = trial(*s)
if category == 1:
category_one.append(1)
else:
category_one.append(0)
if response:
answered.append(1)
else:
answered.append(0)
return((category_one,answered))
def trial(*features):
actr.reset()
for slot,value in actr.permute_list(list(zip(slots,features))):
attribute(slot,value)
actr.schedule_set_buffer_chunk("goal",["state","categorize"], 0)
actr.run(20)
answer = actr.chunk_slot_value(actr.buffer_read("imaginal"),"category")
if isinstance(answer,numbers.Number):
if answer == 1 or answer == 2:
return((answer,True))
else:
actr.model_output("Model responded with invalid category.")
return((0,False))
else:
actr.model_output("Model did not respond or provided a non-numeric category.")
return((0,False))
# create-example-memories is called in the model
# definition to add chunks for the training examples
# to the model's declarative memory. The chunks are
# created with the appropriate slots for the features
# based on the values provided by the modeler to
# run the experiment or the default slots if not
# running the experiment or alternate names were
# not provided.
def create_example_memories():
for s in slots:
actr.extend_possible_slots(s,False)
actr.define_chunks([s,"isa","chunk"])
for c in cat1:
chunk = ["isa","example","category",1]
for slot,value in list(zip(slots,c)):
chunk.append(slot)
chunk.append(value)
actr.add_dm(chunk)
for c in cat2:
chunk = ["isa","example","category",2]
for slot,value in list(zip(slots,c)):
chunk.append(slot)
chunk.append(value)
actr.add_dm(chunk)
actr.add_command("create-example-memories",create_example_memories,"Categorize task function to add the initial example chunks to simulate the training process.")
# Need to load the model after the "create-example-memories" command
# has been added since that command is called during the model
# creation.
actr.load_act_r_model("ACT-R:tutorial;unit8;categorize-model.lisp")