L4: Models in Cognitive Psychology 41

LOs: explain what a model is and list potential goals of modelling efforts (abstraction, simplification, prediction, explanation explicit vs implicit modelling, theory testing); Explain and apply Marr's three levels of analysis (computation (problem), algorithm (rules), implementation (physical), top-down vs bottom up approach)

model

a simplified or idealised representation of a more complex thing

statistical models

a mathematical relationship between variables, that holds under specific assumptions

theoretical cognitive models

description of the relationship between different mental processes, that makes assumptions about the nature of these processes

difference in aims of statistical vs theoretical models

theoretical models try to explain something and provide further predictions from these descriptions but stat models just describe the relationship

cognitive box and arrow models

models that describe the relationship between different mental processes, under the assumption that the mind operates like a multi-staged information processing machine

Broadbent (1958) model- what did he suggest

box and arrow model of attention

• suggested multiple stages

• sensory inputs into retina

• that input goes through a selective filter

• if passes, can go to high level processing

• eventually into working memory

• posited that if an input is attended to, it will go through all of these stages- box arrow box arrow

• if unattended, will go through first box but no further- just be processed in the sensory stage

• classic example of a box and arrow model

Broadbent’s model of attention

inputs into retina → sensory buffer store (if attended, continues) → selective filter → higher level processing → working memory

sensory buffer store

identifies physical characteristics

unlimited capacity

first stage of Broadbent (1958) attention model

selective filter

further processing based on goals

higher level processing

extracts meaning from the input

evolution of box and arrow models

• mind has stages, info goes through stages

• started off simple, but can gradually become very complex

• e..g ppl added to broadbent’s model bc found it did not fulfil purpose

• e.g. Wolfe (2021) visual guidance search model

• choosing most important, essential, central components

how can we test cognitive models

manipulating the input and observing the output can offer glimpse into machination of mind, allowing us to test our models

change input and register output

types of theoretical models

1. informal (box and arrow)

2. formal (computational)

what type of model is box and arrow

informal theoretical

what type of model is computational

formal theoretical

formal cognitive models

a mathematical description of the relationship between mental processes, usually expressed through computer code

• formal cognitive tries to create formula to tell exact mathematical relationship between input and output- computer code simulation of mental processes

why propose should make formal cog models

some suggest box and arrow not fit for purpose

model distinctions

1. theoretical

• informal (box and arrow)

• formal (computational)

2. statistical

George Box quote (1976)

all models are wrong, but some are useful

Alfred Korzybski quote (1931)

the map is not the territory

what do all models do?

make simplifications and abstractions

when we create a model, what is acknowledged?

not going to describe all the info we r describing, only the parts we think are critical for what we are trying to represent

therefore make models are simplifications and abstractions

simplification

make something simpler

abstraction

generating general rules and concepts from specific information

what must models in science produce

some predictions

what can prediction be

directional or numerical

Popper’s key philosophy

• non scientific theories explain after the fact but cannot provide falsifiable predictions

• must be falsifiable to be scientific

how accurate is a model that provides numerical predictions?

can be more or less accurate than a directional one

how do we use informal models to predict and explain? stages plus example

framework → theory → model → hypothesis → data

(arrows looping back other way too)

e.g.:

cognitive psych → early selection theory → broadbent’s filter model → irrelevent stimuli that contain target defining feature will be automatically detected → new gorilla experiment detection rates, t tests

framework

the conceptual system that defines terms and provides context

e.g. cog psych

theory

a scientific proposition that provides relations between phenomena

e.g. early selection theory

model

a schematic representation of a theory, more limited in its scope

e.g. broadbent’s filter model

hypothesis

a narrow testable statement

e.g. irrelevant stimuli that contain target defining feature will be automatically detected

data

collected observations, often as part of an experiment

e.g. new gorilla experiment, detection rates, t tests

what do statistical models do

predict and do not try to explain

what do theoretical models do

predict and try to explain

explanation without exact prediction

• models of schizophrenia can indicate causes but cannot yet predict individual cases

• model may be able to predict group diffs, not individual cases

prediction without explanation

some models can predict whether an individual will develop Alzheimer’s, even though we are not close to understanding the factors that explain Alzheimer’s

informal cognitive models

a verbal description of the relationship between different cognitive procedure

• where often some assumptions are implicit

• often provides only directional predictions

formal/computational models

a mathematical description of the relationship between different cognitive procedure, often instantiated via computer program/simulation

• assumptions are explicit

• often provides numerical predictions

informal vs formal models

• verbal vs mathematical

• implicit vs explicit

• directional vs numerical

how do we use formal models to predict and explain?

framework → theory → specification → implementation → hypothesis → data

(with loops arrows up)

what are parts of how formal models explain that are not part of how informal models explain?

specification and implementation

specification

a formal description of the relations described by a theory

the formal model, comprised of symbolic representations

implementation

a specific instantiation of a specification

a computer program, able to simulate and predict numerical outputs from input

strengths of formal models

1. more accurate predictions

2. counter intuitive predictions

3. benefits of explicit assumptions

strength of formal models: more accurate predictions

• numerical simulation means can see if model provides unreasonable predictions so easier to reject bad models

• can help select which experiments to perform

• can provide more subtle form of hypothesis testing, see how close a model is to predicting an actual result

strength of formal models: counter-intuitive predictions

• model can more clearly describe which predictions follow from a model

• with informal models, it is hard to notice when they make counter intuitive predictions; formal models clearly produce such predictions

• idea of implicit vs explicit assumptions

• reduces hindsight bias

• reveal when intuitions do not match up with theory

coherent motion: are dots going more left or more right? use of modelling + findings

• counterintuitive model where formal helps

• difficult task

• noise = dots moving up and down, neither left nor right

• idea is some kind of evidence accumulation process

• where we are sampling visual field until get enough evidence to make right decision

• evidence accumulation can be measured using decision time

• how long does it take for us to make a decision

• reaction time measure

• question of what happens if have more noise

• intuition wld be that decision time wld be slower bc do not know

• their computational model suggested with more noise, wld get to boundary of leftward decision more quickly. going to have more errors, but correct responses gonna be faster

• so more noise = shorter response times

• this is clearly counterinuitive

• this model cld reveal that if our model is correct, adding more noise wld shorten response time

• and this is what wad found

what is the best kind of prediction? Popper

counterinuitive

uinexpected and more risky so even more impressive

strength of formal models- benefits of explicit assumptions

by making assumptions explicit, we can reveal unanswered questions, flaws in our reasoning, contradictory or unreasonable assumptions

“what i cannot create, i do not understand” - feynman

when assumptions are implicit, sometimes do not notice that they are incorrect or unreasonable

cons of formal models

• require substantial expertise

• transparency: transparent mostly for experts

• comparison: best compared against other computational models

• prediction: sometimes numerical predictions are premature

• progress: changing the model is costly time wise which can limit progress

• theory 1: a computational model may give the semblance of scientific validity (neural network models)

• theory 2: making a model simulate a cognitive task does not neccessarily teach us more about cognition

hype timeline

innovation trigger, then rapid spike up to a peal of inflated expectations, then rapid dip into trough of disillusionment, then steady climb of the slope of enlightenment, then plateau of productivity

David Marr

• 1945-1980

• british mathemetician and neuroscientist

• worked on visual processing

• question: how can we understand information processing systems like the brain?

• biggest legacy was that we can understand and model a system at a number of levels: computation, algorithm, implementation

problem with understanding the brain (Marr)

we can only ever hope to sample from a tiny fraction of its activity, in a tiny fraction of a bit of brain

how did Marr propose we make sense of brain data

break any brain problem into three levels

Marr’s levels of analysis

1. computation

2. algorithm

3. implementation

computation

the problem being solved

algorithm

the steps/rules to solve it

implementation

the actual machinery

what type of approach would Marr prefer?

top-down because then not bogged down by infinite amount of data we find (elephant in the dark)

how should we consider Marr’s levels?

consider all three at same time, up and down, down and up

botttom-up approach: neuroscience.. and AI ( Kriegeskorte & Douglas, 2018)

• implementation: the machinery of neural circuits

→

• rules: what representations and algorithms can we generate, given specific neural circuits?
  

→

• problem: what problems are solved by these algorithms?

exp