QUANTITATIVE MODELS OF MEMORY

• The value of explicit models– Precision of thinking– Explanatory power– Interval- or ratio-scale predictions– The macho factor

• Mathematical models of memory– Assumptions about representation

• What are the stimulus “attributes”?• Are traces separate or integrated?• Nature of item, order, associative info• Local or distributed representation

– Assumptions about process• How is context utilized?• Familiarity match or search?• How does the cue “contact” memory?

• Implementation of models– Encoding and retrieval mechanisms

modeled as equations & flow charts– Model parameters (factors in the

equations) can be fixed, or data-based– “solving” equations through

simulations can produce predictions

• Evaluation of models– Elegance: assumptions should be

psychologically plausible and direct– Goodness-of-Fit: the match between

predicted and observed data– Efficiency: the model predicting the

most phenomena with the fewest parameters wins

– Distinctiveness: No other models would make that prediction

A functional law, though an equation, is not a model!• Power law of practice• Hick’s law of uncertainty and RT

CAPSULE HISTORY OF MEMORY MODELS

• 1955-1965– Mathematical Learning Theory models

specific tasks (e.g., paired-associate learning)• Estes’ (58) Stimulus Sampling Theory

• 1965-1975– Comprehensive models emerge

• The Modal Model (Atkinson & Shiffrin, 68); short-term and long-term episodic

• HAM (Anderson & Bower, 72); list learning and sentence memory

• 1975-1990– “Global” models appear

• Wider range of tasks and processes• All list items and associations are

relevant at retrieval– Distributed-network models of

association developed• The PDP revolution

Search of Associative Memory(Raaihmakers & Shiffrin, 1981)

• Designed for recall and recognition of word lists and associations

• Representation and encoding– Episodic study increases memory trace

strength (image) of association between the studied item and..• the “list context” (a)

(encoding specificity)• Other items in the rehearsal set (b)

(relational processing)• Itself as a potential cue (c)

(item distinctiveness)

– Parameters (a,b,c) determine mean rate of increase in strength for item Wi with

rehearsal time t among n other items

S(C,Wi) = ati/n S(WiWh) = btih/n

S(WiWi) = cti/n

SAM (Cont’d)• Retrieval: recognition task

– Given item Wi as cue, calculate global

familiarity

– For each item in memory Wk:

F(C,Wk) = S(C,Wk) x

S(Wi,Wk)

– Sum over all list items (k=1 to N)Example of associative strengths forImages in memory (studied items)cattle answer radio form

context 0.50 0.30 0.80 0.40cattle 0.30 0.30 0.40 0.10answer 0.30 0.40 0.10 0.10radio 0.40 0.20 0.70 0.30form 0.10 0.10 0.20 0.40metal 0.10 0.05 0.10 0.10pencil 0.20 0.10 0.30 0.10

familiarity for each item given a word cuecue cattle answer radio form sumContext 0.50 0.30 0.80 0.40&cattle 0.15 0.09 0.32 0.12 0.68&answer 0.15 0.12 0.08 0.04 0.39&radio 0.20 0.06 0.56 0.12 0.94&form 0.05 0.03 0.16 0.16 0.40&metal 0.05 0.02 0.08 0.04 0.19&pencil 0.10 0.03 0.24 0.04 0.41

• Recognition in SAM (cont’d)– If summed familiarity exceeds criterion,

item is recognized as old

• Associative recognition– AB pairs strengthen A,B images as

above– At test, pair familiarity obtained by:

F(A) x F(B)

• Recall– Context serves as cue to sample item(s):

Ps(Wi|C) = S(C,Wi)_

Σ[S(C,Wk)]

then, if strength allows “recovery”, item can serve as part of the cue:

Ps(Wi|C,Wh) = _S(C,Wi) x

S(Wh,Wi)__

Σ[S(C,Wk) x

S(Wh,Wk)]

SAM and Performance

• Effects of encoding parameters on performance:– Context (a)

• improves recovery, no effect on sampling in recall

• no effect on recognition. Why?– Interitem associations (b):

• increases familiarity of targets (how?) but not distractors (why not?), so improves recognition

• improves recovery, and sampling selectivity, so improves recall

– Self-strength (c):• Item familiarity increased, no effect on

distractors, so recognition improves• Increases “self-sampling” and so recall

(may be?) impaired (cf. part-list cues)

SAM and Performance (cont’d)

• Effects of “classic” variables:– Study time:

• Associative and item strengths increased, so recall and recognition improve

– Retention interval:• Memory images are permanent, so all

forgetting is retrieval failure through context changes

– Serial position effects:• Smaller rehearsal set for first items, so

stronger strengths (see encoding) and primacy effect

• Recency?– Word Frequency:

• HF words with higher pre-existing associations (d) and easier list associations (b):

b c d Hits FA's d' RecallHF 0.2 0.15 0.075 0.921 0.044 3.12 0.48LF 0.1 0.15 0.035 0.954 0.012 3.93 0.035

Troubles for SAM

• The “mirror effect”– In mixed-frequency lists, LF words show

both higher hits and lower FA’s– Why is this a problem?– How does REM solve the problem?

• The “list strength” effect– In mixed-study-time lists, recall of short-

study items should be worse compared to pure-study-time lists.

– Why should this happen in SAM?– Well, it doesn’t– How does REM solve the problem?

• In Summary:– Models are powerful, but not unfalsifiable– Mix of plausible, less plausible

assumptions about representation & process

– Sometimes “transparent,” sometimes opaque

– Remains relatively unconnected with broader field of memory and cognition