A Bidirectional Associative Memory Explanation of Posttraumatic Stress

Disorder

Tryon, W. W. (1999) Clinical Psychology Review, 19, 789-818.

Introduction• Foa and Kozak (1986), Foa, Steketee, and Rothbaum

(1989), and Jones and Barlow (1990) have reviewed biological, psychodynamic, cognitive/information processing, and behavioral models of posttraumatic stress disorder (PTSD) and found all of them to be deficient in important ways.

• These authors have also provided a form of network theory to advance our understanding of PTSD.

• The BAM network model presented here meets ALL explanatory requirements.

• Full text is at eRes under my name and PSGA8022

• Network theory differs from traditional cognitive theory and its emphasis on a central processing unit (CPU) in that all elements of a fear network theoretically act in reciprocal relationship to each other and is not passively acted upon by a CPU.

• Networks allow one to diagram complex relationships among elements of a fear structure whereas standard cognitive theories require a list of rules regulating the behavior of the CPU to achieve this functionality.

• Traditional cognitive theories cannot account for the relationships among long- and short-term habituation, fear ideation, and treatment outcome (cf. Foz & Kozak, 1986).

• Network theory models complex cognitive and emotional processes.

• More details when you take Cognition & Affect in Fall 2003.

Informal Network Theories• Lang (1977) hypothesized that emotional images entail

propositional constructs about their meaning• He suggested that this visual-semantic network can be

investigated empirically using psychophysiological recording techniques.

• Lang (1979, 1985) demonstrated that fear can be understood as a structure among cognitive propositions based on a memory network that contains information– (a) about external stimulus propositions, – (b) about verbal and nonverbal response propositions

and mediating visceral and somatic events, and – (c) about propositions regarding the meaning of these

stimuli set in context.

Informal Network Theories• The excitatory and inhibitory connections among these

logical propositions constitute the theoretical network that mediates psychophysiological responses to script driven imagery and to escape and avoidance behavior in naturalistic settings.

• This work is important because it introduces the concept of an integrated memory network of stored information.

• Foa and Kozak (1986) extended this line of reasoning to include Rachman’s (1980) concept of “emotional processing” which entails the gradual reduction of emotional responding over time.

• The two key elements are: – (a) activation of fear memory through the presentation

of fear-relevant information, and – (b) presentation of fear-incompatible information.

Explanatory RequirementsJones and Barlow (1990)

• First, the theory must explain the symptom constellation that characterizes PTSD such as the following DSM-IV (APA, 1994) PTSD inclusion criteria: – (a) persistent re-experiencing the traumatic event

through memory, – (b) persistent avoidance of stimuli associated with the

trauma, – (c) general emotional numbing, and – (d) persistent symptoms of arousal.

• Second, the theory must also account for differential symptom severity by explaining why one person develops more severe symptoms than another.

Explanatory RequirementsJones and Barlow (1990)

• Third, Jones and Barlow especially emphasized that a comprehensive PTSD theory must explain why trauma is re-experienced through memory.

• Fourth, a comprehensive theory must explain why some people do not experience PTSD after trauma while others do. – This is actually a variation on the second point

that insists on a good account of individual differences.

Explanatory RequirementsBrewin, Dalgleish, and Joseph (1996)

• 1) The theory must account for the diagnostic characteristics of PTSD as described by DSM-IV.

• 2) The theory must explain individual differences in symptom severity. (Same as Jones & Barlow)

• 3) The theory must stipulate whether PTSD symptoms signify the presence of an abnormal or a normal process.– If an abnormal process is indicated, then the theory

must explain the basis of the abnormality; – In what way do the processes underlying PTSD differ

from the norm. • 4) A comprehensive theory must explain why patients

diagnosed with PTSD are frequently comorbid for depression, generalized anxiety, substance abuse, andsomatization disorder.

• 5) A comprehensive theory must make novel predictions in addition to providing a more comprehensive explanation than other theories.

Bidirectional Associative Memory Model• The BAM was selected as a PTSD model in part

because– It is a general associative mechanism designed

to form and recall memories. – It belongs to a class of CNN models known as

attractor neural networks – It is a relatively simple system and is therefore

parsimonious. – It uses only matrix algebra and therefore can be

simulated using readily available software

Bidirectional Associative Memory Model• These networks are especially interesting because

their behavior can be visually understood in terms of a topographical map. – From one point of view, these networks are

governed by hill climbing and are constrained to only move in directions that are “higher” than their present state.

– From another point of view, attractor networks are governed by gradient descent and therefore are constrained to only move In directions that are “lower” than their present state like water running down hill from.

– The latter perspective is more popular and characterizes the BAM.

Figure 1. An outer product matrix forming synaptic connections in the Bidirectional Associative Memory model.

Vector B

1 -3 -5 7

2 2 -6 -10 14

Vector A -4 -4 12 20 -28

6 6 -18 -30 42

-8 -8 24 40 -56

Step 1: Encode Memories:Three A-B Memory Pairs

A1

1 0 1 0 1 0 1 0 1 0 B1

1 1 1 1 0 0 0 0

A2

1 1 0 0 1 1 0 0 1 1 B2

1 1 1 0 0 0 1 1

A3

1 1 1 1 0 0 0 0 1 1 B3

1 0 1 0 1 0 1 0

Step 2: Convert 0,1 to –1, +1To Balance Around Zero

A1

1 -1 1 -1 1 -1 1 -1 1 -1 B1

1 1 1 1 -1 -1 -1 -1

A2

1 1 -1 -1 1 1 -1 -1 1 1 B2

1 1 1 -1 -1 -1 1 1

A3

1 1 1 1 -1 -1 -1 -1 1 1 B3

1 -1 1 -1 1 -1 1 -1

Step 3:Create Memories Using Equation 1

M = XT Y

Where T means to Transpose Row to Column

Memory For First Pair

Y1X1T 1 1 1 1 -1 -1 -1 -1------ ------ ------ ------ ------ ------ ------ ------ ------ ------

1 1 1 1 1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 11 1 1 1 1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 11 1 1 1 1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 11 1 1 1 1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 11 1 1 1 1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 1

Memory For Second Pair

Y2X2T 1 1 1 -1 -1 -1 1 1------ ------ ------ ------ ------ ------ ------ ------ ------ ------

1 1 1 1 -1 -1 -1 1 11 1 1 1 -1 -1 -1 1 1-1 -1 -1 -1 1 1 1 -1 -1-1 -1 -1 -1 1 1 1 -1 -11 1 1 1 -1 -1 -1 1 11 1 1 1 -1 -1 -1 1 1-1 -1 -1 -1 1 1 1 -1 -1-1 -1 -1 -1 1 1 1 -1 -11 1 1 1 -1 -1 -1 1 11 1 1 1 -1 -1 -1 1 1

Memory For Third Pair Y3

X3T 1 -1 1 -1 1 -1 1 -1------ ------ ------ ------ ------ ------ ------ ------ ------ ------

1 1 -1 1 -1 1 -1 1 -11 1 -1 1 -1 1 -1 1 -11 1 -1 1 -1 1 -1 1 -11 1 -1 1 -1 1 -1 1 -1-1 -1 1 -1 1 -1 1 -1 1-1 -1 1 -1 1 -1 1 -1 1-1 -1 1 -1 1 -1 1 -1 1-1 -1 1 -1 1 -1 1 -1 11 1 -1 1 -1 1 -1 1 -11 1 -1 1 -1 1 -1 1 -1

Step 4: Add Matrices, Element by Element

J------ ------ ------ ------ ------ ------ ------ ------ ------ ------

3 1 3 -1 -1 -3 1 -1 1 -1 1 -3 1 -1 3 1 1 -1 1 1 1 -1 -1 -3 -1 -3 -1 -1 3 1 1 -1 1 3 1 1 -3 -1 -1 1

I -1 1 -1 -1 -1 1 1 3 -1 1 -1 3 -1 1 -3 -1 -3 -1 -3 1 1 3 -1 1 3 1 3 -1 -1 -3 1 -1 1 -1 1 -3 1 -1 3 1

Interpretation• This memory matrix can also be described as a

"correlation matrix" because it associates all A-B pairs.

• If the row and column elements are thought of as neurons, then it is appropriate to think of the matrix elements as synaptic weights connecting these two sets of neurons

• Positive values represent excitation and • Negative values represent inhibition.

Recall• Calculate Response B from Stimulus A using matrix

equation B = A M.• Apply Threshold Function

• If B > 0 then B = 1• If B <= 0 then B = 0

• If correct answer is not obtained, then reverse direction and reconstruct the Stimulus from the Response using matrix equation A = B MT where T means to Transpose columns and rows.

• Reapply the Threshold function.• Calculate B as before using matrix equation B = A M.• Either the correct answer is returned or the “nearest”

correct answer keeps being returned.

Recall Generalization

• Presenting a stimulus other than one of the three used to create associative pairs will return the “closest” response.

• The actual response depends upon the stimulus and memory matrix properties.

• The bidirectional associative memory recall process explains many of the memory distortions associated with eyewitnesses.

Dialectical Memory• Dialectical reasoning involves opposites.• It is what gives Freudian Psychodynamics its life.

– Connectionism unites Behaviorism and Psychoanalysis.• Thoughts automatically suggest their opposite. • For example, success suggests failure and failure suggests

success, war suggests peace and vice versa.• Rychlak (1976, 1981, 1994) emphasized the centrality of

dialectical reasoning in human cognition. • The BAM suggests that the dialectical nature of thought is

also a memory property since the BAM automatically and simultaneously stores the complement of a memory along with the memory and gives bidirectional access to them both.

• For example, the complement of A = 101010 is Ac

= 010101. Notice that the 1’s and 0’s have been exchanged.

Dialectical Memory• Storing memory for the single A1-B1 association enables

the following four associations: – A1 to retrieve B1, – B1 to retrieve A1, – A1c to retrieve B1c, and – B1c to retrieve A1c.

• These four associations form two reversible dialectical pairs.

• Reversibility refers to the A-B and B-A symmetry. • Dialectical pairs refer to the fact that encoding A enables

Ac to be an effective stimulus and B enables Bc to be an effective stimulus.

• This dialectical property is inherent in the BAM and consequently no special theorization is required to model this cognitive facet.

BAM Energy Function• The BAM energy function is important because it

governs the memory recall process. • Memory formation creates a memory well• Imagine placing a heavy ball on a flat rubber

sheet.• The indentation creates a memory well with a

surrounding basin of attraction.• The energy function mathematically defines the

depth of the memory well is:• E = -AMBT

BAM Energy Function• E represents energy and is defined to be negative by the

minus sign so as to create energy wells.• Omitting the minus sign would create energy hills and

memory retrieval would be described in terms of hill climbing rather than in terms of gradient descent into a memory well.

• It is conventional to choose energy wells and to describe memory systems as relaxing into lower energy states during memory retrieval.

• These energy (E) values constitute a third coordinate, along with the A and B vectors thus enabling a 3D visualization of the memory surface. Because E is in decimal notation, we need to transform the A and B vectors into decimal equivalents to obtain the three coordinates necessary for the 3D plot.

BAM Energy Function• A complete picture of the memory field requires

that energy values be calculated for all possible A and B codes.

• The topography of this surface deterministically controls all aspects of memory recall.

• Its shape determines which direction a locus of memory recall will move from each and every possible point as this locus must always move down hill and consequently memory wells are also called attractors.

Memory Removal• The dialectical property enables one to remove an A-B

association from memory by forming memory for A-Bc or for Ac-B.

• This principle suggests a possible therapeutic strategy.• Forming an A-Bc pair for a PTSD victim could be attempted

by associating stimulus features with positive rather than negative cognitions and emotions.

• It is also possible to delete a memory by subtracting its memory matrix or the equivalent operation of adding the quantity -AT B to M.

• These mathematical operations do not correspond simply to any obvious therapeutic procedure.

• However, they do emphasize that memory removal (forgetting) is an active process that involves storage of incompatible information.

Clinical Topics Seminar