Retracing the Rational Analysis of Memory Justin Li Computer - - PowerPoint PPT Presentation

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Retracing the Rational Analysis of Memory Justin Li Computer - - PowerPoint PPT Presentation

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Retracing the Rational Analysis of Memory Justin Li Computer Science and Engineering University of Michigan justinnh@umich.edu 2014-06-19 Introduction Problem Models Summary , What is this talk about? Goal: (re)examine and formalize

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Retracing the Rational Analysis of Memory

Justin Li

Computer Science and Engineering University of Michigan justinnh@umich.edu 2014-06-19

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Introduction Problem Models Summary ,

What is this talk about?

Goal:

◮ (re)examine and formalize the goal of memory mechanisms ◮ unify mechanisms such as cued and spontaneous retrieval,

working and semantic memory activation, etc.

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

The Rational Analysis of Memory

Anderson (1990) performed a rational analysis of memory: Goal Environment Constraints Optimization

2014-06-19

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Introduction Problem Models Summary ,

The Rational Analysis of Memory

Anderson (1990) performed a rational analysis of memory: Goal provide the agent with knowledge it is most likely to need Environment Constraints Optimization

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

The Rational Analysis of Memory

Anderson (1990) performed a rational analysis of memory: Goal provide the agent with knowledge it is most likely to need Environment one where probability of need is a function of recency and frequency Constraints Optimization

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

The Rational Analysis of Memory

Anderson (1990) performed a rational analysis of memory: Goal provide the agent with knowledge it is most likely to need Environment one where probability of need is a function of recency and frequency Constraints memories are accessed sequentially at fixed cost Optimization

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

The Rational Analysis of Memory

Anderson (1990) performed a rational analysis of memory: Goal provide the agent with knowledge it is most likely to need Environment one where probability of need is a function of recency and frequency Constraints memories are accessed sequentially at fixed cost Optimization stop retrieval when cost > probability of need ∗ gain

2014-06-19

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Introduction Problem Models Summary ,

Bayesian Memory

Goal: return element m ∈ M with the highest probability of need P(m) Given: set of context elements C ⊂ M Find: arg max

m∈M

P(m|C) = arg max

m∈M

P(m)P(C|m) P(C)

= arg max

m∈M

P(m)P(C|m)

2014-06-19

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Introduction Problem Models Summary ,

Bayesian Memory

arg max

m∈M

P(m)P(C|m) What does this mean? P(m) probability of need of element m (ie. the prior) P(C|m) probability of need of the context C given that m is needed (ie. the likelihood)

2014-06-19

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Introduction Problem Models Summary ,

ACT-R’s Memory Mechanisms

◮ Cued Retrieval ◮ Partial Match ◮ Spreading Activation

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Introduction Problem Models Summary ,

Cued Retrieval

Assuming the context C is the set of cues: arg max

m∈M

P(C|m)P(m)

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Introduction Problem Models Summary ,

Cued Retrieval

Symbolic Long Term Memories

Semantic Episodic Procedural

Symbolic Short-Term Memory

Reinforce- ment Chunking Semantic Learning Episodic Learning A p p r a i s a l D e t e c t

  • r

Decision Procedure Clustering Perception LT Visual Memory ST Visual Memory Action

Body

2014-06-19

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Introduction Problem Models Summary ,

Cued Retrieval

Symbolic Long Term Memories

Semantic Episodic Procedural

Symbolic Short-Term Memory

Reinforce- ment Chunking Semantic Learning Episodic Learning A p p r a i s a l D e t e c t

  • r

Decision Procedure Clustering Perception LT Visual Memory ST Visual Memory Action

Body

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

Cued Retrieval

Assuming the context C is the set of cues: arg max

m∈M

P(C|m)P(m) We want ∀m, P(C|m1) = P(C|m2) Take P(c|m) =

      

1, if ∀c ∈ C is a child of m 0,

  • therwise

2014-06-19

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Introduction Problem Models Summary ,

Partial Match

Assuming the context C is the set of cues: arg max

m∈M

P(C|m)P(m) We want P(C|m) to be:

◮ proportional to the number of c ∈ C that is a child of m ◮ inversely proportional the number of children that m has

2014-06-19

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Introduction Problem Models Summary ,

Spreading Activation

Assuming the context C is the working memory: arg max

m∈M

P(C|m)P(m)

2014-06-19

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Introduction Problem Models Summary ,

Spreading Activation

Symbolic Long Term Memories

Semantic Episodic Procedural

Symbolic Short-Term Memory

Reinforce- ment Chunking Semantic Learning Episodic Learning A p p r a i s a l D e t e c t

  • r

Decision Procedure Clustering Perception LT Visual Memory ST Visual Memory Action

Body

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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Introduction Problem Models Summary ,

Spreading Activation

Assuming the context C is the working memory: arg max

m∈M

P(C|m)P(m) Note there is no cue – this model could also spontaneous

2014-06-19

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Introduction Problem Models Summary ,

Bayesian Networks

Problems:

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Introduction Problem Models Summary ,

Bayesian Networks

Problems:

◮ What is P(m)?

◮ in ACT-R, base-level activation is ln(P(m)) ◮ other options? ◮ working memory activation or semantic memory activation? 2014-06-19

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Introduction Problem Models Summary ,

Bayesian Networks

Problems:

◮ What is P(m)?

◮ in ACT-R, base-level activation is ln(P(m)) ◮ other options? ◮ working memory activation or semantic memory activation?

◮ What is P(C|m)?

◮ in a Bayes net, all external factors ◮ inference is NP-hard ◮ semantic networks are not Bayesian networks (ie. acyclic) 2014-06-19

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Introduction Problem Models Summary ,

Nuggets and Coal

Nuggets

◮ Memory retrieval can be

cast in a Bayesian framework

◮ This framework provides

explanations for multiple memory mechanisms Coal

◮ Bayesian inference fails on

semantic networks

◮ Additional assumptions

needed to make inference tractable and correct

2014-06-19

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Introduction Problem Models Summary ,

Questions?

Symbolic Long Term Memories

Semantic Episodic Procedural

Symbolic Short-Term Memory

Reinforce- ment Chunking Semantic Learning Episodic Learning A p p r a i s a l D e t e c t

  • r

Decision Procedure Clustering Perception LT Visual Memory ST Visual Memory Action

Body

2014-06-19

  • Li. Retracing the Rational Analysis of Memory

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