Presentation on theme: "MODELING PARAGIGMS IN ACT-R -Adhineth Mahanama.V."— Presentation transcript:
MODELING PARAGIGMS IN ACT-R -Adhineth Mahanama.V
Introduction Key Claim of Rules of the Mind (Anderson, 1993): Cognitive skills are realized by production rules What does this mean? – What predictions does it make about learning? – How does it help explain learning phenomena?
What is ACT-R? ACT-R is a cognitive architecture, a theory about how human cognition works. Looks like a (procedural) programming language. Constructs based on assumptions about human cognitions.
What is ACT-R? ACT-R is an integrated cognitive architecture. Brings together not just different aspects of cognition, but of Cognition Perception Action Runs in real time. Learns. Robust behavior in the face of error, the unexpected, and the unknown.
What is ACT-R? ACT-R is a framework Researchers can create models that are written in ACT-R including ACT-Rs assumptions about cognition. The researchers assumptions about the task. The assumptions are tested against data. Reaction time Accuracy Neurological data (fMRI)
Main claims of ACT-R 1There are two long-term memory stores, declarative memory and procedural memory. 2The basic units in declarative memory are chunks. 3 The basic units in procedural memory are production rules.
Procedural Module Procedural memory: Knowledge about how to do something. How to type the letter Q. How to drive. How to perform addition.
Procedural Module Made of condition-action data structures called production rules. Each production rule takes 50ms to fire. Serial bottleneck in this parallel system.
Declarative Module Declarative memory: Facts Washington, D.C. is the capital of the U.S. 2+3=5. Knowledge a person might be expected to have to solve a problem. Called chunks
Declarative Knowledge Terms Declarative Knowledge – Is the Working Memory of a production system A chunk is an element of declarative knowledge – Type indicates the slots or attributes – In Jess, the chunks are called facts and the chunk types are called templates
Declarative-Procedural Distinction Declarative knowledge – Includes factual knowledge that people can report or describe, but can be non-verbal – Stores inputs of perception & includes visual memory – Is processed & transformed by procedural knowledge – Thus, it can be used flexibly, in multiple ways Procedural knowledge – Is only manifest in peoples behavior, not open to inspection, cannot be directly verbalized – Is processed & transformed by fixed processes of the cognitive architecture – It is more specialized & efficient
Knowledge representation: Procedural vs. declarative This has long been a feature of ACT theories Cognition emerges as interaction between procedural and declarative knowledge Declarative memory contains chunks Structured configurations of small set of elements Sometimes described as containing facts; but real issue is not content, but how they are accessed Procedural memory: production rules Asymmetric condition-action pairs Match on buffers, modify buffers
Buffers The procedural module accesses the other modules through buffers. For each module (visual, declarative, etc), a dedicated buffer serves as the interface with that module. The contents of the buffers at any given time represent the state of ACT-R at that time.
Environment Productions Retrieval Buffer Matching Selection Execution Visual Buffer Manual Buffer Manual Module Visual Module Declarative Module Goal Buffer ACT-R 5.0: Buffers and modules Match and modify buffers
The chunk in declarative memory To use a chunk, production rule is invoked and it requests it from declarative memory. Con figural & hierarchical structure -> different parts of have different roles -> chunks can have sub chunks A fraction addition problem contains fractions, fractions contain a numerator & denominator Goal-independent & symmetric (chunks are retrieved to achieve some goals) – Rules can be represented as declarative chunks – You can think of declarative rules but only think with procedural rules
Paradigms Five modeling paradigms are discussed in ACT-R. Instance learning: User previous experiences to guide choices. Competing strategies: Several strategies compete to solve a problem. Strategies with best probability of success for the lowest cost will be used often. Individual difference. Perceptual & motor process. Specialization of Task-Independent cognitive strategies.
Chunk Activation Activation of Chunk i Base-level activation (Higher if used recently) Attentional weighting of Element j of Chunk i Strength of association of Element j to Chunk i j A i = B i + W j S ji
Base-level Activation The base level activation B i of chunk C i reflects a context-independent estimation of how likely C i is to match a production, i.e. B i is an estimate of the log odds that C i will be used. Two factors determine B i : frequency of using C i recency with which C i was used B i = ln ( ) B i = ln ( ) P(C i ) P(C i ) A i = B i base activation =
Probability of Retrieval The probability of retrieving a chunk is given by P i = 1 / (1 + exp(-(A i - )/s))
Retrieval Time The time to retrieve a chunk is given by T i = F exp(-A i )
Partial Matching The mismatch penalty is a measure of the amount of control over memory retrieval: MP = 0 is free association; MP very large means perfect matching; intermediate values allow some mismatching in search of a memory match. Similarity values between desired value k specified by the production and actual value l present in the retrieved chunk. This provides generalization properties similar to those in neural networks; the similarity value is essentially equivalent to the dot- product between distributed representations. similarity value mismatch penalty ( ) * +
Chunk Activation base activation =+ Activation makes chunks available to the degree that past experiences indicate that they will be useful at the particular moment. Base-level: general past usefulness Associative Activation: relevance to the general context Matching Penalty: relevance to the specific match required Noise: stochastic is useful to avoid getting stuck in local minima Higher activation = fewer errors and faster retrievals associative strength source activation ( ) * similarity value mismatch penalty ( ) * ++ noise
Chunk Activation The activation of a chunk is a sum of base- level activation, reflecting its general usefulness in the past, and an associative activation, reflecting its relevance in the current context.
Production choice and utility learning Only a single production can fire at a time (a serial bottleneck); the production with the highest utility is selected The parameters P and C are incrementally adjusted as function of experience Expected Utility = PG-C P = Successes/ (Successes + Failures) C = cost of achieving goal if production selected (effort) G = value of current goal
3(2x - 5) = 9 6x - 15 = 92x - 5 = 36x - 5 = 9 Use ACT-R theory to individualize instruction Cognitive Model: A system that can solve problems in the various ways students can If goal is solve a(bx+c) = d Then rewrite as abx + ac = d If goal is solve a(bx+c) = d Then rewrite as abx + c = d If goal is solve a(bx+c) = d Then rewrite as bx+c = d/a Model Tracing: Follows student through their individual approach to a problem -> context-sensitive instruction
Source Activation The source activations W j reflect the amount of attention given to elements, i.e. fillers, of the current goal. ACT-R assumes a fixed capacity for source activation W= W j reflects an individual difference parameter. associative strength source activation ( ) + * + W j * S ji j
Associative Strengths The association strength S ji between chunks C j and C i is a measure of how often C i was needed (retrieved) when C j was element of the goal, i.e. S ji estimates the log likelihood ratio of C j being a source of activation if C i was retrieved. associative strength source activation ( ) + * + W j * S ji
--> SPECILIZATION OF TASK-INDEPENDENT COGNITIVE STRATIGIES
Some composition principles 1. Perceptual-Motor Buffers: Avoid compositions that will result in jamming when one tries to build two operations on the same buffer into the same production. 2. Retrieval Buffer: Except for failure tests procedural out and build more specific productions. 3. Safe Productions: Production will not produce any result that the original productions did not produce.
Short-term Memories Chunks (flat structures) in buffers One chunk/buffer Chunk types with fixed slots Goal, Declarative Memory, Perception All persistent until replaced/modified Long-term identifiers for each chunk Provides hierarchical structure declarative memory red #3 x #9 #45 goal perception #3 #45 visualization
Summary Features of cognition explained by ACT-R production rules: – Procedural knowledge: modular, limited generality, goal structured, asymmetric – Declarative knowledge: flexible, verbal or visual, less efficient
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