Explanation and Simulation in Cognitive Science Simulation and computational modeling Symbolic models Connectionist models Comparing symbolism and connectionism Hybrid architectures Cognitive architectures
Simulation and Computational Modeling With detailed and explicit cognitive theories, we can implement the theory as a computational model And then execute the model to: Simulate cognitive capacity Derive predictions from the theory The predictions can then be compared to empirical data
Questions What kinds of theories are amenable to simulation? What techniques work for simulation? Is simulating the mind different from simulating the weather?
The Mind & the Weather The mind may just be a complex dynamic system, but it isn t amenable to generic simulation techniques: The relation between theory and implementation is indirect: theories tend to be rather abstract The relation between simulation results and empirical data is indirect: simulations tend to be incomplete The need to simulate helps make theories more concrete But improvement of the simulation must be theory-drive, not just an attempt to capture the data
Symbolic Models High-level functions (e.g., problem solving, reasoning, language) appear to involve explicit symbol manipulation Example: Chess and shopping seem to involve representation of aspects of the world and systematic manipulation of those representations
Central Assumptions Mental representations exist Representations are structured Representations are semantically interpretable
What s in a representation? Representation must consist of symbols Symbols must have parts Parts must have independent meanings Those meanings must contribute to the meanings of the symbols which contain the e.g., 34 contains 3 and 4, parts which have independent meanings the meaning of 34 is a function of the meaning of 3 in the tens position and 4 in the units position
In favor of structured mental representations Productivity It is through structuring that thought is productive (finite number of elements, infinite number of possible combinations) Systematicity If you think John loves Mary, you can think Mary loves John Compositionality The meaning of John loves Mary is a function of its parts, and their modes of combination Rationality If you know A and B is true, then you can infer A is true Fodor & Pylyshyn (1988)
What do you do with them? Suppose we accept that there are symbolic representations How can they be manipulated? by a computing machine Any such approach has three components A representational system A processing strategy A set of predefined machine operations
Automata Theory Identifies a family of increasingly powerfu computing machines Finite state automata Push down automata Turning machines
Automata, in brief (Figure 2.2 in Green et al., Chapter 2) This FSA takes as input a sequence of on and off messages, and accepts any sequence ending with an on A PDA adds a stack: an infinite-capacity, limited access memory, so that what a machine does depends on input, current state, plus the memory
A Turing machine changes this memory to allow any location to be accessed at any time. An the State transition function specifies read/write instructions, as well as which state to move to next. Any effective procedure can be implemented on an appropriately programmed Turing machine And Universal Turing machines can emulate any Turing machine, via a description on the tape of the machine and its inputs Hence, philosophical disputes: Is the brain Turing powerful? Does machine design matter or not?
More practical architectures Von Neumann machines: Strictly less powerful than Turing machines (finite memory) Distinguished area of memory for stored programs Makes them conceptually easier to use than TMs Special memory location points to next-instruction on each processing cycle: fetch instruction, move pointer to next instruction, execute current instruction
Production Systems Introduced by Newell & Simon (1972) Cyclic processor with two main memory structures Long term memory with rules (~productions) Working memory with symbolic representation of current system state Example: IF goal (sweeten(x) AND available (sugar) THEN action (add(sugar, X)) and retract (goal(sweeten(x)))
Recognize phase (pattern matching) Find all rules in LTM that match elements in WM Act phase (conflict resolution) Choose one matching rule, execute, update WM and (possibly) perform action Complex sequences of behavior can thus result Power of pattern matcher can be varied, allowing different use of WM Power of conflict resolution will influence behavior given multiple matches Most specific This works well for proble -solving. Would it work for pole-balancing?
Connectionist Models The basic assumption There are many processors connected together, and operating simultaneously Processors: units, nodes, artificial neurons
A connectionist network is A set of nodes, connected in some fashion Nodes have varying activation levels Nodes interact via the flow of activation along the connections Connections are usually directed (one-way flow), and weighted (strength and nature of interaction; positive weight = excitatory; negative = inhibitory) A node s activation will be computed from the weighted sum of its inputs
Local vs. Distributed Representation Parallel Distributed Processing is a (the?) major branch of connectionis In principle, a connectionist node could have an interpretable meaning E.g., active when red input, or grandmother, or whatever However, an individual PDP node will not have such an interpretable meaning Activation over whole set of nodes corresponds to red Individual node participates in many such representations
PDP PDP systems lack systematicity and compositionality Three main types of networks: Associative Feed-forward Recurrent
Associative To recognize and reconstruct patterns Present activation pattern to subset of units Let network settle in stable activation pattern (reconstruction of previously learned state)
Feedforwar Not for reconstruction, but for mapping from one domain to another Nodes are organized into layers Activation spreads through layers in sequence A given layer can be thought of as an activation vector Simplest case: Input layer (stimulus) Output layer (response) Two layer networks are very restricted in power. Intermediate (hidden) layers gain most of the additional computational power needed.
Recurrent Feedforward nets compute mappings given current input only. Recurrent networks allow mapping to take into account previous input. Jordan (1986) and Elman (1990) introduced networks with: Feedback links from output or hidden layers to context units, and Feedforward links from the context units to the hidden units Jordan network output depends on current input and previous output Elman network output depends on current input and whole of previous input history
Key Points about PDP It s not just that a net can recognize a pattern or perform a mapping It s the fact that it can learn to do so, on the basis of limited data And the way that networks respond to damage is crucial
Learning Present network with series of training patterns Adjust the weights on connections so that the patterns are encoded in the weights Most training algorithms perform small adjustments to the weights per trial, but require many presentations of the training set to reach a reasonable degree of performance There are many different learning algorithms
Learning (contd.) Associative nets support Hebbian learning rule: Adjust weight of connection by amount proportional to the correlation in activity of corresponding nodes So if both active, increase weight; if both inactive, increase weight; if they differ, decrease weight Important because this is biologically plausible and very effective
Learning (contd.) Feedforward and recurrent nets often exploit the backpropagation of error rule Actual output compared to expected output Difference computed and propagated back to input, layer by layer, requiring weight adjustments Note: unlike Hebb, this is supervised learning
Psychological Relevance Given a network of fixed size, if there are two few units to encode the training set, then interference occurs This is suboptimal, but is better than nothing, since at least approximate answers are provided And this is the flipside of generalization, which provides output for unseen input E.g., weep! wept; bid! bid
Damage Either remove a proportion of connections Or introduce random noise into activati propagati And behavior can simulate that of people with various forms of neurological damage Graceful degradation : impairment, but residual function
Example of Damage Hinton & Shallice (1991), Plaut & Shallice (1993) on deep dyslexia: Visual error ( cat read as cot ) Semantic error ( cat read as dog ) Networks constructed for orthography-tophonology mapping, lesioned in various ways, producing behavior similar to human subjects
Symbolic Networks Though distributed representations have proved very important, some researchers prefer localist approaches Semantic networks: Frequently used in AI-based approaches, and in cognitive approaches which focus on conceptual knowledge One node per concept; typed links between concepts Inference: link-following
Production systems with spreading activati Anderson s work (ACT, ACT*, ACT-R) Symbolic networks with continuous activation values ACT-R never removes working memory elements; activation instead decays over time Productions chosen on basis of (co-) activation
Interactive Activation Networks Essentially, localist connectionist networks Featuring self-excitatory and lateral inhibitory links, which ensure that there s always a winner in a competition (e.g., McClelland & Rumelhart s model of letter perception) Appropriate combinations of levels, with feedback loops in them, allow modeling of complex datadriven and expectation-driven bahavior
Comparing Symbolism & Connectionism As is so often the case in science, the two approaches were initially presented as exclusive alternatives
Connectionist: Interference Generalization Graceful degradation Symbolists complain: Connectionists don t capture structured information Network computation is opaque Networks are merely implementation-level
Symbolic Productive Systematic Compositional Connectionists complain Symbolists don t relate assumed structures to brain They relate them to von Neumann machines
Connectionists can claim: Complex rule-oriented behavior *emerges* from interaction of subsymbolic behavior So symbolic models describe, but do not explai
Symbolists can claim: Though PDP models can learn implicit rules, the learning mechanisms are usually no neurally plausible after all Performance is highly dependent on exact choice of architecture
Hybrid Architectures But really, the truth is that different tasks demand different technologies Hybrid approaches explicitly assume: Neither connectionist nor symbolic approach is flawed Their techniques are compatible
Two main hybrid options: Physically hybrid models: Contain subsystems of both types Issues: interfacing, modularity (e.g., use Interactive Activation Network to integrate results) Non-physically hybrid models Subsystems of only one type, but described two ways Issue: levels of description (e.g., connectionist production systems)
Cognitive Architectures Most modeling is aimed at specific processes or tasks But it has been argued that: Most real tasks involve many cognitive processes Most cognitive processes are used in many tasks Hence, we need unified theories of cognition
Examples ACT-R (Anderson) Soar (Newell) Both based on production system technology Task-specific knowledge coded into the productions Single processing mechanism, single learning mechanis
Like computer architectures, cognitive architectures tend to make some tasks easy, at the price of making other hard Unlike computer architectures, cognitive architectures must include learning mechanisms But note that the unified approaches sacrifice genuine task-appropriateness and perhaps also biological plausibility
A Cognitive Architecture is: A fixed arrangement of particular functional components A processing strategy