slpCOVIS {catlearn}

COVIS category learning model

Description

COmpetition between Verbal and Implicit Systems model of category learning (Ashby et al. 1998), as described in Ashby et al. (2011). The current implementation supports two-category experiments, and uses only single-dimension, not-below-chance, rules in the Explicit system.

Usage

slpCOVIS(st, tr, crx = TRUE, respt = FALSE, rgive = TRUE, xtdo = FALSE)

Arguments

st

List of model parameters

tr

R-by-C matrix of training items

crx

Boolean. Explicit System. If set to TRUE, the current rule is included in the random selection of a rule to receive a weight increase from the Possion distribution. If set to FALSE, the current rule is not included in this random selection.

respt

Set to FALSE for the behaviour described in Note 5; behaviour when TRUE is undocumented

rgive

Set to TRUE; FALSE is undocumented

xtdo

Set to FALSE; TRUE is undocumented

Details

The coverage in this help file is relatively brief; for a more extensive tutorial, see Inkster et al. (n.d.).

The function works as a stateful list processor (slp; see Wills et al., 2017). Specifically, it takes a matrix (tr) as an argument, where each row is one trial for the network, and the columns specify the input representation. It returns a List containing the predictions made by the model and the final state of the model, hence its description as a 'stateful' list processor.

Argument st must be a list containing the following information. Parameter names given in brackets in the descriptions below follow the naming conventions of Ashby et al. (2011), and Edmunds & Wills (2016). Equation numbers are from Ashby et al. (2011); where there is no equation, the page number is given instead.

Explicit system variables:

envar - (sigma^2_E) - p. 68 - Variance of the noise distribution used to determine which response the explicit system makes on the current trial. See Note 4, below.

decbound - (C) - Eq. 1 - location of the decision bound on a single dimension. In the current implementation of slpCOVIS, this location is the same for all dimensions.

corcon - (delta_c) - Eq. 2 - constant by which to increase current rule saliency in the case of a correct response.

errcon - (delta_e) - Eq. 3 - constant by which to decrease current rule saliency in the case of an incorrect response.

perscon - (gamma) - Eq. 4 - perseveration constant, i.e. value to add to the salience of the current rule to obtain its rule weight.

lambda - (lambda) - Eq. 5 - Mean of the Poission distribution. A value randomly sampled from the Poisson distribution is added to a randomly-selected rule when calculating the weights for new rule selection.

decsto - (a) - Eq. 7 - decision stochasticity when using rule weights to select the rule for the next trial. For Ashby et al. (2011)'s implementation, a = 1. For other uses, see Edmunds & Wills (2016).

Procedural system variables:

sconst - (alpha) - Eq. 8 - scaling constant for cortical unit activation. See Note 3, below.

invar - (sigma^2_p) - Eq. 9 - Variance of the normally-distributed noise used to calculate striatal unit activation.

dbase - (D_base) - Eq. 10 - baseline dopamine level.

alphaw - (alpha_w) - Eq. 10 - Learning rate parameter in force when striatal activation is above the NMDA threshold, and dopamine is above baseline.

betaw - (beta_w) - Eq. 10 - Learning rate parameter in force when striatal activation is above the NMDA threshold, and dopamine is below baseline.

gammaw - (gamma_w) - Eq. 10 - Learning rate parameter in force when striatal activation is between the AMPA and NMDA thresholds.

nmda - (theta_NMDA) - Eq. 10 - Activation threshold for post-synaptic NMDA.

ampa - (theta_AMPA) - Eq. 10 - Activation threshold for post-synaptic AMPA. See Note 1, below.

wmax - (w_max) - Eq. 10 - Intended upper weight limit for a cortico-striatal link. See Note 2, below.

prep - ( P_(n-1) ) - Eq. 12 - predicted reward value immediately prior to first trial. If unsure, set to zero.

prer - ( R_(n-1) ) - Eq. 12 - obtained reward value immediately prior to first trial. If unsure, set to zero.

Competition / decision system variables:

emaxval - p.77 - The maximum possible value of the the Explicit system's discriminant variable. For example, if the stimulus value varies from zero to one, and C (see above) is 0.5, then the maximum value is 1-0.5 = 0.5

etrust - (theta_E) - Eq. 15 - trust in the explicit system immediately prior to first trial. If unsure, set to .99.

itrust - (theta_P) - p. 77 - trust in the procedural system immediately prior to first trial. If unsure, set to .01. See also Note 7, below.

ocp - (delta_OC) - Eq. 15 - constant used to increase trust in the Explicit system after it suggests a response that turns out to be correct.

oep - (delta_OE) - Eq. 16 - constant used to decrease trust in the Explicit system after it suggests a response that turns out to be incorrect.

Initial state of model:

initrules - vector of length stimdim, representing the initial salience of each single-dimensional rule in the Explicit system.

crule - a number indicating which rule is in use immediately prior to the first trial (1 = dimension 1, 2 = dimension 2, etc). If this is not meaningful in the context of your simulation, set it to zero, and ensure ctrl = 1 in the first row of your training matrix (see below). This will then randomly pick an initial rule.

initsy - matrix of stimdim rows and two columns - contains the initial values for the cortico-striatal connection strengths.

scups - matrix of stimdim columns and as many rows as you wish to have cortical input units. Each row represents the position of a cortical unit in N-dimensional stimulus space.

And finally, a couple of things slpCOVIS needs to interpret your tr matrix (see below):

stimdim - number of stimulus dimensions in the input representation.

colskip - skip the first N columns of the tr array, where N = colskip. colskip should be set to the number of optional columns you have added to matrix tr, PLUS ONE. So, if you have added no optional columns, colskip = 1. This is because the first (non-optional) column contains the control values, see below.

Argument tr must be a matrix, where each row is one trial presented to the network. Trials are always presented to the model in the order specified. The columns must be as described below, in the order described below:

ctrl - vector of control codes. Available codes are: 0 = normal trial, 1 = reset network (i.e. set back to the state defined in list st and randomly select an initial rule for the Explicit System using Eq. 7) , 2 = Freeze learning. Control codes are actioned before the trial is processed.

opt1, opt2, ... - optional columns, which may have any names you wish, and you may have as many as you like, but they must be placed after the ctrl column, and before the remaining columns (see below). These optional columns are ignored by this function, but you may wish to use them for readability. For example, you might include columns for block number, trial number, and stimulus ID number. The argument colskip (see above) must be set to the number of optional columns plus 1.

x1, x2, ... - stimulus input to the model; there must be one column for each stimulus dimension.

t1 - teaching signal to model. If the correct response is Category 1, t = 1. If the correct response is Category 2, t = -1. Experiments with something other than two categories are not supported in the current implementation.

optend1, optend2, ... - optional columns, which may have any names you wish, and you may have as many as you like, but they must be placed after the t1 column. These optional columns are ignored by this function, but may help with cross-compatibility with other model implementations. For example, the additional 't' and 'm' columns of input representations generated for slpALCOVE will be safely ignored by slpCOVIS.

Value

Returns a List containing eight components:

foutmat

A two-column matrix, representing the model's response on each trial. For any given trial, [1,0] indicates a Category 1 response; [0,1] indicates a Category 2 response. Responses are reported in this manner to facilitate cross-compatibility with models that produce response probabilities on each trial.

frules

Explicit system - rule saliences after final trial

fsystr

Procedural system - cortico-striatal synaptic strengths after final trial)

fetrust

Decision system - trust in explicit system after final trial

fitrust

Decision system - trust in procedural system after final trial

frule

Explicit system - rule used by explicit system on final trial

fprep

Implicit system - predicted reward value on final trial

fprer

Implicit system - obtained reward value on final trial

Note

1. Ashby et al. (2011) state (p. 74) that the intended operation of COVVIS is theta_NMDA > theta_AMPA, but the values they report are theta_NMDA = .0022, theta_AMPA = .01.

2. Ashby et al. (2011) did not specify a value for w_max; Edmunds & Wills (2016) assumed the intended value was 1.

3. Ashby et al. (2011) do not use Eq. 8 in their simulation, they manually set sensory cortex activation to 1 for the presented stimulus and 0 for all the others (p. 78). They thus do not have a value for alpha. Edmunds & Wills (2016) set alpha to 0.14, which produces similar behaviour for 0,1 coded stimulus dimensions, without having to manually set the activations.

4. In Ashby et al. (2011) and Edmunds & Wills (2016), sigma^2_E is set to zero. In this implementation of slpRW, positive values should also work but have not been extensively tested.

5. In the descriptions provided by Ashby et al. (2011, p. 69 & p. 75), there is some ambiguity about the meaning of the term 'response' - does this mean the response of a system (e.g. the Explicit system), or the overall response (i.e. the output of the decision system). In the current implementation, the response of the Explicit System is compared to the feedback to determine whether the Explicit System was correct or incorrect, and the response of the Procedural System is compared to the feedback to determine whether the Procedural System was correct or incorrect.

6. It seems that in Ashby et al.'s (2011) simulations, each dimension generates only one single-dimension rule for a two-category problem, rather than two as one might expect (e.g. small = A, large = B, but also large = A, small = B). Rules that would produce below-chance responding are excluded from the rule set.

7. Ashby et al. (2011) state that theta_E + theta_P = 1. However, slpCOVIS does not perform this check on the initial state, so it is important to check this manually.

Author(s)

Angus Inkster, Andy Wills, Charlotte Edmunds

References

Ashby, F.G., Alfonso-Reese, L.A., Turken, A.U. & Waldron, E.M. (1998). A neuropsychological theory of multiple systems in category learning. Psychological Review, 105, 442-481.

Ashby, F.G., Paul, E.J., & Maddox, W.T. (2011). COVIS. In Pothos, E.M. & Wills, A.J. (2011). Formal approaches in categorization. Cambridge, UK: Cambridge University Press.

Edmunds, C.E.R., & Wills, A.J. (2016). Modeling category learning using a dual-system approach: A simulation of Shepard, Hovland and Jenkins (1961) by COVIS. In A. Papfragou, D. Grodner, D. Mirman, & J.C. Trueswell (Eds.). Proceedings of the 38th Annual Conference of the Cognitive Science Society (pp. 69-74). Austin, TX: Cognitive Science Society.

Inkster, A.B., Edmunds, C.E.R., & Wills, A.J. (n.d.). A distributed-collaboration resource for dual-process modeling in category learning. Manuscript in preparation.

Pothos, E.M. & Wills, A.J.(2011). Formal approaches in Categorisation.Cambridge: University Press.

Wills, A.J., O'Connell, G., Edmunds, C.E.R., & Inkster, A.B.(2017). Progress in modeling through distributed collaboration: Concepts, tools, and category-learning examples. Psychology of Learning and Motivation, 66, 79-115.