uncfam_gamma: Kachergis 2012 with a free familiarity exponent

In XSLmodels: Run and Optimize Cross-Situational Word Learning Models

Kachergis 2012 with a free familiarity exponent

Description

A variant of uncfam() (Kachergis et al. 2012's uncertainty- and familiarity-biased associative model) that decouples familiarity's contribution to a trial's attentional allocation from uncertainty's. uncfam()'s allocation weight for pair (w, o) is exp(B * entropy) * assocs – entropy gets a free, tunable exponent (B), but familiarity (assocs, the pair's current association strength) enters linearly, with an implicit weight of 1 and no free parameter of its own. This adds one parameter, gamma, raising familiarity to a free power instead: assocs^gamma * exp(B * entropy). gamma = 1 is identical to uncfam(); gamma < 1 dampens the "rich get richer" effect (diminishing returns on an already-strong pairing); gamma > 1 amplifies it (winner-take-all).

Usage

uncfam_gamma(X, B, C, gamma)

Arguments

X	Associative weight to distribute
B	Weighting of uncertainty vs. familiarity
C	Decay
gamma	Familiarity exponent (1 = identical to uncfam())

Details

Cross-validated against all of xsl_datasets (SSE to human 18AFC accuracy, the package's standard model-comparison objective), uncfam_gamma() beats plain uncfam() in every fold of a 5-fold split (mean test SSE 0.48 vs. 0.56), with a best-fit gamma around 0.3 – i.e. familiarity's pull dampens with diminishing returns when explaining how well people learn from a passively-received training sequence. A separate analysis fitting this same free-gamma substrate to active cross-situational word learning (Kachergis, Yu, & Shiffrin's paradigm where learners choose which items to see named next, rather than receiving a fixed passive sequence) found a best-fit gamma around 2 instead – amplified, not dampened. Both contexts agree that familiarity should get its own free exponent rather than uncfam()'s hard-coded linear one, but disagree on which direction it bends: the process governing moment-to-moment choice of what to study next doesn't appear to be simply the same one governing how much is learned from a given, already-fixed sequence.

Value

An object of class xslMod

Examples

mod <- uncfam_gamma(X = .1, C = 1, B = .98, gamma = 1)
xsl_run(mod, get_example_ambiguous_condition())

# gamma = 1 reproduces uncfam() exactly
sse_gamma1 <- xsl_run(uncfam_gamma(X = .1, C = 1, B = .98, gamma = 1),
                      get_example_ambiguous_condition())$sse
sse_uncfam <- xsl_run(uncfam(X = .1, C = 1, B = .98),
                      get_example_ambiguous_condition())$sse
isTRUE(all.equal(sse_gamma1, sse_uncfam))

mod <- uncfam_gamma(X = .1, C = 1, B = .98, gamma = 0.3) # dampened familiarity
xsl_run(mod, get_example_ambiguous_condition())

XSLmodels documentation built on Oct. 18, 2026, 5:08 p.m.