oral-tradition
IB-transmission-prior-attractor
Iterated serial reproduction behaves as a Markov chain whose STATIONARY distribution equals the transmitters' shared prior: chains started from 2.63, 4.19 and 5.76 cm all converged to the same value within about 20 transmissions.
Observed quantities
start points 2.63 / 4.19 / 5.76 cm -> converge within ~20 trials to one shared prior
01
Primary source
- Xu & Griffiths 2008/2010 (report cites '2008/10'; exact venue(s) unverified in report)
02
Boundary of this block
'Stationary distribution IS the prior' is exact only UNDER the Bayesian iterated-learning MODEL; the convergence itself is what is measured. The modulation knob lambda = 1/(1+sigma_x^2/sigma_0^2) is a model parameter, not a separate measurement.
03
Connections
Outgoing
- relates to Softmax self-attention (the Transformer's core operation) is exactly ONE update step of a continuous modern Hopfield network with an exponential energy — i.e. associative-memory attractor retrieval — with pattern-storage capacity scaling ~2^(d/2) and the softmax inverse-temperature beta as the retrieval-sharpness knob. the two domains where 'attractor' is mathematically EXACT: Markov stationary here, Hopfield fixed point there
- relates to SOCIAL transmission (imitating others) homogenizes cultural material toward a shared attractor while SOLO transmission does not: in a sung-melody transmission experiment, social chains converged and solo chains did not. social iterated transmission is what drives the population to the shared prior
Incoming
- relates from Softmax self-attention (the Transformer's core operation) is exactly ONE update step of a continuous modern Hopfield network with an exponential energy — i.e. associative-memory attractor retrieval — with pattern-storage capacity scaling ~2^(d/2) and the softmax inverse-temperature beta as the retrieval-sharpness knob. the two domains where the attractor is mathematically exact (Hopfield fixed point ~ Markov stationary / shared prior)
- relates from Crows acquire dangerous-human recognition mostly by HORIZONTAL social learning: naive birds that had mobbed alongside knowledgeable birds later scolded at roughly 8x the control rate (27.8% of 54 vs 3.3% of 181). cross-domain: iterated transmission of a representation across individuals
- relates from In cued recall of oral-tradition-like verse, a rhyme cue alone yields P=.19 and a meaning cue alone P=.14, but the TWO cues together yield P=.97 — the constraints combine MULTIPLICATIVELY (superadditively), far above the ~.33 an additive model predicts. multi-constraint error-correction is the mechanism that sharpens convergence toward the shared prior
- relates from SOCIAL transmission (imitating others) homogenizes cultural material toward a shared attractor while SOLO transmission does not: in a sung-melody transmission experiment, social chains converged and solo chains did not. a large behavioral instance of convergence to a shared prior under social transmission