Introduction · 04 / 04
Glossary
The terms used across these pages, several of them coined in the paper.
The words used across these pages, explained without symbols.
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The words, in plain language
Logic replicantThe whole model: a map-drawing formula plus a set of vortices.
Feature spaceThe original description of an example: its list of measurements.
Space QThe new map that the formula draws. Two dimensions give a picture; more dimensions can give more accuracy.
Leietanic functionThe map-drawing formula. A map counts as leietanic when it separates the classes better than the original measurements did.
QuonAn example once it has been placed on the new map.
VortexA figurative whirlpool planted on the map. It belongs to one class and claims the territory where its pull is strongest.
Low-entropy isolationA region of the map that contains examples of a single class. Training tries to create these.
Compact logicA rule with few exceptions that uses several measurements at once, like "more calories burned than eaten".
Finite-state machineAny rule you can write as a lookup table of states, inputs and outputs. The replicant can imitate all of them.
TrainingNudging the formula and the vortices, thousands of small steps at a time, until every territory holds one class.
Terms
Logic replicantA tuple \(\langle L, V\rangle\) of a leietanic function and a set of vortices that replicates the hidden classification logic of a problem.
Feature space \(X\)The original space of the instances, \(X\subset\mathbb{R}^F\) with \(F\) features.
Space \(Q\)The transformed space, \(Q\subset\mathbb{R}^D\). \(D\) is chosen freely; \(D=2\) allows plotting.
Leietanic function \(L\)The transformation \(L\colon X\to Q\). A transformation is leietanic when it lowers the isolation measure \(B\) relative to the original space.
QuonAn instance after transformation, \(\boldsymbol{q}=L(\boldsymbol{x})\): a point of \(Q\).
VortexA scalar field in \(Q\) with a centre \(\boldsymbol{v}\), a density \(\rho\) and an intensity \(\Phi\), assigned to one class. It claims the region where its field is the greatest.
Scalar field of a class \(U_c\)The sum of the fields of the class's vortices. The class with the greatest \(U_c(\boldsymbol{q})\) is the prediction.
Low-entropy isolation (LEI)An area of \(Q\) where instances of essentially one class are found, so local entropy is low. Training aims to produce them.
Homogeneous / heterogeneous fields\(W_{\text{hom}}\) sums the interactions of a quon with same-class quons, \(W_{\text{het}}\) with other-class quons.
Isolation measure \(B\)\(B=(\Gamma_{\text{het}}-\Gamma_{\text{hom}})/(\Gamma_{\text{het}}+\Gamma_{\text{hom}})\), from \(1\) (fully mixed) to \(-1\) (perfectly isolated classes).
Compact logicA logic that identifies the elements of a class by a relation involving more than one feature at a time, with few exceptions.
DFSMDeterministic finite-state machine, a quintuple \(\langle I,O,S,\delta,\lambda\rangle\) of inputs, outputs, states, a transition function and an output function.
\(S\), \(R\)The two structural sizes of the leietanic function: \(S\) matrices \(\boldsymbol{\Lambda}_s\) and \(R\) folded terms per matrix.
\(|V|\), \(K\)Total number of vortices and number of vortices per class, \(|V|=|C|\cdot K\).