Design principles
The logic replicant was designed from scratch around four functional principles. The paper states them as hypotheses and provides the evidence for each.
Four plain promises the logic replicant is designed to keep, and the bets behind them.
Four promises
The model is smooth enough for the standard "nudge it a little, check, repeat" training used everywhere in modern machine learning.
Anything you could write down as a lookup table of inputs and answers, the replicant can reproduce. That covers every digital circuit and every game with fixed rules.
Instead of grouping look-alikes, it fits a formula that imitates the real reason behind the classes.
The learned logic can be drawn as a two-dimensional map: coloured islands for the classes, with every example plotted on it.
Three bets
Behind these promises are three bets about the world. First, that for most classification problems a simple rule exists that links the measurements to the class. Second, that this rule reflects the real mechanism at work, be it physics, biology or convention. Third, that the rule can be captured by a mathematical formula that redraws the data onto a map where the classes come apart. The experiments on the evidence pages are the test of these bets.
Two goals at once
Most tools give you either accuracy or an explanation. Ensembles of decision trees are accurate but opaque; a self-organising map gives a picture but weak predictions; a small neural network predicts well but shows nothing. The logic replicant aims to give both, so that a researcher facing a new problem has a good first solution and a picture of what it found.
Four principles
The model can take advantage of modern general optimisation methods, specifically the Adam variation of stochastic gradient descent. Its derivative is not continuous everywhere, but it is in most places, which is what gradient methods need. Training.
A deterministic finite-state machine maps categorical inputs to a deterministic output class with the help of states. Replicating any DFSM means replicating any deterministic logic on categorical variables, hence any combinational logic. Proof sketch.
Prediction is based on the logic that decides which inputs map to which outputs, beyond feature similarity. A parametric function \(L\) is fitted during training to be a good-enough approximation of the real function that describes the problem, using a strategy of low-entropy isolations. The strategy.
The replicant can generate two-dimensional plots of the classification logic, showing which instances are close or far under that logic and where the class limits are. Unlike t-SNE or SOM projections, the plot is directly tied to the learned logic. Interpretability.
Three underlying hypotheses
Behind these principles are three hypotheses about classification problems:
- It is possible to find a simple logic that correlates an instance's features with its right class.
- This logic replicates the real mechanism, cause or reason that determines how features are evaluated to identify the class.
- This logic can be represented by a mathematical function that maps the feature space \(X\) to a continuous space \(Q\) where classification is easier.
Two objectives
The design pursues two goals at once, which existing models usually offer only one at a time: consistently good predictive accuracy in multiclass classification, and a graphical explanation of the learned problem. Ensembles such as random forests and XGBoost offer accuracy without an interpretable view; a single self-organising map offers a view without competitive accuracy; a small multilayer perceptron is accurate but opaque. The logic replicant is meant to be a starting point for a researcher facing a new problem: a good solution in itself, or at worst a baseline for comparing an ad hoc method.