Matlab and Mathematica scripts used to perform the simulations and analyses shown in
Di Antonio G, Raglio S and Mattia M. 2023. Ranking and serial thinking: A geometric solution.
The following codes are used to reproduce the results in Figure 6-7-8.
The "MatlabLibrary" folder must be added to the path in order to run all other scripts. It contains codes related to network settings and dynamics.
The "Single_Run" folder contains codes to train and test a single network on the Transitive inference task and check it inside.
The "Multiple_Runs" folder contains codes related to results averaged over multiple task realizations and network structures.
For Figure 3-4-5 the code used to produce the presented results in the following folders:
"Fig3_GMLlearning", simulations and related plots (PDF files) of the Perceptron-like shallow networks learning via classical conditioning (pseudo-inverse approach equivalent to delta rule learning) a transitive inference task. Each subfolder is associated to a different sensory noise. The Matlab scripts to run are computeAndTestGMLOnAverage.m.
"Fig4_NonLinear", simulations of GML learned on Immediate serial-recall and Biased transitive inference. The corresponding scripts for running these simulations are Perceptron_SerialRecall.m and Perceptron_BiasedTI.m. Additionally, Perceptron_DiffTrials.m can be used to reproduce Supplementary Figure 1.
"Fig5_IntegratorOnGML", simulations and related plots (PDF files) of the stochastic dynamics associated to the projection on the geometric mental line of the neural state of the network receiving as input the symbolic distance of the presented pairs of items. The Matlab script to run is plotIntegratorOnGML.m. In the subfolder "Mathematica" can be found the script FPTofWienerProcWithTwoAbsorbBarr.nb used to computed and plot the theoretical derivations related to the average reaction times and accuracy.