Logic replicant: a new machine learning algorithm for multiclass classification in small datasets

Abstract Multiclass classification with small datasets often presents a significant challenge for conventional machine learning (ML) algorithms, predicting with an accuracy affected by this context of data scarcity. To remedy this, this papers presents a novel ML model based on a differentiable deterministic finite-state machine (DFSM) that improves the prediction performance compared with state-of-the-art multiclass classifiers applied in this ambit of small data per class. The proposed model uses a logic-arithmetic function that replicates the inherent classification logic of the problem rather than finding patterns of feature similarity. Our algorithm, called logic replicant, allows to learn problems that other classification models cannot. As the logic replicant is a DFSM it can learn any combinational logic, but it goes beyond this point learning other types of problems such as handwritten-digit recognition, and the detection of mice with Down syndrome based on the presence of 77 proteins. Our ML algorithm is also easy to interpret using quantitative diagrams, in comparison to less interpretable algorithms such as artificial neural networks, random forest, and others. The results obtained with different data sets related to math, physics, biology and image recognition show that our design based on a logic-arithmetic function and being a DFSM improves the generalisation capacity (better prediction accuracy) of the logic replicant compared to other state-of-the-art ML approaches.