The paper

Publication

Logic replicant: a new machine learning algorithm for multiclass classification in small datasets. Pedro Corral, Roberto Centeno and Víctor Fresno. UNED Research Group in Natural Language Processing and Information Retrieval, Universidad Nacional de Educación a Distancia, c/Juan del Rosal 16, Madrid 28040, Spain. Machine Learning: Science and Technology 6 (2025) 025012, IOP Publishing. Open access under a Creative Commons Attribution 4.0 licence.

Timeline

Received 28 October 2024 · Revised 4 March 2025 · Accepted 1 April 2025 · Published 11 April 2025

Keywords

logic replicant, explainable machine learning algorithm, graphical interpretation, new machine learning model, small datasets, improved predictions

Corresponding author

Pedro Corral · ORCID 0000-0003-1908-6986

Abstract

In one paragraph: the paper presents a new machine learning model for sorting things into several classes. Instead of looking for examples that resemble each other, it fits a formula that imitates the actual rule behind the classes. Because of how it is built, it can in principle learn any rule that can be written as a table, and it also learns messier problems such as recognising handwritten digits or telling groups of mice apart from their proteins. Its results can be drawn as a picture, unlike those of neural networks or random forests. On four very different problems it predicted more accurately than the established methods it was compared with.

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 paper 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.

How to cite

Corral P, Centeno R and Fresno V 2025 Logic replicant: a new machine learning algorithm for multiclass classification in small datasets Mach. Learn.: Sci. Technol. 6 025012

@article{Corral2025LogicReplicant,
  author    = {Corral, Pedro and Centeno, Roberto and Fresno, V{\'i}ctor},
  title     = {Logic replicant: a new machine learning algorithm for
               multiclass classification in small datasets},
  journal   = {Machine Learning: Science and Technology},
  volume    = {6},
  number    = {2},
  pages     = {025012},
  year      = {2025},
  publisher = {IOP Publishing},
  doi       = {10.1088/2632-2153/adc86e}
}

Data, funding and licence

Data availability

The data that support the findings are openly available at github.com/pedrocorral/logic-replicant-datasets. Individual sets: 8-bit parity, Down syndrome mice (figshare), nucleosynthesis, handwritten digits (UCI).

Funding

Spanish Ministry of Science, Innovation and Universities, project FairTransNLP PID2021-124361OB-C32, funded by MCIN/AEI/10.13039/501100011033 and by ERDF, EU, A way of making Europe.

Licence

Original content of the paper under CC BY 4.0. The figures on this site are reproduced from the paper under that licence.