Data Evolution by Wittgenstein's Rule Following

2026-06-21

AI Summary

This work addresses the challenge of generating new datasets from sequences of historical datasets that adhere to implicit rules and preserve family resemblance, rather than relying on simple sampling or augmentation. Inspired by Wittgenstein’s notions of rule-following and family resemblance, the authors propose a data evolution framework grounded in structured descriptors capturing geometric, distributional, clustering, and labeling characteristics. Generation is guided in descriptor space through trajectory extrapolation, historical averaging, hybrid recombination, and differentiable optimization. This approach uniquely introduces the philosophical concept of rule-following into data generation, enabling semantically coherent dataset continuation across varying sizes and dimensions without assuming direct transformations of prior data. Experiments demonstrate its effectiveness in producing structurally sound and semantically consistent supervised and unsupervised datasets on both synthetic and image benchmarks.

Abstract

This paper introduces Wittgenstein's Rule Following (WRF) data evolution, a framework in philomatics for evolving or generating a new dataset from a sequence of previously observed datasets. The method is inspired by Ludwig Wittgenstein's rule-following considerations and his notion of family resemblance in Philosophical Investigations. Unlike standard synthetic data generation, where the goal is usually to sample from or augment a fixed distribution, WRF aims to continue the implicit rule expressed by a historical sequence of datasets while preserving resemblance to the previous datasets. WRF represents each dataset by structural descriptors rather than pointwise correspondences. These descriptors summarize geometric, distributional, clustering, and, in the supervised case, label-based properties of the data. The method predicts a rule-following target by extrapolating descriptor trajectories and a family-resemblance target by averaging historical descriptors. Candidate datasets are then generated from the observed history through balanced or bounded mixture recombination, scored according to these targets, and optionally refined through differentiable optimization in descriptor space. The proposed framework allows both sample size and feature dimension to vary over time and does not assume that the next dataset is a direct transformation of the last one. Simulations on synthetic and image datasets show that WRF can generate meaningful continuations of evolving datasets in both unsupervised and supervised settings.

Problem

• data evolution
• rule following
• family resemblance
• dataset generation
• structural descriptors

Innovation

• Wittgenstein's Rule Following
• data evolution
• structural descriptors
• family resemblance
• synthetic data generation