Papers › Real-valued continued fraction of straight lines

Real-valued continued fraction of straight lines

16 Dec 2024arXiv:2412.16191archive 2025-07-28

Vijay Prakash S

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

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Tasks

Image Classificationimage-classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Image Classification Fashion-MNIST Continued fraction of straight lines Accuracy 84.12 #33 of 34 Archive leaderboard report
Image Classification Fashion-MNIST Continued fraction of straight lines NMI 74.4 #33 of 34 Archive leaderboard report
Image Classification Fashion-MNIST Continued fraction of straight lines Trainable Parameters 7870 #33 of 34 Archive leaderboard report

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Methods

a-m-lines

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