Ryosuke Masuya

Ryosuke Masuya, Yuichi Ike, Hiroshi Kera

Vanishing component analysis (VCA) computes approximate generators of vanishing ideals of samples, which are further used for extracting nonlinear features of the samples. Recent studies have shown that normalization of approximate generators plays an important role and different normalization leads to generators of different properties. In this paper, inspired by recent self-supervised frameworks, we propose a contrastive normalization method for VCA, where we impose the generators to vanish on the target samples and to be normalized on the transformed samples. We theoretically show that a contrastive normalization enhances the discriminative power of VCA, and provide the algebraic interpretation of VCA under our normalization. Numerical experiments demonstrate the effectiveness of our method. This is the first study to tailor the normalization of approximate generators of vanishing ideals to obtain discriminative features.

Hanato Kikuchi, Ryosuke Masuya, Kazuhiko Kawamoto et al.

Learning parity functions, more general modular addition, is a challenging machine learning task due to its input sensitivity. A recent study substantially scaled modular addition learning in both the number of summands and the modulus. Its key idea is to increase zeros in training sequences, reducing the effective number of summands and thus controlling training difficulty; however, this induces covariate shift between training and test input distributions. This study theoretically and empirically analyzes this side effect and proposes a covariate-shift-free method for modular addition. Specifically, we introduce an auxiliary modulus $Kq$ during training, which reduces wrap-around frequency and problem difficulty while preserving the same input distribution across training and testing. Experiments show strong scalability and sample efficiency: even for large input length $N$, large modulus $q$, and small datasets -- where the sparse method fails to learn -- our method achieves equal or better match accuracy and relaxed $τ$-accuracy. For example, at $N=64$ and $q=974269$, our method trained on 100K samples achieves $97.0\%$ $τ$-accuracy at $τ=0.05$, while the sparse method achieves only $9.5\%$ with the same data size and $93.9\%$ even when extended to 1M samples.