arXiv subjects

Hiroshi Kera

Publications and source records attributed to Hiroshi Kera.

At least 37 records · Page 2Linked to original sources

arXiv2025

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation

This paper studies the concept and the computation of approximately vanishing ideals of a finite set of data points. By data points, we mean that the points contain some uncertainty, which is a key motivation for the approximate treatment. A careful review of the existing border basis concept for an exact treatment motivates a new adaptation of the border basis concept for an approximate treatment. In the study of approximately vanishing polynomials, the normalization of polynomials plays a vital role. So far, the most common normalization in computational commutative algebra uses the coefficient norm of a polynomial. Inspired by recent developments in machine learning, the present paper proposes and studies the use of gradient-weighted normalization. The gradient-weighted semi-norm evaluates the gradient of a polynomial at the data points. This data-driven nature of gradient-weighted normalization produces, on the one hand, better stability against perturbation and, on the other hand, very significantly, invariance of border bases with respect to scaling the data points. Neither property is achieved with coefficient normalization. In particular, we present an example of the lack of scaling invariance with respect to coefficient normalization, which can cause an approximate border basis computation to fail. This is extremely relevant because scaling of the point set is often recommended for preprocessing the data. Further, we use an existing algorithm with coefficient normalization to show that it is easily adapted to gradient-weighted normalization. The analysis of the adapted algorithm only requires tiny changes, and the time complexity remains the same. Finally, we present numerical experiments on three affine varieties to demonstrate the superior stability of our data-driven normalization over coefficient normalization. We obtain robustness to perturbations and invariance to scaling.

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arXiv2025

CALT: A Library for Computer Algebra with Transformer

Recent advances in artificial intelligence have demonstrated the learnability of symbolic computation through end-to-end deep learning. Given a sufficient number of examples of symbolic expressions before and after the target computation, Transformer models - highly effective learners of sequence-to-sequence functions - can be trained to emulate the computation. This development opens up several intriguing challenges and new research directions, which require active contributions from the symbolic computation community. In this work, we introduce Computer Algebra with Transformer (CALT), a user-friendly Python library designed to help non-experts in deep learning train models for symbolic computation tasks.

cs.LG↗

arXiv2025

Adversarial Training from Mean Field Perspective

Although adversarial training is known to be effective against adversarial examples, training dynamics are not well understood. In this study, we present the first theoretical analysis of adversarial training in random deep neural networks without any assumptions on data distributions. We introduce a new theoretical framework based on mean field theory, which addresses the limitations of existing mean field-based approaches. Based on this framework, we derive (empirically tight) upper bounds of $\ell_q$ norm-based adversarial loss with $\ell_p$ norm-based adversarial examples for various values of $p$ and $q$. Moreover, we prove that networks without shortcuts are generally not adversarially trainable and that adversarial training reduces network capacity. We also show that network width alleviates these issues. Furthermore, we present the various impacts of the input and output dimensions on the upper bounds and time evolution of the weight variance.

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arXiv2025

Cross-Model Transfer of Task Vectors via Few-Shot Orthogonal Alignment

Task arithmetic enables efficient model editing by representing task-specific changes as vectors in parameter space. Task arithmetic typically assumes that the source and target models are initialized from the same pre-trained parameters. This assumption limits its applicability in cross-model transfer settings, where models are independently pre-trained on different datasets. To address this challenge, we propose a method based on few-shot orthogonal alignment, which aligns task vectors to the parameter space of a differently pre-trained target model. These transformations preserve key properties of task vectors, such as norm and rank, and are learned using only a small number of labeled examples. We evaluate the method using two Vision Transformers pre-trained on YFCC100M and LAION400M, and test on eight classification datasets. Experimental results show that our method improves transfer accuracy over direct task vector application and achieves performance comparable to few-shot fine-tuning, while maintaining the modularity and reusability of task vectors. Our code is available at https://github.com/kawakera-lab/CrossModelTransfer.

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arXiv2025

Adapter Merging with Centroid Prototype Mapping for Scalable Class-Incremental Learning

We propose Adapter Merging with Centroid Prototype Mapping (ACMap), an exemplar-free framework for class-incremental learning (CIL) that addresses both catastrophic forgetting and scalability. While existing methods involve a trade-off between inference time and accuracy, ACMap consolidates task-specific adapters into a single adapter, thus achieving constant inference time across tasks without sacrificing accuracy. The framework employs adapter merging to build a shared subspace that aligns task representations and mitigates forgetting, while centroid prototype mapping maintains high accuracy by consistently adapting representations within the shared subspace. To further improve scalability, an early stopping strategy limits adapter merging as tasks increase. Extensive experiments on five benchmark datasets demonstrate that ACMap matches state-of-the-art accuracy while maintaining inference time comparable to the fastest existing methods. The code is available at https://github.com/tf63/ACMap.

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arXiv2025

Undertrained Image Reconstruction for Realistic Degradation in Blind Image Super-Resolution

Most super-resolution (SR) models struggle with real-world low-resolution (LR) images. This issue arises because the degradation characteristics in the synthetic datasets differ from those in real-world LR images. Since SR models are trained on pairs of high-resolution (HR) and LR images generated by downsampling, they are optimized for simple degradation. However, real-world LR images contain complex degradation caused by factors such as the imaging process and JPEG compression. Due to these differences in degradation characteristics, most SR models perform poorly on real-world LR images. This study proposes a dataset generation method using undertrained image reconstruction models. These models have the property of reconstructing low-quality images with diverse degradation from input images. By leveraging this property, this study generates LR images with diverse degradation from HR images to construct the datasets. Fine-tuning pre-trained SR models on our generated datasets improves noise removal and blur reduction, enhancing performance on real-world LR images. Furthermore, an analysis of the datasets reveals that degradation diversity contributes to performance improvements, whereas color differences between HR and LR images may degrade performance. 11 pages, (11 figures and 2 tables)

eess.IV↗

arXiv2025

Wide Two-Layer Networks can Learn from Adversarial Perturbations

Adversarial examples have raised several open questions, such as why they can deceive classifiers and transfer between different models. A prevailing hypothesis to explain these phenomena suggests that adversarial perturbations appear as random noise but contain class-specific features. This hypothesis is supported by the success of perturbation learning, where classifiers trained solely on adversarial examples and the corresponding incorrect labels generalize well to correctly labeled test data. Although this hypothesis and perturbation learning are effective in explaining intriguing properties of adversarial examples, their solid theoretical foundation is limited. In this study, we theoretically explain the counterintuitive success of perturbation learning. We assume wide two-layer networks and the results hold for any data distribution. We prove that adversarial perturbations contain sufficient class-specific features for networks to generalize from them. Moreover, the predictions of classifiers trained on mislabeled adversarial examples coincide with those of classifiers trained on correctly labeled clean samples. The code is available at https://github.com/s-kumano/perturbation-learning.

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arXiv2024

Learning to Compute Gröbner Bases

Solving a polynomial system, or computing an associated Gröbner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the worst case. This paper is the first to address the learning of Gröbner basis computation with Transformers. The training requires many pairs of a polynomial system and the associated Gröbner basis, raising two novel algebraic problems: random generation of Gröbner bases and transforming them into non-Gröbner ones, termed as backward Gröbner problem. We resolve these problems with 0-dimensional radical ideals, the ideals appearing in various applications. Further, we propose a hybrid input embedding to handle coefficient tokens with continuity bias and avoid the growth of the vocabulary set. The experiments show that our dataset generation method is a few orders of magnitude faster than a naive approach, overcoming a crucial challenge in learning to compute Gröbner bases, and Gröbner computation is learnable in a particular class.

math.AC↗

arXiv2024

Low-Quality Image Detection by Hierarchical VAE

To make an employee roster, photo album, or training dataset of generative models, one needs to collect high-quality images while dismissing low-quality ones. This study addresses a new task of unsupervised detection of low-quality images. We propose a method that not only detects low-quality images with various types of degradation but also provides visual clues of them based on an observation that partial reconstruction by hierarchical variational autoencoders fails for low-quality images. The experiments show that our method outperforms several unsupervised out-of-distribution detection methods and also gives visual clues for low-quality images that help humans recognize them even in thumbnail view.

cs.CV↗

arXiv2024

Identifying Important Group of Pixels using Interactions

To better understand the behavior of image classifiers, it is useful to visualize the contribution of individual pixels to the model prediction. In this study, we propose a method, MoXI ($\textbf{Mo}$del e$\textbf{X}$planation by $\textbf{I}$nteractions), that efficiently and accurately identifies a group of pixels with high prediction confidence. The proposed method employs game-theoretic concepts, Shapley values and interactions, taking into account the effects of individual pixels and the cooperative influence of pixels on model confidence. Theoretical analysis and experiments demonstrate that our method better identifies the pixels that are highly contributing to the model outputs than widely-used visualization by Grad-CAM, Attention rollout, and Shapley value. While prior studies have suffered from the exponential computational cost in the computation of Shapley value and interactions, we show that this can be reduced to quadratic cost for our task. The code is available at https://github.com/KosukeSumiyasu/MoXI.

cs.CV↗

arXiv2024

VarteX: Enhancing Weather Forecast through Distributed Variable Representation

Weather forecasting is essential for various human activities. Recent data-driven models have outperformed numerical weather prediction by utilizing deep learning in forecasting performance. However, challenges remain in efficiently handling multiple meteorological variables. This study proposes a new variable aggregation scheme and an efficient learning framework for that challenge. Experiments show that VarteX outperforms the conventional model in forecast performance, requiring significantly fewer parameters and resources. The effectiveness of learning through multiple aggregations and regional split training is demonstrated, enabling more efficient and accurate deep learning-based weather forecasting.

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arXiv2024

Theoretical Understanding of Learning from Adversarial Perturbations

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

cs.LG↗

arXiv2023

Monomial-agnostic computation of vanishing ideals

In the last decade, the approximate basis computation of vanishing ideals has been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term order remain essential gaps between the two fields. In this study, we present the first $\textit{monomial-agnostic}$ basis computation, which works fully numerically with proper normalization and without term order. This is realized by gradient normalization, a newly proposed data-dependent normalization that normalizes a polynomial with the magnitude of gradients at given points. The data-dependent nature of gradient normalization brings various significant advantages: i) efficient resolution of the spurious vanishing problem, the scale-variance issue of approximately vanishing polynomials, without accessing coefficients of terms, ii) scaling-consistent basis computation, ensuring that input scaling does not lead to an essential change in the output, and iii) robustness against input perturbations, where the upper bound of error is determined only by the magnitude of the perturbations. Existing studies did not achieve any of these. As further applications of gradient information, we propose a monomial-agnostic basis reduction method and a regularization method to manage positive-dimensional ideals.

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arXiv2023

Fourier Analysis on Robustness of Graph Convolutional Neural Networks for Skeleton-based Action Recognition

Using Fourier analysis, we explore the robustness and vulnerability of graph convolutional neural networks (GCNs) for skeleton-based action recognition. We adopt a joint Fourier transform (JFT), a combination of the graph Fourier transform (GFT) and the discrete Fourier transform (DFT), to examine the robustness of adversarially-trained GCNs against adversarial attacks and common corruptions. Experimental results with the NTU RGB+D dataset reveal that adversarial training does not introduce a robustness trade-off between adversarial attacks and low-frequency perturbations, which typically occurs during image classification based on convolutional neural networks. This finding indicates that adversarial training is a practical approach to enhancing robustness against adversarial attacks and common corruptions in skeleton-based action recognition. Furthermore, we find that the Fourier approach cannot explain vulnerability against skeletal part occlusion corruption, which highlights its limitations. These findings extend our understanding of the robustness of GCNs, potentially guiding the development of more robust learning methods for skeleton-based action recognition.

cs.CV↗

arXiv2023

Improving Zero-Shot Action Recognition using Human Instruction with Text Description

Zero-shot action recognition, which recognizes actions in videos without having received any training examples, is gaining wide attention considering it can save labor costs and training time. Nevertheless, the performance of zero-shot learning is still unsatisfactory, which limits its practical application. To solve this problem, this study proposes a framework to improve zero-shot action recognition using human instructions with text descriptions. The proposed framework manually describes video contents, which incurs some labor costs; in many situations, the labor costs are worth it. We manually annotate text features for each action, which can be a word, phrase, or sentence. Then by computing the matching degrees between the video and all text features, we can predict the class of the video. Furthermore, the proposed model can also be combined with other models to improve its accuracy. In addition, our model can be continuously optimized to improve the accuracy by repeating human instructions. The results with UCF101 and HMDB51 showed that our model achieved the best accuracy and improved the accuracies of other models.

cs.CV↗

arXiv2023

Exploiting Frequency Spectrum of Adversarial Images for General Robustness

In recent years, there has been growing concern over the vulnerability of convolutional neural networks (CNNs) to image perturbations. However, achieving general robustness against different types of perturbations remains challenging, in which enhancing robustness to some perturbations (e.g., adversarial perturbations) may degrade others (e.g., common corruptions). In this paper, we demonstrate that adversarial training with an emphasis on phase components significantly improves model performance on clean, adversarial, and common corruption accuracies. We propose a frequency-based data augmentation method, Adversarial Amplitude Swap, that swaps the amplitude spectrum between clean and adversarial images to generate two novel training images: adversarial amplitude and adversarial phase images. These images act as substitutes for adversarial images and can be implemented in various adversarial training setups. Through extensive experiments, we demonstrate that our method enables the CNNs to gain general robustness against different types of perturbations and results in a uniform performance against all types of common corruptions.

cs.CV↗

arXiv2023

Approximate Vanishing Ideal Computations at Scale

The vanishing ideal of a set of points $X = \{\mathbf{x}_1, \ldots, \mathbf{x}_m\}\subseteq \mathbb{R}^n$ is the set of polynomials that evaluate to $0$ over all points $\mathbf{x} \in X$ and admits an efficient representation by a finite subset of generators. In practice, to accommodate noise in the data, algorithms that construct generators of the approximate vanishing ideal are widely studied but their computational complexities remain expensive. In this paper, we scale up the oracle approximate vanishing ideal algorithm (OAVI), the only generator-constructing algorithm with known learning guarantees. We prove that the computational complexity of OAVI is not superlinear, as previously claimed, but linear in the number of samples $m$. In addition, we propose two modifications that accelerate OAVI's training time: Our analysis reveals that replacing the pairwise conditional gradients algorithm, one of the solvers used in OAVI, with the faster blended pairwise conditional gradients algorithm leads to an exponential speed-up in the number of features $n$. Finally, using a new inverse Hessian boosting approach, intermediate convex optimization problems can be solved almost instantly, improving OAVI's training time by multiple orders of magnitude in a variety of numerical experiments.

cs.LG↗

arXiv2022

Vanishing Component Analysis with Contrastive Normalization

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.

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