arXiv subjects

Mao Nishino

Publications and source records attributed to Mao Nishino.

8 recordsLinked to original sources

arXiv2026

Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics

A metric space $Z$ gives rise to three natural classes of infinite-dimensional metric spaces associated to $Z$: $p$-Wasserstein spaces of probability measures on $Z$, nonlinear Lebesgue $L^p$-spaces of $Z$-valued maps, and $p$-Gromov-Wasserstein spaces of $Z$-valued kernels. The latter class, referred to as $Z$-Gromov-Wasserstein ($Z$-GW) spaces, extends the classical Gromov-Wasserstein framework from metric measure spaces to more general, possibly attributed, network-like structures, and unifies many GW-type distances that nowadays play a significant role in metric geometry, data science and machine learning. In this article we develop a unified metric-geometric theory of these three classes of spaces, with a particular focus on the $Z$-GW spaces. Our first main result identifies a fundamental submetry structure linking them: the nonlinear Lebesgue space maps via a submetry onto the $Z$-GW space, which in turn maps via a submetry onto the Wasserstein space. This structure provides a mechanism for transferring geometric information among the three spaces. We apply this framework to geodesics and Alexandrov curvature. For $1<p<\infty$, we prove that geodesicity of $Z$ is equivalent to geodesicity of each of the three associated spaces; in the endpoint case $p=1$, all three associated spaces are geodesic, even when $Z$ is not. We also characterize geodesics in the $Z$-GW space as generalized interpolations, extending a known characterization in the classical setting due to Sturm. Finally, we give a complete classification of Alexandrov curvature bounds for these spaces in terms of the curvature of $Z$. Thus, while the main focus of the paper is a new metric-geometric theory of $Z$-GW spaces, the submetry framework also extends classical theorems for Wasserstein and Gromov-Wasserstein spaces and yields new geometric consequences for nonlinear Lebesgue spaces.

math.MG↗

arXiv2026

Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models

As Large Language Models (LLMs) are increasingly integrated into agentic workflows, their unpredictability stemming from numerical instability has emerged as a critical reliability issue. While recent studies have demonstrated the significant downstream effects of these instabilities, the root causes and underlying mechanisms remain poorly understood. In this paper, we present a rigorous analysis of how unpredictability is rooted in the finite numerical precision of floating-point representations, tracking how rounding errors propagate, amplify, or dissipate through Transformer computation layers. Specifically, we identify a chaotic "avalanche effect" in the early layers, where minor perturbations trigger binary outcomes: either rapid amplification or complete attenuation. Beyond specific error instances, we demonstrate that LLMs exhibit universal, scale-dependent chaotic behaviors characterized by three distinct regimes: 1) a stable regime, where perturbations fall below an input-dependent threshold and vanish, resulting in constant outputs; 2) a chaotic regime, where rounding errors dominate and drive output divergence; and 3) a signal-dominated regime, where true input variations override numerical noise. We validate these findings extensively across multiple datasets and model architectures.

cs.AI↗

arXiv2025

The Z-Gromov-Wasserstein Distance

The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly complex structure (such as node and edge-attributed graphs), several variants of GW distance have been introduced in the recent literature. With a view toward establishing a general framework for the theory of GW-like distances, this paper considers a vast generalization of the notion of a metric measure space: for an arbitrary metric space $Z$, we define a $Z$-network to be a measure space endowed with a kernel valued in $Z$. We introduce a method for comparing $Z$-networks by defining a generalization of GW distance, which we refer to as $Z$-Gromov-Wasserstein ($Z$-GW) distance. This construction subsumes many previously known metrics and offers a unified approach to understanding their shared properties. This paper demonstrates that the $Z$-GW distance defines a metric on the space of $Z$-networks which retains desirable properties of $Z$, such as separability, completeness, and geodesicity. Many of these properties were unknown for existing variants of GW distance that fall under our framework. Our focus is on foundational theory, but our results also include computable lower bounds and approximations of the distance which will be useful for practical applications.

math.MG↗

arXiv2025

A Benamou-Brenier Proximal Splitting Method for Constrained Unbalanced Optimal Transport

The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the Fisher-Rao metric, the resulting model is referred to as the Wasserstein-Fisher-Rao (WFR) setting, and allows for the comparison between any two positive measures without the need for equalized total mass. In recent work, we introduced a constrained variant of this model, in which affine integral equality constraints are imposed along the measure path. In the present paper, we propose a further generalization of this framework, which allows for constraints that apply not just to the density path but also to the momentum and source terms, and incorporates affine inequalities in addition to equality constraints. We prove, under suitable assumptions on the constraints, the well-posedness of the resulting class of convex variational problems. The paper is then primarily devoted to developing an effective numerical pipeline that tackles the corresponding constrained optimization problem based on finite difference discretizations and parallel proximal schemes. Our proposed framework encompasses standard balanced and unbalanced optimal transport, as well as a multitude of natural and practically relevant constraints, and we highlight its versatility via several synthetic and real data examples.

math.OC↗

arXiv2025

Universal and Transferable Adversarial Attack on Large Language Models Using Exponentiated Gradient Descent

As large language models (LLMs) are increasingly deployed in critical applications, ensuring their robustness and safety alignment remains a major challenge. Despite the overall success of alignment techniques such as reinforcement learning from human feedback (RLHF) on typical prompts, LLMs remain vulnerable to jailbreak attacks enabled by crafted adversarial triggers appended to user prompts. Most existing jailbreak methods either rely on inefficient searches over discrete token spaces or direct optimization of continuous embeddings. While continuous embeddings can be given directly to selected open-source models as input, doing so is not feasible for proprietary models. On the other hand, projecting these embeddings back into valid discrete tokens introduces additional complexity and often reduces attack effectiveness. We propose an intrinsic optimization method which directly optimizes relaxed one-hot encodings of the adversarial suffix tokens using exponentiated gradient descent coupled with Bregman projection, ensuring that the optimized one-hot encoding of each token always remains within the probability simplex. We provide theoretical proof of convergence for our proposed method and implement an efficient algorithm that effectively jailbreaks several widely used LLMs. Our method achieves higher success rates and faster convergence compared to three state-of-the-art baselines, evaluated on five open-source LLMs and four adversarial behavior datasets curated for evaluating jailbreak methods. In addition to individual prompt attacks, we also generate universal adversarial suffixes effective across multiple prompts and demonstrate transferability of optimized suffixes to different LLMs.

cs.LG↗

arXiv2025

Path constrained unbalanced optimal transport

Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently natural to require paths of distributions to satisfy additional conditions. Inspired by this, we introduce a model for dynamical OT which incorporates constraints on the space of admissible paths into the framework of unbalanced OT, where the source and target measures are allowed to have a different total mass. Our main results establish, for several general families of constraints, the existence of solutions to the variational problem which defines this path constrained unbalanced optimal transport framework. These results are primarily concerned with distributions defined on a Euclidean space, but we extend them to distributions defined over parallelizable Riemannian manifolds as well. We also consider metric properties of our framework, showing that, for certain types of constraints, our model defines a metric on the relevant space of distributions. This metric is shown to arise as a geodesic distance of a Riemannian metric, obtained through an analogue of Otto's submersion in the classical OT setting.

math.OC↗

arXiv2025

Adversarial Attack on Large Language Models using Exponentiated Gradient Descent

As Large Language Models (LLMs) are widely used, understanding them systematically is key to improving their safety and realizing their full potential. Although many models are aligned using techniques such as reinforcement learning from human feedback (RLHF), they are still vulnerable to jailbreaking attacks. Some of the existing adversarial attack methods search for discrete tokens that may jailbreak a target model while others try to optimize the continuous space represented by the tokens of the model's vocabulary. While techniques based on the discrete space may prove to be inefficient, optimization of continuous token embeddings requires projections to produce discrete tokens, which might render them ineffective. To fully utilize the constraints and the structures of the space, we develop an intrinsic optimization technique using exponentiated gradient descent with the Bregman projection method to ensure that the optimized one-hot encoding always stays within the probability simplex. We prove the convergence of the technique and implement an efficient algorithm that is effective in jailbreaking several widely used LLMs. We demonstrate the efficacy of the proposed technique using five open-source LLMs on four openly available datasets. The results show that the technique achieves a higher success rate with great efficiency compared to three other state-of-the-art jailbreaking techniques. The source code for our implementation is available at: https://github.com/sbamit/Exponentiated-Gradient-Descent-LLM-Attack

cs.LG↗

arXiv2025

Mechanistic Understandings of Representation Vulnerabilities and Engineering Robust Vision Transformers

While transformer-based models dominate NLP and vision applications, their underlying mechanisms to map the input space to the label space semantically are not well understood. In this paper, we study the sources of known representation vulnerabilities of vision transformers (ViT), where perceptually identical images can have very different representations and semantically unrelated images can have the same representation. Our analysis indicates that imperceptible changes to the input can result in significant representation changes, particularly in later layers, suggesting potential instabilities in the performance of ViTs. Our comprehensive study reveals that adversarial effects, while subtle in early layers, propagate and amplify through the network, becoming most pronounced in middle to late layers. This insight motivates the development of NeuroShield-ViT, a novel defense mechanism that strategically neutralizes vulnerable neurons in earlier layers to prevent the cascade of adversarial effects. We demonstrate NeuroShield-ViT's effectiveness across various attacks, particularly excelling against strong iterative attacks, and showcase its remarkable zero-shot generalization capabilities. Without fine-tuning, our method achieves a competitive accuracy of 77.8% on adversarial examples, surpassing conventional robustness methods. Our results shed new light on how adversarial effects propagate through ViT layers, while providing a promising approach to enhance the robustness of vision transformers against adversarial attacks. Additionally, they provide a promising approach to enhance the robustness of vision transformers against adversarial attacks.

cs.CV↗