Tootfinder

Two-dimensional Rademacher walk
Satyaki Bhattacharya, Stanislav Volkov
https://arxiv.org/abs/2506.16259 https://arxiv.org/pdf/2506.16…

Two-dimensional Rademacher walk
We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (2023) to $\mathbb{Z}^2$ (for $d\ge 3$, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Englander and Volkov (2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the $n$th step is $a_n$ where $\{a_n\}$ is a given sequence of positive …

Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
Jiyoung Park, Abhishek Roy, Jonathan W. Siegel, Anirban Bhattacharya
https://arxiv.org/abs/2506.06160

Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the recent success of varying step-size methods in the Euclidean setting, we undertake a study of such algorithms in the Riemannian setting. We show that varying step-size acceleration can be achieved in non-negatively curved Riemannian manifolds under geodesic s…

A deep shotgun method for solving high-dimensional parabolic partial differential equations
Wenjun Xu, Wenzhong Zhang
https://arxiv.org/abs/2506.15481 http…

A deep shotgun method for solving high-dimensional parabolic partial differential equations
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most existing methods requires simulating multiple trajectories of stochastic processes with a small step size of time discretization to ensure accuracy, hence having limited performance, especially when solving on a large time interval. To address such issue, we propos…

Improving population size adapting CMA-ES algorithm on step-size blow-up in weakly-structured multimodal functions
Chandula Fernando, Kushani De Silva
https://arxiv.org/abs/2506.00825

Improving population size adapting CMA-ES algorithm on step-size blow-up in weakly-structured multimodal functions
Multimodal optimization requires both exploration and exploitation. Exploration identifies promising attraction basins, while exploitation finds the best solutions within these basins. The balance between exploration and exploitation can be maintained by adjusting parameter settings. The population size adaptation covariance matrix adaption evolutionary strategy algorithm (PSA-CMA-ES) achieves this balance by dynamically adjusting population size. PSA-CMA-ES performs well on well-structured mul…

This https://arxiv.org/abs/2504.01759 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dyna…

This https://arxiv.org/abs/2502.13943 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence
Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the …

Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states
Zijun Zhao, Shuhang Li, Francesco A. Evangelista
https://arxiv.org/abs/2506.13693

Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states
We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for systems with strongly correlated ground and excited states. The EOM step scales as $O(N^5)$ with the basis set size $N$, allowing for efficient calculation of spect…

This https://arxiv.org/abs/2505.21700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Rethinking Chunk Size For Long-Document Retrieval: A Multi-Dataset Analysis
Chunking is a crucial preprocessing step in retrieval-augmented generation (RAG) systems, significantly impacting retrieval effectiveness across diverse datasets. In this study, we systematically evaluate fixed-size chunking strategies and their influence on retrieval performance using multiple embedding models. Our experiments, conducted on both short-form and long-form datasets, reveal that chunk size plays a critical role in retrieval effectiveness -- smaller chunks (64-128 tokens) are optim…

This https://arxiv.org/abs/2504.01759 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Alpha-Beta HMM: Hidden Markov Model Filtering with Equal Exit Probabilities and a Step-Size Parameter
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we propose the $αβ$-HMM algorithm, which simplifies the state transition model to a Markov chain with equal exit probabilities and introduces a step-size parameter to balance the influence of observational data and the model. By analyzing the algorithm's dyna…

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Haiquan Zhao, Chengjin Li
https://arxiv.org/abs/2506.00403 https://

Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation
Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks. The existing work has completed the steady state error analysis of the GSP LMS algorithm and GSP RLS algorithm in Gaussian noise scenarios, and a range of values for the step size of the GSP LMS algorithm has also been given. Meanwhile, the transient error a…

Statistical microlocal analysis in two-dimensional X-ray CT
Anuj Abhishek, Alexander Katsevich, James W. Webber
https://arxiv.org/abs/2506.05113 https://…

Statistical microlocal analysis in two-dimensional X-ray CT
In many imaging applications it is important to assess how well the edges of the original object, $f$, are resolved in an image, $f^\text{rec}$, reconstructed from the measured data, $g$. In this paper we consider the case of image reconstruction in 2D X-ray Computed Tomography (CT). Let $f$ be a function describing the object being scanned, and $g=Rf + η$ be the Radon transform data in $\mathbb{R}^2$ corrupted by noise, $η$, and sampled with step size $\simε$. Conventional microlocal analys…

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
Matteo Ferrari, Ilaria Perugia, Enrico Zampa
https://arxiv.org/abs/2506.05886

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findin…

This https://arxiv.org/abs/2502.03701 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

First-ish Order Methods: Hessian-aware Scalings of Gradient Descent
Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural scaling, which often necessitates expensive line searches or heuristic tuning to determine an appropriate step size. In this paper, we address this limitation by incorporating Hessian information to scale the gradient direction. By accounting for the curvatur…