Tootfinder

This is the third full build iteration of my miniature #QRP unun supporting both EFHW and "random wire" antennas. At this point, it is still fiddly to build, but I'd expect an experienced #HamRadio DIY / homebrew enthusiast to find the build not terribly difficult.
There's nothing…

Iteration Steps of 3x 1 Problem
Youchun Luo
https://arxiv.org/abs/2506.23070 https://arxiv.org/pdf/2506.23070

Iteration Steps of 3x+1 Problem
On the 3x+1 problem, given a positive integer $N$, let $D\left( N \right) $, $O\left( N \right) $, $E\left( N \right) $ be the total iteration steps, the odd iteration steps and the even iteration steps when $N$ iterates to 1(except 1) respectively. Trivially, we have $D\left( N \right) =O\left( N \right) +E\left( N \right) $. In this paper, we propose a so-called weak residue conjecture(i.e., $\frac{2^{E\left( N \right)}}{3^{O\left( N \right)}\cdot N}\le 2$). We prove that if 3x+1 conjecture i…

A Denotational Semantics for Quantum Loops
Nicola Assolini, Alessandra Di Pierro
https://arxiv.org/abs/2506.23320 https://arxiv.org/p…

A Denotational Semantics for Quantum Loops
Programming a quantum computer, i.e., implementing quantum algorithms on a quantum processor-based copmputer architecture, is a task that can be addressed (just as for classical computers) at different levels of abstraction. This paper proposes a denotational semantics for high-level quantum programming constructs, focusing on the conceptual meaning of quantum-controlled branching and iteration. We introduce a denotational domain where a mathematical meaning of a quantum control flow with loops…

An Empirical Study on the Amount of Changes Required for Merge Request Acceptance
Samah Kansab, Mohammed Sayagh, Francis Bordeleau, Ali Tizghadam
https://arxiv.org/abs/2507.23640

An Empirical Study on the Amount of Changes Required for Merge Request Acceptance
Code review (CR) is essential to software development, helping ensure that new code is properly integrated. However, the CR process often involves significant effort, including code adjustments, responses to reviewers, and continued implementation. While past studies have examined CR delays and iteration counts, few have investigated the effort based on the volume of code changes required, especially in the context of GitLab Merge Requests (MRs), which remains underexplored. In this paper, we d…

Bootstrap Policy Iteration for Stochastic LQ Tracking with Multiplicative Noise
Jiayu Chen, Zhenhui Xu, Xinghu Wang
https://arxiv.org/abs/2508.20394 https://

Bootstrap Policy Iteration for Stochastic LQ Tracking with Multiplicative Noise
This paper studies the optimal tracking control problem for continuous-time stochastic linear systems with multiplicative noise. The solution framework involves solving a stochastic algebraic Riccati equation for the feedback gain and a Sylvester equation for the feedforward gain. To enable model-free optimal tracking, we first develop a two-phase bootstrap policy iteration (B-PI) algorithm, which bootstraps a stabilizing control gain from the trivially initialized zero-value start and proceeds…

lifeXplore at the Lifelog Search Challenge 2020
Andreas Leibetseder, Klaus Schoeffmann
https://arxiv.org/abs/2508.21397 https://arxiv.org/pdf/2508.21397

lifeXplore at the Lifelog Search Challenge 2020
Since its first iteration in 2018, the Lifelog Search Challenge (LSC) - an interactive competition for retrieving lifelogging moments - is co-located at the annual ACM International Conference on Multimedia Retrieval (ICMR) and has drawn international attention. With the goal of making an ever growing public lifelogging dataset searchable, several teams develop systems for quickly solving time-limited queries during the challenge. Having participated in both previous LSC iterations, i.e. LSC201…

Some open questions and conjectures about visibility and iteration in bounded convex domains in $\mathbb C^N$
Filippo Bracci, Ahmed Yekta \"Okten
https://arxiv.org/abs/2507.19967

Some open questions and conjectures about visibility and iteration in bounded convex domains in $\mathbb C^N$
In this note, we propose some open problems and questions about bounded convex domains in $\C^N$, specifically about visibility and iteration theory.

Budda Baker 'excited' for Cardinals' future despite 'more losing than winning' over first eight seasons https://www.nfl.com/news/budda-baker-excited-for-cardinals-future-despite-more-losing-t…

An iterated random function with Lipschitz number one
Aaron Abrams, Henry Landau, Zeph Landau, James Pommersheim, Eric Zaslow
https://arxiv.org/abs/2506.22420

An iterated random function with Lipschitz number one
Consider the set of functions $f_θ(x)=|θ-x|$ on $\mathbb{R}$. Define a Markov process that starts with a point $x_0 \in \mathbb{R}$ and continues with $x_{k+1}=f_{θ_{k+1}}(x_{k})$ with each $θ_{k+1}$ picked from a fixed bounded distribution $μ$ on $\mathbb{R}^+$. We prove the conjecture of G. Letac that if $μ$ is not supported on a lattice, then this process has a unique stationary distribution $π_μ$ and any distribution converges under iteration to $π_μ$ (in the weak-$^*$ t…

Thermal-phototactic bioconvection in a forward scattering algal suspension
S. K. Rajput, M. K. Panda, A. Rathi
https://arxiv.org/abs/2506.23224 https://

Thermal-phototactic bioconvection in a forward scattering algal suspension
Bioconvection induced by phototaxis and thermal gradients in an anisotropic (forward) scattering algal suspension is investigated in this article. The suspension is illuminated by collimated irradiation from above and heated either from top or bottom. The linear theory is deployed on the steady state of the proposed bioconvective system and resulting eigen value problem is solved using fourth-order accurate finite-difference scheme based on Newton-Raphson-Kantorovich iteration. The results indi…

Block Coordinate Descent Network Simplex for Optimal Transport
Lingrui Li, Nobuo Yamashita
https://arxiv.org/abs/2506.21231 https://a…

Block Coordinate Descent Network Simplex for Optimal Transport
We propose the Block Coordinate Descent Network Simplex (BCDNS) method for solving large-scale discrete Optimal Transport (OT) problems. BCDNS integrates the Network Simplex (NS) algorithm with a block coordinate descent (BCD) strategy, decomposing the full problem into smaller subproblems per iteration and reusing basis variables to ensure feasibility. We prove that BCDNS terminates in a finite number of iterations with an exact optimal solution, and we characterize its per-iteration complexit…

Singular functions obtained via random function iteration
Cristian Mitrea, Alef E. Sterk
https://arxiv.org/abs/2508.16327 https://arxiv.org/pdf/2508.16327

Singular functions obtained via random function iteration
In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed. Using Bernoulli measures on the space of binary sequences we show that sequences generated by the iteration process almost surely diverge to either plus or minus infinity. The function that assigns to each initial point the probability that the iterates diverg…

Got a #Switch2 and I have to say I’m really enjoying it. Playing my way through #Skyrim for the first time—well I’ve played it before but never got too far. I aim to actually play it far this time.
Switch 2 feels so much more like what I feel the original Switch should’ve been. It’s an iteration …

Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration
Junkai Wang, Yuxuan Zhao, Mi Zhou, Fumin Zhang
https://arxiv.org/abs/2508.19398

Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration
The region of attraction is a key metric of the robustness of systems. This paper addresses the numerical solution of the generalized Zubov's equation, which produces a special Lyapunov function characterizing the robust region of attraction for perturbed systems. To handle the highly nonlinear characteristic of the generalized Zubov's equation, we propose a physics-informed neural network framework that employs a policy iteration training scheme with rollout to approximate the viscosity soluti…

EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation
Daniel Appelo, Jeffrey W. Banks, William D. Henshaw, Ngan Le, Donald W. Schwendeman
https://arxiv.org/abs/2507.18282

EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of an iteration. At each iteration, the solution to the wave equation is filtered in time. As the iteration progresses, the filtered solution generally contains relatively larger and larger proportions of eigenmodes whose eigenvalues are near a chosen target fr…

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
Eike Neumann
https://arxiv.org/abs/2506.21481 https://

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
We study the problem of deciding whether a point escapes a closed subset of $\mathbb{R}^d$ under the iteration of a continuous map $f \colon \mathbb{R}^d \to \mathbb{R}^d$ in the bit-model of real computation. We give a sound partial decision method for this problem which is complete in the sense that its halting set contains the halting set of all sound partial decision methods for the problem. Equivalently, our decision method terminates on all problem instances whose answer is robust under a…

Quantum Power Iteration Unified Using Generalized Quantum Signal Processing
Viktor Khinevich, Yasunori Lee, Nobuyuki Yoshioka, Wataru Mizukami
https://arxiv.org/abs/2507.11142

Quantum Power Iteration Unified Using Generalized Quantum Signal Processing
We present a unifying framework for quantum power-method-based algorithms through the lens of generalized quantum signal processing (GQSP): we apply GQSP to realize quantum analogues of classical power iteration, power Lanczos, inverse iteration, and folded spectrum methods, all within a single coherent framework. Our approach is efficient in terms of the number of queries to the block encoding of a Hamiltonian. Also, our approach can avoid Suzuki-Trotter decomposition. We constructed quantum c…

An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function
Lingyi Chen, Deheng Yuan, Wenyi Zhang, Hao Wu, Huihui Wu
https://arxiv.org/abs/2507.19920

An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function
We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables a…

The latest #qemu just dropped. The biggest #emulation feature #Linaro worked on was the next iteration of the Scalable Matrix Extensions (FEAT_SME2) which you can currently only see in the wild on

\textit{FedABC}: Attention-Based Client Selection for Federated Learning with Long-Term View
Wenxuan Ye, Xueli An, Junfan Wang, Xueqiang Yan, Georg Carle
https://arxiv.org/abs/2507.20871

\textit{FedABC}: Attention-Based Client Selection for Federated Learning with Long-Term View
Native AI support is a key objective in the evolution of 6G networks, with Federated Learning (FL) emerging as a promising paradigm. FL allows decentralized clients to collaboratively train an AI model without directly sharing their data, preserving privacy. Clients train local models on private data and share model updates, which a central server aggregates to refine the global model and redistribute it for the next iteration. However, client data heterogeneity slows convergence and reduces mo…

Unfolding Iterators: Specification and Verification of Higher-Order Iterators, in OCaml
Ion Chirica, M\'ario Pereira
https://arxiv.org/abs/2506.20310 h…

Unfolding Iterators: Specification and Verification of Higher-Order Iterators, in OCaml
Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic approach to the specification and deductive verification of higher-order iterators, written in the OCaml language. Our methodology follows two key principles: first, the usage of the Gospel specification language to describe the general behaviour of any iterati…

Utility-Driven Speculative Decoding for Mixture-of-Experts
Anish Saxena, Po-An Tsai, Hritvik Taneja, Aamer Jaleel, Moinuddin Qureshi
https://arxiv.org/abs/2506.20675

Utility-Driven Speculative Decoding for Mixture-of-Experts
GPU memory bandwidth is the main bottleneck for low-latency Large Language Model (LLM) inference. Speculative decoding leverages idle GPU compute by using a lightweight drafter to propose K tokens, which the LLM verifies in parallel, boosting token throughput. In conventional dense LLMs, all model weights are fetched each iteration, so speculation adds no latency overhead. Emerging Mixture of Experts (MoE) models activate only a subset of weights per token, greatly reducing data movement. Howev…

Complexity of PXP scars revisited
Pawel Caputa, Xuhao Jiang, Sinong Liu
https://arxiv.org/abs/2506.21156 https://arxiv.org/pdf/2506.2…

Complexity of PXP scars revisited
We revisit a quantum quench scenario in which either a scarring or thermalizing initial state evolves under the PXP Hamiltonian. Within this framework, we study the time evolution of spread complexity and related quantities in the Krylov basis. We find that the Lanczos coefficients $b_n$, as functions of the iteration number $n$, exhibit a characteristic arched growth and decay, followed by erratic oscillations which we refer to as buttress. The arched profile predominantly arises from contribu…

Figured out what I was doing wrong in the curve25519 refactoring: the state signal I was using to dispatch register file reads also glitched high for one cycle (not sure if this is technically a glitch since it's synchronous but whatever) at the end of each main loop iteration.
This is harmless if you have combinatorial reads, but if you have synchronous reads with latency it leads to the "read data ready" signal being asserted an extra time and some extra math operation…

Robust Recursive Query Parallelism in Graph Database Management Systems
Anurag Chakraborty, Semih Saliho\u{g}lu
https://arxiv.org/abs/2508.19379 https://ar…

Robust Recursive Query Parallelism in Graph Database Management Systems
Efficient multi-core parallel processing of recursive join queries is critical for achieving good performance in graph database management systems (GDBMSs). Prior work adopts two broad approaches. First is the state of the art morsel-driven parallelism, whose vanilla application in GDBMSs parallelizes computations at the source node level. Second is to parallelize each iteration of the computation at the frontier level. We show that these approaches can be seen as part of a design space of mors…

Chain-of-Experts: Unlocking the Communication Power of Mixture-of-Experts Models
Zihan Wang, Rui Pan, Jiarui Yao, Robert Csordas, Linjie Li, Lu Yin, Jiajun Wu, Tong Zhang, Manling Li, Shiwei Liu
https://arxiv.org/abs/2506.18945

Chain-of-Experts: Unlocking the Communication Power of Mixture-of-Experts Models
We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts dur…

A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria
Zhong Zheng, Xin Yu, Shiqian Ma, Lingzhou Xue
https://arxiv.org/abs/2508.19234 https://

A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria
This paper studies the nonsmooth and nonconvex composite optimization on Riemannian manifolds. We propose a new inexact manifold proximal linear algorithm (IManPL) that incorporates both high- and low-accuracy conditions. At each iteration, IManPL solves convex subproblems on tangent spaces inexactly, guided by two adaptive stopping criteria. We establish convergence guarantees and show that IManPL achieves the best iteration complexity for solving the nonsmooth manifold composite optimization.…

One of SF's last live #punkrock music havens #TheeParkside threatened with closure as new #landlord bids $300k over bar's attempt to buy its shedlike building structure along 17th St. across from Jackson Playground at fo…

Choosing iteration maps for the parallel Pollard rho method
Finn Rudolph
https://arxiv.org/abs/2506.12844 https://arxiv.org/pdf/2506.…

Choosing iteration maps for the parallel Pollard rho method
Pollard's rho method finds a prime factor $p$ of an integer $N$ by searching for a collision in a map of the form $x \mapsto x^{2k} + c$ modulo $N$. This search can be parallelized to multiple machines, which may use distinct parameters $k$ and $c$. In this paper, we give an asymptotic estimate for the expected running time of the parallel rho method depending on the choice of $k$ for each machine. We also prove that $k = 1$ is the best choice for one machine, if nothing about $p$ is known in a…

AI Product Value Assessment Model: An Interdisciplinary Integration Based on Information Theory, Economics, and Psychology
Yu yang
https://arxiv.org/abs/2508.16714 https://

AI Product Value Assessment Model: An Interdisciplinary Integration Based on Information Theory, Economics, and Psychology
In recent years, breakthroughs in artificial intelligence (AI) technology have triggered global industrial transformations, with applications permeating various fields such as finance, healthcare, education, and manufacturing. However, this rapid iteration is accompanied by irrational development, where enterprises blindly invest due to technology hype, often overlooking systematic value assessments. This paper develops a multi-dimensional evaluation model that integrates information theory's e…

Yeah, I knew some lovely people who worked at Twitter too. And did you know they once had unfettered API access and anyone could create their own client? Some of us loved that so much we built things that helped legitimise them as an open platform. And then one day they just switched that off.
Legitimacy is gold to venture-capital-funded startups. They need people with it to convince everyday folks that this latest iteration of the same old rug pull is different. Until they’ve grown s…

Cory Doctorow (@pluralistic@mamot.fr)
Attached: 1 image I can't wait to use Bluesky, but I will not be joining Bluesky. As much as I trust and respect the Bluesky executives and board members I am acquainted with, I believe the service itself is insufficiently enshittification-resistant to trust: https://pluralistic.net/2024/12/14/fire-exits/#graceful-failure-modes If you'd like an essay-formatted version of this thread to read or share, here's a link to it on pluralistic.net, my surveillance-free, ad-free, tracker-free blog: h…

@… finance apps have been this way for years and are only getting worse. QuickBooks Online is even worse as you pay for the account and can’t remove all the ads from the dashboard. In their latest iteration they are now appearing on every screen excepts reports, and I fully expect for them to show up there as well. This following yet another price increase for features …

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Jonathan A. Moran, Pablo G. Morato
https://arxiv.org/abs/2508.18170

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Reliability assessment of engineering systems is often hindered by the need to evaluate limit-state functions through computationally expensive simulations, rendering standard sampling impractical. An effective solution is to approximate the limit-state function with a surrogate model iteratively refined through active learning, thereby reducing the number of expensive simulations. At each iteration, an acquisition strategy selects the next sample by balancing two competing goals: exploration, …

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
Hee Jun Yang, Min Jung Kim, Yeoneung Kim
https://arxiv.org/abs/2507.15455

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control. The method alternates between solving linear second-order PDEs under fixed feedback policies and updating the controls via pointwise minimax optimization using automatic differentiation. Under standard Lipschitz and unif…

Monotonicity properties of hyperbolic projections in holomorphic iteration
Argyrios Christodoulou, Konstantinos Zarvalis
https://arxiv.org/abs/2506.19562 h…

Monotonicity properties of hyperbolic projections in holomorphic iteration
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity properties akin to those present in continuous dynamics. Our techniques are purely hyperbolic-geometric in nature and provide the general framework for analysing projections of arbitrary sequences onto curves.

Overly academic/distanced ethical discussions
Had a weird interaction with @/brainwane@social.coop just now. I misinterpreted one of their posts quoting someone else and I think the combination of that plus an interaction pattern where I'd assume their stance on something and respond critically to that ended up with me getting blocked. I don't have hard feelings exactly, and this post is only partly about this particular person, but I noticed something interesting by the end of the conversation that had been bothering me. They repeatedly criticized me for assuming what their position was, but never actually stated their position. They didn't say: "I'm bothered you assumed my position was X, it's actually Y." They just said "I'm bothered you assumed my position was X, please don't assume my position!" I get that it's annoying to have people respond to a straw man version of your argument, but when I in response asked some direct questions about what their position was, they gave some non-answers and then blocked me. It's entirely possible it's a coincidence, and they just happened to run out of patience on that iteration, but it makes me take their critique of my interactions a bit less seriously. I suspect that they just didn't want to hear what I was saying, while at the same time they wanted to feel as if they were someone who values public critique and open discussion of tricky issues (if anyone reading this post also followed our interaction and has a different opinion of my behavior, I'd be glad to hear it; it's possible In effectively being an asshole here and it would be useful to hear that if so).
In any case, the fact that at the end of the entire discussion, I'm realizing I still don't actually know their position on whether they think the AI use case in question is worthwhile feels odd. They praised the system on several occasions, albeit noting some drawbacks while doing so. They said that the system was possibly changing their anti-AI stance, but then got mad at me for assuming this meant that they thought this use-case was justified. Maybe they just haven't made up their mind yet but didn't want to say that?
Interestingly, in one of their own blog posts that got linked in the discussion, they discuss a different AI system, and despite listing a bunch of concrete harms, conclude that it's okay to use it. That's fine; I don't think *every* use of AI is wrong on balance, but what bothered me was that their post dismissed a number of real ethical issues by saying essentially "I haven't seen calls for a boycott over this issue, so it's not a reason to stop use." That's an extremely socially conformist version of ethics that doesn't sit well with me. The discussion also ended up linking this post: https://chelseatroy.com/2024/08/28/does-ai-benefit-the-world/ which bothered me in a related way. In it, Troy describes classroom teaching techniques for introducing and helping students explore the ethics of AI, and they seem mostly great. They avoid prescribing any particular correct stance, which is important when teaching given the power relationship, and they help students understand the limitations of their perspectives regarding global impacts, which is great. But the overall conclusion of the post is that "nobody is qualified to really judge global impacts, so we should focus on ways to improve outcomes instead of trying to judge them." This bothers me because we actually do have a responsibility to make decisive ethical judgments despite limitations of our perspectives. If we never commit to any ethical judgment against a technology because we think our perspective is too limited to know the true impacts (which I'll concede it invariably is) then we'll have to accept every technology without objection, limiting ourselves to trying to improve their impacts without opposing them. Given who currently controls most of the resources that go into exploration for new technologies, this stance is too permissive. Perhaps if our objection to a technology was absolute and instantly effective, I'd buy the argument that objecting without a deep global view of the long-term risks is dangerous. As things stand, I think that objecting to the development/use of certain technologies in certain contexts is necessary, and although there's a lot of uncertainly, I expect strongly enough that the overall outcomes of objection will be positive that I think it's a good thing to do.
The deeper point here I guess is that this kind of "things are too complicated, let's have a nuanced discussion where we don't come to any conclusions because we see a lot of unknowns along with definite harms" really bothers me.

The Minnesota assassinations, the attempted arson at Governor Shapiro's home, and the violent arrest of Senator Padilla are all straight out of the Jim Crow terrorism playbook. Same goes with cops aiming for journalists covering the ICE protests.
None of these are new tactics, just a new iteration.
-- Max Kennerly

Adaptive Benders decomposition and enhanced SDDP for multistage stochastic programs with block-separable multistage recourse
Nicol\`o Mazzi, Ken Mckinnon, Hongyu Zhang
https://arxiv.org/abs/2507.21624 …

Adaptive Benders decomposition and enhanced SDDP for multistage stochastic programs with block-separable multistage recourse
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first decomposes the full problem into a reduced master problem and subproblems using Adaptive Benders decomposition. The subproblems are then solved by an enhanced SDDP. The enhancement includes (1) valid bounds at each iteration, (2) a path exploration rule, (3) c…

Real-Time Iteration Scheme for Diffusion Policy
Yufei Duan, Hang Yin, Danica Kragic
https://arxiv.org/abs/2508.05396 https://arxiv.org/pdf/2508.05396

Real-Time Iteration Scheme for Diffusion Policy
Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand addi…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A unified worst case for classical simplex and policy iteration pivot rules
Yann Disser, Nils Mosis

An Iterative PDE Based Illumination Restoration Scheme for Image Enhancement
Dragos-Patru Covei
https://arxiv.org/abs/2506.12560 https://

An Iterative PDE Based Illumination Restoration Scheme for Image Enhancement
We present a novel iterative scheme for restoring uneven illumination in grayscale images. Our approach solves, at each global iteration, a nonlinear elliptic equation for an auxiliary field $u$ and then updates the illumination via an explicit time-marching step driven by the logarithmic potential of $u$. We establish existence and uniqueness of the discrete subproblems, analyze convergence of the fixed point iteration, and demonstrate performance on standard test images, reporting PSNR and SS…

Statistical Theory of Multi-stage Newton Iteration Algorithm for Online Continual Learning
Xinjia Lu, Chuhan Wang, Qian Zhao, Lixing Zhu, Xuehu Zhu
https://arxiv.org/abs/2508.07419

Statistical Theory of Multi-stage Newton Iteration Algorithm for Online Continual Learning
We focus on the critical challenge of handling non-stationary data streams in online continual learning environments, where constrained storage capacity prevents complete retention of historical data, leading to catastrophic forgetting during sequential task training. To more effectively analyze and address the problem of catastrophic forgetting in continual learning, we propose a novel continual learning framework from a statistical perspective. Our approach incorporates random effects across …

There may be exactly $n$ $Q$-points
Lorenz Halbeisen, Silvan Horvath, Tan \"Ozalp
https://arxiv.org/abs/2507.15123 https://arxiv…

There may be exactly $n$ $Q$-points
We generalize the main result of arXiv:2505.17960 and show the consistency of the statement ``There are exactly $n$ $Q$-points up to isomorphism" for any finite $n$. Furthermore, we show that the above statement for $n=2$ can alternatively be obtained by a length-$ω_2$ countable support iteration of Matet-Mathias forcing restricted to a Matet-adequate family.

Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity
Qi-Long Shi, Rui Wang, Wei Xiong, Peng-Cheng Li
https://arxiv.org/abs/2506.16217

Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity
In this paper, we present a detailed study of axial gravitational perturbations of the regular black hole solution in asymptotically safe gravity, as proposed in \cite{Bonanno:2023rzk}. We analyze the quasinormal mode (QNM) spectrum of this black hole using two numerical techniques: the Bernstein spectral method and the asymptotic iteration method (AIM). These approaches allow us to compute QNM frequencies with high accuracy, even for higher overtones. Our results show that the fundamental mode…

From SALAMANDRA to SALAMANDRATA: BSC Submission for WMT25 General Machine Translation Shared Task
Javier Garcia Gilabert, Xixian Liao, Severino Da Dalt, Ella Bohman, Audrey Mash, Francesca De Luca Fornaciari, Irene Baucells, Joan Llop, Miguel Claramunt Argote, Carlos Escolano, Maite Melero
https://arxiv.org/abs/2508.12774

From SALAMANDRA to SALAMANDRATA: BSC Submission for WMT25 General Machine Translation Shared Task
In this paper, we present the SALAMANDRATA family of models, an improved iteration of SALAMANDRA LLMs (Gonzalez-Agirre et al., 2025) specifically trained to achieve strong performance in translation-related tasks for 38 European languages. SALAMANDRATA comes in two scales: 2B and 7B parameters. For both versions, we applied the same training recipe with a first step of continual pre-training on parallel data, and a second step of supervised fine-tuning on high-quality instructions. The BSC subm…

Convergence of Fast Policy Iteration in Markov Games and Robust MDPs
Keith Badger, Marek Petrik, Jefferson Huang
https://arxiv.org/abs/2508.06661 https://a…

Convergence of Fast Policy Iteration in Markov Games and Robust MDPs
Markov games and robust MDPs are closely related models that involve computing a pair of saddle point policies. As part of the long-standing effort to develop efficient algorithms for these models, the Filar-Tolwinski (FT) algorithm has shown considerable promise. As our first contribution, we demonstrate that FT may fail to converge to a saddle point and may loop indefinitely, even in small games. This observation contradicts the proof of FT's convergence to a saddle point in the original pape…

Widest Path Games and Maximality Inheritance in Bounded Value Iteration for Stochastic Games
Kittiphon Phalakarn, Yun Chen Tsai, Ichiro Hasuo
https://arxiv.org/abs/2508.06088 ht…

Widest Path Games and Maximality Inheritance in Bounded Value Iteration for Stochastic Games
For model checking stochastic games (SGs), bounded value iteration (BVI) algorithms have gained attention as efficient approximate methods with rigorous precision guarantees. However, BVI may not terminate or converge when the target SG contains end components. Most existing approaches address this issue by explicitly detecting and processing end components--a process that is often computationally expensive. An exception is the widest path-based BVI approach previously studied by Phalakarn et a…

🔧 #Generators excel at lazy iteration and memory efficiency, implementing Iterator interface for foreach loops
⚡ #Fibers enable cooperative multitasking and nested suspension, perfect for #CLI

Collaborative Editable Model
Kaiwen Tang, Aitong Wu, Yao Lu, Guangda Sun
https://arxiv.org/abs/2506.14146 https://arxiv.org/pdf/2506.…

Collaborative Editable Model
Vertical-domain large language models (LLMs) play a crucial role in specialized scenarios such as finance, healthcare, and law; however, their training often relies on large-scale annotated data and substantial computational resources, impeding rapid development and continuous iteration. To address these challenges, we introduce the Collaborative Editable Model (CoEM), which constructs a candidate knowledge pool from user-contributed domain snippets, leverages interactive user-model dialogues c…

PromptCanvas: Composable Prompting Workspaces Using Dynamic Widgets for Exploration and Iteration in Creative Writing
Rifat Mehreen Amin, Oliver Hans K\"uhle, Daniel Buschek, Andreas Butz
https://arxiv.org/abs/2506.03741

PromptCanvas: Composable Prompting Workspaces Using Dynamic Widgets for Exploration and Iteration in Creative Writing
We introduce PromptCanvas, a concept that transforms prompting into a composable, widget-based experience on an infinite canvas. Users can generate, customize, and arrange interactive widgets representing various facets of their text, offering greater control over AI-generated content. PromptCanvas allows widget creation through system suggestions, user prompts, or manual input, providing a flexible environment tailored to individual needs. This enables deeper engagement with the creative proce…

Revisiting Randomization in Greedy Model Search
Xin Chen, Jason M. Klusowski, Yan Shuo Tan, Chang Yu
https://arxiv.org/abs/2506.15643 https://

Revisiting Randomization in Greedy Model Search
Combining randomized estimators in an ensemble, such as via random forests, has become a fundamental technique in modern data science, but can be computationally expensive. Furthermore, the mechanism by which this improves predictive performance is poorly understood. We address these issues in the context of sparse linear regression by proposing and analyzing an ensemble of greedy forward selection estimators that are randomized by feature subsampling -- at each iteration, the best feature is s…

A Chebyshev--Jackson series based block SS--RR algorithm for computing partial eigenpairs of real symmetric matrices
Zhongxiao Jia, Tianhang Liu
https://arxiv.org/abs/2508.20456

A Chebyshev--Jackson series based block SS--RR algorithm for computing partial eigenpairs of real symmetric matrices
This paper considers eigenpair computations of large symmetric matrices with the desired eigenvalues lying in a given interval using the contour integral-based block SS--RR method, a Rayleigh--Ritz projection onto a certain subspace generated by moment matrices. Instead of using a numerical quadrature to approximately compute the moments by solving a number of large shifted complex linear systems at each iteration, we make use of the Chebyshev--Jackson (CJ) series expansion to approximate the m…

Necklaces, permutations, and periodic critical orbits for quadratic polynomials
Matthew Baker, Andrea Chen, Sophie Li, Matthew Qian
https://arxiv.org/abs/2508.12924 https://

Necklaces, permutations, and periodic critical orbits for quadratic polynomials
Let $G_n$ denote the $n^{\rm th}$ Gleason polynomial, whose roots correspond to parameters $c$ such that the critical point $0$ is periodic of exact period $n$ under iteration of $z^2 + c$, and let $\bar{G}_n$ denote the reduction of $G_n$ modulo $2$. Buff, Floyd, Koch, and Parry made the surprising observation that the number of real roots of $G_n$ is equal to the number of irreducible factors of $\bar{G}_n$ for all $n$. We provide a bijective proof for this result by first providing explicit …

Power Stabilization for AI Training Datacenters
Esha Choukse, Brijesh Warrier, Scot Heath, Luz Belmont, April Zhao, Hassan Ali Khan, Brian Harry, Matthew Kappel, Russell J. Hewett, Kushal Datta, Yu Pei, Caroline Lichtenberger, John Siegler, David Lukofsky, Zaid Kahn, Gurpreet Sahota, Andy Sullivan, Charles Frederick, Hien Thai, Rebecca Naughton, Daniel Jurnove, Justin Harp, Reid Carper, Nithish Mahalingam, Srini Varkala, Alok Gautam Kumbhare, Satyajit Desai, Venkatesh Ramamurthy, Prane…

Power Stabilization for AI Training Datacenters
Large Artificial Intelligence (AI) training workloads spanning several tens of thousands of GPUs present unique power management challenges. These arise due to the high variability in power consumption during the training. Given the synchronous nature of these jobs, during every iteration there is a computation-heavy phase, where each GPU works on the local data, and a communication-heavy phase where all the GPUs synchronize on the data. Because compute-heavy phases require much more power than…

Outer symplectic billiard map at infinity
Peter Albers, Ana Chavez Caliz, Serge Tabachnikov
https://arxiv.org/abs/2508.15142 https://arxiv.org/pdf/2508.151…

Outer symplectic billiard map at infinity
We show that the second iteration $T^2$ of the outer symplectic billiard map with respect to a convex domain $M$ in a symplectic vector space is approximated by an explicit Hamiltonian flow for points far away from $M$. More precisely, denote by $N$ the symplectic polar dual of the symmetrization $M\ominus M$ of $M$. If we write $N$ as the unit level set of a 1-homogeneous function $H$, then the difference between $T^2$ and the time-2-Hamiltonian flow of $H$ applied to a point $x$ is smaller …

AI-Driven Tools in Modern Software Quality Assurance: An Assessment of Benefits, Challenges, and Future Directions
Ihor Pysmennyi, Roman Kyslyi, Kyrylo Kleshch
https://arxiv.org/abs/2506.16586

AI-Driven Tools in Modern Software Quality Assurance: An Assessment of Benefits, Challenges, and Future Directions
Traditional quality assurance (QA) methods face significant challenges in addressing the complexity, scale, and rapid iteration cycles of modern software systems and are strained by limited resources available, leading to substantial costs associated with poor quality. The object of this research is the Quality Assurance processes for modern distributed software applications. The subject of the research is the assessment of the benefits, challenges, and prospects of integrating modern AI-orient…

Faster Fixed-Point Methods for Multichain MDPs
Matthew Zurek, Yudong Chen
https://arxiv.org/abs/2506.20910 https://arxiv.org/pdf/2506…

Faster Fixed-Point Methods for Multichain MDPs
We study value-iteration (VI) algorithms for solving general (a.k.a. multichain) Markov decision processes (MDPs) under the average-reward criterion, a fundamental but theoretically challenging setting. Beyond the difficulties inherent to all average-reward problems posed by the lack of contractivity and non-uniqueness of solutions to the Bellman operator, in the multichain setting an optimal policy must solve the navigation subproblem of steering towards the best connected component, in additi…

Information Entropy-Based Scheduling for Communication-Efficient Decentralized Learning
Jaiprakash Nagar, Zheng Chen, Marios Kountouris, Photios A. Stavrou
https://arxiv.org/abs/2507.17426

Information Entropy-Based Scheduling for Communication-Efficient Decentralized Learning
This paper addresses decentralized stochastic gradient descent (D-SGD) over resource-constrained networks by introducing node-based and link-based scheduling strategies to enhance communication efficiency. In each iteration of the D-SGD algorithm, only a few disjoint subsets of nodes or links are randomly activated, subject to a given communication cost constraint. We propose a novel importance metric based on information entropy to determine node and link scheduling probabilities. We validate …

Deciding Termination of Simple Randomized Loops
\'El\'eanore Meyer, J\"urgen Giesl
https://arxiv.org/abs/2506.18541 https://

Deciding Termination of Simple Randomized Loops
We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all programs that consist of a single loop, with a linear loop guard and a loop body composed of two linear commuting and diagonalizable updates. In each iteration of the loop, the update to be carried out is picked at random, according to a fixed probability. We s…

On spurious fixed points in iterative maximum likelihood reconstruction for quantum tomography
Florian Oberender
https://arxiv.org/abs/2508.14549 https://a…

On spurious fixed points in iterative maximum likelihood reconstruction for quantum tomography
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density matrix in practice. Contradicting these practical observations, we will show that convergence to a true solution is not guaranteed in general by constructing examples for spurious fixed points. To deal with this newly found problem, we then provide a criterion…

There’s a specific kind of cognitive dissonance that comes from watching a woman of color who seemed to have been intellectually reared in progressive circles endear herself to this iteration of the Republican Party
https://slate.com/news-and-politics/20

The One Thing You Need to Know to Understand Usha Vance
Usha Vance isn’t a mystery.

Learning Interior Point Method for AC and DC Optimal Power Flow
Farshad Amani, Amin Kargarian, Ramachandran Vaidyanathan
https://arxiv.org/abs/2508.19146 https://

Learning Interior Point Method for AC and DC Optimal Power Flow
This paper proposes a feasibility-guaranteed learning interior point method (L-IPM) to solve both AC and DC optimal power flow (OPF) problems. Given the criticality of OPF, the proposed L-IPM uses a hybrid learning model approach rather than relying solely on a simple black-box prediction. The traditional IPM follows a central path from an initial point to the optimal solution. However, each iteration involves solving large linear systems, which becomes increasingly expensive as the matrices gr…

Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
Zhicheng Yang, Zhijiang Guo, Yinya Huang, Yongxin Wang, Dongchun Xie, Yiwei Wang, Xiaodan Liang, Jing Tang
https://arxiv.org/abs/2508.13755

Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
Reinforcement Learning with Verifiable Reward (RLVR) has emerged as a powerful paradigm for unlocking reasoning capabilities in large language models, yet its full potential is hindered by two under-explored dimensions: Depth-the hardest problem a model can sample; Breadth-the number of instances consumed in a single iteration. We dissect the popular GRPO algorithm and reveal a systematic bias: the cumulative-advantage disproportionately weights samples with medium accuracy, while down-weightin…

Fourth-Order Compact FDMs for Steady and Time-Dependent Nonlinear Convection-Diffusion Equations
Qiwei Feng, Catalin Trenchea
https://arxiv.org/abs/2507.18799 https://

Checkmate: Zero-Overhead Model Checkpointing via Network Gradient Replication
Ankit Bhardwaj, Weiyang Wang, Jeremy Carin, Adam Belay, Manya Ghobadi
https://arxiv.org/abs/2507.13522

Checkmate: Zero-Overhead Model Checkpointing via Network Gradient Replication
This paper presents Checkmate, a system that enables per-iteration checkpointing in DNN training without any training slowdown. The traditional approach to checkpointing requires a pause in training to copy model states to a separate location, allowing the state to be restored in the event of failure. This approach fundamentally has a tradeoff between the frequency of checkpoints and the cost of a failure. We avoid this tradeoff; our key insight is that in data-parallel training, all informatio…

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
Jiarui Gan, Rupak Majumdar
https://arxiv.org/abs/2506.07186

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this poses new representational and algorithmic challenges as the number of possible histories grows exponentially with the number of time steps. We focus on computing $(ε, δ)$-optimal CEs -- solutions that achieve a value within $ε$ of an optimal CE, while al…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- From Optimization to Control: Quasi Policy Iteration
Mohammad Amin Sharifi Kolarijani, Peyman Mohajerin Esfahani

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[3/3]:
- StoryEnsemble: Enabling Dynamic Exploration & Iteration in the Design Process with AI and Forward...
Sangho Suh, Michael Lai, Kevin Pu, Steven P. Dow, Tovi Grossman

Higher arithmetic on the ordinals
Adrian Ducourtial
https://arxiv.org/abs/2508.13334 https://arxiv.org/pdf/2508.13334…

Higher arithmetic on the ordinals
We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are discussed.

Language Models Improve When Pretraining Data Matches Target Tasks
David Mizrahi, Anders Boesen Lindbo Larsen, Jesse Allardice, Suzie Petryk, Yuri Gorokhov, Jeffrey Li, Alex Fang, Josh Gardner, Tom Gunter, Afshin Dehghan
https://arxiv.org/abs/2507.12466

Language Models Improve When Pretraining Data Matches Target Tasks
Every data selection method inherently has a target. In practice, these targets often emerge implicitly through benchmark-driven iteration: researchers develop selection strategies, train models, measure benchmark performance, then refine accordingly. This raises a natural question: what happens when we make this optimization explicit? To explore this, we propose benchmark-targeted ranking (BETR), a simple method that selects pretraining documents based on similarity to benchmark training examp…

Two-dimensional greedy randomized Kaczmarz methods for solving large-scale linear systems
Tao Li, Meng-Long Xiao, Xin-Fang Zhang
https://arxiv.org/abs/2506.20940

Two-dimensional greedy randomized Kaczmarz methods for solving large-scale linear systems
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like constant, for solving large-scale linear systems. From the greedy selection strategy with grasping two larger entries of the residual vector at each iteration, we then devise a two-dimensional greedy randomized Kaczmarz method. To improve the above methods further,…

Forward Reverse Kernel Regression for the Schr\"{o}dinger bridge problem
Denis Belomestny, John. Schoenmakers
https://arxiv.org/abs/2507.00640 https:/…

Forward Reverse Kernel Regression for the Schrödinger bridge problem
In this paper, we study the Schrödinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schrödinger potentials in a nonparametric way. In particular, we use kernel based Monte Carlo regression in the context of Picard iteration of a corresponding fixed point problem. By preserving in the iteration positivity and contractivity …

A Generalized Alternating Anderson Acceleration Method
Yunhui He, Santolo Leveque
https://arxiv.org/abs/2508.10158 https://arxiv.org/pdf/2508.10158

A Generalized Alternating Anderson Acceleration Method
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and nonlinear problems. This allows flexibility to use different combinations of fixed-point iteration and Anderson iteration. We present a convergence analysis of the proposed scheme for accelerating the Richardson iteration in the linear case, with a focus on spe…

Information Preserving Line Search via Bayesian Optimization
Robin Labryga, Tomislav Prusina, S\"oren Laue
https://arxiv.org/abs/2507.15485 https://…

Information Preserving Line Search via Bayesian Optimization
Line search is a fundamental part of iterative optimization methods for unconstrained and bound-constrained optimization problems to determine suitable step lengths that provide sufficient improvement in each iteration. Traditional line search methods are based on iterative interval refinement, where valuable information about function value and gradient is discarded in each iteration. We propose a line search method via Bayesian optimization, preserving and utilizing otherwise discarded inform…

It’s exactly four weeks ago today that the Jeffrey Epstein story broke,
or re-broke in its current form.
On Friday, July 11, the world learned of the tense meeting that took place at the White House that previous Wednesday,
in which FBI Deputy Director Dan Bongino clashed with Attorney General Pam Bondi over the handling of the Epstein files.
Bongino was so incensed that he didn’t go to work that Friday
and threatened to resign.
He has, at least for now…

On Epstein, Even MAGA World Can Smell That Trump Is Hiding Something
We’re four weeks into the current iteration of the Epstein scandal. And there is no way it’s going away.

Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration
Chaofeng Guan, Shitao Li, Gaojun Luo, Zhi Ma, Hong Wang
https://arxiv.org/abs/2507.05567

Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration
The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest error coefficients achieve the best possible asymptotic frame error rate (AFER) among all optimal linear codes under maximum likelihood decoding. Such codes are referred to as AFER-optimal linear codes. The Griesmer bound is essential for determining the optimality of linear codes. However, establishing tight lower bou…

Non-Euclidean Enriched Contraction Theory for Monotone Operators and Monotone Dynamical Systems
Diego Deplano, Sergio Grammatico, Mauro Franceschelli
https://arxiv.org/abs/2506.17990

Non-Euclidean Enriched Contraction Theory for Monotone Operators and Monotone Dynamical Systems
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and underpinning the stability analysis of numerous dynamical models - by focusing on a non-Euclidean vector space equipped with the diagonally weighted supremum norm. By extending the state of the art, we introduce the notion of enriched weak contractivity, which …

Structured Program Synthesis using LLMs: Results and Insights from the IPARC Challenge
Shraddha Surana, Ashwin Srinivasan, Michael Bain
https://arxiv.org/abs/2506.13820

Structured Program Synthesis using LLMs: Results and Insights from the IPARC Challenge
The IPARC Challenge, inspired by ARC, provides controlled program synthesis tasks over synthetic images to evaluate automatic program construction, focusing on sequence, selection, and iteration. This set of 600 tasks has resisted automated solutions. This paper presents a structured inductive programming approach with LLMs that successfully solves tasks across all IPARC categories. The controlled nature of IPARC reveals insights into LLM-based code generation, including the importance of prior…

The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations
Binbin Du, Shenxiang Cheng, Yue Yu, Chuanjun Chen
https://arxiv.org/abs/2507.12036

The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations
This article presents a detailed analysis of the Arrow-Hurwicz iteration applied to the solution of the incompressible Navier-Stokes equations, discretized by a divergence-free mixed virtual element method. Under a set of appropriate assumptions, it is rigorously demonstrated that the method exhibits geometric convergence, with a contraction factor that remains independent of the mesh sizes. A series of numerical experiments are conducted to validate the theoretical findings and to assess the c…

Dominating numbers at singular cardinals
Yusuke Hayashi
https://arxiv.org/abs/2508.12018 https://arxiv.org/pdf/2508.12018

Dominating numbers at singular cardinals
We study the generalized dominating number $\mathfrak{d}_μ$ at a singular cardinal $μ$ of cofinality $κ$. We show two lower bounds: in ZFC, $\mathrm{cf}([μ]^κ,\subseteq) \leq \mathfrak{d}_μ$, and under mild cardinal-arithmetic assumptions, $2^{<μ} \leq \mathfrak{d}_μ$. We also clarify when $\mathfrak{d}_μ$ can differ from $2^μ$: assuming GCH and $κ= \mathrm{cf}(μ) > ω$, a finite-support iteration of Cohen forcing of length $μ^{++}$ yields $\mathfrak{d}_μ < 2^μ$. On the other han…

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
Qi Feng, Gu Wang
https://arxiv.org/abs/2506.08121 https://…

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By …

Accelerating Newton-Schulz Iteration for Orthogonalization via Chebyshev-type Polynomials
Ekaterina Grishina, Matvey Smirnov, Maxim Rakhuba
https://arxiv.org/abs/2506.10935

Accelerating Newton-Schulz Iteration for Orthogonalization via Chebyshev-type Polynomials
The problem of computing optimal orthogonal approximation to a given matrix has attracted growing interest in machine learning. Notable applications include the recent Muon optimizer or Riemannian optimization on the Stiefel manifold. Among existing approaches, the Newton-Schulz iteration has emerged as a particularly effective solution, as it relies solely on matrix multiplications and thus achieves high computational efficiency on GPU hardware. Despite its efficiency, the method has inherent …

Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization
Dongxuan Zhu, Weihuan Huang, Caihua Chen
https://arxiv.org/abs/2507.18277

Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization
We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive sampling strategy for gradient estimation. We provide a complexity analysis demonstrating that the new algorithm, adaNAPG, achieves both the optimal iteration complexity and the optimal sample complexity as outlined in the existing literature. Additionally, we …

Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications
Valentin Leplat, Salman Ahmadi-Asl, JunJun Pan, Ning Zheng
https://arxiv.org/abs/2508.16979

Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications
We develop iterative methods to compute the Moore-Penrose pseudoinverse of quaternion matrices directly in $\mathbb{H}$. We introduce a damped Newton-Schulz (NS) iteration, proving its convergence under spectral scaling $X_0=αA^H$ with $α\in(0,2/\|A\|_2^2)$. We derive higher-order hyperpower NS schemes with optimized factorizations. Beyond NS, we propose a randomized sketch-and-project method (RSP-Q) and a conjugate gradient on normal equations (CGNE-Q). Numerically, spectrally-scal…

Reference-Free Iterative Learning Model Predictive Control with Neural Certificates
Wataru Hashimoto, Kazumune Hashimoto, Masako Kishida, Shigemasa Takai
https://arxiv.org/abs/2507.14025

Reference-Free Iterative Learning Model Predictive Control with Neural Certificates
In this paper, we propose a novel reference-free iterative learning model predictive control (MPC). In the proposed method, a certificate function based on the concept of Control Lyapunov Barrier Function (CLBF) is learned using data collected from past control executions and used to define the terminal set and cost in the MPC optimization problem at the current iteration. This scheme enables the progressive refinement of the MPC's terminal components over successive iterations. Unlike existing…

Parallel Polyhedral Projection Method for the Convex Feasibility Problem
Pablo Barros, Roger Behling, Vincent Guigues
https://arxiv.org/abs/2506.15895 http…

Parallel Polyhedral Projection Method for the Convex Feasibility Problem
In this paper, we introduce and study the Parallel Polyhedral Projection Method (3PM) and the Approximate Parallel Polyhedral Projection Method (A3PM) for finding a point in the intersection of finitely many closed convex sets. Each iteration has two phases: parallel projections onto the target sets (exact in 3PM, approximate in A3PM), followed by an exact or approximate projection onto a polyhedron defined by supporting half-spaces. These strategies appear novel, as existing methods largely fo…

Shifted HSS preconditioners for the indefinite Helmholtz equation
Colin J Cotter, Kars Knook, Joshua Hope-Collins
https://arxiv.org/abs/2506.18694 https://…

Shifted HSS preconditioners for the indefinite Helmholtz equation
We provide a preconditioning approach for the indefinite Helmholtz equation discretised using finite elements, based upon a Hermitian Skew-Hermitian Splitting (HSS) iteration applied to the shifted operator, and prove that the preconditioner is k- and mesh-robust when O(k) HSS iterations are performed. The HSS iterations involve solving a shifted operator that is suitable for approximation by multigrid using standard smoothers and transfer operators, leading to a fully scalable algorithm. We ar…

Frank-Wolfe algorithm for star-convex functions
R. Diaz Millan, Orizon Pereira Ferreira, Julien Ugon
https://arxiv.org/abs/2507.17272 https://arxiv.org/pdf…

Frank-Wolfe algorithm for star-convex functions
We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of \emph{star-convex functions}, which retain essential geometric properties despite the lack of convexity. We establish iteration-complexity bounds of $\mathcal{O}(1/k)$ for both the objective values and the duality gap under star-convexity, using diminishing, Armijo…

Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees
Max L. N. Goncalves, Geovani N. Grapiglia
https://arxiv.org/abs/2507.17556 https://

Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees
In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function, significantly reducing the overall computational cost. We propose a novel adaptive procedure for deterministically adjusting the sample size used for gradient (or gradient and Hessian) approximations. Furthermore, we establish worst-case iteration complexity bounds for o…

A parameterized block-splitting preconditioner for indefinite least squares problem
Davod Khojasteh Salkuyeh
https://arxiv.org/abs/2507.16938 https://arxiv…

A parameterized block-splitting preconditioner for indefinite least squares problem
We present a stationary iteration based upon a block splitting for a class of indefinite least squares problem. Convergence of the proposed method is investigated and optimal value of the involving parameter is used. The induced preconditioner is applied to accelerate the convergence of the GMRES method for solving the problem. We also analysed the eigenpair distribution of the preconditioned matrix. Some numerical are presented to show the effectiveness of the preconditioner. Numerical compari…

Error estimates and adaptivity for a least-squares method applied to the Monge-Amp\`ere equation
Alexandre Caboussat, Anna Peruso, Marco Picasso
https://arxiv.org/abs/2507.17569

Error estimates and adaptivity for a least-squares method applied to the Monge-Ampère equation
We introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge--Ampère equation on convex polygonal domains in $\mathbb{R}^2$. At each iteration, our iterative scheme decouples the problem into (i) a pointwise nonlinear minimization problem and (ii) a linear biharmonic variational problem. For the latter, we derive an equivalence to a biharmonic problem with Navier boundary conditions and solve it via mixed piecewise-linear finite elemen…

An inertial iteratively regularized extragradient method for bilevel variational inequality problems
M. Marques Alves, Kangming Chen, Ellen H. Fukuda
https://arxiv.org/abs/2507.16640

An inertial iteratively regularized extragradient method for bilevel variational inequality problems
We study a bilevel variational inequality problem where the feasible set is itself the solution set of another variational inequality. Motivated by the difficulty of computing projections onto such sets, we consider a regularized extragradient method, as proposed by Samadi and Yousefian (2025), which operates over a simpler constraint set. Building on this framework, we introduce an inertial variant (called IneIREG) that incorporates momentum through extrapolation steps. We establish iteration-…

Computing stabilizing feedback gains for stochastic linear systems via policy iteration method
Xinpei Zhang, Guangyan Jia
https://arxiv.org/abs/2508.05214 https://

Computing stabilizing feedback gains for stochastic linear systems via policy iteration method
In recent years, stabilizing unknown dynamical systems has became a critical problem in control systems engineering. Addressing this for linear time-invariant (LTI) systems is an essential fist step towards solving similar problems for more complex systems. In this paper, we develop a model-free reinforcement learning algorithm to compute stabilizing feedback gains for stochastic LTI systems with unknown system matrices. This algorithm proceeds by solving a series of discounted stochastic linea…

Dissipativity-based time domain decomposition for optimal control of hyperbolic PDEs
B\'alint Farkas, Birgit Jacob, Manuel Schaller, Merlin Schmitz
https://arxiv.org/abs/2507.07812

Dissipativity-based time domain decomposition for optimal control of hyperbolic PDEs
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state and adjoint equation, as a sum of dissipative operators, which enables a Peaceman-Rachford-type fixed-point iteration. The iteration steps may be understood and implemented as solutions of many decoupled, and therefore highly parallelizable, time-distributed …

Stochastic gradient descent based variational inference for infinite-dimensional inverse problems
Jiaming Sui, Junxiong Jia, Jinglai Li
https://arxiv.org/abs/2506.08380

Stochastic gradient descent based variational inference for infinite-dimensional inverse problems
This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the target posterior distribution using a constant-rate stochastic gradient descent (cSGD) iteration. Specifically, we introduce a randomization strategy that incorporates stochastic gradient noise, allowing the cSGD iteration to be viewed as a discrete-time process.…

First Order Algorithm on an Optimization Problem with Improved Convergence when Problem is Convex
Chee-Khian Sim
https://arxiv.org/abs/2508.13302 https://a…

First Order Algorithm on an Optimization Problem with Improved Convergence when Problem is Convex
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can be nonsmooth. The algorithm is shown to have an iteration complexity of $\mathcal{O}(ε^{-2})$ to find an $ε$-approximate solution to the problem, and this complexity improves to $\mathcal{O}(ε^{-2/3})$ when the objective function turns out to be convex. W…

Stabilization of BiCGSTAB by the generalized residual cutting method
Toshihiko Abe
https://arxiv.org/abs/2508.13536 https://arxiv.org/pdf/2508.13536…

Stabilization of BiCGSTAB by the generalized residual cutting method
The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations. Then based on RC the generalized residual cutting (GRC) method has been introduced, which can be applied to more general sparse linear systems problems. In this paper, we show that GRC can stabilize the BiCGSTAB, which is also an iterative algorithm for solving …

A polynomial projective algorithm for convex feasibility problems with positive-definite constraints
Sergei Chubanov
https://arxiv.org/abs/2506.15484 https…

A polynomial projective algorithm for convex feasibility problems with positive-definite constraints
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of the algorithm, either a feasible solution is found or a suitable valid inequality inducing a projective transformation allowing to bring the solution set closer to the center of an associated spectraplex. The closeness to the center is measured in terms of a…

Glocal Smoothness: Line Search can really help!
Curtis Fox, Aaron Mishkin, Sharan Vaswani, Mark Schmidt
https://arxiv.org/abs/2506.12648 https://

Glocal Smoothness: Line Search can really help!
Iteration complexities for first-order optimization algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are achieved using fixed step sizes. But many objective functions that arise in practice have regions with small Lipschitz constants where larger step sizes can be used. Many local Lipschitz assumptions have been proposed, which have lead to results showing that adaptive step sizes and/or line searches yield improved convergence ra…

Faster stochastic cubic regularized Newton methods with momentum
Yiming Yang, Chuan He, Xiao Wang, Zheng Peng
https://arxiv.org/abs/2507.13003 https://

Faster stochastic cubic regularized Newton methods with momentum
Cubic regularized Newton (CRN) methods have attracted signiffcant research interest because they offer stronger solution guarantees and lower iteration complexity. With the rise of the big-data era, there is growing interest in developing stochastic cubic regularized Newton (SCRN) methods that do not require exact gradient and Hessian evaluations. In this paper, we propose faster SCRN methods that incorporate gradient estimation with small, controlled errors and Hessian estimation with momentum…