Tootfinder

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.

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 …

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…

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…

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…

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

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…

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…

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…

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…

@… 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 …

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…

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…

Symmetry breaking in time-dependent billiards
Anne K\'etri Pasquinelli da Fonseca, Edson Denis Leonel
https://arxiv.org/abs/2505.20488 https://

Symmetry breaking in time-dependent billiards
We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When inelastic collisions are introduced between the particle and the boundary, the velocity reaches a plateau after the crossover iteration. The system presents the expected behavior for this type of transition, including scale invariance, critical exponents relate…

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…

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.

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…

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.

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…

I’m late to the party but congratulations @…!
Christian Selig, developer of Apollo, joins Digg https://techcrunch.c…

Apollo for Reddit dev Christian Selig to join Digg as an advisor | TechCrunch
Christian Selig, the iOS developer who ran the beloved third-party Reddit client Apollo, is joining the new iteration of Digg as an advisor. Earlier this

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 …

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

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…

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…

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

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…

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…

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…

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…

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…

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…

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…

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…

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,…

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 …

Data warehouses, lakes, lakehouses, and more – our choices significantly affect operational costs and development speed. Join Lars Albertsson at Berlin Buzzwords to explore how different data processing paradigms impact deployment, failure handling, and data quality. Learn strategies to minimise costs and latency, bridge between paradigms, and enhance development iteration and operational efficiency.
Learn more:

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…

Numerical and data-driven modeling of spall failure in polycrystalline ductile materials
Indrashish Saha, Lori Graham-Brady
https://arxiv.org/abs/2507.03706

Numerical and data-driven modeling of spall failure in polycrystalline ductile materials
Developing materials with tailored mechanical performance requires iteration over a large number of proposed designs. When considering dynamic fracture, experiments at every iteration are usually infeasible. While high-fidelity, physics-based simulations can potentially reduce experimental efforts, they remain computationally expensive. As a faster alternative, key dynamic properties can be predicted directly from microstructural images using deep-learning surrogate models. In this work, the sp…

A near-complete resolution of the exponential-time complexity of k-opt for the traveling salesman problem
Sophia Heimann, Hung P. Hoang, Stefan Hougardy
https://arxiv.org/abs/2507.12304

A near-complete resolution of the exponential-time complexity of k-opt for the traveling salesman problem
The $k$-opt algorithm is one of the simplest and most widely used heuristics for solving the traveling salesman problem. Starting from an arbitrary tour, the $k$-opt algorithm improves the current tour in each iteration by exchanging up to $k$ edges. The algorithm continues until no further improvement of this kind is possible. For a long time, it remained an open question how many iterations the $k$-opt algorithm might require for small values of $k$, assuming the use of an optimal pivot rule.…

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…

Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity
Wanjin Feng, Xingyu Gao, Wenqian Du, Hailong Shi, Peilin Zhao, Pengcheng Wu, Chunyan Miao
https://arxiv.org/abs/2506.12087

Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity
Spiking Neural Networks (SNNs) often suffer from high time complexity $O(T)$ due to the sequential processing of $T$ spikes, making training computationally expensive. In this paper, we propose a novel Fixed-point Parallel Training (FPT) method to accelerate SNN training without modifying the network architecture or introducing additional assumptions. FPT reduces the time complexity to $O(K)$, where $K$ is a small constant (usually $K=3$), by using a fixed-point iteration form of Leaky Inte…

The escaping set in transcendental dynamics
Walter Bergweiler, Lasse Rempe
https://arxiv.org/abs/2507.11370 https://arxiv.org/pdf/250…

The escaping set in transcendental dynamics
The escaping set of an entire function consists of the points in the complex plane that tend to infinity under iteration. This set plays a central role in the dynamics of transcendental entire functions. The goal of this survey is to explain this role, to summarise some of the main results in the area, and to identify a number of open questions.

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 …

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…

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…

Finding the Smallest Possible Exact Aggregation of a Markov Chain
Patrick Sonnentag
https://arxiv.org/abs/2507.11157 https://arxiv.or…

Finding the Smallest Possible Exact Aggregation of a Markov Chain
Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed for analysis by reducing the size of the state space. So far, most approximative algorithms focused on finding approximations, which are, again, Markov chains. We remove this restriction and present an algorithm using the Arnoldi iteration. Further, we show tha…

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…

So i just threw together a first iteration of the switch engine PCB schematic in one crazed allnighter (thanks non 24 hour sleep schedules lol, its 0900 and I'm almost ready for bed).
It's missing some details like mounting holes and such, plus a few odds and ends like a 2.5V LDO and level shifter on the rs232 console, but I think it's 80% or so done. Lots of copy paste from kup-lulz and lcbringup which was of course the intent, those projects were intended to de-risk the s…

This https://arxiv.org/abs/2410.08476 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNI_…

JingZhao: A Framework for Rapid NIC Prototyping in the Domain-Specific-Network Era
The network is becoming domain-specific, which requires on-demand design of the network protocols, as well as the microarchitecture of the NIC. However, to develop such a NIC is not that easy. Since the scissor gap between network speed and the growth of CPU frequency is expanding, most of the protocols need to be offloaded to hardware. The process of designing, verifying and optimizing a domain-specific NIC usually takes great effort, which hinders the rapid iteration of new protocols and algo…

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 …

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Wenjin Qin, Hailin Wang, Jingyao Hou, Jianjun Wang
https://arxiv.org/abs/2506.09594 https:/…

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale high-order tensor data. To alleviate these issue, assisted by the Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies, this article first devises two fast and accurate randomized algorithms for low-rank tensor approx…

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…

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…

Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation
Bugra Kilictas, Faruk Alpay
https://arxiv.org/abs/2507.07868 https://

Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation
This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchical sub-games at each iteration level. Building upon Alpay Algebra IV's empathetic embedding concept, we introduce a nested game-theoretic structure where the alignment process between AI systems and documents becomes a meta-game containing embedded decision problems. We formalize this through a composite operator $ϕ(\…

This https://arxiv.org/abs/2505.12990 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

From Theory to Practice: Analyzing VQPM for Quantum Optimization of QUBO Problems
The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a comprehensive theoretical and numerical analysis of VQPM by investigating its convergence, robustness, and qubit locking mechanisms. We present detailed strategies for applying VQPM to QUBO problems by leveraging these locking mechanisms. Based on the simulations for e…

This https://arxiv.org/abs/2408.05197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal eigenfunction and show that the corresponding Rayleigh quotients converge to the principal eigenvalue. We also propose a related iterative method for an eigenvalue problem arising from a model for optimal insulation and provide some partial results.

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…

Full normalization for $\kappa^ $-supercompactness
Farmer Schlutzenberg
https://arxiv.org/abs/2506.08287 https://arxiv.org/pdf/2506.0…

Full normalization for $κ^+$-supercompactness
We extend the normalization results of the author's paper "Full normalization for transfinite stacks" [5] to mice at the level of $κ^+$-supercompactness: given a normal iteration strategy $Σ$ for such a mouse $M$, with both $M$ and $Σ$ satisfying certain condensation properties, we extend $Σ$ to a strategy $Σ^*$ for stacks of normal trees, such that every iterate via $Σ^*$ is in fact a normal iterate via $Σ$.

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…

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 …

This https://arxiv.org/abs/2505.11862 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Q-Policy: Quantum-Enhanced Policy Evaluation for Scalable Reinforcement Learning
We propose Q-Policy, a hybrid quantum-classical reinforcement learning (RL) framework that mathematically accelerates policy evaluation and optimization by exploiting quantum computing primitives. Q-Policy encodes value functions in quantum superposition, enabling simultaneous evaluation of multiple state-action pairs via amplitude encoding and quantum parallelism. We introduce a quantum-enhanced policy iteration algorithm with provable polynomial reductions in sample complexity for the evaluat…

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…

K-ADAPT-VQE: Optimizing Molecular Ground State Searches by Chunking Operators
Tatiana Bespalova, Oumaya Ladhari, Guido Masella
https://arxiv.org/abs/2506.09658

K-ADAPT-VQE: Optimizing Molecular Ground State Searches by Chunking Operators
Classical simulation of molecular systems is limited by exponential scaling, a hurdle quantum algorithms like Variational Quantum Eigensolvers (VQEs) aim to overcome. Although ADAPT-VQE enhances VQEs by dynamically building ansätze, it can remain computationally intensive. This work presents K-ADAPT-VQE, which improves efficiency by adding operators in chunks of K at each iteration. Our results from simulating small molecular systems show that K-ADAPT-VQE substantially reduces the total number…

AFLOW4: heading toward disorder
Simon Divilov, Hagen Eckert, Scott D. Thiel, Sean D. Griesemer, Rico Friedrich, Nicholas H. Anderson, Michael J. Mehl, David Hicks, Marco Esters, Nico Hotz, Xiomara Campilongo, Arrigo Calzolari, Stefano Curtarolo
https://arxiv.org/abs/2507.03422

AFLOW4: heading toward disorder
AFLOW4 is the latest iteration of the AFLOW toolkit, specifically tailored to study high-entropy disordered materials. This upgrade includes innovative features like the Soliquidy module, based on the Euclidean transport cost between disordered and ordered material states. AFLOW4 can calculate dielectric functions to understand optical and electronic properties of disordered ceramics. The newly introduced human-readable data export feature ensures the uncomplicated incorporation of AFLOW4 in di…

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…

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 …

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…

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…

Cost-Efficient LLM Training with Lifetime-Aware Tensor Offloading via GPUDirect Storage
Ziqi Yuan, Haoyang Zhang, Yirui Eric Zhou, Apoorve Mohan, I-Hsin Chung, Seetharami Seelam, Jian Huang
https://arxiv.org/abs/2506.06472

Cost-Efficient LLM Training with Lifetime-Aware Tensor Offloading via GPUDirect Storage
We present the design and implementation of a new lifetime-aware tensor offloading framework for GPU memory expansion using low-cost PCIe-based solid-state drives (SSDs). Our framework, TERAIO, is developed explicitly for large language model (LLM) training with multiple GPUs and multiple SSDs. Its design is driven by our observation that the active tensors take only a small fraction (1.7% on average) of allocated GPU memory in each LLM training iteration, the inactive tensors are usually large…

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-…

Variational quantum algorithms with invariant probabilistic error cancellation on noisy quantum processors
Yulin Chi, Hongyi Shi, Wen Zheng, Haoyang Cai, Yu Zhang, Xinsheng Tan, Shaoxiong Li, Jianwei Wang, Jiangyu Cui, Man-Hong Yung, Yang Yu
https://arxiv.org/abs/2506.07039

Variational quantum algorithms with invariant probabilistic error cancellation on noisy quantum processors
In the noisy intermediate-scale quantum era, emerging classical-quantum hybrid optimization algorithms, such as variational quantum algorithms (VQAs), can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits. However, these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors. These difficulties can only be partially addressed without error correction by optimizing h…

This https://arxiv.org/abs/2503.21224 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlo
Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs with Polish state and action spaces, assuming access to a generative model of the environment. We propose a novel family of multilevel Monte Carlo (MLMC) algorithms that integrate fixed-point iteration with MLMC techniques and a generic stochastic approximat…

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 …

Low-rank Momentum Factorization for Memory Efficient Training
Pouria Mahdavinia, Mehrdad Mahdavi
https://arxiv.org/abs/2507.08091 https://arxiv.org/pdf/2507.08091 https://arxiv.org/html/2507.08091
arXiv:2507.08091v1 Announce Type: new
Abstract: Fine-tuning large foundation models presents significant memory challenges due to stateful optimizers like AdamW, often requiring several times more GPU memory than inference. While memory-efficient methods like parameter-efficient fine-tuning (e.g., LoRA) and optimizer state compression exist, recent approaches like GaLore bridge these by using low-rank gradient projections and subspace moment accumulation. However, such methods may struggle with fixed subspaces or computationally costly offline resampling (e.g., requiring full-matrix SVDs). We propose Momentum Factorized SGD (MoFaSGD), which maintains a dynamically updated low-rank SVD representation of the first-order momentum, closely approximating its full-rank counterpart throughout training. This factorization enables a memory-efficient fine-tuning method that adaptively updates the optimization subspace at each iteration. Crucially, MoFaSGD leverages the computed low-rank momentum factors to perform efficient spectrally normalized updates, offering an alternative to subspace moment accumulation. We establish theoretical convergence guarantees for MoFaSGD, proving it achieves an optimal rate for non-convex stochastic optimization under standard assumptions. Empirically, we demonstrate MoFaSGD's effectiveness on large language model alignment benchmarks, achieving a competitive trade-off between memory reduction (comparable to LoRA) and performance compared to state-of-the-art low-rank optimization methods. Our implementation is available at https://github.com/pmahdavi/MoFaSGD.
toXiv_bot_toot

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…

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.…

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…

Theoretical analysis and numerical solution to a vector equation $Ax-\|x\|_1x=b$
Yuezhi Wang, Gwi Soo Kim, Jie Meng
https://arxiv.org/abs/2507.04971 https:…

Theoretical analysis and numerical solution to a vector equation $Ax-\|x\|_1x=b$
Theoretical and computational properties of a vector equation $Ax-\|x\|_1x=b$ are investigated, where $A$ is an invertible $M$-matrix and $b$ is a nonnegative vector. Existence and uniqueness of a nonnegative solution is proved. Fixed-point iterations, including a relaxed fixed-point iteration and Newton iteration, are proposed and analyzed. A structure-preserving doubling algorithm is proved to be applicable in computing the required solution, the convergence is at least linear wit…

Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver
Xiaopeng Zhu, Zhongyi Huang
https://arxiv.org/abs/2506.15185

Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an special energy functional minimization with total variation(TV) regularization. The minimization problem is solved by Adam algorithm, which only requires solving one forward problem and no adjoint problem in each iteration. In order to deal with the irregularity o…

Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
Yassine Nabou, Lahcen El Bourkhissi, Sebastian U. Stich, Tuomo Valkonen
https://arxiv.org/abs/2506.12397

Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is selected, and the smooth components of the objective are linearized along the chosen block in a Gauss-Newton approach. For the monotone variant, we establish a global sublinear convergence rate to a stationary point under the assumption of bounded iterates. …

Faber polynomials in a deltoid region and power iteration momentum methods
Peter Cowal, Nicholas F. Marshall, Sara Pollock
https://arxiv.org/abs/2507.01885

Faber polynomials in a deltoid region and power iteration momentum methods
We consider a region in the complex plane enclosed by a deltoid curve inscribed in the unit circle, and define a family of polynomials $P_n$ that satisfy the same recurrence relation as the Faber polynomials for this region. We use this family of polynomials to give a constructive proof that $z^n$ is approximately a polynomial of degree $\sim\sqrt{n}$ within the deltoid region. Moreover, we show that $|P_n| \le 1$ in this deltoid region, and that, if $|z| = 1+\varepsilon$, t…

Rate of metastability of an iterative algorithm for quadratic optimization
Paulo Firmino
https://arxiv.org/abs/2506.11342 https://arx…

Rate of metastability of an iterative algorithm for quadratic optimization
In this paper, relying on methods from proof mining, we provide a quantitative analysis of a theorem due to Xu, stating that an iteration strongly converges to the solution of a well known quadratic optimization problem. Rates of metastability and some rates of asymptotic regularity were obtained. We get quadratic rates of asymptotic regularity for particular sequences.

Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters
Mathukumalli Vidyasagar
https://arxiv.org/abs/2506.11904 https://…

Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters
In this paper, we present a unified algorithm for stochastic optimization that makes use of a "momentum" term; in other words, the stochastic gradient depends not only on the current true gradient of the objective function, but also on the true gradient at the previous iteration. Our formulation includes the Stochastic Heavy Ball (SHB) and the Stochastic Nesterov Accelerated Gradient (SNAG) algorithms as special cases. In addition, in our formulation, the momentum term is allowed to vary as a f…

An optimal two-side Robin-Robin domain decomposition method for H(div)-elliptic problem
Na Xuyang
https://arxiv.org/abs/2506.12485 https://

An optimal two-side Robin-Robin domain decomposition method for H(div)-elliptic problem
In this paper, we develop a new two-side Robin-Robin domain decomposition method for H(div)-elliptic problem. Numerical results show that the convergence rate of the new algorithm only depends on $H/h$, where $H$ is diameter of subdomains and $h$ is the mesh size. Besides, an algebraic system of Robin boundary conditions is derived from the iterative method. We solve it by MINRES and get asymptotically stable iteration numbers as well.

SVD method for sparse recovery
Long Li, Liang Ding
https://arxiv.org/abs/2506.11379 https://arxiv.org/pdf/2506.11379

SVD method for sparse recovery
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding algorithms and their accelerated variants. However, these algorithms rely on Landweber iteration, which can be computationally intensive. Therefore, there is a pressing need to develop a more efficient algorithm for sparsity regularization. The Singular Value Dec…

Faithful-Newton Framework: Bridging Inner and Outer Solvers for Enhanced Optimization
Alexander Lim, Fred Roosta
https://arxiv.org/abs/2506.13154 https://

Faithful-Newton Framework: Bridging Inner and Outer Solvers for Enhanced Optimization
While Newton-type methods are known for their fast local convergence and strong empirical performance, achieving theoretically favorable global convergence compared to first-order methods remains a key challenge. For instance, surprisingly, for simple strongly convex problems, no straightforward variant of Newton's method matches the global complexity of gradient descent. Although sophisticated variants can improve iteration complexity over gradient descent for various problems, they often invo…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
P. C. N. Verheijen, D. Goswami, M. Lazar
https://arxiv.org/abs/2506.11608 https://…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that penalizes each constraint individually and performs weight updates at every ADMM iteration. We provide a numerical stability analysis, methods for parameter selection and infeasibility detection. The algorithm is implemented in c with efficient linear algebra pac…

Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction
Andrea Cristofari, Marianna De Santis, Stefano Lucidi, Giampaolo Liuzzi
https://arxiv.org/abs/2506.11929

Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of $p$th-order models regularized with a power $p+1$ of the norm of the step. Through a tailored search procedure, several trial points are generated at each iteration and they can be added to the current set if a decrease is obtained for at least one objective func…

A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
Elisabetta Carlini, Valentina Coscetti
https://arxiv.org/abs/2506.10509

A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the resulting discrete problem, we implement a Learning Value Algorithm, prove its convergence, and propose an acceleration strategy based on a Policy iteration method. Finally, we present numerical experiments that validate the effectiveness of the proposed schemes an…

A Cubic Regularization Method for Multiobjective Optimization
Douglas S. Gon\c{c}alves, Max L. N. Gon\c{c}alves, Jefferson G. Melo
https://arxiv.org/abs/2506.08181

A Cubic Regularization Method for Multiobjective Optimization
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective function is minimized. This model allows approximations for the first- and second-order derivatives, which must satisfy suitable error conditions. One interesting feature of the proposed algorithm is that the regularization parameter of the model and the accura…

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems
Barsha Shaw, Md Abu Talhamainuddin Ansary
https://arxiv.org/abs/2507.07674

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems
This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth multi-objective optimization problems. Moreover, the proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At every iteration of the proposed method, a subproblem is solved to identify a suitable d…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
Xi Chen, Jinyan Fan
https://arxiv.org/abs/2507.05623 h…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via orthogonal spherical smoothing and propose a derivative-free regularization algorithm for solving the problem. At each iteration, a regularized augmented Lagrangian subproblem is solved to obtain a Newton-like step. If a sufficient decrease in the merit function of…

An inexact inertial projective splitting algorithm with strong convergence
M. Marques Alves, J. E. Navarro Caballero, R. T. Marcavillaca
https://arxiv.org/abs/2507.05382

An inexact inertial projective splitting algorithm with strong convergence
We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of the iterates is ensured by projections onto the intersection of appropriately defined half-spaces, even in the absence of inertial effects. We also establish iteration-complexity results for the proposed PS method, which likewise hold without requiring inerti…

This https://arxiv.org/abs/2403.18213 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Long-Term Open-Pit Mine Planning with Large Neighbourhood Search
We present a Large Neighbourhood Search based approach for solving complex long-term open-pit mine planning problems. An initial feasible solution, generated by a sliding windows heuristic, is improved through repeated solves of a restricted mixed-integer program. Each iteration leaves only a subset of the variables in the planning model free to take on new values. We form these subsets through the use of neighbourhood formation strategies that exploit model structure. We show that our approach…

A variable dimension sketching strategy for nonlinear least-squares
Stefania Bellavia, Greta Malaspina, Benedetta Morini
https://arxiv.org/abs/2506.03965 h…

A variable dimension sketching strategy for nonlinear least-squares
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model.…

This https://arxiv.org/abs/2501.04034 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mirror Descent Methods with Weighting Scheme for Outputs for Constrained Variational Inequality Problems
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints. To solve these problems, we propose mirror descent-type methods with a weighting scheme for the generated points in each iteration of the algorithms. This scheme assigns smaller weights to the initial points and larger weights to the most recent points, thus i…