Gradient_Descent
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Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regression
2025-09-26 18:02:58Haodong Liang, Yanhao Jin, Krishnakumar Balasubramanian, Lifeng LaiAbstract
We study instrumental variable regression (IVaR) under differential privacy constraints. Classical IVaR methods (like two-stage least squares regression) rely on solving moment equations that directly use sensitive covariates and instruments, creating significant risks of privacy leakage and posing challenges in designing algorithms that are both statistically efficient and differentially private. We propose a noisy two-state gradient descent algorithm that ensures $\rho$-zero-concentrated differential privacy by injecting carefully calibrated noise into the gradient updates. Our analysis establishes finite-sample convergence rates for the proposed method, showing that the algorithm achieves consistency while preserving privacy. In particular, we derive precise bounds quantifying the trade-off among privacy parameters, sample size, and iteration-complexity. To the best of our knowledge, this is the first work to provide both privacy guarantees and provable convergence rates for instrumental variable regression in linear models. We further validate our theoretical findings with experiments on both synthetic and real datasets, demonstrating that our method offers practical accuracy-privacy trade-offs.
Abstract (translated)
我们研究了在差分隐私约束下的工具变量回归（IVaR）。传统的IVaR方法（如两阶段最小二乘法回归）依赖于直接使用敏感协变量和工具变量求解矩方程，这带来了显著的隐私泄露风险，并且在设计既统计有效又满足差分隐私算法方面存在挑战。我们提出了一种带有噪声的两阶段梯度下降算法，通过向梯度更新中注入精心校准的噪音来确保$\rho$-零集中差分隐私。我们的分析建立了所提方法的有限样本收敛率，表明该算法在保持隐私的同时实现了渐近一致性。特别地，我们推导了精确界来量化隐私参数、样本量和迭代复杂性之间的权衡关系。据我们所知，这是首次为线性模型中的工具变量回归同时提供隐私保证和可证明的收敛速率的研究工作。我们进一步通过在合成数据集和真实数据集上的实验验证了理论发现，并表明我们的方法提供了实用的精度-隐私权衡。
URL
https://arxiv.org/abs/2509.22794
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Global Convergence in Neural ODEs: Impact of Activation Functions
2025-09-26 14:54:48Tianxiang Gao, Siyuan Sun, Hailiang Liu, Hongyang GaoAbstract
Neural Ordinary Differential Equations (ODEs) have been successful in various applications due to their continuous nature and parameter-sharing efficiency. However, these unique characteristics also introduce challenges in training, particularly with respect to gradient computation accuracy and convergence analysis. In this paper, we address these challenges by investigating the impact of activation functions. We demonstrate that the properties of activation functions, specifically smoothness and nonlinearity, are critical to the training dynamics. Smooth activation functions guarantee globally unique solutions for both forward and backward ODEs, while sufficient nonlinearity is essential for maintaining the spectral properties of the Neural Tangent Kernel (NTK) during training. Together, these properties enable us to establish the global convergence of Neural ODEs under gradient descent in overparameterized regimes. Our theoretical findings are validated by numerical experiments, which not only support our analysis but also provide practical guidelines for scaling Neural ODEs, potentially leading to faster training and improved performance in real-world applications.
Abstract (translated)
神经普通微分方程（ODE）由于其连续性特性和参数共享效率，在各种应用中取得了成功。然而，这些独特的特性也给训练带来了挑战，特别是在梯度计算精度和收敛分析方面。在本文中，我们通过研究激活函数的影响来解决这些问题。我们证明了激活函数的属性，特别是平滑性和非线性，对于训练动态至关重要。平滑激活函数保证了正向和反向ODE的全局唯一解，而足够的非线性对于保持训练过程中的神经切核（NTK）谱特性是必不可少的。这些性质共同使得我们在超参数化条件下通过梯度下降方法建立了Neural ODEs的全局收敛性。我们的理论发现得到了数值实验的支持，不仅验证了我们的分析，而且还为扩展Neural ODEs提供了实用指南，这可能导致更快的训练速度和在实际应用中的性能提升。
URL
https://arxiv.org/abs/2509.22436
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Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning
2025-09-26 13:28:53Naicheng He, Kaicheng Guo, Arjun Prakash, Saket Tiwari, Ruo Yu Tao, Tyrone Serapio, Amy Greenwald, George KonidarisAbstract
We investigate why deep neural networks suffer from \emph{loss of plasticity} in deep continual learning, failing to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. To characterize the necessary condition for successful training, we introduce the notion of $\tau$-trainability and show that current plasticity preserving algorithms can be unified under this framework. Targeting spectral collapse directly, we then discuss the Kronecker factored approximation of the Hessian, which motivates two regularization enhancements: maintaining high effective feature rank and applying $L2$ penalties. Experiments on continual supervised and reinforcement learning tasks confirm that combining these two regularizers effectively preserves plasticity.
Abstract (translated)
我们研究了深度神经网络在深层连续学习中为何会遭受\emph{可塑性丧失}，即无法在不重新初始化参数的情况下学习新任务。我们展示了这种失败是由新任务初始时Hessian谱坍缩所导致的，在此过程中有意义的曲率方向消失，梯度下降变得无效。为了描述成功训练的必要条件，我们引入了$\tau$-可训练性的概念，并表明当前保持可塑性的算法可以在这一框架下统一起来。针对直接解决谱坍缩的问题，接下来我们讨论Hessian的Kronecker因子近似方法，这促使了两种正则化增强策略：维持高有效特征秩和应用$L2$惩罚项。在连续监督学习和强化学习任务上的实验确认，结合这两种正则化器可以有效地保持可塑性。
URL
https://arxiv.org/abs/2509.22335
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Analysis of approximate linear programming solution to Markov decision problem with log barrier function
2025-09-24 06:36:11Donghwan Lee, Hyukjun Yang, Bum Geun ParkAbstract
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact that it leads to an inequality-constrained optimization problem, which is generally more challenging to solve effectively compared with Bellman-equation-based methods. The purpose of this paper is to establish a theoretical foundation for solving LP-based MDPs in a more effective and practical manner. Our key idea is to leverage the log-barrier function, widely used in inequality-constrained optimization, to transform the LP formulation of the MDP into an unconstrained optimization problem. This reformulation enables approximate solutions to be obtained easily via gradient descent. While the method may appear simple, to the best of our knowledge, a thorough theoretical interpretation of this approach has not yet been developed. This paper aims to bridge this gap.
Abstract (translated)
解决马尔可夫决策问题（MDPs）主要有两种方法：基于贝尔曼方程的动态规划和线性规划（LP）。动态规划方法是最广泛使用的方法，构成了经典和现代强化学习（RL）的基础。相比之下，虽然线性规划方法被采用得较少，但它们最近在离线强化学习等领域引起了关注。线性规划方法相对较少被使用的部分原因在于，它会导致一个带有不等式约束的优化问题，而相对于基于贝尔曼方程的方法而言，这类问题通常更难有效解决。 本文旨在为以更加有效和实用的方式解决基于LP的MDPs提供理论基础。我们的核心思想是利用广泛用于处理不等式约束优化问题中的对数障碍函数，将MDP的线性规划表示转换为无约束优化问题。这种重述使得通过梯度下降方法可以轻松获得近似解。虽然这种方法可能看似简单，据我们所知，迄今为止还没有对其进行全面的理论解释。本文旨在填补这一空白。
URL
https://arxiv.org/abs/2509.19800
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Deep Learning as the Disciplined Construction of Tame Objects
2025-09-22 17:00:40Gilles Bareilles, Allen Gehret, Johannes Aspman, Jana Lep\v{s}ov\'a, Jakub Mare\v{c}ekAbstract
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.
Abstract (translated)
可以将深度学习模型视为所谓的“温和几何”（tame geometry）中的函数组合。在这篇阐述性笔记中，我们概述了处于温和几何学（又称o-最小性）、优化理论以及深度学习理论与实践交汇处的一些主题。为此，我们将逐步介绍用于在一般非光滑、非凸但符合温和条件的框架下构建随机梯度下降收敛保证的概念和工具。这说明了温和几何如何成为研究AI系统特别是深度学习系统的自然数学框架。
URL
https://arxiv.org/abs/2509.18025
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Hyperbolic Optimization
2025-09-20 07:53:10Yanke Wang, Kyriakos FlourisAbstract
This work explores optimization methods on hyperbolic manifolds. Building on Riemannian optimization principles, we extend the Hyperbolic Stochastic Gradient Descent (a specialization of Riemannian SGD) to a Hyperbolic Adam optimizer. While these methods are particularly relevant for learning on the Poincaré ball, they may also provide benefits in Euclidean and other non-Euclidean settings, as the chosen optimization encourages the learning of Poincaré embeddings. This representation, in turn, accelerates convergence in the early stages of training, when parameters are far from the optimum. As a case study, we train diffusion models using the hyperbolic optimization methods with hyperbolic time-discretization of the Langevin dynamics, and show that they achieve faster convergence on certain datasets without sacrificing generative quality.
Abstract (translated)
这项工作探讨了双曲流形上的优化方法。基于黎曼优化原则，我们将双曲随机梯度下降（黎曼随机梯度下降的一种特例）扩展为双曲Adam优化器。虽然这些方法特别适用于庞加莱球面上的学习，但它们也可能在欧几里得和其他非欧几里得环境中提供好处，因为所选择的优化鼓励学习庞加莱嵌入。这种表示反过来可以在训练初期参数远离最优解时加速收敛。作为案例研究，我们使用双曲优化方法和朗之万动力学的双曲时间离散化来训练扩散模型，并展示了它们在某些数据集上可以实现更快的收敛速度而不牺牲生成质量。
URL
https://arxiv.org/abs/2509.25206
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Reverse Engineering of Music Mixing Graphs with Differentiable Processors and Iterative Pruning
2025-09-19 12:55:58Sungho Lee, Marco Mart\'inez-Ram\'irez, Wei-Hsiang Liao, Stefan Uhlich, Giorgio Fabbro, Kyogu Lee, Yuki MitsufujiAbstract
Reverse engineering of music mixes aims to uncover how dry source signals are processed and combined to produce a final mix. We extend the prior works to reflect the compositional nature of mixing and search for a graph of audio processors. First, we construct a mixing console, applying all available processors to every track and subgroup. With differentiable processor implementations, we optimize their parameters with gradient descent. Then, we repeat the process of removing negligible processors and fine-tuning the remaining ones. This way, the quality of the full mixing console can be preserved while removing approximately two-thirds of the processors. The proposed method can be used not only to analyze individual music mixes but also to collect large-scale graph data that can be used for downstream tasks, e.g., automatic mixing. Especially for the latter purpose, efficient implementation of the search is crucial. To this end, we present an efficient batch-processing method that computes multiple processors in parallel. We also exploit the "dry/wet" parameter of the processors to accelerate the search. Extensive quantitative and qualitative analyses are conducted to evaluate the proposed method's performance, behavior, and computational cost.
Abstract (translated)
音乐混音的逆向工程旨在揭示干声源信号是如何被处理和组合以生成最终混音的。我们扩展了先前的工作，反映混合的组成特性，并寻找音频处理器图。首先，我们构建一个混音控制台，在每个轨道和子组上应用所有可用的处理器。利用可微分的处理器实现方式，我们用梯度下降法优化它们的参数。然后，我们会重复删除不重要的处理器并微调剩余处理器的过程。这样可以在移除约三分之二的处理器的同时保持整个混音控制台的质量。 提出的方法不仅可以用于分析单个音乐混音，还可以收集大规模图数据以供下游任务使用，例如自动混音。特别是为了后者的用途，高效的搜索实现至关重要。为此，我们提供了一种高效的批量处理方法，在其中可以并行计算多个处理器。此外，我们利用处理器的“干/湿”参数来加速搜索过程。 进行了广泛的定量和定性分析以评估所提出的方法性能、行为及其计算成本。
URL
https://arxiv.org/abs/2509.15948
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Information Geometry of Variational Bayes
Abstract
We highlight a fundamental connection between information geometry and variational Bayes (VB) and discuss its consequences for machine learning. Under certain conditions, a VB solution always requires estimation or computation of natural gradients. We show several consequences of this fact by using the natural-gradient descent algorithm of Khan and Rue (2023) called the Bayesian Learning Rule (BLR). These include (i) a simplification of Bayes' rule as addition of natural gradients, (ii) a generalization of quadratic surrogates used in gradient-based methods, and (iii) a large-scale implementation of VB algorithms for large language models. Neither the connection nor its consequences are new but we further emphasize the common origins of the two fields of information geometry and Bayes with a hope to facilitate more work at the intersection of the two fields.
Abstract (translated)
我们强调了信息几何与变分贝叶斯（VB）之间的基本联系，并讨论了这对机器学习的含义。在某些条件下，VB解总是需要估计或计算自然梯度。通过使用Khan和Rue (2023)提出的称为贝叶斯学习规则(BLR)的自然梯度下降算法，我们展示了这一事实的几个后果。这包括(i) 贝叶斯法则作为自然梯度相加的简化形式；(ii) 对基于梯度方法中使用的二次代理的推广；以及(iii) 大规模实现适用于大型语言模型的VB算法。虽然这种联系及其影响并不新鲜，但我们进一步强调了信息几何和贝叶斯这两个领域共同起源的重要性，并希望这能够促进两个领域交叉点上更多工作的开展。
URL
https://arxiv.org/abs/2509.15641
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A Universal Banach--Bregman Framework for Stochastic Iterations: Unifying Stochastic Mirror Descent, Learning and LLM Training
2025-09-17 17:50:59Johnny R. Zhang (Independent Researcher), Xiaomei Mi (University of Manchester), Gaoyuan Du (Amazon), Qianyi Sun (Microsoft), Shiqi Wang (Meta), Jiaxuan Li (Amazon), Wenhua Zhou (Independent Researcher)Abstract
Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert spaces, relying on inner-product frameworks and orthogonality. This paradigm fails to capture non-Euclidean settings, such as mirror descent on simplices, Bregman proximal methods for sparse learning, natural gradient descent in information geometry, or Kullback--Leibler-regularized language model training. Unlike Euclidean-based Hilbert-space methods, this approach embraces general Banach spaces. This work introduces a pioneering Banach--Bregman framework for stochastic iterations, establishing Bregman geometry as a foundation for next-generation optimization. It (i) provides a unified template via Bregman projections and Bregman--Fejer monotonicity, encompassing stochastic approximation, mirror descent, natural gradient, adaptive methods, and mirror-prox; (ii) establishes super-relaxations ($\lambda > 2$) in non-Hilbert settings, enabling flexible geometries and elucidating their acceleration effect; and (iii) delivers convergence theorems spanning almost-sure boundedness to geometric rates, validated on synthetic and real-world tasks. Empirical studies across machine learning (UCI benchmarks), deep learning (e.g., Transformer training), reinforcement learning (actor--critic), and large language models (WikiText-2 with distilGPT-2) show up to 20% faster convergence, reduced variance, and enhanced accuracy over classical baselines. These results position Banach--Bregman geometry as a cornerstone unifying optimization theory and practice across core AI paradigms.
Abstract (translated)
随机优化为现代人工智能的可扩展性提供了动力，涵盖了机器学习、深度学习、强化学习和大型语言模型训练等多个领域。然而，现有的理论主要局限于希尔伯特空间，并依赖于内积框架和正交性。这种范式无法捕捉非欧几里得场景下的情况，比如单纯形上的镜像下降法、稀疏学习的布雷格曼近似方法、信息几何中的自然梯度下降或带Kullback-Leibler正则化的语言模型训练。不同于基于欧氏空间的希尔伯特空间方法，这种方法采用了一般巴拿赫空间。这项工作引入了一个开创性的巴拿赫-布雷格曼框架用于随机迭代，确立了布雷格曼几何作为下一代优化的基础。它（i）通过布雷格曼投影和布雷格曼-Féjer单调性提供了一个统一的模板，涵盖了随机近似、镜像下降法、自然梯度、自适应方法和镜像-普罗克；（ii）在非希尔伯特空间设置中建立了超松弛化($\lambda > 2$)，使得灵活的几何结构成为可能，并阐明了它们加速效果；以及（iii）提供了涵盖几乎必然有界性到几何速率的收敛定理，通过合成和现实世界任务进行了验证。跨机器学习（UCI基准测试）、深度学习（例如Transformer训练）、强化学习（演员-评论家方法）和大型语言模型（使用distilGPT-2的WikiText-2）进行的经验研究表明，在经典基线之上实现了高达20%更快的收敛速度，减少了方差，并提高了精度。这些结果将巴拿赫-布雷格曼几何确立为在核心AI范式中统一优化理论和实践的一个基石。
URL
https://arxiv.org/abs/2509.14216
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Repulsive Trajectory Modification and Conflict Resolution for Efficient Multi-Manipulator Motion Planning
2025-09-17 10:20:19Junhwa Hong, Beomjoon Lee, Woojin Lee, Changjoo NamAbstract
We propose an efficient motion planning method designed to efficiently find collision-free trajectories for multiple manipulators. While multi-manipulator systems offer significant advantages, coordinating their motions is computationally challenging owing to the high dimensionality of their composite configuration space. Conflict-Based Search (CBS) addresses this by decoupling motion planning, but suffers from subsequent conflicts incurred by resolving existing conflicts, leading to an exponentially growing constraint tree of CBS. Our proposed method is based on repulsive trajectory modification within the two-level structure of CBS. Unlike conventional CBS variants, the low-level planner applies a gradient descent approach using an Artificial Potential Field. This field generates repulsive forces that guide the trajectory of the conflicting manipulator away from those of other robots. As a result, subsequent conflicts are less likely to occur. Additionally, we develop a strategy that, under a specific condition, directly attempts to find a conflict-free solution in a single step without growing the constraint tree. Through extensive tests including physical robot experiments, we demonstrate that our method consistently reduces the number of expanded nodes in the constraint tree, achieves a higher success rate, and finds a solution faster compared to Enhanced CBS and other state-of-the-art algorithms.
Abstract (translated)
我们提出了一种高效的运动规划方法，旨在为多个机械臂高效地寻找无碰撞轨迹。虽然多机械臂系统提供了显著的优势，但由于其复合配置空间的高维度，协调它们的动作在计算上具有挑战性。基于冲突的搜索（CBS）通过解耦运动规划来解决这个问题，但这种方法会因解决现有冲突而产生后续冲突，导致CBS约束树呈指数级增长。 我们的方法建立在CBS双层结构中使用排斥轨迹修改的基础上。与传统的CBS变体不同，低级别计划者采用人工势场中的梯度下降方法。该势场生成排斥力，引导冲突机械臂远离其他机器人的轨迹。因此，后续冲突发生的可能性降低。 此外，在特定条件下，我们开发了一种策略，尝试在一步内直接找到无冲突的解决方案，而无需增长约束树。 通过包括物理机器人实验在内的广泛测试，我们证明了我们的方法能够持续减少约束树中的扩展节点数量，并且相比增强版CBS和其他最先进的算法，成功概率更高、更快地找到了解决方案。
URL
https://arxiv.org/abs/2509.13882
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Complexity Bounds for Smooth Convex Multiobjective Optimization
Abstract
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. The progress metric is the Pareto stationarity gap $\mathcal{G}(x)$ (the norm of an optimal convex combination of gradients). Our contributions are fourfold. (i) For strongly convex objectives, any span first-order method (iterates lie in the span of past gradients) exhibits linear convergence no faster than $\exp(-\Theta(T/\sqrt{\kappa}))$ after $T$ oracle calls, where $\kappa$ is the condition number, implying $\Theta(\sqrt{\kappa}\log(1/\varepsilon))$ iterations; this matches classical accelerated upper bounds. (ii) For convex problems and oblivious one-step methods (a fixed scalarization with pre-scheduled step sizes), we prove a lower bound of order $1/T$ on the best gradient norm among the first $T$ iterates. (iii) Although accelerated gradient descent is outside this restricted class, it is an oblivious span method and attains the same $1/T$ upper rate on a fixed scalarization. (iv) For convex problems and general span methods with adaptive scalarizations, we establish a universal lower bound of order $1/T^{2}$ on the gradient norm of the final iterate after $T$ steps, highlighting a gap between known upper bounds and worst-case guarantees. All bounds hold on non-degenerate instances with distinct objectives and non-singleton Pareto fronts; rates are stated up to universal constants and natural problem scaling.
Abstract (translated)
我们研究了在具有$m$个目标的光滑多目标优化中寻找$\varepsilon$-Pareto平稳点的oracle复杂度。衡量指标是Pareto平稳间隙$\mathcal{G}(x)$（即梯度最优凸组合的范数）。我们的贡献有四个方面： (i) 对于强凸的目标函数，任何span一阶方法（迭代值位于过去梯度张成的空间内）在进行了$T$次oracle调用后最多显示线性收敛速度$\exp(-\Theta(T/\sqrt{\kappa}))$，其中$\kappa$是条件数。这需要$\Theta(\sqrt{\kappa}\log(1/\varepsilon))$轮迭代，与经典的加速上限相匹配。 (ii) 对于凸问题和无记忆单步方法（固定标量化且预设步长），我们证明了在前$T$次迭代中最佳梯度范数的下界为$\Theta(1/T)$。 (iii) 虽然加速梯度下降超出了这个受限类别，但它是无记忆span方法，在固定的标量化上达到了同样的$\Theta(1/T)$上限。 (iv) 对于凸问题和一般span方法，如果采用自适应标量化，则在进行了$T$步之后，最终迭代的梯度范数具有下界$\Theta(1/T^2)$。这揭示了已知的上界与最坏情况保证之间的差距。 所有这些界限适用于目标不相同且非单点Pareto前沿的情况；速率表达到了通用常量和自然问题标度为止。
URL
https://arxiv.org/abs/2509.13550
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From Next Token Prediction to World Models -- Preliminary Results
2025-09-16 14:03:58Carlos N\'u\~nez-Molina, Vicen\c{c} G\'omez, Hector GeffnerAbstract
We consider the problem of learning propositional STRIPS world models from action traces alone, using a deep learning architecture (transformers) and gradient descent. The task is cast as a supervised next token prediction problem where the tokens are the actions, and an action $a$ may follow an action sequence if the hidden effects of the previous actions do not make an action precondition of $a$ false. We show that a suitable transformer architecture can faithfully represent propositional STRIPS world models, and that the models can be learned from sets of random valid (positive) and invalid (negative) action sequences alone. A number of experiments are reported.
Abstract (translated)
我们考虑仅从动作轨迹学习命题STRIPS世界模型的问题，使用深度学习架构（如变换器）和梯度下降方法。这个问题被转化为一个监督式的下一个标记预测问题，其中的标记是动作，并且动作$a$可以跟随某个动作序列的前提条件是在之前的动作所产生的隐含效应不使动作$a$的前提条件变为假的情况下。 我们展示了一种合适的变换器架构能够忠实地表示命题STRIPS世界模型，并表明仅从随机生成的有效（正样本）和无效（负样本）的动作序列集合中就可以学习到这些模型。报告了一系列的实验结果。
URL
https://arxiv.org/abs/2509.13389
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Graph Algorithm Unrolling with Douglas-Rachford Iterations for Image Interpolation with Guaranteed Initialization
2025-09-15 13:43:55Xue Zhang, Bingshuo Hu, Gene CheungAbstract
Conventional deep neural nets (DNNs) initialize network parameters at random and then optimize each one via stochastic gradient descent (SGD), resulting in substantial risk of poor-performing local this http URL on the image interpolation problem and leveraging a recent theorem that maps a (pseudo-)linear interpolator {\Theta} to a directed graph filter that is a solution to a MAP problem regularized with a graph shift variation (GSV) prior, we first initialize a directed graph adjacency matrix A based on a known interpolator {\Theta}, establishing a baseline this http URL, towards further gain, we learn perturbation matrices P and P(2) from data to augment A, whose restoration effects are implemented via Douglas-Rachford (DR) iterations, which we unroll into a lightweight interpretable neural this http URL results demonstrate state-of-the-art image interpolation results, while drastically reducing network parameters.
Abstract (translated)
传统的深度神经网络（DNN）在网络参数初始化时采用随机方式，然后通过随机梯度下降（SGD）优化每个参数，这会导致陷入次优局部极小值的风险。本文针对图像插值问题，并利用最近的一个定理，该定理将一个线性或伪线性插值器{\Theta}映射为带有图移变差（GSV）先验的极大似然估计（MAP）问题的解所对应的有向图滤波器。首先，我们基于已知的插值器{\Theta}初始化了一个有向图邻接矩阵A，以此建立一个基准点。 为了进一步提高性能，我们从数据中学习到扰动矩阵P和P(2)，用以增强矩阵A，其恢复效果通过道格拉斯-拉奇福德（DR）迭代来实现，并将其展开成轻量级可解释的神经网络。实验结果表明，在大幅减少网络参数的同时，达到了最先进的图像插值性能。
URL
https://arxiv.org/abs/2509.11926
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MAPGD: Multi-Agent Prompt Gradient Descent for Collaborative Prompt Optimization
2025-09-14 17:28:52Yichen Han, Bojun Liu, Zhengpeng zhou, Guanyu Liu, Zeng Zhang, Yang Yang, Wenli Wang, Isaac N Shi, Yunyan, Lewei He, Tianyu ShiAbstract
Prompt engineering is crucial for leveraging large language models (LLMs), but existing methods often rely on a single optimization trajectory, limiting adaptability and efficiency while suffering from narrow perspectives, gradient conflicts, and high computational cost. We propose MAPGD (Multi-Agent Prompt Gradient Descent), a framework integrating multi-agent collaboration with gradient-based optimization. MAPGD features specialized agents for task clarity, example selection, format design, and stylistic refinement; semantic gradient coordination to resolve conflicts; bandit-based candidate selection for efficient exploration-exploitation; and theoretical convergence guarantees. Experiments on classification, generation, and reasoning tasks show MAPGD outperforms single-agent and random baselines in accuracy and efficiency. Ablations confirm the benefits of gradient fusion, agent specialization, and conflict resolution, providing a unified, gradient-inspired multi-agent approach to robust and interpretable prompt optimization.
Abstract (translated)
提示工程对于充分利用大型语言模型（LLM）至关重要，但现有方法往往依赖单一的优化路径，这限制了其适应性和效率，并且容易出现视野狭窄、梯度冲突和计算成本过高的问题。我们提出了MAPGD（多代理提示梯度下降），这是一种结合了多代理协作与基于梯度优化的框架。MAPGD的特点包括：专门负责任务清晰性、示例选择、格式设计和风格精炼的代理；用于解决冲突的语义梯度协调；基于强盗算法的选择候选方案以实现高效的探索-利用平衡；以及理论上的收敛保证。在分类、生成和推理任务上的实验表明，MAPGD比单一代理和随机基线方法在准确性和效率方面表现更优。消融分析证实了梯度融合、代理专门化及冲突解决带来的益处，为稳健且可解释的提示优化提供了一种统一的、以梯度为基础的多代理方法。
URL
https://arxiv.org/abs/2509.11361
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Gradient Free Deep Reinforcement Learning With TabPFN
2025-09-14 13:09:58David Schiff, Ofir Lindenbaum, Yonathan EfroniAbstract
Gradient based optimization is fundamental to most modern deep reinforcement learning algorithms, however, it introduces significant sensitivity to hyperparameters, unstable training dynamics, and high computational costs. We propose TabPFN RL, a novel gradient free deep RL framework that repurposes the meta trained transformer TabPFN as a Q function approximator. Originally developed for tabular classification, TabPFN is a transformer pre trained on millions of synthetic datasets to perform inference on new unseen datasets via in context learning. Given an in context dataset of sample label pairs and new unlabeled data, it predicts the most likely labels in a single forward pass, without gradient updates or task specific fine tuning. We use TabPFN to predict Q values using inference only, thereby eliminating the need for back propagation at both training and inference. To cope with the model's fixed context budget, we design a high reward episode gate that retains only the top 5% of trajectories. Empirical evaluations on the Gymnasium classic control suite demonstrate that TabPFN RL matches or surpasses Deep Q Network on CartPole v1, MountainCar v0, and Acrobot v1, without applying gradient descent or any extensive hyperparameter tuning. We discuss the theoretical aspects of how bootstrapped targets and non stationary visitation distributions violate the independence assumptions encoded in TabPFN's prior, yet the model retains a surprising generalization capacity. We further formalize the intrinsic context size limit of in context RL algorithms and propose principled truncation strategies that enable continual learning when the context is full. Our results establish prior fitted networks such as TabPFN as a viable foundation for fast and computationally efficient RL, opening new directions for gradient free RL with large pre trained transformers.
Abstract (translated)
基于梯度的优化是大多数现代深度强化学习算法的基础，然而它引入了对超参数的高度敏感性、不稳定的训练动态以及高昂的计算成本。我们提出了一种新的无梯度深度RL框架——TabPFN RL，该框架重新利用元训练过的变压器模型TabPFN作为Q函数逼近器。最初为表格分类设计的TabPFN是一个在数百万个合成数据集上预训练的Transformer模型，能够通过上下文学习来推断新未见的数据集。给定包含样本标签对的上下文数据集和新的无标签数据，它可以在单次前向传递中预测最可能的标签，无需进行梯度更新或特定任务的微调。 我们在不使用反向传播的情况下，利用TabPFN仅通过推理来预测Q值。为了应对模型固定的上下文预算限制，我们设计了一个高奖励集束门（high reward episode gate），该机制保留了前5%的轨迹。在Gymnasium经典控制套件上的实证评估表明，在不应用梯度下降或进行大量超参数调整的情况下，TabPFN RL在CartPole v1、MountainCar v0和Acrobot v1环境中的表现与深度Q网络相当甚至更优。 我们讨论了如何通过自举目标（bootstrapped targets）以及非静态访问分布破坏TabPFN先验中编码的独立性假设的问题，尽管如此，模型仍然保持了令人惊讶的一般化能力。此外，我们形式化地定义了在上下文RL算法中的内在上下文大小限制，并提出了原理性的截断策略，在上下文满时允许持续学习。 我们的研究结果表明，基于拟合网络（如TabPFN）可以作为快速且计算效率高的强化学习的基础框架，为使用大型预训练变换器进行无梯度的强化学习开辟了新的方向。
URL
https://arxiv.org/abs/2509.11259
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Decoupling Search and Learning in Neural Net Training
Abstract
Gradient descent typically converges to a single minimum of the training loss without mechanisms to explore alternative minima that may generalize better. Searching for diverse minima directly in high-dimensional parameter space is generally intractable. To address this, we propose a framework that performs training in two distinct phases: search in a tractable representation space (the space of intermediate activations) to find diverse representational solutions, and gradient-based learning in parameter space by regressing to those searched representations. Through evolutionary search, we discover representational solutions whose fitness and diversity scale with compute--larger populations and more generations produce better and more varied solutions. These representations prove to be learnable: networks trained by regressing to searched representations approach SGD's performance on MNIST, CIFAR-10, and CIFAR-100. Performance improves with search compute up to saturation. The resulting models differ qualitatively from networks trained with gradient descent, following different representational trajectories during training. This work demonstrates how future training algorithms could overcome gradient descent's exploratory limitations by decoupling search in representation space from efficient gradient-based learning in parameter space.
Abstract (translated)
梯度下降通常会收敛到训练损失中的单一最小值，而没有探索可能更好泛化的替代极小值的机制。在高维参数空间中直接搜索多样性的极小值通常是不可行的。为了解决这个问题，我们提出了一种框架，在两个不同的阶段进行训练：首先在可处理的表现形式空间（中间激活的空间）中寻找多样化的表示解；然后通过基于梯度的学习方法在参数空间中回归到这些找到的表示上进行学习。 通过进化搜索，我们可以发现那些其适应性和多样性与计算资源成比例增长的表示解——更大的种群和更多的世代会产生更好且更加多样的解决方案。这些表示证明是可学得的：通过回归至搜索到的表示来训练的网络在MNIST、CIFAR-10和CIFAR-100数据集上的性能与随机梯度下降法（SGD）相当。随着搜索计算资源的增加，性能会提升直至饱和。 由此产生的模型在训练过程中遵循不同的表示轨迹，这区别于通过梯度下降方法训练得到的网络。这项工作展示了未来训练算法如何能够通过将表示空间中的搜索和参数空间中基于梯度的学习解耦来克服梯度下降探索上的限制。
URL
https://arxiv.org/abs/2509.10973
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Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method
Abstract
Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on dense matrix multiplications. Due to their differentiable nature, they can be integrated with neural networks and jointly trained using gradient descent algorithms, resulting in more efficient systems. Furthermore, signal processing algorithms have significantly fewer parameters than neural networks, allowing the application of the Newton-Raphson method. This method offers faster and more robust convergence than gradient descent at the cost of quadratic storage. This paper presents a method to emulate analogue levelling amplifiers using a feed-forward digital compressor with parameters optimised via the Newton-Raphson method. We demonstrate that a digital compressor can successfully approximate the behaviour of our target unit, the Teletronix LA-2A. Different strategies for computing the Hessian matrix are benchmarked. We leverage parallel algorithms for recursive filters to achieve efficient training on modern GPUs. The resulting model is made into a VST plugin and is open-sourced at this https URL.
Abstract (translated)
最近，通过数字信号处理算法进行自动微分以实现虚拟模拟建模的方法变得越来越受欢迎。这些算法通常比依赖密集矩阵乘法的黑盒神经网络更具有计算效率。由于它们是可微的，因此可以与神经网络集成，并使用梯度下降算法联合训练，从而生成更为高效的系统。此外，信号处理算法相较于神经网络拥有较少的参数量，这使得能够应用牛顿-拉夫森方法。此方法虽然以二次存储为代价，但比梯度下降法提供更快且更稳健的收敛速度。 本文提出了一种使用前馈数字压缩器来模拟类比电平放大器的方法，并利用牛顿-拉夫森方法优化参数。我们展示了通过这种方式，一个数字压缩器可以成功地近似目标单元——Teletronix LA-2A的行为表现。文章还对计算海森矩阵的不同策略进行了基准测试。我们利用递归滤波器的并行算法来实现在现代GPU上的高效训练。最终模型被制作成VST插件，并在以下网址开源：[此链接](https://这个URL需要你根据实际情况提供)。 请注意，上述翻译中的最后一句话提到的链接应当由原文作者或发布者提供一个具体的、可访问的实际地址。
URL
https://arxiv.org/abs/2509.10706
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Privacy-Preserving Decentralized Federated Learning via Explainable Adaptive Differential Privacy
2025-09-12 20:52:41Fardin Jalil Piran, Zhiling Chen, Yang Zhang, Qianyu Zhou, Jiong Tang, Farhad ImaniAbstract
Decentralized federated learning faces privacy risks because model updates can leak data through inference attacks and membership inference, a concern that grows over many client exchanges. Differential privacy offers principled protection by injecting calibrated noise so confidential information remains secure on resource-limited IoT devices. Yet without transparency, black-box training cannot track noise already injected by previous clients and rounds, which forces worst-case additions and harms accuracy. We propose PrivateDFL, an explainable framework that joins hyperdimensional computing with differential privacy and keeps an auditable account of cumulative noise so each client adds only the difference between the required noise and what has already been accumulated. We evaluate on MNIST, ISOLET, and UCI-HAR to span image, signal, and tabular modalities, and we benchmark against transformer-based and deep learning-based baselines trained centrally with Differentially Private Stochastic Gradient Descent (DP-SGD) and Renyi Differential Privacy (RDP). PrivateDFL delivers higher accuracy, lower latency, and lower energy across IID and non-IID partitions while preserving formal (epsilon, delta) guarantees and operating without a central server. For example, under non-IID partitions, PrivateDFL achieves 24.42% higher accuracy than the Vision Transformer on MNIST while using about 10x less training time, 76x lower inference latency, and 11x less energy, and on ISOLET it exceeds Transformer accuracy by more than 80% with roughly 10x less training time, 40x lower inference latency, and 36x less training energy. Future work will extend the explainable accounting to adversarial clients and adaptive topologies with heterogeneous privacy budgets.
Abstract (translated)
去中心化的联邦学习由于模型更新可能通过推理攻击和成员推断等方式泄露数据，因此面临着隐私风险。随着多个客户端之间的交互增加，这种担忧也在加剧。差分隐私（Differential Privacy）提供了一种原则性的保护方法，通过注入校准噪声来确保在资源受限的物联网设备上保密信息的安全性。然而，在缺乏透明度的情况下，黑盒训练无法追踪之前客户端和轮次中已经注入的噪声，这迫使每次必须增加最坏情况下的噪音量，并损害了准确性。 我们提出了一种名为PrivateDFL的可解释框架，该框架结合了超维度计算（Hyperdimensional Computing）与差分隐私技术，并维护了一个可以审计的累计噪声记录，使得每个客户端只需添加所需噪声与其之前累积噪声之间的差异部分。我们在MNIST、ISOLET和UCI-HAR数据集上进行了测试，涵盖图像、信号和表格模态，并将PrivateDFL与其他基于转换器（Transformer）和深度学习且使用中心化训练的Differentially Private Stochastic Gradient Descent (DP-SGD) 和 Renyi Differential Privacy (RDP) 方法进行基准比较。结果表明，在保持正式的(epsilon, delta)保证的同时，PrivateDFL在IID和非IID数据分区上都提供了更高的准确率、更低的延迟和能耗，并且无需中央服务器支持。 具体而言，在处理非IID数据分区时，与视觉转换器相比，PrivateDFL在MNIST数据集上的准确性提高了24.42%，训练时间减少了约10倍，推理延迟降低了76倍，训练能量消耗减少了11倍；而在ISOLET数据集上，PrivateDFL的准确率超出转换器模型80%以上，并且训练时间减少大约10倍、推理延迟降低40倍以及训练能耗减少36倍。 未来的工作计划将可解释性账目扩展到对抗客户端和自适应拓扑结构中具有异构隐私预算的情况。
URL
https://arxiv.org/abs/2509.10691
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zkUnlearner: A Zero-Knowledge Framework for Verifiable Unlearning with Multi-Granularity and Forgery-Resistance
2025-09-08 23:50:35Nan Wang, Nan Wu, Xiangyu Hui, Jiafan Wang, Xin YuanAbstract
As the demand for exercising the "right to be forgotten" grows, the need for verifiable machine unlearning has become increasingly evident to ensure both transparency and accountability. We present {\em zkUnlearner}, the first zero-knowledge framework for verifiable machine unlearning, specifically designed to support {\em multi-granularity} and {\em forgery-resistance}. First, we propose a general computational model that employs a {\em bit-masking} technique to enable the {\em selectivity} of existing zero-knowledge proofs of training for gradient descent algorithms. This innovation enables not only traditional {\em sample-level} unlearning but also more advanced {\em feature-level} and {\em class-level} unlearning. Our model can be translated to arithmetic circuits, ensuring compatibility with a broad range of zero-knowledge proof systems. Furthermore, our approach overcomes key limitations of existing methods in both efficiency and privacy. Second, forging attacks present a serious threat to the reliability of unlearning. Specifically, in Stochastic Gradient Descent optimization, gradients from unlearned data, or from minibatches containing it, can be forged using alternative data samples or minibatches that exclude it. We propose the first effective strategies to resist state-of-the-art forging attacks. Finally, we benchmark a zkSNARK-based instantiation of our framework and perform comprehensive performance evaluations to validate its practicality.
Abstract (translated)
随着人们对于“被遗忘权”的需求增加，确保透明度和问责制的可验证机器遗忘技术的重要性也日益凸显。我们提出了一种名为{\em zkUnlearner}的零知识框架，这是第一个专门用于支持{\em多粒度}和{\em防伪造}的可验证机器遗忘系统。 首先，我们提出了一个通用计算模型，并使用一种称为{\em位掩码}的技术来使现有的针对梯度下降算法训练过程的零知识证明具备选择性。这一创新不仅能够实现传统的基于样本级别的遗忘，还支持更为高级的特征级别和类别级别遗忘。我们的模型可以转换为算术电路，确保与广泛范围内的零知识证明系统兼容。此外，我们方法在效率和隐私方面克服了现有技术的关键限制。 其次，伪造攻击对遗忘过程的可靠性构成严重威胁。特别是在随机梯度下降优化过程中，来自被遗忘数据或包含此类数据的小批量中的梯度可以通过使用不包含这些数据样本或小批量的数据来伪造。我们提出了有效抵抗当前最先进的伪造攻击的战略。 最后，我们采用基于zkSNARK（零知识简洁非交互式知识论证）的实例化框架，并进行了全面性能评估以验证其实际应用价值。
URL
https://arxiv.org/abs/2509.07290
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Intraoperative 2D/3D Registration via Spherical Similarity Learning and Inference-Time Differentiable Levenberg-Marquardt Optimization
2025-09-08 17:10:43Minheng Chen, Youyong KongAbstract
Intraoperative 2D/3D registration aligns preoperative 3D volumes with real-time 2D radiographs, enabling accurate localization of instruments and implants. A recent fully differentiable similarity learning framework approximates geodesic distances on SE(3), expanding the capture range of registration and mitigating the effects of substantial disturbances, but existing Euclidean approximations distort manifold structure and slow convergence. To address these limitations, we explore similarity learning in non-Euclidean spherical feature spaces to better capture and fit complex manifold structure. We extract feature embeddings using a CNN-Transformer encoder, project them into spherical space, and approximate their geodesic distances with Riemannian distances in the bi-invariant SO(4) space. This enables a more expressive and geometrically consistent deep similarity metric, enhancing the ability to distinguish subtle pose differences. During inference, we replace gradient descent with fully differentiable Levenberg-Marquardt optimization to accelerate convergence. Experiments on real and synthetic datasets show superior accuracy in both patient-specific and patient-agnostic scenarios.
Abstract (translated)
术中2D/3D配准将术前的三维体积与实时二维影像对齐，使得手术器械和植入物的位置能够被精确地定位。最近提出的一种完全可微相似性学习框架，在SE(3)上近似测地距离，从而扩大了注册范围并减轻了重大干扰的影响；然而，现有的欧几里得近似方法会扭曲流形结构，并减缓收敛速度。为了解决这些问题，我们探索在非欧几里得球面特征空间中进行相似性学习，以更好地捕捉和拟合复杂的流形结构。我们使用CNN-Transformer编码器提取特征嵌入，将其投影到球面上，并通过SO(4)双不变量空间中的黎曼距离来近似它们的测地距离。这使得深度相似度度量更具表现力且几何一致性更强，从而增强了区分细微姿态差异的能力。在推理过程中，我们用完全可微的Levenberg-Marquardt优化方法替代梯度下降法，以加快收敛速度。实验证明，在真实和合成数据集上进行测试时，无论是患者特定的情况还是无差别情况，该方法均表现出更高的准确性。
URL
https://arxiv.org/abs/2509.06890
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