Gradient_Descent
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Curriculum-Guided Antifragile Reinforcement Learning for Secure UAV Deconfliction under Observation-Space Attacks
2025-06-26 10:10:41Deepak Kumar Panda, Adolfo Perrusquia, Weisi GuoAbstract
Reinforcement learning (RL) policies deployed in safety-critical systems, such as unmanned aerial vehicle (UAV) navigation in dynamic airspace, are vulnerable to out-ofdistribution (OOD) adversarial attacks in the observation space. These attacks induce distributional shifts that significantly degrade value estimation, leading to unsafe or suboptimal decision making rendering the existing policy fragile. To address this vulnerability, we propose an antifragile RL framework designed to adapt against curriculum of incremental adversarial perturbations. The framework introduces a simulated attacker which incrementally increases the strength of observation-space perturbations which enables the RL agent to adapt and generalize across a wider range of OOD observations and anticipate previously unseen attacks. We begin with a theoretical characterization of fragility, formally defining catastrophic forgetting as a monotonic divergence in value function distributions with increasing perturbation strength. Building on this, we define antifragility as the boundedness of such value shifts and derive adaptation conditions under which forgetting is stabilized. Our method enforces these bounds through iterative expert-guided critic alignment using Wasserstein distance minimization across incrementally perturbed observations. We empirically evaluate the approach in a UAV deconfliction scenario involving dynamic 3D obstacles. Results show that the antifragile policy consistently outperforms standard and robust RL baselines when subjected to both projected gradient descent (PGD) and GPS spoofing attacks, achieving up to 15% higher cumulative reward and over 30% fewer conflict events. These findings demonstrate the practical and theoretical viability of antifragile reinforcement learning for secure and resilient decision-making in environments with evolving threat scenarios.
Abstract (translated)
强化学习（RL）策略在无人驾驶航空器（UAV）导航等安全关键系统中的应用，面对动态空域中观察空间的分布外（OOD）对抗攻击时表现出脆弱性。这些攻击导致价值估计出现显著偏差，从而引发不安全或次优决策，使现有策略变得不稳定。为了应对这一漏洞，我们提出了一种抗脆性的RL框架，该框架能够适应增量式对抗扰动的课程训练。该框架引入了一个模拟攻击者，逐步增加观察空间中的干扰强度，从而使强化学习代理能够在更广泛的OOD观察中进行自适应和泛化，并且可以预测以前未见过的攻击。 我们从理论上对脆弱性进行了描述，正式定义了灾难性遗忘为随着扰动强度增强价值函数分布之间的单调发散。在此基础上，我们将抗脆性定义为这样的价值转移是有限度的，并推导出在哪些适应条件下可以使这种遗忘稳定下来。我们的方法通过使用Wasserstein距离最小化来进行迭代专家指导的批评对齐来强制执行这些限制，该过程是在逐步受到扰动的观察中进行的。 我们在涉及动态3D障碍物规避的UAV场景中进行了实验评估。结果显示，在面对投影梯度下降（PGD）和GPS欺骗攻击时，抗脆性策略在标准RL基准线的基础上累计奖励提高了高达15%，冲突事件减少了超过30%。这些发现证明了抗脆性强化学习对于具有不断变化威胁环境中的安全和弹性决策制定的实用性和理论可行性。 总之，该研究为强化学习算法的安全性和稳健性提供了一种新的方法，并展示了在面对动态且复杂的OOD攻击时，通过适应训练来提高策略鲁棒性的潜力。
URL
https://arxiv.org/abs/2506.21129
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Robust Policy Switching for Antifragile Reinforcement Learning for UAV Deconfliction in Adversarial Environments
2025-06-26 10:06:29Deepak Kumar Panda, Weisi GuoAbstract
The increasing automation of navigation for unmanned aerial vehicles (UAVs) has exposed them to adversarial attacks that exploit vulnerabilities in reinforcement learning (RL) through sensor manipulation. Although existing robust RL methods aim to mitigate such threats, their effectiveness has limited generalization to out-of-distribution shifts from the optimal value distribution, as they are primarily designed to handle fixed perturbation. To address this limitation, this paper introduces an antifragile RL framework that enhances adaptability to broader distributional shifts by incorporating a switching mechanism based on discounted Thompson sampling (DTS). This mechanism dynamically selects among multiple robust policies to minimize adversarially induced state-action-value distribution shifts. The proposed approach first derives a diverse ensemble of action robust policies by accounting for a range of perturbations in the policy space. These policies are then modeled as a multiarmed bandit (MAB) problem, where DTS optimally selects policies in response to nonstationary Bernoulli rewards, effectively adapting to evolving adversarial strategies. Theoretical framework has also been provided where by optimizing the DTS to minimize the overall regrets due to distributional shift, results in effective adaptation against unseen adversarial attacks thus inducing antifragility. Extensive numerical simulations validate the effectiveness of the proposed framework in complex navigation environments with multiple dynamic three-dimensional obstacles and with stronger projected gradient descent (PGD) and spoofing attacks. Compared to conventional robust, non-adaptive RL methods, the antifragile approach achieves superior performance, demonstrating shorter navigation path lengths and a higher rate of conflict-free navigation trajectories compared to existing robust RL techniques
Abstract (translated)
无人驾驶飞机（UAV）导航的自动化程度提高，使其更容易受到通过操纵传感器来利用强化学习（RL）漏洞的对抗性攻击。尽管现有的鲁棒RL方法旨在减轻此类威胁，但由于它们主要设计用于处理固定扰动，因此在面对偏离最优价值分布的变化时，其效果有限且泛化能力不足。为了克服这一限制，本文提出了一种基于折扣Thompson采样（DTS）切换机制的抗脆弱性RL框架，以增强对更广泛分布变化的适应性。此机制通过动态选择多个鲁棒策略来最小化对抗性引起的状态-动作值分布的变化。 所提出的这种方法首先通过对策略空间中一系列扰动进行建模，导出一组多样化的行动鲁棒策略集合。然后将这些策略作为多臂赌博机（MAB）问题进行处理，在此过程中使用DTS根据非平稳的伯努利奖励来优化选择策略，从而有效适应不断变化的对抗性策略。 此外，本文还提供了一个理论框架，通过优化DTS以最小化由于分布变化导致的整体遗憾值，使得该方法能够有效地对抗未见过的对抗性攻击，并因此具有抗脆弱性。大量的数值模拟验证了所提出的框架在复杂导航环境中的有效性，包括存在多个动态三维障碍物的情况，以及更强烈的投影梯度下降（PGD）和欺骗攻击的情况下。 与传统的鲁棒、非适应性的RL方法相比，该抗脆弱性方法展示了更优的性能：其生成的导航路径更短，并且冲突自由的导航轨迹比例更高。这表明，在面对复杂和动态变化的对抗环境中，所提出的框架能够更好地保护UAV的安全性和稳定性。
URL
https://arxiv.org/abs/2506.21127
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Can Gradient Descent Simulate Prompting?
2025-06-26 04:06:20Eric Zhang, Leshem Choshen, Jacob AndreasAbstract
There are two primary ways of incorporating new information into a language model (LM): changing its prompt or changing its parameters, e.g. via fine-tuning. Parameter updates incur no long-term storage cost for model changes. However, for many model updates, prompting is significantly more effective: prompted models can generalize robustly from single examples and draw logical inferences that do not occur under standard fine-tuning. Can models be modified so that fine-tuning does emulate prompting? This paper describes a method for meta-training LMs such that gradient updates emulate the effects of conditioning on new information. Our approach uses tools from gradient-based meta-learning but uses an LM's own prompted predictions as targets, eliminating the need for ground-truth labels. Subsequent gradient descent training recovers some (and occasionally all) of prompted model performance -- showing improvement on the ``reversal curse'' tasks, and answering questions about text passages after a single gradient update. These results suggest that, with appropriate initialization, gradient descent can be surprisingly expressive. Our results suggest new avenues for long-context modeling and offer insight into the generalization capabilities of gradient-based learning.
Abstract (translated)
将新信息融入语言模型（LM）主要有两种方式：更改其提示或调整其参数，例如通过微调来实现。参数更新不会产生长期存储成本。然而，在许多模型更新的情况下，使用提示更加有效：经过提示的模型可以从单个示例中稳健地泛化，并得出逻辑推断，而这些在标准微调过程中并不会发生。是否可以修改模型使微调的效果模拟出提示的效果呢？ 本文描述了一种方法，即通过元训练LM的方式使得梯度更新能够模仿对新信息条件化的效果。我们的方法使用基于梯度的元学习工具，但以语言模型自身受到提示后的预测作为目标，从而消除了对真实标签的需求。后续的梯度下降训练可以恢复一些（有时甚至是全部）由提示带来的模型性能——在“逆转诅咒”任务中表现出改善，并且仅通过一次梯度更新即可回答关于文本段落的问题。这些结果表明，在适当的初始化下，梯度下降具有惊人的表达能力。 我们的研究成果为长上下文建模提供了新的途径，并对基于梯度的学习泛化能力提供了见解。
URL
https://arxiv.org/abs/2506.20989
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Toward Decision-Oriented Prognostics: An Integrated Estimate-Optimize Framework for Predictive Maintenance
2025-06-24 15:10:15Zhuojun Xie, Adam Abdin, Yiping FangAbstract
Recent research increasingly integrates machine learning (ML) into predictive maintenance (PdM) to reduce operational and maintenance costs in data-rich operational settings. However, uncertainty due to model misspecification continues to limit widespread industrial adoption. This paper proposes a PdM framework in which sensor-driven prognostics inform decision-making under economic trade-offs within a finite decision space. We investigate two key questions: (1) Does higher predictive accuracy necessarily lead to better maintenance decisions? (2) If not, how can the impact of prediction errors on downstream maintenance decisions be mitigated? We first demonstrate that in the traditional estimate-then-optimize (ETO) framework, errors in probabilistic prediction can result in inconsistent and suboptimal maintenance decisions. To address this, we propose an integrated estimate-optimize (IEO) framework that jointly tunes predictive models while directly optimizing for maintenance outcomes. We establish theoretical finite-sample guarantees on decision consistency under standard assumptions. Specifically, we develop a stochastic perturbation gradient descent algorithm suitable for small run-to-failure datasets. Empirical evaluations on a turbofan maintenance case study show that the IEO framework reduces average maintenance regret up to 22% compared to ETO. This study provides a principled approach to managing prediction errors in data-driven PdM. By aligning prognostic model training with maintenance objectives, the IEO framework improves robustness under model misspecification and improves decision quality. The improvement is particularly pronounced when the decision-making policy is misaligned with the decision-maker's target. These findings support more reliable maintenance planning in uncertain operational environments.
Abstract (translated)
最近的研究越来越多地将机器学习（ML）融入预测性维护（PdM），以减少数据密集型操作环境中的运营和维护成本。然而，由于模型规格不匹配导致的不确定性继续限制了其在工业领域的广泛应用。本文提出了一种基于传感器驱动预测的PdM框架，在该框架中，经济权衡下的决策制定在一个有限的决策空间内进行。我们探讨了两个关键问题：（1）更高的预测准确性是否必然会导致更好的维护决策？（2）如果不尽然，如何减轻预测误差对后续维护决策的影响？ 首先，我们展示了在传统的估计然后优化（ETO）框架中，概率预测中的错误可能导致不一致和次优的维护决策。为了解决这个问题，我们提出了一个集成估计-优化（IEO）框架，该框架联合调优预测模型的同时直接针对维护结果进行最优化。我们在标准假设下建立了理论上的有限样本保证，以确保决策的一致性。具体来说，我们开发了一种适合于小规模运行至故障数据集的随机扰动梯度下降算法。 在对涡轮风扇维护案例的研究中，实证评估表明IEO框架相比于ETO减少了高达22%的平均维护遗憾（即未达到最佳维护效果的程度）。这项研究提供了一个基于数据驱动PdM管理预测误差的原则性方法。通过将诊断模型训练与维护目标相结合，IEO框架在模型规格不匹配的情况下提高了鲁棒性和决策质量。这种改进尤其明显于当决策策略与决策者的目标不一致时。 这些发现支持了在不确定的操作环境中进行更可靠的维护规划。
URL
https://arxiv.org/abs/2506.19698
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Optimization-Induced Dynamics of Lipschitz Continuity in Neural Networks
2025-06-23 12:49:13R\'ois\'in Luo, James McDermott, Christian Gagn\'e, Qiang Sun, Colm O'RiordanAbstract
Lipschitz continuity characterizes the worst-case sensitivity of neural networks to small input perturbations; yet its dynamics (i.e. temporal evolution) during training remains under-explored. We present a rigorous mathematical framework to model the temporal evolution of Lipschitz continuity during training with stochastic gradient descent (SGD). This framework leverages a system of stochastic differential equations (SDEs) to capture both deterministic and stochastic forces. Our theoretical analysis identifies three principal factors driving the evolution: (i) the projection of gradient flows, induced by the optimization dynamics, onto the operator-norm Jacobian of parameter matrices; (ii) the projection of gradient noise, arising from the randomness in mini-batch sampling, onto the operator-norm Jacobian; and (iii) the projection of the gradient noise onto the operator-norm Hessian of parameter matrices. Furthermore, our theoretical framework sheds light on such as how noisy supervision, parameter initialization, batch size, and mini-batch sampling trajectories, among other factors, shape the evolution of the Lipschitz continuity of neural networks. Our experimental results demonstrate strong agreement between the theoretical implications and the observed behaviors.
Abstract (translated)
李普希茨连续性表征了神经网络对小输入扰动的最坏情况敏感度；然而，在使用随机梯度下降（SGD）进行训练时，其动力学特性（即随时间的变化过程）仍然研究不足。我们提出了一种严格的数学框架来模拟在使用SGD训练过程中李普希茨连续性的随时间变化过程。该框架利用随机微分方程（SDEs）系统捕捉确定性和随机力的影响。 我们的理论分析识别了驱动演变的三个主要因素： (i) 由优化动力学引起的梯度流向参数矩阵操作员范数雅可比矩阵的投影； (ii) 由于小批量采样中的随机性产生的梯度噪声对操作员范数雅可比矩阵的投影； (iii) 梯度噪声向参数矩阵操作员范数海森矩阵的投影。 此外，我们的理论框架还揭示了诸如嘈杂监督、参数初始化、批次大小和小批量采样轨迹等因素如何塑造神经网络李普希茨连续性随时间的变化。实验结果表明，理论推断与观察到的行为之间有很强的一致性。
URL
https://arxiv.org/abs/2506.18588
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Quantum-Classical Hybrid Quantized Neural Network
2025-06-23 02:12:36Wenxin Li, Chuan Wang, Hongdong Zhu, Qi Gao, Yin Ma, Hai Wei, Kai WenAbstract
Here in this work, we present a novel Quadratic Binary Optimization (QBO) model for quantized neural network training, enabling the use of arbitrary activation and loss functions through spline interpolation. We introduce Forward Interval Propagation (FIP), a method designed to tackle the challenges of non-linearity and the multi-layer composite structure in neural networks by discretizing activation functions into linear subintervals. This approach preserves the universal approximation properties of neural networks while allowing complex nonlinear functions to be optimized using quantum computers, thus broadening their applicability in artificial intelligence. We provide theoretical upper bounds on the approximation error and the number of Ising spins required, by deriving the sample complexity of the empirical risk minimization problem, from an optimization perspective. A significant challenge in solving the associated Quadratic Constrained Binary Optimization (QCBO) model on a large scale is the presence of numerous constraints. When employing the penalty method to handle these constraints, tuning a large number of penalty coefficients becomes a critical hyperparameter optimization problem, increasing computational complexity and potentially affecting solution quality. To address this, we employ the Quantum Conditional Gradient Descent (QCGD) algorithm, which leverages quantum computing to directly solve the QCBO problem. We prove the convergence of QCGD under a quantum oracle with randomness and bounded variance in objective value, as well as under limited precision constraints in the coefficient matrix. Additionally, we provide an upper bound on the Time-To-Solution for the QCBO solving process. Experimental results using a coherent Ising machine (CIM) demonstrate a 94.95% accuracy on the Fashion MNIST classification task, with only 1.1-bit precision.
Abstract (translated)
在这项工作中，我们提出了一种新颖的二次二进制优化（QBO）模型用于量化神经网络训练，并通过样条插值实现任意激活和损失函数的应用。我们还引入了前向区间传播（FIP），这是一种旨在解决非线性和多层复合结构带来的挑战的方法，它将激活函数离散化为线性子区间。这种方法保留了神经网络的通用近似性质，同时允许使用量子计算机对复杂的非线性功能进行优化，从而扩大其在人工智能领域的适用范围。 我们从优化的角度推导出经验风险最小化问题的样本复杂度，并提供理论上的误差上限和所需的伊辛自旋数量，以此来衡量近似的精度。解决与QBO模型相关的二次约束二进制优化（QCBO）问题的一个重大挑战在于存在大量的约束条件。在使用惩罚方法处理这些限制时，调整大量惩罚系数成为一个关键的超参数优化问题，并可能增加计算复杂性和影响解决方案质量。 为了解决这个问题，我们采用了量子条件梯度下降（QCGD）算法，该算法利用量子计算机直接解决QCBO问题。我们在随机量子Oracle和目标值有界方差以及系数矩阵精度有限的情况下证明了QCGD的收敛性，并提供了QCBO求解过程的时间复杂度上限。 实验结果表明，在使用相干伊辛机（CIM）处理Fashion MNIST分类任务时，仅采用1.1位精度就达到了94.95%的准确率。
URL
https://arxiv.org/abs/2506.18240
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Robustness Evaluation of OCR-based Visual Document Understanding under Multi-Modal Adversarial Attacks
2025-06-19 15:38:31Dong Nguyen Tien, Dung D. LeAbstract
Visual Document Understanding (VDU) systems have achieved strong performance in information extraction by integrating textual, layout, and visual signals. However, their robustness under realistic adversarial perturbations remains insufficiently explored. We introduce the first unified framework for generating and evaluating multi-modal adversarial attacks on OCR-based VDU models. Our method covers six gradient-based layout attack scenarios, incorporating manipulations of OCR bounding boxes, pixels, and texts across both word and line granularities, with constraints on layout perturbation budget (e.g., IoU >= 0.6) to preserve plausibility. Experimental results across four datasets (FUNSD, CORD, SROIE, DocVQA) and six model families demonstrate that line-level attacks and compound perturbations (BBox + Pixel + Text) yield the most severe performance degradation. Projected Gradient Descent (PGD)-based BBox perturbations outperform random-shift baselines in all investigated models. Ablation studies further validate the impact of layout budget, text modification, and adversarial transferability.
Abstract (translated)
视觉文档理解（VDU）系统通过整合文本、布局和视觉信号，在信息提取方面取得了显著的性能。然而，这些系统的鲁棒性在面对现实中的对抗性扰动时仍不够充分研究。我们介绍了首个用于生成和评估基于OCR的VDU模型多模态对抗攻击的统一框架。我们的方法涵盖了六种基于梯度的布局攻击场景，包括对OCR边界框、像素和文本（从单词级别到行级别）的操作，并在布局干扰预算（例如IoU >= 0.6）上设置了约束条件以保持现实性。通过四个数据集（FUNSD、CORD、SROIE、DocVQA）及六种模型家族的实验结果表明，行级别的攻击和复合扰动（边界框+像素+文本）导致性能下降最为严重。基于投影梯度下降（PGD）的边界框扰动在所有研究的模型中均优于随机偏移基线。进一步的消融研究表明了布局预算、文本修改以及对抗迁移性的影响力。
URL
https://arxiv.org/abs/2506.16407
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Rethinking LLM Training through Information Geometry and Quantum Metrics
2025-06-18 19:17:47Riccardo Di SipioAbstract
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via natural gradient descent. Though often impractical, this geometric lens clarifies phenomena such as sharp minima, generalization, and observed scaling laws. We argue that curvature-aware approaches deepen our understanding of LLM training. Finally, we speculate on quantum analogies based on the Fubini-Study metric and Quantum Fisher Information, hinting at efficient optimization in quantum-enhanced systems.
Abstract (translated)
在大型语言模型（LLMs）中的优化过程发生在具有非欧几里得结构的高维参数空间中。信息几何学利用费雪信息度量来描绘这一景观，从而使通过自然梯度下降进行更原理性的学习成为可能。尽管这种方法通常难以实现，但它有助于阐明诸如尖锐极小值、泛化和观察到的扩展规律等现象。我们认为，考虑到曲率的方法能加深我们对LLMs训练的理解。最后，基于富比尼-施图迪度量（Fubini-Study metric）和量子费雪信息（Quantum Fisher Information），我们推测出在量子增强系统中的有效优化可能存在的类比关系。
URL
https://arxiv.org/abs/2506.15830
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Ken Utilization Layer: Hebbian Replay Within a Student's Ken for Adaptive Knowledge Tracing
2025-06-18 00:06:28Grey Kuling, Marinka ZitnikAbstract
We introduce KUL-KT, a biologically inspired architecture for knowledge tracing (KT), combining Hebbian memory encoding with gradient-based consolidation in a scalable, input-agnostic framework. KUL-KT adapts the principle of memory consolidation in neural systems, to student modeling by introducing two key innovations: (i) a time-decaying Hebbian memory update that enables graceful forgetting, and (ii) a novel Loss-aligned Internal Target (LIT) method to compute an ideal internal state, allowing continual learning without backpropagation through time. The architecture consists of a fast Hebbian memory that captures each learner interaction via a single associative update, and a slower linear network that consolidates recalled samples through gradient descent. This design enables few-shot personalization and natural forgetting without storing raw data or relying on large cohort training. Operating entirely in embedding space, KUL-KT supports both structured (tabular) and unstructured (short-answer) inputs. Empirically, KUL-KT outperforms strong baselines on ten public KT benchmarks in rank-sensitive metrics such as nDCG and Recall@10. In a classroom deployment, KUL-KT personalized quizzes from short-answer data, leading to improved learner-perceived helpfulness and reduced difficulty (p < 0.05). Ablation studies confirm that Hebbian decay and LIT are critical for continual adaptation. Compared to a strong graph-based KT model, KUL-KT trains 1.75x faster and uses 99.01\% less memory. These results position KUL-KT as a biologically grounded, memory-efficient, and input-flexible framework for personalized learning at scale.
Abstract (translated)
我们介绍了KUL-KT，这是一种生物启发的知识追踪（KT）架构，它结合了海布记忆编码与基于梯度的巩固机制，并在一个可扩展且不受输入限制的框架中实现了这一点。KUL-KT通过引入两个关键创新，将神经系统的记忆巩固原理应用到学生建模上：(i) 一种随时间衰减的海布记忆更新方式，使优雅遗忘成为可能；(ii) 一种新颖的目标与损失对齐内部目标（LIT）方法来计算理想内部状态，从而允许不通过时间反向传播进行持续学习。该架构包括一个快速的海布记忆，每次捕捉到每个学习者互动时都会通过单一联想更新来进行记录，以及一个较慢的线性网络，它通过梯度下降巩固被召回的数据样本。这种设计使得少量个性化和自然遗忘成为可能，同时不需要存储原始数据或依赖大规模群体训练。整个操作完全在嵌入空间中进行，KUL-KT支持结构化（表格）和非结构化（简答题）输入。 实验上，在十个公开的知识追踪基准测试中，KUL-KT在nDCG和Recall@10等敏感排名的度量标准上超过了强大的基线模型。在一个教室部署案例中，KUL-KT利用简答题数据为每位学生个性化测验，提高了学习者感知到的帮助效果，并降低了难度（p < 0.05）。删减研究证实了海布衰减和LIT对于持续适应性至关重要。与一个强大的基于图的KT模型相比，KUL-KT训练速度快1.75倍且内存使用量减少了99.01%。 这些结果表明，KUL-KT作为一种生物基础、记忆效率高并且输入灵活的知识追踪框架，在大规模个性化学习中具有重要位置。
URL
https://arxiv.org/abs/2507.00032
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Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization
2025-06-17 17:56:42Xuemin Chi, Hakan Girgin, Tobias L\"ow, Yangyang Xie, Teng Xue, Jihao Huang, Cheng Hu, Zhitao Liu, Sylvain CalinonAbstract
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: this https URL
Abstract (translated)
生成机器人与各种形状物体交互的运动是一个复杂的问题，这个问题进一步因机器人的几何结构和多种期望行为而变得更加困难。当前的机器人编程工具（如逆向动力学、碰撞避免和操作规划）通常将这些问题视为约束优化问题，但许多现有的求解器往往专注于特定领域或无法有效利用几何约束条件。我们提出了一种高效的一阶方法——增广拉格朗日谱投影梯度下降法（ALSPG），该方法通过欧几里得投影、闵可夫斯基和以及基函数来利用几何投影。 研究表明，通过使用几何约束而非全部约束和梯度，ALSPG在实时性能上有了显著的提高。与二次优化方法（如iLQR）相比，在无约束情况下，ALSPG依然具有竞争力。我们通过玩具示例、广泛的仿真验证了我们的方法，并且通过实际实验展示了其在7轴Franka机器人、6轴P-Rob机器人以及1:10比例模型汽车上的有效性。 源代码、实验数据和视频可在项目网页上获得：[此链接](this https URL)。
URL
https://arxiv.org/abs/2506.14865
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A Study of Hybrid and Evolutionary Metaheuristics for Single Hidden Layer Feedforward Neural Network Architecture
2025-06-17 04:12:58Gautam Siddharth Kashyap, Md Tabrez Nafis, Samar WazirAbstract
Training Artificial Neural Networks (ANNs) with Stochastic Gradient Descent (SGD) frequently encounters difficulties, including substantial computing expense and the risk of converging to local optima, attributable to its dependence on partial weight gradients. Therefore, this work investigates Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) - two population-based Metaheuristic Optimizers (MHOs) - as alternatives to SGD to mitigate these constraints. A hybrid PSO-SGD strategy is developed to improve local search efficiency. The findings indicate that the hybrid PSO-SGD technique decreases the median training MSE by 90 to 95 percent relative to conventional GA and PSO across various network sizes (e.g., from around 0.02 to approximately 0.001 in the Sphere function). RMHC attains substantial enhancements, reducing MSE by roughly 85 to 90 percent compared to GA. Simultaneously, RS consistently exhibits errors exceeding 0.3, signifying subpar performance. These findings underscore that hybrid and evolutionary procedures significantly improve training efficiency and accuracy compared to conventional optimization methods and imply that the Building Block Hypothesis (BBH) may still be valid, indicating that advantageous weight structures are retained during evolutionary search.
Abstract (translated)
使用随机梯度下降（SGD）训练人工神经网络（ANNs）经常遇到诸如计算成本高昂和可能陷入局部最优解等问题，这些问题归因于其对权重偏导数的依赖。因此，本研究探讨了粒子群优化（PSO）和遗传算法（GAs）——两种基于种群的元启发式优化器（MHOs），作为SGD的替代方案以缓解这些限制。开发了一种混合PSO-SGD策略来提高局部搜索效率。研究表明，与传统的GA和PSO相比，该混合PSO-SGD技术在各种网络规模下将中位训练均方误差（MSE）降低了90%到95%，例如，在Sphere函数中的误差从大约0.02降至约0.001。 RMHC（随机重启Hill-Climbing算法）也取得了显著改进，与GA相比，它使MSE减少了约85%至90%。同时，RS（随机搜索）始终表现出超过0.3的错误率，表明其性能不佳。这些发现强调了混合和进化方法在训练效率和准确性方面相较于传统优化方法有明显改善，并暗示构建块假设（BBH）可能仍然有效，这意味着有利的权重结构在进化搜索中得以保留。
URL
https://arxiv.org/abs/2506.15737
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Attention-based Adversarial Robust Distillation in Radio Signal Classifications for Low-Power IoT Devices
2025-06-13 15:39:01Lu Zhang, Sangarapillai Lambotharan, Gan Zheng, Guisheng Liao, Basil AsSadhan, Fabio RoliAbstract
Due to great success of transformers in many applications such as natural language processing and computer vision, transformers have been successfully applied in automatic modulation classification. We have shown that transformer-based radio signal classification is vulnerable to imperceptible and carefully crafted attacks called adversarial examples. Therefore, we propose a defense system against adversarial examples in transformer-based modulation classifications. Considering the need for computationally efficient architecture particularly for Internet of Things (IoT)-based applications or operation of devices in environment where power supply is limited, we propose a compact transformer for modulation classification. The advantages of robust training such as adversarial training in transformers may not be attainable in compact transformers. By demonstrating this, we propose a novel compact transformer that can enhance robustness in the presence of adversarial attacks. The new method is aimed at transferring the adversarial attention map from the robustly trained large transformer to a compact transformer. The proposed method outperforms the state-of-the-art techniques for the considered white-box scenarios including fast gradient method and projected gradient descent attacks. We have provided reasoning of the underlying working mechanisms and investigated the transferability of the adversarial examples between different architectures. The proposed method has the potential to protect the transformer from the transferability of adversarial examples.
Abstract (translated)
由于Transformer在自然语言处理和计算机视觉等众多应用中的巨大成功，它们已经被成功应用于自动调制分类中。我们已经证明了基于Transformer的无线电信号分类对精心设计且难以察觉的对抗性样本攻击非常脆弱。因此，我们提出了一种针对基于Transformer的调制分类中对抗性示例的防御系统。考虑到计算效率架构的需求，特别是在物联网（IoT）应用或在电力供应有限的环境中操作设备的情况下，我们提出了一个用于调制分类的小型化变压器。然而，在小型化变压器中可能无法实现增强鲁棒性的方法，例如基于Transformer中的对抗训练。通过证明这一点，我们提出了一种新的紧凑型变压器，可以在存在对抗性攻击时提高其健壮性。新方法旨在将来自稳健大型Transformer的对抗注意力图转移到紧凑型Transformer中。在考虑的白盒场景（包括快速梯度法和投影梯度下降攻击）下，所提方法优于现有的最先进技术。我们提供了该方法背后的工作机制的理由，并探讨了不同架构之间对抗样本的可迁移性。所提出的方法有望保护变压器免受对抗样本传输的影响。
URL
https://arxiv.org/abs/2506.11892
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Vision Transformer with Adversarial Indicator Token against Adversarial Attacks in Radio Signal Classifications
2025-06-13 15:21:54Lu Zhang, Sangarapillai Lambotharan, Gan Zheng, Guisheng Liao, Xuekang Liu, Fabio Roli, Carsten MapleAbstract
The remarkable success of transformers across various fields such as natural language processing and computer vision has paved the way for their applications in automatic modulation classification, a critical component in the communication systems of Internet of Things (IoT) devices. However, it has been observed that transformer-based classification of radio signals is susceptible to subtle yet sophisticated adversarial attacks. To address this issue, we have developed a defensive strategy for transformer-based modulation classification systems to counter such adversarial attacks. In this paper, we propose a novel vision transformer (ViT) architecture by introducing a new concept known as adversarial indicator (AdvI) token to detect adversarial attacks. To the best of our knowledge, this is the first work to propose an AdvI token in ViT to defend against adversarial attacks. Integrating an adversarial training method with a detection mechanism using AdvI token, we combine a training time defense and running time defense in a unified neural network model, which reduces architectural complexity of the system compared to detecting adversarial perturbations using separate models. We investigate into the operational principles of our method by examining the attention mechanism. We show the proposed AdvI token acts as a crucial element within the ViT, influencing attention weights and thereby highlighting regions or features in the input data that are potentially suspicious or anomalous. Through experimental results, we demonstrate that our approach surpasses several competitive methods in handling white-box attack scenarios, including those utilizing the fast gradient method, projected gradient descent attacks and basic iterative method.
Abstract (translated)
变压器在自然语言处理和计算机视觉等多个领域的显著成功，为物联网设备通信系统中的自动调制分类应用铺平了道路。然而，观察发现基于变压器的无线电信号分类容易受到细微而复杂的对抗性攻击的影响。为了应对这一问题，我们开发了一种防御策略，用于保护基于变压器的调制分类系统的免受此类对抗性攻击。在本文中，我们提出了一种新的视觉变压器（ViT）架构，通过引入一种名为“对抗指示符”(AdvI)标记的新概念来检测对抗性攻击。据我们所知，这是首次提议使用带有AdvI标记的ViT来防御对抗性攻击。 我们将对抗训练方法与基于AdvI标记的检测机制相结合，在统一的神经网络模型中同时实现了训练时间防护和运行时防护，从而简化了系统的架构复杂度，相比单独使用的检测模型而言更为简单。通过研究注意力机制的操作原理，我们展示了提出的AdvI标记在ViT中的关键作用：它影响注意权重，并且突出显示输入数据中可能可疑或异常的区域或特征。 实验结果显示，我们的方法在处理包括快速梯度法、投影梯度下降攻击和基本迭代法在内的白盒攻击场景方面超越了多种竞争性方法。
URL
https://arxiv.org/abs/2507.00015
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Machine Learning-Based Quantification of Vesicoureteral Reflux with Enhancing Accuracy and Efficiency
2025-06-13 07:09:12Muhyeeddin Alqaraleh, Mowafaq Salem Alzboon, Mohammad Subhi Al-Batah, Lana Yasin Al Aesa, Mohammed Hasan Abu-Arqoub, Rashiq Rafiq Marie, Firas Hussein AlsmadAbstract
Vesicoureteral reflux (VUR) is traditionally assessed using subjective grading systems, which introduces variability in diagnosis. This study investigates the use of machine learning to improve diagnostic consistency by analyzing voiding cystourethrogram (VCUG) images. A total of 113 VCUG images were reviewed, with expert grading of VUR severity. Nine image-based features were selected to train six predictive models: Logistic Regression, Decision Tree, Gradient Boosting, Neural Network, and Stochastic Gradient Descent. The models were evaluated using leave-one-out cross-validation. Analysis identified deformation patterns in the renal calyces as key indicators of high-grade VUR. All models achieved accurate classifications with no false positives or negatives. High sensitivity to subtle image patterns characteristic of different VUR grades was confirmed by substantial Area Under the Curve (AUC) values. The results suggest that machine learning can offer an objective and standardized alternative to current subjective VUR assessments. These findings highlight renal calyceal deformation as a strong predictor of severe cases. Future research should aim to expand the dataset, refine imaging features, and improve model generalizability for broader clinical use.
Abstract (translated)
输尿管膀胱反流（Vesicoureteral reflux，简称 VUR）的传统评估方法依赖于主观分级系统，这会导致诊断的一致性较差。本研究探讨了利用机器学习技术分析排尿膀胱造影（Voiding Cystourethrogram，VCUG）图像来提高诊断一致性的可能性。研究团队审查了总共113幅 VCUG 图像，并由专家对其 VUR 的严重程度进行了分级。随后选择了九个基于图像的特征，用于训练六种预测模型：逻辑回归、决策树、梯度提升、神经网络和随机梯度下降。通过留一交叉验证（leave-one-out cross-validation）方法评估这些模型的效果。 分析发现，在肾盏中观察到的变形模式是高级别 VUR 的关键指标之一。所有模型均能够准确分类，且无误报或漏报情况发生。通过对不同级别的VUR特有的细微图像特征具有高度敏感性的确认（通过显著的曲线下面积值即AUC值得出），证实了机器学习方法在识别这些特征上的有效性。 研究结果表明，机器学习可以为当前主观评估 VUR 的方式提供一个客观且标准化的选择方案。此外，该研究表明肾盏变形是严重病例的重要预测因素。未来的研究应该致力于扩大数据集规模、优化成像特征以及改进模型的泛化能力，从而使其在更广泛的临床应用中更具实用性。
URL
https://arxiv.org/abs/2506.11508
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Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers
2025-06-12 16:50:45Yixiao Huang, Hanlin Zhu, Tianyu Guo, Jiantao Jiao, Somayeh Sojoudi, Michael I. Jordan, Stuart Russell, Song MeiAbstract
Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This mathematical structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.
Abstract (translated)
大型语言模型（LLMs）可以通过微调获得新知识，但这一过程表现出一种令人费解的二元性：这些模型可以从新的事实中进行显著地概括推理，但也容易产生不正确的信息。然而，导致这种现象的原因尚不清楚。在本项工作中，我们提出两种行为都源于单一机制，即跨背景推理（OCR）：即使没有因果关系，也能够通过关联概念推断出结论的能力。我们的实验涵盖了五个知名的大规模语言模型，并确认了 OCR 确实驱动着概括和幻觉的产生，这取决于相关联的概念是否具有因果联系。 为了建立这一现象的严谨理论理解，我们随后将 OCR 形式化为一个合成的事实回忆任务。通过实验，我们证明了一层单一头部注意力机制且输出和值矩阵因子分解的变压器能够学会解决该任务，而权重合并的模型则不能，这突显了矩阵分解的关键作用。 我们的理论分析表明，OCR 能力可以归因于梯度下降的隐含偏置，这种偏置倾向于选择使组合输出-值矩阵的核范数最小化的解决方案。这一数学结构解释了为什么模型能够以高样本效率学会将事实与结论关联起来，无论这些关联是因果关系还是仅仅偶然相关。 最终，我们的工作为理解 OCR 现象提供了理论基础，并提供了一种新的视角来分析和缓解知识注入带来的不良行为。
URL
https://arxiv.org/abs/2506.10887
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SPBA: Utilizing Speech Large Language Model for Backdoor Attacks on Speech Classification Models
2025-06-10 02:01:00Wenhan Yao, Fen Xiao, Xiarun Chen, Jia Liu, YongQiang He, Weiping WenAbstract
Deep speech classification tasks, including keyword spotting and speaker verification, are vital in speech-based human-computer interaction. Recently, the security of these technologies has been revealed to be susceptible to backdoor attacks. Specifically, attackers use noisy disruption triggers and speech element triggers to produce poisoned speech samples that train models to become vulnerable. However, these methods typically create only a limited number of backdoors due to the inherent constraints of the trigger function. In this paper, we propose that speech backdoor attacks can strategically focus on speech elements such as timbre and emotion, leveraging the Speech Large Language Model (SLLM) to generate diverse triggers. Increasing the number of triggers may disproportionately elevate the poisoning rate, resulting in higher attack costs and a lower success rate per trigger. We introduce the Multiple Gradient Descent Algorithm (MGDA) as a mitigation strategy to address this challenge. The proposed attack is called the Speech Prompt Backdoor Attack (SPBA). Building on this foundation, we conducted attack experiments on two speech classification tasks, demonstrating that SPBA shows significant trigger effectiveness and achieves exceptional performance in attack metrics.
Abstract (translated)
深度语音分类任务，包括关键词识别和说话人验证，在基于语音的人机交互中至关重要。然而，最近的研究揭示了这些技术的安全性容易受到后门攻击的威胁。具体来说，攻击者利用噪声干扰触发器和语音元素触发器来生成中毒语音样本，使模型变得脆弱。不过，由于触发函数本身的限制，这些方法通常只能创建有限数量的后门。 在本文中，我们提出了一种策略，即通过专注于语音中的音色和情感等元素，并借助于语音大语言模型（SLLM）生成多样化的触发器来实施语音后门攻击。增加触发器的数量可能会不成比例地提高中毒率，导致攻击成本上升而每个触发器的成功率降低。 为了应对这一挑战，我们引入了多重梯度下降算法（MGDA）作为缓解策略，并提出了名为“Speech Prompt Backdoor Attack”（SPBA）的新型攻击方法。基于此基础，我们在两个语音分类任务上进行了攻击实验，结果表明SPBA展示了显著的触发器有效性，并在攻击指标方面取得了卓越性能。 该研究的主要贡献包括： 1. 提出了一种新的后门攻击策略，利用多样化的语音元素来增加模型中毒的可能性。 2. 引入了MGDA作为缓解方法，旨在减少此类攻击的影响。 3. 通过实验验证了SPBA的有效性和效率，在实际应用中具有重要的安全意义。
URL
https://arxiv.org/abs/2506.08346
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Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks
2025-06-09 04:04:08Xiaojun zhou, Chunna Zhao, Yaqun Huang, Chengli Zhou, Junjie Ye, Kemeng XiangAbstract
Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due to insufficient theoretical research, at present, there is no fractional-order matrix differentiation method that is perfectly compatible with automatic differentiation (Autograd) technology. Therefore, we propose a fractional-order matrix differentiation calculation method. This method is introduced by the definition of the integer-order Jacobian matrix. We denote it as fractional-order Jacobian matrix differentiation (${\bf{J}^\alpha }$). Through ${\bf{J}^\alpha }$, we can carry out the matrix-based fractional-order chain rule. Based on the Linear module and the fractional-order differentiation, we design the fractional-order Autograd technology to enable the use of fractional-order differentiation in hidden layers, thereby enhancing the practicality of fractional-order differentiation in deep learning. In the experiment, according to the PyTorch framework, we design fractional-order Linear (FLinear) and replace this http URL in the multilayer perceptron with FLinear. Through the qualitative analysis of the training set and validation set $Loss$, the quantitative analysis of the test set indicators, and the analysis of time consumption and GPU memory usage during model training, we verify the superior performance of ${\bf{J}^\alpha }$ and prove that it is an excellent fractional-order gradient descent method in the field of deep learning.
Abstract (translated)
分数阶微分具有许多与整数阶微分不同的特性。这些特性可以应用于人工神经网络的优化算法，从而获得更好的结果。然而，由于理论研究不足，在目前阶段还没有一种完全兼容自动微分（Autograd）技术的分数阶矩阵微分方法。因此，我们提出了一种分数阶矩阵微分计算方法。这种方法通过整数阶雅可比矩阵的定义引入，并将其标记为分数阶雅可比矩阵微分（${\bf{J}^\alpha }$）。利用 ${\bf{J}^\alpha }$ ，我们可以进行基于矩阵的分数阶链式法则运算。结合线性模块和分数阶微分，我们设计了分数阶Autograd技术，以使隐藏层能够使用分数阶微分，从而增强分数阶微分在深度学习中的实用性。 通过根据PyTorch框架设计分数阶Linear（FLinear）并将其替换多层感知机网络中的相应部分，我们在实验中通过对训练集和验证集$Loss$的定性分析、测试集指标的定量分析以及模型训练过程中时间消耗和GPU内存使用的分析，验证了${\bf{J}^\alpha }$ 的优越性能，并证明它是深度学习领域中一种优秀的分数阶梯度下降方法。
URL
https://arxiv.org/abs/2506.07408
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Can Biologically Plausible Temporal Credit Assignment Rules Match BPTT for Neural Similarity? E-prop as an Example
2025-06-07 19:32:15Yuhan Helena Liu, Guangyu Robert Yang, Christopher J. CuevaAbstract
Understanding how the brain learns may be informed by studying biologically plausible learning rules. These rules, often approximating gradient descent learning to respect biological constraints such as locality, must meet two critical criteria to be considered an appropriate brain model: (1) good neuroscience task performance and (2) alignment with neural recordings. While extensive research has assessed the first criterion, the second remains underexamined. Employing methods such as Procrustes analysis on well-known neuroscience datasets, this study demonstrates the existence of a biologically plausible learning rule -- namely e-prop, which is based on gradient truncation and has demonstrated versatility across a wide range of tasks -- that can achieve neural data similarity comparable to Backpropagation Through Time (BPTT) when matched for task accuracy. Our findings also reveal that model architecture and initial conditions can play a more significant role in determining neural similarity than the specific learning rule. Furthermore, we observe that BPTT-trained models and their biologically plausible counterparts exhibit similar dynamical properties at comparable accuracies. These results underscore the substantial progress made in developing biologically plausible learning rules, highlighting their potential to achieve both competitive task performance and neural data similarity.
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理解大脑如何学习可能需要研究生物上合理的学习规则。这些规则通常会模仿梯度下降学习，以遵守诸如局部性等生物学约束条件。为了被认为是一个合适的脑模型，这类规则必须满足两个关键标准：（1）良好的神经科学任务表现；以及（2）与神经记录数据的契合度。尽管许多研究已经评估了第一个标准，但第二个标准则相对较少被探讨。 通过在知名神经科学研究数据集中应用诸如普罗克鲁斯特斯分析等方法，本研究证明了一个生物上合理的学习规则——即基于梯度截断的e-prop（Efficient Propagation），它能够跨广泛任务展示出灵活性。当准确率相匹配时，该学习规则可以达到与通过时间反向传播算法（Backpropagation Through Time, BPTT）相似的神经数据一致性。 此外，我们的研究还揭示了模型架构和初始条件对于确定神经相似度的影响可能比具体的学习规则更为重要。我们进一步观察到，在准确率相同的情况下，使用BPTT训练得到的模型及其生物合理学习规则对应的模型表现出类似的动态特性。 这些结果突显了在开发生物学上合理的学习规则方面所取得的重大进展，并强调其不仅能够实现竞争性的任务表现，还能达到与神经记录数据相似性。
URL
https://arxiv.org/abs/2506.06904
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Gradient Similarity Surgery in Multi-Task Deep Learning
2025-06-06 14:40:50Thomas Borsani, Andrea Rosani, Giuseppe Nicosia, Giuseppe Di FattaAbstract
The multi-task learning ($MTL$) paradigm aims to simultaneously learn multiple tasks within a single model capturing higher-level, more general hidden patterns that are shared by the tasks. In deep learning, a significant challenge in the backpropagation training process is the design of advanced optimisers to improve the convergence speed and stability of the gradient descent learning rule. In particular, in multi-task deep learning ($MTDL$) the multitude of tasks may generate potentially conflicting gradients that would hinder the concurrent convergence of the diverse loss functions. This challenge arises when the gradients of the task objectives have either different magnitudes or opposite directions, causing one or a few to dominate or to interfere with each other, thus degrading the training process. Gradient surgery methods address the problem explicitly dealing with conflicting gradients by adjusting the overall gradient trajectory. This work introduces a novel gradient surgery method, the Similarity-Aware Momentum Gradient Surgery (SAM-GS), which provides an effective and scalable approach based on a gradient magnitude similarity measure to guide the optimisation process. The SAM-GS surgery adopts gradient equalisation and modulation of the first-order momentum. A series of experimental tests have shown the effectiveness of SAM-GS on synthetic problems and $MTL$ benchmarks. Gradient magnitude similarity plays a crucial role in regularising gradient aggregation in $MTDL$ for the optimisation of the learning process.
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多任务学习（MTL）范式旨在通过单个模型同时学习多个任务，捕捉这些任务共有的更高层次、更具普遍性的隐含模式。在深度学习领域，反向传播训练过程中的一大挑战是设计高级优化器以提升梯度下降学习规则的收敛速度和稳定性。特别是在多任务深度学习（MTDL）中，众多的任务可能会产生潜在冲突的梯度，阻碍各个多样化的损失函数的同时收敛。这一挑战源于任务目标的梯度在幅度或方向上的差异，导致某些梯度占据主导地位或是相互干扰，从而破坏训练过程。梯度手术方法通过调整整体梯度轨迹来明确解决冲突梯度的问题。 本文介绍了一种新的梯度手术方法——相似性感知动量梯度手术（SAM-GS），它基于梯度幅度的相似性测量提供了一个有效且可扩展的方式来引导优化过程。SAM-GS手术采用梯度均衡化和一阶动量调节的方式进行操作。一系列实验测试表明，SAM-GS在合成问题以及多任务学习基准上表现出了有效性。梯度幅度相似性在MTDL中对于正则化梯度聚合以优化学习过程起着关键作用。
URL
https://arxiv.org/abs/2506.06130
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Grokking Beyond the Euclidean Norm of Model Parameters
2025-06-06 03:44:28Pascal Jr Tikeng Notsawo, Guillaume Dumas, Guillaume RabusseauAbstract
Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed.
Abstract (translated)
"Grokking"（灵悟）是指在使用基于梯度的方法优化人工神经网络时，在过度拟合之后出现的延迟泛化现象。在这项工作中，我们展示了通过正则化可以诱导出灵悟现象，这种正则化既可以是显式的也可以是隐式的。更具体地说，当存在一个具有某种性质P（例如稀疏或低秩权重）且在感兴趣的问题上能够泛化的模型时，使用带有小但非零的针对该性质P的梯度下降和正则化（例如L1或者核范数正则化），会导致灵悟现象的发生。这扩展了之前的工作，这些工作表明即使是很小的非零权重衰减也能导致灵悟。 此外，我们的分析还显示，通过增加深度进行过度参数化使得模型能够在不显式使用正则化的情况下实现或避免灵悟，这是在浅层网络中不可能做到的。我们进一步展示了当模型被调整以向不同的性质P（例如稀疏性）泛化时，L2范数不能可靠地作为泛化的代理指标：因为在没有权重衰减的情况下，L2范数会在许多情况下增长，但模型仍然可以实现泛化。 此外，我们还表明可以通过单纯的数据选择来放大灵悟现象，而不改变其他的超参数。
URL
https://arxiv.org/abs/2506.05718
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