Gradient_Descent
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Deciphering Trajectory-Aided LLM Reasoning: An Optimization Perspective
2025-05-26 10:52:17Junnan Liu, Hongwei Liu, Linchen Xiao, Shudong Liu, Taolin Zhang, Zihan Ma, Songyang Zhang, Kai ChenAbstract
We propose a novel framework for comprehending the reasoning capabilities of large language models (LLMs) through the perspective of meta-learning. By conceptualizing reasoning trajectories as pseudo-gradient descent updates to the LLM's parameters, we identify parallels between LLM reasoning and various meta-learning paradigms. We formalize the training process for reasoning tasks as a meta-learning setup, with each question treated as an individual task, and reasoning trajectories serving as the inner loop optimization for adapting model parameters. Once trained on a diverse set of questions, the LLM develops fundamental reasoning capabilities that can generalize to previously unseen questions. Extensive empirical evaluations substantiate the strong connection between LLM reasoning and meta-learning, exploring several issues of significant interest from a meta-learning standpoint. Our work not only enhances the understanding of LLM reasoning but also provides practical insights for improving these models through established meta-learning techniques.
Abstract (translated)
我们提出了一种新颖的框架，通过元学习的角度来理解大规模语言模型（LLMs）的推理能力。我们将推理轨迹视为对LLM参数进行伪梯度下降更新，并在此过程中发现了LLM推理与各种元学习范式之间的相似性。我们将用于推理任务的训练过程形式化为一个元学习设置，在这种设置中，每个问题都被视为独立的任务，而推理轨迹则作为内循环优化以适应模型参数。经过一系列多样化的提问训练后，LLM能够发展出可以推广到未见过的问题的基本推理能力。 大量的实证评估证实了LLM推理与元学习之间存在强有力的联系，并探讨了一些从元学习角度来看具有重要意义的问题。我们的工作不仅增强了对LLM推理的理解，还为通过已建立的元学习技术改进这些模型提供了实用见解。
URL
https://arxiv.org/abs/2505.19815
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Diagnosing and Mitigating Modality Interference in Multimodal Large Language Models
2025-05-26 07:31:32Rui Cai, Bangzheng Li, Xiaofei Wen, Muhao Chen, Zhe ZhaoAbstract
Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities across tasks, yet they often exhibit difficulty in distinguishing task-relevant from irrelevant signals, particularly in tasks like Visual Question Answering (VQA), which can lead to susceptibility to misleading or spurious inputs. We refer to this broader limitation as the Cross-Modality Competency Problem: the model's inability to fairly evaluate all modalities. This vulnerability becomes more evident in modality-specific tasks such as image classification or pure text question answering, where models are expected to rely solely on one modality. In such tasks, spurious information from irrelevant modalities often leads to significant performance degradation. We refer to this failure as Modality Interference, which serves as a concrete and measurable instance of the cross-modality competency problem. We further design a perturbation-based causal diagnostic experiment to verify and quantify this problem. To mitigate modality interference, we propose a novel framework to fine-tune MLLMs, including perturbation-based data augmentations with both heuristic perturbations and adversarial perturbations via Projected Gradient Descent (PGD), and a consistency regularization strategy applied to model outputs with original and perturbed inputs. Experiments on multiple benchmark datasets (image-heavy, text-heavy, and VQA tasks) and multiple model families with different scales demonstrate significant improvements in robustness and cross-modality competency, indicating our method's effectiveness in boosting unimodal reasoning ability while enhancing performance on multimodal tasks.
Abstract (translated)
多模态大型语言模型（MLLMs）在各种任务中展示了令人印象深刻的性能，但它们经常难以区分与任务相关的信号和不相关的信号，特别是在如视觉问答（VQA）这样的任务中。这会导致这些模型容易受到误导性或错误输入的影响。我们将这种更广泛的问题称为跨模态胜任力问题：即模型无法公平评估所有模式的能力。在特定于某一模式的任务（如图像分类或纯文本问答）中，这一脆弱性变得更为明显，在这类任务中，模型应仅依赖一种模式。在这种情况下，来自不相关模式的错误信息通常会导致性能显著下降。我们将这种失败称为模态干扰，这是跨模态胜任力问题的一个具体而可量化的实例。 为了验证和量化这个问题，我们设计了一个基于扰动的因果诊断实验。为减轻模态干扰，我们提出了一种新颖的微调MLLM框架，包括基于数据增强的启发式和对抗性扰动（通过投影梯度下降实现），以及应用于模型输出的一致性正则化策略，这些输出是基于原始输入和扰动后输入生成的。 在多个基准数据集上进行实验（图像密集型、文本密集型及VQA任务）以及不同规模的多种模型家族显示了显著的鲁棒性和跨模态胜任力改进。这表明我们的方法不仅能够增强单一模式推理能力，还能提高多模式任务的表现。
URL
https://arxiv.org/abs/2505.19616
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Minimalist Softmax Attention Provably Learns Constrained Boolean Functions
2025-05-26 05:33:26Jerry Yao-Chieh Hu, Xiwen Zhang, Maojiang Su, Zhao Song, Han LiuAbstract
We study the computational limits of learning $k$-bit Boolean functions (specifically, $\mathrm{AND}$, $\mathrm{OR}$, and their noisy variants), using a minimalist single-head softmax-attention mechanism, where $k=\Theta(d)$ relevant bits are selected from $d$ inputs. We show that these simple $\mathrm{AND}$ and $\mathrm{OR}$ functions are unsolvable with a single-head softmax-attention mechanism alone. However, with teacher forcing, the same minimalist attention is capable of solving them. These findings offer two key insights: Architecturally, solving these Boolean tasks requires only minimalist attention, without deep Transformer blocks or FFNs. Methodologically, one gradient descent update with supervision suffices and replaces the multi-step Chain-of-Thought (CoT) reasoning scheme of [Kim and Suzuki, ICLR 2025] for solving Boolean problems. Together, the bounds expose a fundamental gap between what this minimal architecture achieves under ideal supervision and what is provably impossible under standard training.
Abstract (translated)
我们研究了使用简约的单头softmax注意力机制（其中$ k=\Theta(d) $相关的位从$d$个输入中被选出）来学习$k$-位布尔函数（特别是$\mathrm{AND}$、$\mathrm{OR}$及其噪声变体）的计算极限。结果显示，这些简单的$\mathrm{AND}$和$\mathrm{OR}$函数仅靠单头softmax注意力机制是无法解决的。然而，在使用教师强制训练的情况下，相同的简约注意力机制能够解决这些问题。 这些发现提供了两个关键见解：从架构的角度来看，解决布尔任务只需要简约注意机制，而不需要深层Transformer块或全连接层（FFNs）。从方法论角度来看，一次带有监督的梯度下降更新足以替代[Kim和Suzuki, ICLR 2025]为解决布尔问题提出的多步骤链式思考（CoT）推理方案。总的来说，这些界限揭示了在理想监督下这种最小架构所能实现的效果与在标准训练条件下无法证明可能之间存在着一个根本性的差距。
URL
https://arxiv.org/abs/2505.19531
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Navigating loss manifolds via rigid body dynamics: A promising avenue for robustness and generalisation
2025-05-26 05:26:21Mohammed D. Belgoumri, Mohamed Reda Bouadjenek, Hakim Hacid, Imran Razzak, Sunil AryalAbstract
Training large neural networks through gradient-based optimization requires navigating high-dimensional loss landscapes, which often exhibit pathological geometry, leading to undesirable training dynamics. In particular, poor generalization frequently results from convergence to sharp minima that are highly sensitive to input perturbations, causing the model to overfit the training data while failing to generalize to unseen examples. Furthermore, these optimization procedures typically display strong dependence on the fine structure of the loss landscape, leading to unstable training dynamics, due to the fractal-like nature of the loss surface. In this work, we propose an alternative optimizer that simultaneously reduces this dependence, and avoids sharp minima, thereby improving generalization. This is achieved by simulating the motion of the center of a ball rolling on the loss landscape. The degree to which our optimizer departs from the standard gradient descent is controlled by a hyperparameter, representing the radius of the ball. Changing this hyperparameter allows for probing the loss landscape at different scales, making it a valuable tool for understanding its geometry.
Abstract (translated)
通过基于梯度的优化训练大型神经网络需要在高维损失景观中导航，而这种景观通常具有病态几何形状，导致不理想的训练动态。特别是，由于模型收敛于对输入扰动高度敏感的尖锐极小值，从而过拟合训练数据并无法泛化到未见示例，因此经常导致较差的一般性（泛化能力）。此外，这些优化过程通常强烈依赖于损失景观的精细结构，导致不稳定的训练动态，这是由于损失表面具有分形特性。在这项工作中，我们提出了一种替代的优化器，该优化器同时减少了这种依赖关系并避免了尖锐极小值，从而提高了泛化能力。这通过模拟一个球心在损失景观上滚动的运动来实现。我们的优化器与标准梯度下降方法的区别程度由超参数表示（即球体的半径）控制。改变这个超参数可以在不同尺度下探测损失景观，使其成为了解其几何形状的重要工具。
URL
https://arxiv.org/abs/2505.19527
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CloneShield: A Framework for Universal Perturbation Against Zero-Shot Voice Cloning
2025-05-25 12:22:00Renyuan Li, Zhibo Liang, Haichuan Zhang, Tianyu Shi, Zhiyuan Cheng, Jia Shi, Carl Yang, Mingjie TangAbstract
Recent breakthroughs in text-to-speech (TTS) voice cloning have raised serious privacy concerns, allowing highly accurate vocal identity replication from just a few seconds of reference audio, while retaining the speaker's vocal authenticity. In this paper, we introduce CloneShield, a universal time-domain adversarial perturbation framework specifically designed to defend against zero-shot voice cloning. Our method provides protection that is robust across speakers and utterances, without requiring any prior knowledge of the synthesized text. We formulate perturbation generation as a multi-objective optimization problem, and propose Multi-Gradient Descent Algorithm (MGDA) to ensure the robust protection across diverse utterances. To preserve natural auditory perception for users, we decompose the adversarial perturbation via Mel-spectrogram representations and fine-tune it for each sample. This design ensures imperceptibility while maintaining strong degradation effects on zero-shot cloned outputs. Experiments on three state-of-the-art zero-shot TTS systems, five benchmark datasets and evaluations from 60 human listeners demonstrate that our method preserves near-original audio quality in protected inputs (PESQ = 3.90, SRS = 0.93) while substantially degrading both speaker similarity and speech quality in cloned samples (PESQ = 1.07, SRS = 0.08).
Abstract (translated)
最近在文本到语音（TTS）声音克隆领域的突破引发了严重的隐私担忧，仅通过几秒钟的参考音频即可实现高度准确的声音身份复制，并保留发言人的声音真实性。本文介绍了CloneShield，这是一个专门设计用于防御零样本声音克隆的通用时域对抗性扰动框架。我们的方法提供了一种无需任何关于合成文本的先验知识就能在不同说话人和话语中保持稳健性的保护方式。我们通过将扰动生成形式化为一个多目标优化问题，并提出多梯度下降算法（MGDA）来确保对各种话语具有鲁棒性的保护措施。 为了保留用户自然的听觉感知，我们将对抗性扰动分解为梅尔频谱图表示，并针对每个样本进行微调。这种设计在保证不可察觉的同时，还能保持对零样本克隆输出的强大破坏效果。我们在三个最先进的零样本TTS系统、五个基准数据集以及来自60名人类听众的评估中进行了实验，结果表明我们的方法可以保留受保护输入接近原始音频的质量（PESQ = 3.90, SRS = 0.93），同时大幅降低克隆样本中的说话人相似性和语音质量（PESQ = 1.07, SRS = 0.08）。
URL
https://arxiv.org/abs/2505.19119
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Efficient Data Selection at Scale via Influence Distillation
2025-05-25 09:08:00Mahdi Nikdan, Vincent Cohen-Addad, Dan Alistarh, Vahab MirrokniAbstract
Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a $\textit{landmark-based approximation}$: influence is precisely computed for a small subset of "landmark" samples and then efficiently propagated to all other samples to determine their weights. We validate Influence Distillation by applying it to instruction tuning on the Tulu V2 dataset, targeting a range of tasks including GSM8k, SQuAD, and MMLU, across several models from the Llama and Qwen families. Experiments show that Influence Distillation matches or outperforms state-of-the-art performance while achieving up to $3.5\times$ faster selection.
Abstract (translated)
有效数据选择对于现代大型语言模型（LLM）的高效训练至关重要。本文介绍了影响蒸馏（Influence Distillation），这是一种新颖且数学上合理化的数据选择框架，利用二阶信息来优化加权训练样本的方式。通过提炼每个样本对目标分布的影响，我们的方法为LLM微调分配特定于模型的权重，从而指导其在目标领域的性能表现。我们推导了这两种最常用优化器（梯度下降和Adam）下的最优权重。 为了确保可扩展性和降低计算成本，我们提出了一种基于地标样例的近似方法：精确地为一小部分“地标”样本计算影响值，并然后高效传播到所有其他样本上以确定其权重。我们在Tulu V2数据集上的指令调优任务中验证了影响蒸馏的有效性，针对包括GSM8k、SQuAD和MMLU等不同任务类型，并覆盖来自Llama和Qwen家族的多个模型。 实验结果表明，通过影响蒸馏选择训练数据能够与现有最佳方法相匹敌或超越其性能表现，同时实现高达3.5倍更快的选择速度。
URL
https://arxiv.org/abs/2505.19051
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LoTA-QAF: Lossless Ternary Adaptation for Quantization-Aware Fine-Tuning
2025-05-24 14:47:28Junyu Chen, Junzhuo Li, Zhen Peng, Wenjie Wang, Yuxiang Ren, Long Shi, Xuming HuAbstract
Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in data types between the low-precision quantized weights (e.g., 4-bit) and the high-precision adaptation weights (e.g., 16-bit). This mismatch limits the computational efficiency advantage offered by quantized weights during inference. Second, potential accuracy degradation when merging these high-precision adaptation weights into the low-precision quantized weights, as the adaptation weights often necessitate approximation or truncation. Third, as far as we know, no existing methods support the lossless merging of adaptation while adjusting all quantized weights. To address these challenges, we introduce lossless ternary adaptation for quantization-aware fine-tuning (LoTA-QAF). This is a novel fine-tuning method specifically designed for quantized LLMs, enabling the lossless merging of ternary adaptation weights into quantized weights and the adjustment of all quantized weights. LoTA-QAF operates through a combination of: i) A custom-designed ternary adaptation (TA) that aligns ternary weights with the quantization grid and uses these ternary weights to adjust quantized weights. ii) A TA-based mechanism that enables the lossless merging of adaptation weights. iii) Ternary signed gradient descent (t-SignSGD) for updating the TA weights. We apply LoTA-QAF to Llama-3.1/3.3 and Qwen-2.5 model families and validate its effectiveness on several downstream tasks. On the MMLU benchmark, our method effectively recovers performance for quantized models, surpassing 16-bit LoRA by up to 5.14\%. For task-specific fine-tuning, 16-bit LoRA achieves superior results, but LoTA-QAF still outperforms other methods.
Abstract (translated)
量化和微调对于在资源受限的边缘设备上部署大型语言模型（LLMs）至关重要。然而，对量化模型进行微调带来了显著的挑战，主要原因是： 首先，低精度量化权重（例如4位）与高精度适应权重（例如16位）之间存在数据类型不匹配的问题。这种不匹配限制了在推理过程中量化权重提供的计算效率优势。 其次，在将这些高精度适应权重合并到低精度量化权重时可能出现准确度下降的情况，因为适应权重往往需要近似或截断处理。 第三，据我们所知，目前尚无任何方法支持在调整所有量化权重的同时进行无损融合适应过程。 为解决上述挑战，我们提出了一种面向量化感知微调（QAT）的无损三值适应技术（LoTA-QAF）。这是一种专门针对量化LLMs设计的新颖微调方法，它能够实现将三值适应权重无损地合并到量化权重中，并调整所有量化权重。LoTA-QAF通过以下组合方式运行： i) 设计了一种自定义的三值适应（TA），该机制使三值权重与量化网格对齐，并使用这些三值权重来调整量化权重。 ii) 基于TA的机制，使得可以无损地融合适应权重。 iii) 用于更新TA权重的三值有符号梯度下降法（t-SignSGD）。 我们将LoTA-QAF应用于Llama-3.1/3.3和Qwen-2.5模型家族，并在多个下游任务上验证了其有效性。在MMLU基准测试中，我们的方法有效恢复了量化模型的性能，比16位低秩适应（LoRA）高出最多5.14%。对于特定任务的微调而言，虽然16位LoRA表现出色，但LoTA-QAF仍然优于其他方法。 这种方法在保持计算效率的同时提高了量化LLMs的精度和灵活性，在资源受限设备上的应用前景广阔。
URL
https://arxiv.org/abs/2505.18724
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Accelerating Learned Image Compression Through Modeling Neural Training Dynamics
2025-05-23 17:03:13Yichi Zhang, Zhihao Duan, Yuning Huang, Fengqing ZhuAbstract
As learned image compression (LIC) methods become increasingly computationally demanding, enhancing their training efficiency is crucial. This paper takes a step forward in accelerating the training of LIC methods by modeling the neural training dynamics. We first propose a Sensitivity-aware True and Dummy Embedding Training mechanism (STDET) that clusters LIC model parameters into few separate modes where parameters are expressed as affine transformations of reference parameters within the same mode. By further utilizing the stable intra-mode correlations throughout training and parameter sensitivities, we gradually embed non-reference parameters, reducing the number of trainable parameters. Additionally, we incorporate a Sampling-then-Moving Average (SMA) technique, interpolating sampled weights from stochastic gradient descent (SGD) training to obtain the moving average weights, ensuring smooth temporal behavior and minimizing training state variances. Overall, our method significantly reduces training space dimensions and the number of trainable parameters without sacrificing model performance, thus accelerating model convergence. We also provide a theoretical analysis on the Noisy quadratic model, showing that the proposed method achieves a lower training variance than standard SGD. Our approach offers valuable insights for further developing efficient training methods for LICs.
Abstract (translated)
随着学习型图像压缩（LIC）方法计算需求的增加，提高其训练效率变得至关重要。本文通过建模神经网络训练动力学来加速LIC方法的训练过程。我们首先提出了一个基于敏感度感知的真实和虚拟嵌入训练机制（STDET），该机制将LIC模型参数聚类成少数几种不同的模式，在每个模式内，参数可以表示为参考参数的仿射变换。通过进一步利用各模式内部在训练过程中稳定的关联关系及参数敏感性，我们逐步嵌入非参考参数，从而减少可训练参数的数量。 此外，我们还引入了采样后移动平均（SMA）技术，该技术从随机梯度下降(SGD)训练中插值出采样的权重，以此来获取移动平均权重，确保时间行为的平滑性并最小化训练状态方差。总体而言，我们的方法在不牺牲模型性能的前提下显著减少了训练空间维度和可训练参数的数量，从而加速了模型收敛速度。 我们还对噪声二次模型进行了理论分析，表明所提出的方法比标准SGD实现了更低的训练方差。本文的研究为开发更高效的LIC训练方法提供了有价值的见解。
URL
https://arxiv.org/abs/2505.18107
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Attention with Trained Embeddings Provably Selects Important Tokens
2025-05-22 21:00:09Diyuan Wu, Aleksandr Shevchenko, Samet Oymak, Marco MondelliAbstract
Token embeddings play a crucial role in language modeling but, despite this practical relevance, their theoretical understanding remains limited. Our paper addresses the gap by characterizing the structure of embeddings obtained via gradient descent. Specifically, we consider a one-layer softmax attention model with a linear head for binary classification, i.e., $\texttt{Softmax}( p^\top E_X^\top ) E_X v = \frac{ \sum_{i=1}^T \exp(p^\top E_{x_i}) E_{x_i}^\top v}{\sum_{j=1}^T \exp(p^\top E_{x_{j}}) }$, where $E_X = [ E_{x_1} , \dots, E_{x_T} ]^\top$ contains the embeddings of the input sequence, $p$ is the embedding of the $\mathrm{\langle cls \rangle}$ token and $v$ the output vector. First, we show that, already after a single step of gradient training with the logistic loss, the embeddings $E_X$ capture the importance of tokens in the dataset by aligning with the output vector $v$ proportionally to the frequency with which the corresponding tokens appear in the dataset. Then, after training $p$ via gradient flow until convergence, the softmax selects the important tokens in the sentence (i.e., those that are predictive of the label), and the resulting $\mathrm{\langle cls \rangle}$ embedding maximizes the margin for such a selection. Experiments on real-world datasets (IMDB, Yelp) exhibit a phenomenology close to that unveiled by our theory.
Abstract (translated)
令牌嵌入在语言建模中扮演着关键角色，尽管具有实际重要性，但对其理论理解仍然有限。我们的论文通过表征经梯度下降获得的嵌入结构来填补这一空白。具体来说，我们考虑了一个单层softmax注意力模型，并带有用于二分类的线性头部，即 $\texttt{Softmax}( p^\top E_X^\top ) E_X v = \frac{\sum_{i=1}^T \exp(p^\top E_{x_i}) E_{x_i}^\top v}{\sum_{j=1}^T \exp(p^\top E_{x_{j}})}$，其中 $E_X = [ E_{x_1}, \dots, E_{x_T}]^\top$ 包含输入序列的嵌入，$p$ 是 $\mathrm{\langle cls \rangle}$ 令牌的嵌入，而 $v$ 是输出向量。首先，我们证明即使经过一次梯度训练（使用逻辑损失），嵌入 $E_X$ 已经通过与输出向量 $v$ 的比例对齐来捕捉数据集中令牌的重要性，这种对齐方式与其在数据集中的出现频率成正比。然后，在通过梯度流训练 $p$ 直到收敛之后，softmax 会选择句子中重要的令牌（即那些能预测标签的令牌），并且最终产生的 $\mathrm{\langle cls \rangle}$ 嵌入会最大化这样的选择所带来的间隔。在现实世界数据集（IMDB、Yelp）上的实验展示了与我们理论揭示的现象学非常接近的结果。
URL
https://arxiv.org/abs/2505.17282
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Decouple and Orthogonalize: A Data-Free Framework for LoRA Merging
2025-05-21 16:34:37Shenghe Zheng, Hongzhi Wang, Chenyu Huang, Xiaohui Wang, Tao Chen, Jiayuan Fan, Shuyue Hu, Peng YeAbstract
With more open-source models available for diverse tasks, model merging has gained attention by combining models into one, reducing training, storage, and inference costs. Current research mainly focuses on model merging for full fine-tuning, overlooking the popular LoRA. However, our empirical analysis reveals that: a) existing merging methods designed for full fine-tuning perform poorly on LoRA; b) LoRA modules show much larger parameter magnitude variance than full fine-tuned weights; c) greater parameter magnitude variance correlates with worse merging performance. Considering that large magnitude variances cause deviations in the distribution of the merged parameters, resulting in information loss and performance degradation, we propose a Decoupled and Orthogonal merging approach(DO-Merging). By separating parameters into magnitude and direction components and merging them independently, we reduce the impact of magnitude differences on the directional alignment of the merged models, thereby preserving task information. Furthermore, we introduce a data-free, layer-wise gradient descent method with orthogonal constraints to mitigate interference during the merging of direction components. We provide theoretical guarantees for both the decoupling and orthogonal components. And we validate through extensive experiments across vision, language, and multi-modal domains that our proposed DO-Merging can achieve significantly higher performance than existing merging methods at a minimal cost. Notably, each component can be flexibly integrated with existing methods, offering near free-lunch improvements across tasks.
Abstract (translated)
随着开源模型的增多，能够为各种任务服务，模型合并（将多个模型整合成一个）越来越受到关注。通过这种方法可以减少训练、存储和推理的成本。然而，当前的研究主要集中在全面微调（full fine-tuning）上的模型合并上，而忽略了流行的LoRA方法。我们的实证分析表明： a) 为全面微调设计的现有合并方法在处理LoRA时表现不佳； b) LoRA模块显示出比完全微调权重更大的参数幅度变化； c) 更大的参数幅度变化与较差的合并性能相关联。 考虑到大范围的幅度差异会导致合并参数分布中的偏差，从而导致信息丢失和性能下降，我们提出了一种解耦正交合并方法（Decoupled and Orthogonal merging, DO-Merging）。通过将参数分解为幅度和方向分量，并独立地对它们进行合并，我们可以减少幅度差异对合并模型方向一致性的负面影响，从而保留任务相关信息。 此外，为了在方向分量的合并过程中减轻干扰，我们引入了一种无数据依赖、逐层梯度下降的方法，该方法带有正交约束。我们为解耦和正交部分都提供了理论保证。通过广泛的实验验证（涵盖视觉、语言以及跨模态领域），我们的DO-Merging方法可以在最低成本下实现比现有合并方法显著更高的性能。 值得注意的是，每个组件都可以灵活地与现有的方法集成，从而在各种任务中提供近乎无代价的改进效果。
URL
https://arxiv.org/abs/2505.15875
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Second-Order Convergence in Private Stochastic Non-Convex Optimization
2025-05-21 15:25:23Youming Tao, Zuyuan Zhang, Dongxiao Yu, Xiuzhen Cheng, Falko Dressler, Di WangAbstract
We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: (i) inaccurate convergence error rate due to overlooking gradient variance in the saddle point escape analysis, and (ii) dependence on auxiliary private model selection procedures for identifying DP-SOSP, which can significantly impair utility, particularly in distributed settings. To address these issues, we propose a generic perturbed stochastic gradient descent (PSGD) framework built upon Gaussian noise injection and general gradient oracles. A core innovation of our framework is using model drift distance to determine whether PSGD escapes saddle points, ensuring convergence to approximate local minima without relying on second-order information or additional DP-SOSP identification. By leveraging the adaptive DP-SPIDER estimator as a specific gradient oracle, we develop a new DP algorithm that rectifies the convergence error rates reported in prior work. We further extend this algorithm to distributed learning with arbitrarily heterogeneous data, providing the first formal guarantees for finding DP-SOSP in such settings. Our analysis also highlights the detrimental impacts of private selection procedures in distributed learning under high-dimensional models, underscoring the practical benefits of our design. Numerical experiments on real-world datasets validate the efficacy of our approach.
Abstract (translated)
我们研究了在差异隐私（DP）随机非凸优化中寻找二阶平稳点（SOSP）的问题。现有方法存在两个关键局限性：(i) 由于忽视了鞍点逃脱分析中的梯度方差，导致收敛误差率不准确；(ii) 需要依赖于辅助的私有模型选择程序来识别DP-SOSP，这在分布式环境中可能会显著损害效用。 为解决这些问题，我们提出了一种基于高斯噪声注入和一般梯度预测器构建的泛化扰动随机梯度下降（PSGD）框架。我们框架的一个核心创新是使用模型漂移距离来确定PSGD是否逃脱了鞍点，并确保在不依赖于二阶信息或额外DP-SOSP识别的情况下收敛到近似局部最小值。 通过利用自适应DP-SPIDER估计算法作为特定的梯度预测器，我们开发了一种新的DP算法，该算法纠正了先前工作中报告的收敛误差率。我们将此算法进一步扩展至任意异构数据分布式的环境中，并为在这种设置下寻找DP-SOSP提供了第一个正式保证。 我们的分析还强调，在高维模型下的分布式学习中私有选择程序带来的负面影响，突显了我们设计的实际应用价值。在现实世界的数据集上的数值实验验证了我们方法的有效性。
URL
https://arxiv.org/abs/2505.15647
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One-Layer Transformers are Provably Optimal for In-context Reasoning and Distributional Association Learning in Next-Token Prediction Tasks
2025-05-21 01:26:44Quan Nguyen, Thanh Nguyen-TangAbstract
We study the approximation capabilities and on-convergence behaviors of one-layer transformers on the noiseless and noisy in-context reasoning of next-token prediction. Existing theoretical results focus on understanding the in-context reasoning behaviors for either the first gradient step or when the number of samples is infinite. Furthermore, no convergence rates nor generalization abilities were known. Our work addresses these gaps by showing that there exists a class of one-layer transformers that are provably Bayes-optimal with both linear and ReLU attention. When being trained with gradient descent, we show via a finite-sample analysis that the expected loss of these transformers converges at linear rate to the Bayes risk. Moreover, we prove that the trained models generalize to unseen samples as well as exhibit learning behaviors that were empirically observed in previous works. Our theoretical findings are further supported by extensive empirical validations.
Abstract (translated)
我们研究了一层变压器在无噪声和有噪声的上下文推理中的下-token预测时的近似能力和在线收敛行为。现有的理论结果主要集中在理解要么第一次梯度步骤，要么样本数量无限时的上下文推理行为上。此外，没有已知的收敛速率或泛化能力。我们的工作通过展示一类一层变压器，在使用线性注意力和ReLU注意力时都是贝叶斯最优的，填补了这些空白。当用梯度下降法训练时，我们通过对有限样本分析显示，这些变压器的预期损失以线性的速度收敛到贝叶斯风险。此外，我们还证明了经过训练的模型能够泛化至未见过的数据，并且表现出与之前工作中观察到的学习行为一致的行为模式。我们的理论发现进一步通过广泛的实证验证得到了支持。
URL
https://arxiv.org/abs/2505.15009
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Tversky Neural Networks: Psychologically Plausible Deep Learning with Differentiable Tversky Similarity
2025-05-21 01:01:48Moussa Koulako Bala Doumbouya, Dan Jurafsky, Christopher D. ManningAbstract
Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception. In contrast, Tversky (1977) proposed an axiomatic theory of similarity based on a representation of objects as sets of features, and their similarity as a function of common and distinctive features. However, this model has not been used in deep learning before, partly due to the challenge of incorporating discrete set operations. We develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive neural network building blocks such as the Tversky projection layer, which unlike the linear projection layer can model non-linear functions such as XOR. Through experiments with image recognition and language modeling, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer, which employs geometric similarity. On the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.5%, and its parameter count by 34.8%. Finally, we propose a unified interpretation of both projection layers as computing similarities of input stimuli to learned prototypes, for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in deep learning, and designing networks that are interpretable under an established theory of psychological similarity.
Abstract (translated)
心理学领域的研究指出，深度学习中基于几何模型的相似性标准在心理上是不合理的，因为其度量属性（如对称性）与人类感知不符。相比之下，Tversky（1977）提出了一种基于对象特征集表示和共同及独特特征函数的相似性公理理论。然而，由于难以将离散集合运算融入其中，这一模型以前未曾应用于深度学习中。 我们开发了Tversky相似性的可微参数化版本，使其可以通过梯度下降进行学习，并推导出神经网络构建模块（如Tversky投影层），这与传统的线性投影层不同，能够模拟非线性函数（例如XOR）。通过图像识别和语言建模的实验表明，Tversky投影层可以替代使用几何相似性的线性投影层。在NABirds图像分类任务中，一个冻结的ResNet-50模型，在添加了Tversky投影层后，相对于线性层适配基线实现了24.7%的相对准确率提升。 当使用Tversky投影层时，GPT-2在PTB上的困惑度降低了7.5%，参数量减少了34.8%。最后，我们提出了对两种投影层进行统一解释的方法，认为它们计算的是输入刺激与学习原型之间的相似性，并为此提出了一种新的可视化技术以突出Tversky投影层的可解释性。 我们的工作为深度学习中的隐含相似性模型提供了新的思考方式，并设计了在心理相似理论下具有良好可解释性的网络结构。
URL
https://arxiv.org/abs/2506.11035
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PhySense: Sensor Placement Optimization for Accurate Physics Sensing
2025-05-19 14:59:11Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng LongAbstract
Physics sensing plays a central role in many scientific and engineering domains, which inherently involves two coupled tasks: reconstructing dense physical fields from sparse observations and optimizing scattered sensor placements to observe maximum information. While deep learning has made rapid advances in sparse-data reconstruction, existing methods generally omit optimization of sensor placements, leaving the mutual enhancement between reconstruction and placement on the shelf. To change this suboptimal practice, we propose PhySense, a synergistic two-stage framework that learns to jointly reconstruct physical fields and to optimize sensor placements, both aiming for accurate physics sensing. The first stage involves a flow-based generative model enhanced by cross-attention to adaptively fuse sparse observations. \correct{Leveraging the reconstruction feedback, }the second stage performs sensor placement via projected gradient descent to satisfy spatial constraints. \correct{We further prove that the learning objectives of the two stages are consistent with classical variance-minimization principles, providing theoretical guarantees.} Extensive experiments across three challenging benchmarks, especially a 3D geometry dataset, indicate PhySense achieves state-of-the-art physics sensing accuracy and discovers informative sensor placements previously unconsidered.
Abstract (translated)
物理学感知在许多科学和工程领域中扮演着核心角色，这通常涉及到两个相互关联的任务：从稀疏观测数据重建密集的物理场以及优化传感器布置以获取最大信息量。虽然深度学习在处理稀疏数据重建方面取得了快速进展，但现有方法一般忽略了传感器布局优化的问题，从而导致了重建与布局之间的协同提升被搁置一旁。为了改变这种次优做法，我们提出了一种名为PhySense的协同两阶段框架，该框架能够同时学习物理场的联合重构和传感器布置的优化，两者都旨在实现准确的物理学感知。 第一阶段涉及一种通过跨注意力增强的流生成模型，用于自适应地融合稀疏观测数据。利用重建反馈，第二阶段则采用投影梯度下降法进行传感器放置以满足空间约束条件。此外，我们还证明了两个阶段的学习目标与经典的方差最小化原理一致，并提供了理论保证。 在三个具有挑战性的基准测试（尤其是3D几何数据集）中的广泛实验表明，PhySense达到了最先进的物理学感知准确度，并且发现了之前未曾考虑的有信息量的传感器布局。
URL
https://arxiv.org/abs/2505.18190
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When majority rules, minority loses: bias amplification of gradient descent
2025-05-19 13:51:49Fran\c{c}ois Bachoc (IMT), J\'er\^ome Bolte (TSE-R), Ryan Boustany (TSE-R), Jean-Michel Loubes (IMT)Abstract
Despite growing empirical evidence of bias amplification in machine learning, its theoretical foundations remain poorly understood. We develop a formal framework for majority-minority learning tasks, showing how standard training can favor majority groups and produce stereotypical predictors that neglect minority-specific features. Assuming population and variance imbalance, our analysis reveals three key findings: (i) the close proximity between ``full-data'' and stereotypical predictors, (ii) the dominance of a region where training the entire model tends to merely learn the majority traits, and (iii) a lower bound on the additional training required. Our results are illustrated through experiments in deep learning for tabular and image classification tasks.
Abstract (translated)
尽管有关机器学习中偏见放大的实证证据越来越多，但其理论基础仍然不甚明了。我们建立了一个用于多数群体和少数群体学习任务的形式框架，展示了标准训练如何倾向于支持多数群体，并产生忽视少数群体特定特征的刻板印象预测模型。假设存在人口不平衡和方差差异的情况下，我们的分析揭示了三个关键发现：(i) “全数据”与刻板印象预测之间的紧密关联；(ii) 训练整个模型往往只是学习多数群体特性的主导区域；以及 (iii) 额外训练所需的最低限度。通过深度学习在表格和图像分类任务中的实验，我们展示了这些结果。
URL
https://arxiv.org/abs/2505.13122
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FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA
2025-05-19 07:32:56Seanie Lee, Sangwoo Park, Dong Bok Lee, Dominik Wagner, Haebin Seong, Tobias Bocklet, Juho Lee, Sung Ju HwangAbstract
Low-Rank Adaptation (LoRA), which introduces a product of two trainable low-rank matrices into frozen pre-trained weights, is widely used for efficient fine-tuning of language models in federated learning (FL). However, when combined with differentially private stochastic gradient descent (DP-SGD), LoRA faces substantial noise amplification: DP-SGD perturbs per-sample gradients, and the matrix multiplication of the LoRA update ($BA$) intensifies this effect. Freezing one matrix (e.g., $A$) reduces the noise but restricts model expressiveness, often resulting in suboptimal adaptation. To address this, we propose FedSVD, a simple yet effective method that introduces a global reparameterization based on singular value decomposition (SVD). In our approach, each client optimizes only the $B$ matrix and transmits it to the server. The server aggregates the $B$ matrices, computes the product $BA$ using the previous $A$, and refactorizes the result via SVD. This yields a new adaptive $A$ composed of the orthonormal right singular vectors of $BA$, and an updated $B$ containing the remaining SVD components. This reparameterization avoids quadratic noise amplification, while allowing $A$ to better capture the principal directions of the aggregate updates. Moreover, the orthonormal structure of $A$ bounds the gradient norms of $B$ and preserves more signal under DP-SGD, as confirmed by our theoretical analysis. As a result, FedSVD consistently improves stability and performance across a variety of privacy settings and benchmarks, outperforming relevant baselines under both private and non-private regimes.
Abstract (translated)
低秩适应（LoRA）通过将两个可训练的低秩矩阵的乘积引入冻结的预训练权重中，被广泛用于联邦学习（FL）中的语言模型高效微调。然而，在与差异隐私随机梯度下降（DP-SGD）结合时，LoRA面临着显著的噪声放大问题：DP-SGD会扰动每个样本的梯度，而LoRA更新的矩阵乘法($BA$)则增强了这一影响。冻结一个矩阵（例如 $A$）虽然可以减少噪音但限制了模型的表现力，往往导致次优适应。 为解决上述问题，我们提出了一种简单且有效的方法FedSVD，该方法基于奇异值分解（SVD）引入了一个全局重参数化。在我们的方法中，每个客户端仅优化矩阵 $B$ 并将其传输到服务器。服务器聚合了所有的 $B$ 矩阵，并使用之前的 $A$ 计算乘积 $BA$ ，然后通过 SVD 重新因子化该结果。这生成了一个新的适应性 $A$，由 $BA$ 的正交右奇异向量组成，并且更新后的 $B$ 包含剩余的 SVD 组件。这种重参数化避免了二次噪声放大，同时允许 $A$ 更好地捕捉聚合更新的主要方向。此外，由于 $A$ 的正交结构，它限制了 $B$ 的梯度范数并在 DP-SGD 下保留更多信号，这一点已被我们的理论分析所证实。 因此，在各种隐私设置和基准测试中，FedSVD 一致提高了稳定性和性能，并且在私人和非私人模式下均超越了相关的基线方法。
URL
https://arxiv.org/abs/2505.12805
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EnvInjection: Environmental Prompt Injection Attack to Multi-modal Web Agents
2025-05-16 22:00:26Xilong Wang, John Bloch, Zedian Shao, Yuepeng Hu, Shuyan Zhou, Neil Zhenqiang GongAbstract
Multi-modal large language model (MLLM)-based web agents interact with webpage environments by generating actions based on screenshots of the webpages. Environmental prompt injection attacks manipulate the environment to induce the web agent to perform a specific, attacker-chosen action--referred to as the target action. However, existing attacks suffer from limited effectiveness or stealthiness, or are impractical in real-world settings. In this work, we propose EnvInjection, a new attack that addresses these limitations. Our attack adds a perturbation to the raw pixel values of the rendered webpage, which can be implemented by modifying the webpage's source code. After these perturbed pixels are mapped into a screenshot, the perturbation induces the web agent to perform the target action. We formulate the task of finding the perturbation as an optimization problem. A key challenge in solving this problem is that the mapping between raw pixel values and screenshot is non-differentiable, making it difficult to backpropagate gradients to the perturbation. To overcome this, we train a neural network to approximate the mapping and apply projected gradient descent to solve the reformulated optimization problem. Extensive evaluation on multiple webpage datasets shows that EnvInjection is highly effective and significantly outperforms existing baselines.
Abstract (translated)
基于多模态大型语言模型（MLLM）的网页代理通过根据网页截图生成动作来与网页环境互动。环境提示注入攻击通过操控环境，诱使网页代理执行特定的、由攻击者选定的动作——称为目标动作。然而，现有的攻击方法在有效性或隐蔽性方面存在局限，或者在现实世界场景中难以实施。在这项工作中，我们提出了一种新的攻击方式EnvInjection，旨在克服这些限制。 我们的攻击通过向渲染后的网页的原始像素值添加干扰来实现，这可以通过修改网页源代码完成。当这些被干扰的像素映射到截图后，干扰会诱使网页代理执行目标动作。我们将寻找这一干扰的任务形式化为一个优化问题。解决这个问题的关键挑战在于，原始像素值与截图之间的映射是非可微分的（non-differentiable），这使得难以将梯度反向传播到干扰上。为了克服这一点，我们训练了一个神经网络来近似该映射，并应用投影梯度下降法来求解重新表述后的优化问题。 在多个网页数据集上的广泛评估表明，EnvInjection具有高度有效性，并且显著优于现有的基准方法。
URL
https://arxiv.org/abs/2505.11717
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Questioning Representational Optimism in Deep Learning: The Fractured Entangled Representation Hypothesis
2025-05-16 16:28:34Akarsh Kumar, Jeff Clune, Joel Lehman, Kenneth O. StanleyAbstract
Much of the excitement in modern AI is driven by the observation that scaling up existing systems leads to better performance. But does better performance necessarily imply better internal representations? While the representational optimist assumes it must, this position paper challenges that view. We compare neural networks evolved through an open-ended search process to networks trained via conventional stochastic gradient descent (SGD) on the simple task of generating a single image. This minimal setup offers a unique advantage: each hidden neuron's full functional behavior can be easily visualized as an image, thus revealing how the network's output behavior is internally constructed neuron by neuron. The result is striking: while both networks produce the same output behavior, their internal representations differ dramatically. The SGD-trained networks exhibit a form of disorganization that we term fractured entangled representation (FER). Interestingly, the evolved networks largely lack FER, even approaching a unified factored representation (UFR). In large models, FER may be degrading core model capacities like generalization, creativity, and (continual) learning. Therefore, understanding and mitigating FER could be critical to the future of representation learning.
Abstract (translated)
现代人工智能领域的许多兴奋之处在于，扩大现有系统的规模会导致性能提升。然而，更好的性能是否必然意味着内部表示也更好呢？虽然代表乐观主义者认为答案是肯定的，但本文对此观点提出了挑战。我们比较了通过开放式演化过程进化的神经网络与使用传统随机梯度下降（SGD）训练的神经网络在生成单个图像这一简单任务上的表现。这种最小设置提供了一个独特的优势：可以轻松地将每个隐藏神经元的完整功能行为可视化为一个图像，从而揭示出网络输出行为是如何通过一个个神经元构建起来的。 结果令人震惊：尽管两种类型的网络都产生了相同的行为输出，但它们的内部表示却大相径庭。SGD训练的网络表现出一种我们称之为“碎片化纠缠表示”（FER）的形式。有趣的是，演化出来的网络在很大程度上缺乏这种“碎片化纠缠表示”，甚至接近于统一因子表示（UFR）。在大规模模型中，“碎片化纠缠表示”可能会削弱核心功能能力，如泛化、创造力和持续学习等。 因此，理解和缓解“碎片化纠缠表示”的问题对于未来代表学习的发展可能至关重要。
URL
https://arxiv.org/abs/2505.11581
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Adaptive Diffusion Policy Optimization for Robotic Manipulation
2025-05-13 09:21:45Huiyun Jiang, Zhuang YangAbstract
Recent studies have shown the great potential of diffusion models in improving reinforcement learning (RL) by modeling complex policies, expressing a high degree of multi-modality, and efficiently handling high-dimensional continuous control tasks. However, there is currently limited research on how to optimize diffusion-based polices (e.g., Diffusion Policy) fast and stably. In this paper, we propose an Adam-based Diffusion Policy Optimization (ADPO), a fast algorithmic framework containing best practices for fine-tuning diffusion-based polices in robotic control tasks using the adaptive gradient descent method in RL. Adaptive gradient method is less studied in training RL, let alone diffusion-based policies. We confirm that ADPO outperforms other diffusion-based RL methods in terms of overall effectiveness for fine-tuning on standard robotic tasks. Concretely, we conduct extensive experiments on standard robotic control tasks to test ADPO, where, particularly, six popular diffusion-based RL methods are provided as benchmark methods. Experimental results show that ADPO acquires better or comparable performance than the baseline methods. Finally, we systematically analyze the sensitivity of multiple hyperparameters in standard robotics tasks, providing guidance for subsequent practical applications. Our video demonstrations are released in this https URL.
Abstract (translated)
最近的研究表明，扩散模型在通过建模复杂的策略、表达高多模态性以及高效处理高维连续控制任务方面，具有显著提升强化学习（RL）的潜力。然而，目前关于如何快速且稳定地优化基于扩散的策略（如Diffusion Policy）的研究还很有限。在这篇论文中，我们提出了一种基于Adam的方法——扩散策略优化(ADPO)，这是一个快速的算法框架，使用自适应梯度下降方法在强化学习中对机器人控制任务中的基于扩散的策略进行微调。自适应梯度法在训练RL中研究较少，更不用说针对基于扩散的政策了。我们确认，在标准机器人任务上的微调总体效果上，ADPO优于其他基于扩散的方法。 具体来说，我们在标准的机器人控制任务上进行了广泛的实验以测试ADPO的有效性，并提供了六种流行的基于扩散的强化学习方法作为基准方法进行对比。实验证明，ADPO在性能上至少达到了与这些基准方法相同的水平，或者更好。最后，我们系统地分析了标准机器人任务中多个超参数的敏感度，为后续的实际应用提供了指导。我们的视频演示可在[此处](https://this.https.URL)查看。
URL
https://arxiv.org/abs/2505.08376
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IRNN: Innovation-driven Recurrent Neural Network for Time-Series Data Modeling and Prediction
2025-05-09 09:43:40Yifan Zhou, Yibo Wang, Chao ShangAbstract
Many real-world datasets are time series that are sequentially collected and contain rich temporal information. Thus, a common interest in practice is to capture dynamics of time series and predict their future evolutions. To this end, the recurrent neural network (RNN) has been a prevalent and effective machine learning option, which admits a nonlinear state-space model representation. Motivated by the resemblance between RNN and Kalman filter (KF) for linear state-space models, we propose in this paper Innovation-driven RNN (IRNN), a novel RNN architecture tailored to time-series data modeling and prediction tasks. By adapting the concept of "innovation" from KF to RNN, past prediction errors are adopted as additional input signals to update hidden states of RNN and boost prediction performance. Since innovation data depend on network parameters, existing training algorithms for RNN do not apply to IRNN straightforwardly. Thus, a tailored training algorithm dubbed input updating-based back-propagation through time (IU-BPTT) is further proposed, which alternates between updating innovations and optimizing network parameters via gradient descent. Experiments on real-world benchmark datasets show that the integration of innovations into various forms of RNN leads to remarkably improved prediction accuracy of IRNN without increasing the training cost substantially.
Abstract (translated)
许多现实世界的数据集都是按时间顺序收集的时间序列数据，包含丰富的时序信息。因此，在实践中一个共同的兴趣是捕捉时间序列的动力学特性并预测它们的未来演变趋势。为此，递归神经网络（RNN）已成为一种普遍且有效的机器学习选项，它可以表示非线性状态空间模型。受RNN与线性状态空间模型中的卡尔曼滤波器（KF）之间的相似性的启发，本文提出了创新驱动式RNN（IRNN），这是一种新型的针对时间序列数据建模和预测任务定制化的RNN架构。通过将“创新”这一概念从KF引入到RNN中，我们采用了过去预测误差作为额外输入信号来更新RNN的状态，并提高了预测性能。由于创新数据依赖于网络参数，现有的适用于RNN的训练算法不能直接应用于IRNN。因此，进一步提出了一种定制化的训练算法——基于输入更新的反向传播通过时间（IU-BPTT），该算法交替进行创新更新和利用梯度下降优化网络参数。在现实世界的基准数据集上的实验表明，在不显著增加训练成本的情况下，将创新整合到各种形式的RNN中可以大大提高IRNN的预测准确性。
URL
https://arxiv.org/abs/2505.05916
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