论文检索

Computer Vision · Image and Video Generation

Qiang Xiang, Shuang Sun, Binglei Li, Dejia Song, Huaxia Li, Yibo Chen, Xu Tang, Yao Hu, Junping Zhang

Diffusion models have demonstrated remarkable capabilities in generating high-quality images. Recent advancements in Layout-to-Image (L2I) generation have leveraged positional conditions and textual descriptions to facilitate precise and controllable image synthesis. Despite overall progress, current L2I methods still exhibit suboptimal performance. Therefore, we propose InstanceAssemble, a novel architecture that incorporates layout conditions via instance-assembling attention, enabling position control with bounding boxes (bbox) and multimodal content control including texts and additional visual content. Our method achieves flexible adaption to existing DiT-based T2I models through light-weighted LoRA modules. Additionally, we propose a Layout-to-Image benchmark, Denselayout, a comprehensive benchmark for layout-to-image generation, containing 5k images with 90k instances in total. We further introduce Layout Grounding Score (LGS), an interpretable evaluation metric to more precisely assess the accuracy of L2I generation. Experiments demonstrate that our InstanceAssemble method achieves state-of-the-art performance under complex layout conditions, while exhibiting strong compatibility with diverse style LoRA modules. The code and pretrained models are publicly available at \url{https://github.com/FireRedTeam/InstanceAssemble}.

Applications · Language, Speech and Dialog

Ki-Joong Kwon, Junho So, Sang-Hoon Lee

While substantial advances have been achieved in TTS for languages such as English and Mandarin, Korean remains comparatively underrepresented due to the lack of rigorous preprocessing methods, systematically constructed datasets, a shortage of standardized Korean TTS benchmarks, and explicitly optimized models for Korean. To address these limitations, we propose a Korean-tailored data-refinement and coreset selection pipeline. It refines speech data and performs textual normalization especially for numerals and English terms, followed by a novel coreset selection strategy that leverages Jamo-based linguistic and phonological features unique to Korean. As a result, we release CoreaSpeech, an efficient and robust Korean speech corpus comprising 700 hours across 21,449 speakers. This refined core subset, evenly balanced across utterances ranging from 0 to 30 seconds, is derived from 2,058 hours of widely used Korean datasets. Building on this, we conducted extensive experiments via cross-lingual fine-tuning with our CoreaSpeech dataset. Furthermore, we introduce a new universal Korean TTS benchmark dataset including clean, noisy, and numeric subsets. Additionally, we demonstrate that our Korean-specific text normalization serves as a plug-and-play module, reliably improving performance regardless of the underlying TTS architecture. We publicly release our dataset, pipeline code, and evaluation benchmarks to support reproducible research and further advances in Korean and multilingual speech synthesis.

Applications · Everything Else

Zhening Li, Armando Solar-Lezama, Yisong Yue, Stephan Zheng

We introduce a new approach to *agent programming*, the development of LLM-based agents. Current approaches to agent programming often entangle two aspects of agent design: the core workflow logic and the inference-time strategy (e.g., tree search). We introduce *probabilistic angelic nondeterminism* (PAN), a programming model that disentangles these two concerns, allowing the programmer to describe the agent workflow and independently experiment with different inference-time strategies by simply changing a few inputs. We provide an implementation of PAN in Python as the EnCompass framework, which uses a Python decorator to compile agent workflow programs into a search space. We present three case studies that demonstrate how the framework lets the programmer quickly improve the reliability of an agent and easily switch between different inference-time strategies, all with little additional coding.

Applications · Language, Speech and Dialog

Abhijnan Nath, Nikhil Krishnaswamy

Large Language Models (LLMs) are increasingly bring deployed in agentic settings where they act as collaborators with humans. Therefore, it is increasingly important to be able to evaluate their abilities to collaborate effectively in multi-turn, multi-party tasks. In this paper, we build on the AI alignment and “safe interruptability” literature to offer novel theoretical insights on collaborative behavior between LLM-driven *collaborator agents* and an *intervention agent*. Our goal is to learn an ideal “partner-aware” collaborator that increases the group’s common-ground (CG)—alignment on task-relevant propositions—by intelligently collecting information provided in *interventions* by a partner agent.We show how LLM agents trained using standard RLHF and related approaches are naturally inclined to ignore possibly well-meaning interventions, which makes increasing group common ground non-trivial in this setting. We employ a two-player Modified-Action MDP to examine this suboptimal behavior of standard AI agents, and propose **Interruptible Collaborative Roleplayer (ICR)**—a novel “partner-aware” learning algorithm to train CG-optimal collaborators. Experiments on multiple collaborative task environments show that ICR, on average, is more capable of promoting successful CG convergence and exploring more diverse solutions in such tasks.

Computer Vision · Everything Else

Aobo Li, Jinjian Wu, Yongxu Liu, Leida Li, Weisheng Dong

Blind Image Quality Assessment (BIQA) has advanced significantly through deep learning, but the scarcity of large-scale labeled datasets remains a challenge. While synthetic data offers a promising solution, models trained on existing synthetic datasets often show limited generalization ability. In this work, we make a key observation that representations learned from synthetic datasets often exhibit a discrete and clustered pattern that hinders regression performance: features of high-quality images cluster around reference images, while those of low-quality images cluster based on distortion types. Our analysis reveals that this issue stems from the distribution of synthetic data rather than model architecture. Consequently, we introduce a novel framework SynDR-IQA, which reshapes synthetic data distribution to enhance BIQA generalization. Based on theoretical derivations of sample diversity and redundancy's impact on generalization error, SynDR-IQA employs two strategies: distribution-aware diverse content upsampling, which enhances visual diversity while preserving content distribution, and density-aware redundant cluster downsampling, which balances samples by reducing the density of densely clustered areas. Extensive experiments across three cross-dataset settings (synthetic-to-authentic, synthetic-to-algorithmic, and synthetic-to-synthetic) demonstrate the effectiveness of our method. The code is available at https://github.com/Li-aobo/SynDR-IQA.

Social Aspects · Trustworthy Machine Learning

Wei Shen, Weiqi Liu, Mingde Chen, Wenke Huang, Mang Ye

Vertical Federated Learning (VFL) has emerged as a critical privacy-preserving learning paradigm, enabling collaborative model training by leveraging distributed features across clients. However, due to privacy concerns, there are few publicly available real-world datasets for evaluating VFL methods, which poses significant challenges to related research. To bridge this gap, we propose MARS-VFL, a unified benchmark for realistic VFL evaluation. It integrates data from practical applications involving collaboration across different features, maintaining compatibility with the VFL setting. Based on this, we standardize the evaluation of VFL methods from the mainstream aspects of efficiency, robustness, and security. We conduct comprehensive experiments to assess different VFL approaches, providing references for unified evaluation. Furthermore, we are the first to unify the evaluation of robustness challenges in VFL and introduce a new method for addressing robustness challenges, establishing standard baselines for future research.

Optimization · Stochastic & Convex Optimization

Pengfei Li, Yuelin Han, Adam Wierman, Shaolei Ren

Fairness and action smoothness are two crucial considerations in many online optimization problems, but they have yet to be addressed simultaneously. In this paper, we study a new and challenging setting of fairness-regularized smoothed online convex optimization with switching costs. First, to highlight the fundamental challenges introduced by the long-term fairness regularizer evaluated based on the entire sequence of actions, we prove that even without switching costs, no online algorithms can possibly achieve a sublinear regret or finite competitive ratio compared to the offline optimal algorithm as the problem episode length $T$ increases. Then, we propose **FairOBD** (Fairness-regularized Online Balanced Descent), which reconciles the tension between minimizing the hitting cost, switching cost, and fairness cost. Concretely, **FairOBD** decomposes the long-term fairness cost into a sequence of online costs by introducing an auxiliary variable and then leverages the auxiliary variable to regularize the online actions for fair outcomes. Based on a new approach to account for switching costs, we prove that **FairOBD** offers a worst-case asymptotic competitive ratio against a novel benchmark---the optimal offline algorithm with parameterized constraints---by considering $T\to\infty$. Finally, we run trace-driven experiments of dynamic computing resource provisioning for socially responsible AI inference to empirically evaluate **FairOBD**, showing that **FairOBD** can effectively reduce the total fairness-regularized cost and better promote fair outcomes compared to existing baseline solutions.

Xiangyu Zhao, Peiyuan Zhang, Kexian Tang, Xiaorong Zhu, Hao Li, Wenhao Chai, Zicheng Zhang, Renqiu Xia, Guangtao Zhai, Junchi Yan 等

Large Multi-modality Models (LMMs) have made significant progress in visual understanding and generation, but they still face challenges in General Visual Editing, particularly in following complex instructions, preserving appearance consistency, and supporting flexible input formats. To study this gap, we introduce RISEBench, the first benchmark for evaluating Reasoning-Informed viSual Editing (RISE). RISEBench focuses on four key reasoning categories: Temporal, Causal, Spatial, and Logical Reasoning. We curate high-quality test cases for each category and propose an robust evaluation framework that assesses Instruction Reasoning, Appearance Consistency, and Visual Plausibility with both human judges and the LMM-as-a-judge approach. We conducted experiments evaluating nine prominent visual editing models, comprising both open-source and proprietary models. The evaluation results demonstrate that current models face significant challenges in reasoning-based editing tasks. Even the most powerful model evaluated, GPT-image-1, achieves an accuracy of merely 28.8%. RISEBench effectively highlights the limitations of contemporary editing models, provides valuable insights, and indicates potential future directions for the field of reasoning-aware visual editing. Our code and data have been released at https://github.com/PhoenixZ810/RISEBench.

Computer Vision · Vision Models & Multimodal

Fujun Han, Peng Ye

Vision-based intrusion detection has multiple applications in practical scenarios, e.g., autonomous driving, intelligent monitoring, and security. Previous works mainly focus on improving the intrusion detection performance, without a comprehensive and in-depth understanding of the intrusion scene. To fill this gap, we explore a novel task called Multimodal Large Language Models based Intrusion Scene Understanding (MLLM-ISU) and report a comprehensive benchmark for the task. Specifically, we first design an effective and automatic visual question-answer generation strategy, constructing a new MLLM-ISU dataset, with 3000 VQA evaluation Pairs, 8925 training Pairs, and six relevant subtasks. Then, we perform a comprehensive assessment on various state-of-the-art proprietary and open-source MLLMs, e.g., DeepSeek-VL2, GPT-4o, Qwen2.5-VL, etc, and find that current MLLMs have weak abilities for this task. Further, in order to improve the intrusion understanding capabilities of current MLLMs, we propose a Post-Training Framework with three sequential training stages, i.e., Intrusion-aware Visual Instruction Pre-training, Intrusion Chain of Thought tuning, and Intrusion-centric VQA tuning, and sufficient experiments and comparisons are conducted to verify the effectiveness of the proposed three-stages training framework. Available datasets and codes: https://github.com/1012537710/MLLM-ISU.

hongyong han, Wei Wang, Gaowei Zhang, Mingjie Li, Yi Wang

Coral reefs are vital yet vulnerable ecosystems that require continuous monitoring to support conservation. While coral reef images provide essential information in coral monitoring, interpreting such images remains challenging due to the need for domain expertise. Visual Question Answering (VQA), powered by Large Vision-Language Models (LVLMs), has great potential in user-friendly interaction with coral reef images. However, applying VQA to coral imagery demands a dedicated dataset that addresses two key challenges: domain-specific annotations and multidimensional questions. In this work, we introduce CoralVQA, the first large-scale VQA dataset for coral reef analysis. It contains 12,805 real-world coral images from 67 coral genera collected from 3 oceans, along with 277,653 question-answer pairs that comprehensively assess ecological and health-related conditions. To construct this dataset, we develop a semi-automatic data construction pipeline in collaboration with marine biologists to ensure both scalability and professional-grade data quality. CoralVQA presents novel challenges and provides a comprehensive benchmark for studying vision-language reasoning in the context of coral reef images. By evaluating several state-of-the-art LVLMs, we reveal key limitations and opportunities. These insights form a foundation for future LVLM development, with a particular emphasis on supporting coral conservation efforts.

Liwei Jiang, Yuanjun Chai, Margaret Li, Mickel Liu, Raymond Fok, Nouha Dziri, Yulia Tsvetkov, Maarten Sap, Yejin Choi

Large language models (LMs) often struggle to generate diverse, human-like creative content, raising concerns about the long-term homogenization of human thought through repeated exposure to similar outputs. Yet scalable methods for evaluating LM output diversity remain limited, especially beyond narrow tasks such as random number or name generation, or beyond repeated sampling from a single model. To address this gap, we introduce Infinity-Chat, a large-scale dataset of 26K diverse, real-world, open-ended user queries that admit a wide range of plausible answers with no single ground truth. We introduce the first comprehensive taxonomy for characterizing the full spectrum of open-ended prompts posed to LMs, comprising 6 top-level categories (e.g., creative content generation, brainstorm & ideation) that further breaks down to 17 subcategories. Using Infinity-Chat, we present a large-scale study of mode collapse in LMs, revealing a pronounced Artificial Hivemind effect in open-ended generation of LMs, characterized by (1) intra-model repetition, where a single model consistently generates similar responses, and more so (2) inter-model homogeneity, where different models produce strikingly similar outputs. Infinity-Chat also includes 31,250 human annotations, across absolute ratings and pairwise preferences, with 25 independent human annotations per example. This enables studying collective and individual-specific human preferences in response to open-ended queries. Our findings show that state-of-the-art LMs, reward models, and LM judges are less well calibrated to human ratings on model generations that elicit differing idiosyncratic annotator preferences, despite maintaining comparable overall quality. Overall, INFINITY-CHAT presents the first large-scale resource for systematically studying real-world open-ended queries to LMs, revealing critical insights to guide future research for mitigating long-term AI safety risks posed by the Artificial Hivemind.

Social Aspects · Accountability, Transparency and Interpretability

Alessandro Serra, Francesco Ortu, Emanuele Panizon, Lucrezia Valeriani, Lorenzo Basile, Alessio Ansuini, Diego Doimo, Alberto Cazzaniga

Recent advances in multimodal training have significantly improved the integration of image understanding and generation within a unified model. This study investigates how vision-language models (VLMs) handle image-understanding tasks, focusing on how visual information is processed and transferred to the textual domain. We compare *native multimodal VLMs*, models trained from scratch on multimodal data to generate both text and images, and *non-native multimodal VLMs*, models adapted from pre-trained large language models or capable of generating only text, highlighting key differences in information flow. We find that in native multimodal VLMs, image and text embeddings are more separated within the residual stream. Moreover, VLMs differ in how visual information reaches text: non-native multimodal VLMs exhibit a distributed communication pattern, where information is exchanged through multiple image tokens, whereas models trained natively for joint image and text generation tend to rely on a single post-image token that acts as a *narrow gate* for visual information. We show that ablating this single token significantly deteriorates image-understanding performance, whereas targeted, token-level interventions reliably steer image semantics and downstream text with fine-grained control.

Computer Vision · Everything Else

Zhenhao Zhang, Ye Shi, Lingxiao Yang, Suting Ni, Qi Ye, Jingya Wang

Understanding and synthesizing realistic 3D hand-object interactions (HOI) is critical for applications ranging from immersive AR/VR to dexterous robotics. Existing methods struggle with generalization, performing well on closed-set objects and predefined tasks but failing to handle unseen objects or open-vocabulary instructions. We introduce OpenHOI, the first framework for open-world HOI synthesis, capable of generating long-horizon manipulation sequences for novel objects guided by free-form language commands. Our approach integrates a 3D Multimodal Large Language Model (MLLM) fine-tuned for joint affordance grounding and semantic task decomposition, enabling precise localization of interaction regions (e.g., handles, buttons) and breakdown of complex instructions (e.g., “Find a water bottle and take a sip”) into executable sub-tasks. To synthesize physically plausible interactions, we propose an affordance-driven diffusion model paired with a training-free physics refinement stage that minimizes penetration and optimizes affordance alignment. Evaluations across diverse scenarios demonstrate OpenHOI’s superiority over state-of-the-art methods in generalizing to novel object categories, multi-stage tasks, and complex language instructions.

Applications · Language, Speech and Dialog

Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, Gao Huang

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs), particularly in mathematics and programming tasks. It is widely believed that, similar to how traditional RL helps agents to explore and learn new strategies, RLVR enables LLMs to continuously self-improve, thus acquiring novel reasoning abilities that exceed the capacity of the corresponding base models. In this study, we take a critical look at \textit{the current state of RLVR} by systematically probing the reasoning capability boundaries of RLVR-trained LLMs across diverse model families, RL algorithms, and math/coding/visual reasoning benchmarks, using pass@\textit{k} at large \textit{k} values as the evaluation metric. While RLVR improves sampling efficiency towards the correct path, we surprisingly find that current training does \emph{not} elicit fundamentally new reasoning patterns. We observe that while RLVR-trained models outperform their base models at smaller values of $k$ (\eg, $k$=1), base models achieve higher pass@$k$ score when $k$ is large. Moreover, we observe that the reasoning capability boundary of LLMs often narrows as RLVR training progresses. Further coverage and perplexity analysis shows that the reasoning paths generated by RLVR models are already included in the base models' sampling distribution, suggesting that their reasoning abilities originate from and are \textit{bounded} by the base model. From this perspective, treating the base model as an upper bound, our quantitative analysis shows that six popular RLVR algorithms perform similarly and remain far from optimal in fully leveraging the potential of the base model. In contrast, we find that distillation can introduce new reasoning patterns from the teacher and genuinely expand the model’s reasoning capabilities. Taken together, our findings suggest that current RLVR methods have not fully realized the potential of RL to elicit genuinely novel reasoning abilities in LLMs. This underscores the need for improved RL paradigms—such as continual scaling and multi-turn agent-environment interaction—to unlock this potential.

Steffen Schotthöfer, Lexie Yang, Stefan Schnake

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical low-rank training scheme enhanced with a novel spectral regularizer that controls the condition number of the low-rank core in each layer. This approach mitigates the sensitivity of compressed models to adversarial perturbations without sacrificing clean accuracy. The method is model- and data-agnostic, computationally efficient, and supports rank adaptivity to automatically compress the network at hand. Extensive experiments across standard architectures, datasets, and adversarial attacks show the regularized networks can achieve over 94 compression while recovering or improving adversarial accuracy relative to uncompressed baselines.

Deep Learning · Graph Neural Networks

Shuaicheng Zhang, Haohui Wang, Junhong Lin, Xiaojie Guo, Yada Zhu, Si Zhang, Dongqi Fu, Dawei Zhou

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for heterophilic graphs. However, we discover that the relationship between graph heterophily and spectral filters is more complex - the optimal filter response varies across frequency components and does not follow a strict monotonic correlation with heterophily degree. This finding challenges conventional fixed filter designs and suggests the need for adaptive filtering to preserve expressiveness in graph embeddings. Formally, natural questions arise: Given a heterophilic graph $\mathcal{G}$ , how and to what extent will the varying heterophily degree of $\mathcal{G}$ affect the performance of GNNs? How can we design adaptive filters to fit those varying heterophilic connections? Our theoretical analysis reveals that the average frequency response of GNNs and graph heterophily degree do not follow a strict monotonic correlation, necessitating adaptive graph filters to guarantee good generalization performance. Hence, we propose HeroFilter, a simple yet powerful GNN, which extracts information across the heterophily spectrum and combines salient representations through adaptive mixing. HeroFilter's superior performance achieves up to 9.2% accuracy improvement over leading baselines across homophilic and heterophilic graphs.

Zhenting Qi, Fan Nie, Alexandre Alahi, James Zou, Himabindu Lakkaraju, Yilun Du, Eric Xing, Sham Kakade, Hanlin Zhang

Modern language model (LM) training has been divided into multiple stages, making it difficult for downstream developers to evaluate the impact of design choices made at each stage. We present EvoLM, a model suite that enables systematic and transparent analysis of LMs' training dynamics across pre-training, continued pre-training, supervised fine-tuning, and reinforcement learning. By training over 100 LMs with 1B and 4B parameters from scratch, we rigorously evaluate both upstream (language modeling) and downstream (problem-solving) reasoning capabilities, including considerations of both in-domain and out-of-domain generalization. Key insights highlight the diminishing returns from excessive pre-training and post-training, the importance and practices of mitigating forgetting during domain-specific continued pre-training, the crucial role of continued pre-training in bridging pre-training and post-training phases, and various intricate trade-offs when configuring supervised fine-tuning and reinforcement learning. To facilitate open research and reproducibility, we release all pre-trained and post-trained models, training datasets for all stages, and our entire training and evaluation pipeline.

Computer Vision · Everything Else

Jiahui Wang, Haiyue Zhu, Haoren Guo, Abdullah Al Mamun, Cheng Xiang, Tong Heng LEE

Recent 6D pose estimation methods demonstrate notable performance but still face some practical limitations. For instance, many of them rely heavily on sensor depth, which may fail with challenging surface conditions, such as transparent or highly reflective materials. In the meantime, RGB-based solutions provide less robust matching performance in low-light and texture-less scenes due to the lack of geometry information. Motivated by these, we propose **SingRef6D**, a lightweight pipeline requiring only a **single RGB** image as a reference, eliminating the need for costly depth sensors, multi-view image acquisition, or training view synthesis models and neural fields. This enables SingRef6D to remain robust and capable even under resource-limited settings where depth or dense templates are unavailable. Our framework incorporates two key innovations. First, we propose a token-scaler-based fine-tuning mechanism with a novel optimization loss on top of Depth-Anything v2 to enhance its ability to predict accurate depth, even for challenging surfaces. Our results show a 14.41% improvement (in $\delta_{1.05}$) on REAL275 depth prediction compared to Depth-Anything v2 (with fine-tuned head). Second, benefiting from depth availability, we introduce a depth-aware matching process that effectively integrates spatial relationships within LoFTR, enabling our system to handle matching for challenging materials and lighting conditions. Evaluations of pose estimation on the REAL275, ClearPose, and Toyota-Light datasets show that our approach surpasses state-of-the-art methods, achieving a 6.1% improvement in average recall.

Tony Bonnaire, Raphaël Urfin, Giulio Biroli, Marc Mezard

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time $\tau_\mathrm{gen}$ at which models begin to generate high-quality samples, and a later time $\tau_\mathrm{mem}$ beyond which memorization emerges. Crucially, we find that $\tau_\mathrm{mem}$ increases linearly with the training set size $n$, while $\tau_\mathrm{gen}$ remains constant. This creates a growing window of training times with $n$ where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when $n$ becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Phuc Tran, Van Vu, Nisheeth K. Vishnoi

A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank approximation, where one aims to preserve the top-$p$ structure of a data-derived matrix while ensuring privacy. Prior work often analyzes Frobenius norm error or changes in reconstruction quality, but these metrics can over- or under-estimate true subspace distortion. The spectral norm, by contrast, captures worst-case directional error and provides the strongest utility guarantees. We establish new high-probability spectral-norm perturbation bounds for symmetric matrices that refine the classical Eckart--Young--Mirsky theorem and explicitly capture interactions between a matrix $A \in \mathbb{R}^{n \times n}$ and an arbitrary symmetric perturbation $E$. Under mild eigengap and norm conditions, our bounds yield sharp estimates for $\| (A + E)_p - A_p \|$, where $A_p$ is the best rank-$p$ approximation of $A$, with improvements of up to a factor of $\sqrt{n}$. As an application, we derive improved utility guarantees for differentially private PCA, resolving an open problem in the literature. Our analysis relies on a novel contour bootstrapping method from complex analysis and extends it to a broad class of spectral functionals, including polynomials and matrix exponentials. Empirical results on real-world datasets confirm that our bounds closely track the actual spectral error under diverse perturbation regimes.