NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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5,812篇论文

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主题: 应用 · chemistry physics and earth sciences · 455 篇论文 · 重置筛选

Quantifying and Alleviating Co-Adaptation in Sparse-View 3D Gaussian Splatting

Kangjie Chen, Yingji Zhong, Zhihao Li, Jiaqi Lin, Youyu Chen, Minghan Qin, Haoqian Wang

展开摘要

3D Gaussian Splatting (3DGS) has demonstrated impressive performance in novel view synthesis under dense-view settings. However, in sparse-view scenarios, despite the realistic renderings in training views, 3DGS occasionally manifests appearance artifacts in novel views. This paper investigates the appearance artifacts in sparse-view 3DGS and uncovers a core limitation of current approaches: the optimized Gaussians are overly-entangled with one another to aggressively fit the training views, which leads to a neglect of the real appearance distribution of the underlying scene and results in appearance artifacts in novel views. The analysis is based on a proposed metric, termed Co-Adaptation Score (CA), which quantifies the entanglement among Gaussians, i.e., co-adaptation, by computing the pixel-wise variance across multiple renderings of the same viewpoint, with different random subsets of Gaussians. The analysis reveals that the degree of co-adaptation is naturally alleviated as the number of training views increases. Based on the analysis, we propose two lightweight strategies to explicitly mitigate the co-adaptation in sparse-view 3DGS: (1) random gaussian dropout; (2) multiplicative noise injection to the opacity. Both strategies are designed to be plug-and-play, and their effectiveness is validated across various methods and benchmarks. We hope that our insights into the co-adaptation effect will inspire the community to achieve a more comprehensive understanding of sparse-view 3DGS.

Poster
Stitch and Tell: A Structured Data Augmentation Method for Spatial Understanding

Hang Yin, Xiaomin He, Peiwen Yuan, Yiwei Li, Jiayi Shi, Wenxiao Fan, Shaoxiong Feng, Kan Li

展开摘要

Existing vision-language models often suffer from spatial hallucinations, i.e., generating incorrect descriptions about the relative positions of objects in an image. We argue that this problem mainly stems from the asymmetric properties between images and text. To enrich the spatial understanding ability of vision-language models, we propose a simple, annotation-free, plug-and-play method named Stitch and Tell (abbreviated as SiTe), which injects structured spatial supervision into multimodal data. It constructs stitched image–text pairs by stitching images along a spatial axis and generating spatially-aware captions or question answer pairs based on the layout of stitched image, without relying on costly advanced models or human involvement. We evaluate SiTe across three architectures including LLaVA-v1.5-7B, LLaVA-Qwen2-1.5B and HALVA-7B, two training datasets, and thirteen benchmarks. Experiments show that SiTe improves spatial understanding tasks such as $\text{MME}_{\text{Position}}$ (+5.50\%) and Spatial-MM (+4.19\%), while maintaining or improving performance on general vision-language benchmarks. Our findings suggest that explicitly injecting spatially-aware structure into training data offers an effective way to mitigate spatial hallucinations and improve spatial understanding, while preserving general vision-language capabilities.

Poster
Interpreting Emergent Features in Deep Learning-based Side-channel Analysis

Sengim Karayalcin, Marina Krček, Stjepan Picek

展开摘要

Side-channel analysis (SCA) poses a real-world threat by exploiting unintentional physical signals to extract secret information from secure devices. Evaluation labs also use the same techniques to certify device security. In recent years, deep learning has emerged as a prominent method for SCA, achieving state-of-the-art attack performance at the cost of interpretability. Understanding how neural networks extract secrets is crucial for security evaluators aiming to defend against such attacks, as only by understanding the attack can one propose better countermeasures. In this work, we apply mechanistic interpretability to neural networks trained for SCA, revealing $\textit{how}$ models exploit $\textit{what}$ leakage in side-channel traces. We focus on sudden jumps in performance to reverse engineer learned representations, ultimately recovering secret masks and moving the evaluation process from black-box to white-box. Our results show that mechanistic interpretability can scale to realistic SCA settings, even when relevant inputs are sparse, model accuracies are low, and side-channel protections prevent standard input interventions.

Poster
Understanding Softmax Attention Layers:\\ Exact Mean-Field Analysis on a Toy Problem

Elvis Dohmatob

展开摘要

Self-attention has emerged as a fundamental component driving the success of modern transformer architectures, which power large language models and various applications. However, a theoretical understanding of how such models actually work is still under active development. The recent work of (Marion et al., 2025) introduced the so-called "single-location regression" problem, which can provably be solved by a simplified self-attention layer but not by linear models, thereby demonstrating a striking functional separation. A rigorous analysis of self-attention with softmax for this problem is challenging due to the coupled nature of the model. In the present work, we use ideas from the classical random energy model in statistical physics to analyze softmax self-attention on the single-location problem. Our analysis yields exact analytic expressions for the population risk in terms of the overlaps between the learned model parameters and those of an oracle. Moreover, we derive a detailed description of the gradient descent dynamics for these overlaps and prove that, under broad conditions, the dynamics converge to the unique oracle attractor. Our work not only advances our understanding of self-attention but also provides key theoretical ideas that are likely to find use in further analyses of even more complex transformer architectures.

Poster
TIDMAD: Time Series Dataset for Discovering Dark Matter with AI Denoising

J. T. Fry, Xinyi Hope Fu, Zhenghao Fu, Kaliroë Mabelle West Pappas, Lindley Winslow, Aobo Li

展开摘要

Dark matter makes up approximately 85\% of total matter in our universe, yet it has never been directly observed in any laboratory on Earth. The origin of dark matter is one of the most important questions in contemporary physics, and a convincing detection of dark matter would be a Nobel-Prize-level breakthrough in fundamental science. The ABRACADABRA experiment was specifically designed to search for dark matter. Although it has not yet made a discovery, ABRACADABRA has produced several dark matter search results widely endorsed by the physics community. The experiment generates ultra-long time-series data at a rate of 10 million samples per second, where the dark matter signal would manifest itself as a sinusoidal oscillation mode within the ultra-long time series. In this paper, we present the TIDMAD --- a comprehensive data release from the ABRACADABRA experiment including three key components: an ultra-long time series dataset divided into training, validation, and science subsets; a carefully-designed denoising score for direct model benchmarking; and a complete analysis framework which produces a physics community-standard dark matter search result suitable for publication as a physics paper. This data release enables core AI algorithms to extract the dark matter signal and produce real physics results thereby advancing fundamental science.

Spotlight
Improving Generative Behavior Cloning via Self-Guidance and Adaptive Chunking

Junhyuk So, Chiwoong Lee, Shinyoung Lee, Jungseul Ok, Eunhyeok Park

展开摘要

Generative Behavior Cloning (GBC) is a simple yet effective framework for robot learning, particularly in multi-task settings. Recent GBC methods often employ diffusion policies with open-loop (OL) control, where actions are generated via a diffusion process and executed in multi-step chunks without replanning. While this approach has demonstrated strong success rates and generalization, its inherent stochasticity can result in erroneous action sampling, occasionally leading to unexpected task failures. Moreover, OL control suffers from delayed responses, which can degrade performance in noisy or dynamic environments. To address these limitations, we propose two novel techniques to enhance the consistency and reactivity of diffusion policies: (1) self-guidance, which improves action fidelity by leveraging past observations and implicitly promoting future-aware behavior; and (2) adaptive chunking, which selectively updates action sequences when the benefits of reactivity outweigh the need for temporal consistency. Extensive experiments show that our approach substantially improves GBC performance across a wide range of simulated and real-world robotic manipulation tasks.

Poster
DrivAerStar: An Industrial-Grade CFD Dataset for Vehicle Aerodynamic Optimization

Jiyan Qiu, Lyulin Kuang, Guan Wang, Yichen Xu, Leiyao Cui, Shaotong Fu, Yixin Zhu, Ruihua Zhang

展开摘要

Vehicle aerodynamics optimization has become critical for automotive electrification, where drag reduction directly determines electric vehicle range and energy efficiency. Traditional approaches face an intractable trade-off: computationally expensive Computational Fluid Dynamics (CFD) simulations requiring weeks per design iteration, or simplified models that sacrifice production-grade accuracy. While machine learning offers transformative potential, existing datasets exhibit fundamental limitations -- inadequate mesh resolution, missing vehicle components, and validation errors exceeding 5% -- preventing deployment in industrial workflows. We present DrivAerStar, comprising 12,000 industrial-grade automotive CFD simulations generated using STAR-CCM+${}^{\textregistered}$ software. The dataset systematically explores three vehicle configurations through 20 Computer Aided Design (CAD) parameters via Free Form Deformation (FFD) algorithms, including complete engine compartments and cooling systems with realistic internal airflow. DrivAerStar achieves wind tunnel validation accuracy below 1.04% -- a five-fold improvement over existing datasets -- through refined mesh strategies with strict wall $y^+$ control. Benchmarks demonstrate that models trained on this data achieve production-ready accuracy while reducing computational costs from weeks to minutes. This represents the first dataset bridging academic machine learning research and industrial CFD practice, establishing a new standard for data-driven aerodynamic optimization in automotive development. Beyond automotive applications, DrivAerStar demonstrates a paradigm for integrating high-fidelity physics simulations with Artificial Intelligence (AI) across engineering disciplines where computational constraints currently limit innovation.

Poster
Mesh Interpolation Graph Network for Dynamic and Spatially Irregular Global Weather Forecasting

Zinan Zheng, Yang Liu, Jia Li

展开摘要

Graph neural networks have shown promising results in weather forecasting, which is critical for human activity such as agriculture planning and extreme weather preparation. However, most studies focus on finite and local areas for training, overlooking the influence of broader areas and limiting their ability to generalize effectively. Thus, in this work, we study global weather forecasting that is irregularly distributed and dynamically varying in practice, requiring the model to generalize to unobserved locations. To address such challenges, we propose a general Mesh Interpolation Graph Network (MIGN) that models the irregular weather station forecasting, consisting of two key designs: (1) learning spatially irregular data with regular mesh interpolation network to align the data; (2) leveraging parametric spherical harmonics location embedding to further enhance spatial generalization ability. Extensive experiments on an up-to-date observation dataset show that MIGN significantly outperforms existing data-driven models. Besides, we show that MIGN has spatial generalization ability, and is capable of generalizing to previously unseen stations.

Poster
Optimized Minimal 3D Gaussian Splatting

Joo Chan Lee, Jong Hwan Ko, Eunbyung Park

展开摘要

3D Gaussian Splatting (3DGS) has emerged as a powerful representation for real-time, high-performance rendering, enabling a wide range of applications. However, representing 3D scenes with numerous explicit Gaussian primitives imposes significant storage and memory overhead. Recent studies have shown that high-quality rendering can be achieved with a substantially reduced number of Gaussians when represented with high-precision attributes. Nevertheless, existing 3DGS compression methods still rely on a relatively large number of Gaussians, focusing primarily on attribute compression. This is because a smaller set of Gaussians becomes increasingly sensitive to lossy attribute compression, leading to severe quality degradation. Since the number of Gaussians is directly tied to computational costs, it is essential to reduce the number of Gaussians effectively rather than only optimizing storage. In this paper, we propose Optimized Minimal Gaussians representation (OMG), which significantly reduces storage while using a minimal number of primitives. First, we determine the distinct Gaussian from the near ones, minimizing redundancy without sacrificing quality. Second, we propose a compact and precise attribute representation that efficiently captures both continuity and irregularity among primitives. Additionally, we propose a sub-vector quantization technique for improved irregularity representation, maintaining fast training with a negligible codebook size. Extensive experiments demonstrate that OMG reduces storage requirements by nearly 50% compared to the previous state-of-the-art and enables 600+ FPS rendering while maintaining high rendering quality. Our source code is available at https://maincold2.github.io/omg/.

Poster
FlowRefiner: A Robust Traffic Classification Framework against Label Noise

Mingwei Zhan, Ruijie Zhao, Xianwen Deng, Zhi Xue, Qi Li, Zhuotao Liu, Guang Cheng, Ke Xu

展开摘要

Network traffic classification is essential for network management and security. In recent years, deep learning (DL) algorithms have emerged as essential tools for classifying complex traffic. However, they rely heavily on high-quality labeled training data. In practice, traffic data is often noisy due to human error or inaccurate automated labeling, which could render classification unreliable and lead to severe consequences. Although some studies have alleviated the label noise issue in specific scenarios, they are difficult to generalize to general traffic classification tasks due to the inherent semantic complexity of traffic data. In this paper, we propose FlowRefiner, a robust and general traffic classification framework against label noise. FlowRefiner consists of three core components: a traffic semantics-driven noise detector, a confidence-guided label correction mechanism, and a cross-granularity robust classifier. First, the noise detector utilizes traffic semantics extracted from a pre-trained encoder to identify mislabeled flows. Next, the confidence-guided label correction module fine-tunes a label predictor to correct noisy labels and construct refined flows. Finally, the cross-granularity robust classifier learns generalized patterns of both flow-level and packet-level, improving classification robustness against noisy labels. We evaluate our method on four traffic datasets with various classification scenarios across varying noise ratios. Experimental results demonstrate that FlowRefiner mitigates the impact of label noise and consistently outperforms state-of-the-art baselines by a large margin. The code is available at https://github.com/NSSL-SJTU/FlowRefiner.

Poster
List-Level Distribution Coupling with Applications to Speculative Decoding and Lossy Compression

Joseph Rowan, Buu Phan, Ashish J Khisti

展开摘要

We study a relaxation of the problem of coupling probability distributions — a list of samples is generated from one distribution and an *accept* is declared if any one of these samples is identical to the sample generated from the other distribution. We propose a novel method for generating samples, which extends the Gumbel-max sampling suggested in Daliri et al. (2025) for coupling probability distributions. We also establish a corresponding lower bound on the acceptance probability, which we call the \emph{list matching lemma}. We next discuss two applications of our setup. First, we develop a new mechanism for multi-draft speculative sampling that is simple to implement and achieves performance competitive with baselines such as SpecTr and SpecInfer across a range of language tasks. Our method also guarantees a certain degree of *drafter invariance* with respect to the output tokens which is not supported by existing schemes. We also provide a theoretical lower bound on the token level acceptance probability. As our second application, we consider distributed lossy compression with side information in a setting where a source sample is compressed and available to multiple decoders, each with independent side information. We propose a compression technique that is based on our generalization of Gumbel-max sampling and show that it provides significant gains in experiments involving synthetic Gaussian sources and the MNIST image dataset.

Poster
ProteinConformers: Benchmark Dataset for Simulating Protein Conformational Landscape Diversity and Plausibility

Yihang Zhou, Chen Wei, Minghao Sun, Jin Song, Yang Li, Lin Wang, Yang Zhang

展开摘要

Understanding the conformational landscape of proteins is essential for elucidating protein function and facilitating drug design. However, existing protein conformation benchmarks fail to capture the full energy landscape, limiting their ability to evaluate the diversity and physical plausibility of AI-generated structures. We introduce ProteinConformers, a large-scale benchmark dataset comprising over 381,000 physically realistic conformations for 87 CASP targets. These were derived from more than 40,000 structural decoys via extensive all-atom molecular dynamics simulations totaling over 6 million CPU hours. Using this dataset, we propose novel metrics to evaluate conformational diversity and plausibility, and systematically benchmark six protein conformation generative models. Our results highlight that leveraging large-scale protein sequence data can enhance a model’s ability to explore conformational space, potentially reducing reliance on MD-derived data. Additionally, we find that PDB and MD datasets influence model performance differently, current models perform well on inter-atomic distance prediction but struggle with inter-residue orientation generation. Overall, our dataset, evaluation metrics, and benchmarking results provide the first comprehensive foundation for assessing generative models in protein conformational modeling. Dataset and instructions are available at https://huggingface.co/ datasets/Jim990908/ProteinConformers/tree/main. Codes are stored at https://github.com/auroua/ProteinConformers. An interactive website locates at https://zhanggroup.org/ProteinConformers.

Poster
UEPI: Universal Energy-Behavior-Preserving Integrators for Energy Conservative/Dissipative Differential Equations

Elena Celledoni, Brynjulf Owren, Chong Shen, Baige Xu, Takaharu Yaguchi

展开摘要

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory. It is known that physical phenomena based on these theories have an energy conservation law or a dissipation law. Therefore, in the simulations of such physical phenomena, numerical methods that preserve the energy-conservation or dissipation laws are desirable. However, because various energy-behavior-preserving numerical methods have been proposed, it is difficult to discover the best one. In this study, we propose a method for learning highly accurate energy-behavior-preserving integrators from data. Numerical results show that our approach certainly learns energy-behavior-preserving numerical methods that are more accurate than existing numerical methods for various differential equations, including chaotic Hamiltonian systems, dissipative systems, and a nonlinear partial differential equation. We also provide universal approximation theorems for the proposed approach.

Poster
Don’t Give Up on Democratizing AI for the Wrong Reasons

Annette Zimmermann, Andrew Zeppa, Srijan Pandey, Kenneth Diao

展开摘要

The claim that the AI community, or society at large, should ‘democratize AI’ has attracted considerable critical attention and controversy. Two core problems have arisen and remain unsolved: conceptual disagreement persists about what democratizing AI means; normative disagreement persists over whether democratizing AI is ethically and politically desirable. We identify eight common AI democratization traps: democratization-skeptical arguments that seem plausible at first glance, but turn out to be misconceptions. We develop arguments about how to resist each trap. We conclude that, while AI democratization may well have drawbacks, we should be cautious about dismissing AI democratization prematurely and for the wrong reasons. We offer a constructive roadmap for developing alternative conceptual and normative approaches to democratizing AI that successfully avoid the traps.

Poster
Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis

Yicong Jiang, Tracy Ke

展开摘要

Vertex hunting (VH) is the task of estimating a simplex from noisy data points and has many applications in areas such as network and text analysis. We introduce a new variant, semi-supervised vertex hunting (SSVH), in which partial information is available in the form of barycentric coordinates for some data points, known only up to an unknown transformation. To address this problem, we develop a method that leverages properties of orthogonal projection matrices, drawing on novel insights from linear algebra. We establish theoretical error bounds for our method and demonstrate that it achieves a faster convergence rate than existing unsupervised VH algorithms. Finally, we apply SSVH to two practical settings---semi-supervised network mixed membership estimation and semi-supervised topic modeling---resulting in efficient and scalable algorithms.

Poster
BoltzNCE: Learning likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation

Rishal Aggarwal, Jacky Chen, Nicholas Matthew Boffi, David Koes

展开摘要

Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to transform a simple prior into a distribution that can be reweighted to match the target using sample likelihoods. Despite the elegance of this approach, obtaining these likelihoods requires computing costly Jacobians during integration, which is impractical for large molecular systems. To overcome this difficulty, we train an energy-based model (EBM) to approximate likelihoods using both noise contrastive estimation (NCE) and score matching, which we show outperforms the use of either objective in isolation. On 2D synthetic systems where failure can be easily visualized, NCE improves mode weighting relative to score matching alone. On alanine dipeptide, our method yields free energy profiles and energy distributions that closely match those obtained using exact likelihoods while achieving $100\times$ faster inference. By training on multiple dipeptide systems, we show that our approach also exhibits effective transfer learning, generalizing to new systems at inference time and achieving at least a $6\times$ speedup over standard MD with only a bit of fine-tuning. While many recent efforts in generative modeling have prioritized models with fast sampling, our work demonstrates the design of models with accelerated likelihoods, enabling the application of reweighting schemes that ensure unbiased Boltzmann statistics at scale. Our code is available at https://github.com/RishalAggarwal/BoltzNCE.

Poster
Unifying Symbolic Music Arrangement: Track-Aware Reconstruction and Structured Tokenization

Longshen Ou, jingwei zhao, Ziyu Wang, Gus Xia, Qihao Liang, Torin Hopkins, Ye Wang

展开摘要

We present a unified framework for automatic multitrack music arrangement that enables a single pre-trained symbolic music model to handle diverse arrangement scenarios, including reinterpretation, simplification, and additive generation. At its core is a segment-level reconstruction objective operating on token-level disentangled content and style, allowing for flexible any-to-any instrumentation transformations at inference time. To support track-wise modeling, we introduce REMI-z, a structured tokenization scheme for multitrack symbolic music that enhances modeling efficiency and effectiveness for both arrangement tasks and unconditional generation. Our method outperforms task-specific state-of-the-art models on representative tasks in different arrangement scenarios---band arrangement, piano reduction, and drum arrangement, in both objective metrics and perceptual evaluations. Taken together, our framework demonstrates strong generality and suggests broader applicability in symbolic music-to-music transformation.

Poster
Thompson Sampling in Function Spaces via Neural Operators

Rafael Oliveira, Xuesong Wang, Kian Ming A. Chai, Edwin V. Bonilla

展开摘要

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Poster
FAIR Universe HiggsML Uncertainty Dataset and Competition

Wahid Bhimji, Ragansu Chakkappai, Po-Wen Chang, Yuan-Tang Chou, Sascha Diefenbacher, Jordan Dudley, Ibrahim Elsharkawy, Steven Farrell, Aishik Ghosh, Cristina Giordano, Isabelle Guyon, Chris Harris, Yota Hashizume, Shih-Chieh Hsu, Elham E Khoda, Claudius Krause, Ang Li, Benjamin Nachman, David Rousseau, Robert Schöfbeck, Maryam Shooshtari, Dennis Schwarz, Ihsan Ullah, Daohan Wang, Yulei Zhang

展开摘要

The FAIR Universe – HiggsML Uncertainty Challenge focused on measuring the physical properties of elementary particles with imperfect simulators. Participants were required to compute and report confidence intervals for a parameter of interest regarding the Higgs boson while accounting for various systematic (epistemic) uncertainties. The dataset is a tabular dataset of 28 features and 280 million instances. Each instance represents a simulated proton-proton collision as observed at CERN’s Large Hadron Collider in Geneva, Switzerland. The features of these simulations were chosen to capture key characteristics of different types of particles. These include primary attributes, such as the energy and three-dimensional momentum of the particles, as well as derived attributes, which are calculated from the primary ones using domain-specific knowledge. Additionally, a label feature designates each instance’s type of proton-proton collision, distinguishing the Higgs boson events of interest from three background sources. As outlined in this paper, the permanent dataset release allows long-term benchmarking of new techniques. The leading submissions, including Contrastive Normalising Flows and Density Ratios estimation through classification, are described. Our challenge has brought together the physics and machine learning communities to advance our understanding and methodologies in handling systematic uncertainties within AI techniques.

Poster
Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacy

Phuc Tran, Van Vu, Nisheeth K. Vishnoi

展开摘要

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.

Oral