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2,245篇论文匹配“Statistical Methods”
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Social Aspects · Privacy

Quentin Sinh, Jan Ramon

We study the problem of computing a U-statistic with a kernel function $f$ of degree $k \geq 2$, i.e., the average of some function $f$ over all $k$-tuples of instances, in a federated learning setting. U-statistics of degree $2$ include several useful statistics such as Kendall's $\tau$ coefficient, the Area under the Receiver-Operator Curve and the Gini mean difference. Existing methods provide solutions only under the lower-utility local differential privacy model and/or scale poorly in the size of the domain discretization. In this work, we propose a protocol that securely computes U-statistics of degree $k \geq 2$ under central differential privacy by leveraging Multi Party Computation (MPC). Our method substantially improves accuracy when compared to prior solutions. We provide a detailed theoretical analysis of its accuracy, communication and computational properties. We evaluate its performance empirically, obtaining favorable results, e.g., for Kendall's $\tau$ coefficient, our approach reduces the Mean Squared Error by up to four orders of magnitude over existing baselines.

Probabilistic Methods · Everything Else

Daniel Csillag, Pedro Dall’Antonia, Claudio Struchiner, Guilherme Tegoni Goedert

Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.

Reinforcement Learning · Everything Else

Zhijian Zhou, Long Li, Xuan Zhang, Zongkai Liu, Yanting Miao, Yuchen Liu, Deshu Chen, Ke Li, Xing Sun, Ruoxi Jiang 等

Reinforcement Learning (RL) has become a cornerstone for enhancing the reasoning capabilities of Large Language Models (LLMs). However, standard actor-critic methods, such as PPO, rely on scalar value functions that estimate only the expectation of cumulative returns. This reduction inherently discards higher-order statistical information (e.g., variance and multimodality), leading to inaccurate value estimation and suboptimal credit assignment in complex tasks. While Distributional RL offers a solution by modeling the full return distribution, its application to LLMs remains challenging due to the computational intractability of value-based operations over large vocabularies and the instability and memory burden of off-policy replay mechanisms. In this paper, we propose DisPPO, a novel on-policy framework that seamlessly integrates non-parametric quantile regression into PPO. Theoretically, we prove that our distributional update operator---composed of the $\lambda$-return Bellman operator and quantile projection---is a contraction mapping in the Wasserstein metric, guaranteeing convergence to a unique fixed point. Empirically, we evaluate DisPPO using Llama and Qwen models across diverse benchmarks, including mathematical reasoning and Text-to-SQL generation. DisPPO consistently outperforms standard PPO and recent group-based baselines in both Pass@1 and Pass@$k$ metrics, demonstrating that distributional critics provide a richer, more robust learning signal for large-scale reasoning models.

General Machine Learning · Transfer, Multitask and Meta-learning

Hongwei Yan, Kanglei Zhou, Yuchen Liu, Qingyu Shi, Yi Zhong, Liyuan Wang

Perception for embodied agents is video-based, often multi-view (ego, exo, or both), and inherently continual, with simultaneous task and viewpoint shifts. Yet continual learning (CL) remains dominated by exo-only recognition tasks, obscuring behavior under these real-world coupled shifts. We introduce **C**ontinual **E**go, **E**xo, and **E**go-**E**xo **L**earning (**CE$^4$L**), a unified multi-view CL benchmark spanning four representative tasks: cross-view referenced skill assessment, temporal action segmentation, cross-view association, and action anticipation \& planning. CE$^4$L highlights challenges largely absent in prior CL benchmarks, including cross-view correspondence, view-dependent asynchrony, and heterogeneous semantic objectives. To this end, we propose **V**ideo **I**ncremental **S**ubspace-routed **T**ask **A**dapters (**VISTA**), a parameter-efficient baseline method that stores task-specific updates in lightweight adapters and performs training-free routing via residual distance to task-specific whitened subspaces estimated from second-order statistics. Extensive experiments demonstrate the significantly varied efficacy of representative CL methods across CE$^4$L settings, while VISTA is consistently competitive and achieves state-of-the-art overall performance.

General Machine Learning · Causality

Yunfeng Wang, Zhiheng Zhang, Zijun Gao

Partial identification provides informative causal guarantees when point identification is impossible, but existing approaches based on optimal transport (OT) become computationally and statistically intractable in high-dimensional settings. This limitation is particularly severe when both potential outcomes and confounders are high-dimensional, where classical OT-based bounds suffer from the curse of dimensionality and unfavorable convergence rates. To address this challenge, we propose a novel estimator that decomposes the transport problem into a low-dimensional signal subspace and a high-dimensional residual subspace. Unlike existing projection-based methods that discard residual information, we recover the residual transport energy using the Sliced Wasserstein distance, which is computationally efficient and robust to high dimensions. We establish interpretable conditions controlling the approximation gap based on residual structure and provide a data-driven rule for signal dimension selection. Empirical results show that our estimator consistently outperforms projection-only baselines by recovering lost transport energy, yielding more informative causal bounds while remaining computationally tractable in high dimensions.

Deep Learning · Large Language Models

Jieming Bian, Lei Wang, Letian Zhang, Jie Xu

Federated Learning (FL) with Low-Rank Adaptation (LoRA) has become a standard for privacy-preserving LLM fine-tuning. However, existing personalized methods predominantly operated under a restrictive Flat-Model Assumption: they addressed client-side *statistical heterogeneity* but treated the model as a monolithic block, ignoring the *functional heterogeneity* across LLM layers. We argue that these two statistical (horizontal) and functional (vertical) dimensions, are *orthogonal in source yet coupled in interaction*, implying that the optimal depth of parameter sharing is functionally dependent on client similarity. To address this, we propose **FedTreeLoRA**, a framework employing tree-structured aggregation for fine-grained, layer-wise alignment. By dynamically constructing an aggregation hierarchy, FedTreeLoRA allows clients to share broad consensus on shallow ’trunks‘ while progressively specializing on deep ‘branches'. Experiments on NLU and NLG benchmarks demonstrate that FedTreeLoRA significantly outperforms state-of-the-art methods by effectively reconciling generalization and personalization.

General Machine Learning · Causality

Bo Peng, Sirui Chen, Jiaguo Tian, Yu Qiao, Chaochao Lu

Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge, we present CauScale, a neural architecture designed for efficient causal discovery that scales inference to graphs with up to 1000 nodes. CauScale improves time efficiency via a reduction unit that compresses data embeddings and improves space efficiency by adopting tied attention weights to avoid maintaining axis-specific attention maps. To keep high causal discovery accuracy, CauScale adopts a two-stream design: a data stream extracts relational evidence from high-dimensional observations, while a graph stream integrates statistical graph priors and preserves key structural signals. CauScale successfully scales to 500-node graphs during training, where prior work fails due to space limitations. Across testing data with varying graph scales and causal mechanisms, \sys achieves 99.6\% mAP on in-distribution data and 84.4\% on out-of-distribution data, while delivering 4$\times$–13,000$\times$ inference speedups over prior methods.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Nikita Kalinin, Ryan McKenna, Jalaj Upadhyay, Christoph Lampert

Matrix factorization mechanisms for differentially private training have emerged as a promising approach to improve model utility under privacy constraints. In practical settings, models are typically trained over multiple epochs, requiring matrix factorizations that account for repeated participation. Existing theoretical upper and lower bounds on multi-epoch factorization error leave a significant gap. In this work, we introduce a new explicit factorization method, Banded Inverse Square Root (BISR), which imposes a banded structure on the inverse correlation matrix. This factorization enables us to derive an explicit and tight characterization of the multi-epoch error. We further prove that BISR achieves asymptotically optimal error by matching the upper and lower bounds. Empirically, BISR performs on par with the state of the art factorization methods, while being simpler to implement, computationally efficient, and easier to analyze.

Deep Learning · Algorithms

Xing Hu, Dawei Yang, Yuan Cheng, Zhixuan Chen, Zukang Xu

The rapid growth in the parameter scale of large language models (LLMs) has created a high demand for efficient compression techniques. As a hardware-agnostic and highly compatible technique, low-rank compression has been widely adopted. However, existing methods typically compress each layer independently by minimizing per-layer reconstruction error, overlooking a critical limitation: the reconstruction error propagates and accumulates through the network, which leads to amplified global deviations from the full-precision baseline. To address this, we propose **Self-Adaptive Error Suppression SVD (SAES-SVD)**, a LLMs compression framework that jointly optimizes intra-layer reconstruction and inter-layer error compensation. SAES-SVD is composed of two novel components: **Cumulative Error-Aware Layer Compression (CEALC),** which formulates the compression objective as a combination of local reconstruction and weighted cumulative error compensation. Based on it, we derive a closed-form low-rank solution relied on second-order activation statistics, which explicitly aligns each layer's output with its full-precision counterpart to compensate for accumulated errors. \ding{183} Adaptive Collaborative Error Suppression (ACES), which automatically adjusts the weighting coefficient to enhance the low-rank structure of the compression objective in CELAC. Specifically, the coefficient is optimized to maximize the ratio between the Frobenius norm of the compressed layer's output and that of the compression objective under a fixed rank, thus ensuring that the rank budget is utilized effectively. Extensive experiments across multiple LLM architectures and tasks show that, without fine-tuning or additional tricks, SAES-SVD consistently improves post-compression performance. For example, at a 0.2 compression ratio on LLaMA-7B, existing methods exhibit an average accuracy drop exceeding 0.05, whereas SAES-SVD restricts the drop to only 0.02. These improvements underscore the potential of SAES-SVD to effectively narrow the gap between compressed models and their full-precision counterparts, paving the way for more reliable compression of LLMs.

Computer Vision · Everything Else

Jungu Cho, Seong Jong Ha, Hae-Gon Jeon

Video scene segmentation aims to detect semantically coherent boundaries in long-form videos, bridging the gap between low-level visual signals and high-level narrative understanding. However, existing methods primarily rely on visual similarity between adjacent shots, which makes it difficult to accurately identify scene boundaries, especially when semantic transitions do not align with visual changes. In this paper, we propose a novel approach that incorporates production-level metadata, specifically genre conventions and shot duration patterns, into video scene segmentation. Our main contributions are three-fold: (1) we leverage textual genre definitions as semantic priors to guide shot-level representation learning during self-supervised pretraining, enabling better capture of narrative coherence; (2) we introduce a duration-aware anchor selection strategy that prioritizes shorter shots based on empirical duration statistics, improving pseudo-boundary generation quality; (3) we propose a test-time shot splitting strategy that subdivides long shots into segments for improved temporal modeling. Experimental results demonstrate state-of-the-art performance on MovieNet-SSeg and BBC datasets. We introduce MovieChat-SSeg, extending MovieChat-1K with manually annotated scene boundaries across 1,000 videos spanning movies, TV series, and documentaries.

Viet-Hoang Tran, Thanh Q. Tran, Thanh Chu, Trung-Khang Tran, Duy-Tung Pham, Tam Le, Tan Nguyen

Tree-Sliced methods have emerged as an efficient and expressive alternative to the traditional Sliced Wasserstein distance, replacing one-dimensional projections with tree-structured metric spaces and leveraging a splitting mechanism to better capture the underlying topological structure of integration domains while maintaining low computational cost. At the core of this framework is the Tree-Sliced Wasserstein (TSW) distance, defined over probability measures in Euclidean spaces, along with several variants designed to enhance its performance. A fundamental distinction between SW and TSW lies in their sampling strategies—a component explored in the context of SW but often overlooked in comparisons. This omission is significant: whereas SW relies exclusively on directional projections, TSW incorporates both directional and positional information through its tree-based construction. This enhanced spatial sensitivity enables TSW to reflect the geometric structure of the underlying data more accurately. Building on this insight, we propose a novel variant of TSW that explicitly leverages positional information in its design. Inspired by the classical Fermat–Weber problem—which seeks a point minimizing the sum of distances to a given set of points—we introduce the Fermat–Weber Tree-Sliced Wasserstein (FW-TSW) distance. By incorporating geometric median principles into the tree construction process, FW-TSW notably further improves the performance of TSW while preserving its low computational cost. These improvements are empirically validated across diverse experiments, including diffusion model training and gradient flow. Our code is available at [https://github.com/thanhquangtran/FW-TSW](https://github.com/thanhquangtran/FW-TSW).

Applications · Time Series

Jongwon Kim, Samuel Yoon, Young Ko, Yerin Kim, Sung Kim, JAEUNG TAE

This paper introduces a methodology for anomaly detection in time series using Time Series Foundation Models (TFMs). While TFMs have achieved strong success in forecasting, their role in anomaly detection remains underexplored. We identify two key challenges when applying TFMs to reconstruction-based anomaly detection and propose solutions. The first challenge is overgeneralization, where TFMs reconstruct both normal and abnormal data with similar accuracy, masking true anomalies. We find that this effect often occurs in data with strong low-frequency components. To address it, we propose a complexity metric, $\alpha$, that reflects how difficult the data is for TFMs and design a Complexity-Aware Ensemble (CAE) that adaptively balances TFMs with a statistical model. The second challenge is overstationarization, caused by instance normalization layers that improve forecasting accuracy but remove essential statistical features such as mean and variance, which are critical for anomaly detection. We resolve this by reintroducing these features into the reconstruction process without retraining the TFMs. Experiments on 23 univariate and 17 multivariate benchmark datasets demonstrate that our method significantly outperforms both deep learning and statistical baselines. Furthermore, we show that our complexity-based metric, $\alpha$, provides a theoretical foundation for improved anomaly detection, and we briefly explore prediction-based anomaly detection using TFMs.

Social Aspects · Accountability, Transparency and Interpretability

Yihong Chen, Xiangxiang Xu, Pontus Stenetorp, Sebastian Riedel, Luca Franceschi

Large language models are becoming general knowledge engines for diverse applications. However, their computations are deeply entangled after training, resisting modularization which complicates interpretability, auditing, and long-term maintenance. We introduce Jet Expansions, a framework for expanding computational graphs using jet operators that generalize truncated Taylor series. Our method systematically decomposes language models into explicit input-to-output computational paths and complementary remainders. This functional decomposition provides a principled, knife-like operator for cutting through entanglement in LLMs, enabling scalable model inspection. We demonstrate how Jet Expansions ground and subsume the popular interpretability technique Logit Lens, reveal a (super-)exponential path structure with respect to recursive residual depth, and support several interpretability applications, including sketching a transformer language model with $n$-gram statistics extracted from its computations and indexing model toxicity levels *without* curated benchmarks.

Applications · Neuroscience, Cognitive Science

Yijie Lu, Zhiyi Pan, Renrui Zhang, Yanhao Jia, Ronggang Wang, Zhaokun Zhou

Spiking Transformer has sparked growing interest, with the Spiking Self-Attention merging spikes with self-attention to deliver both energy efficiency and competitive performance. However, existing work primarily focuses on 2D visual tasks, and in the domain of 3D point clouds, the disorder and complexity of spatial information, along with the scale of the point clouds, present significant challenges. For point clouds, we introduce spiking discrepancy, measuring differences in spike features to highlight key information, and then construct the Spiking Discrepancy Attention Mechanism (SDAM). SDAM contains two variants: the Spiking Element Discrepancy Attention captures local geometric correlations between central points and neighboring points, while the Spiking Intensity Discrepancy Attention characterizes structural patterns of point clouds based on macroscopic spike statistics. Moreover, we propose a Spatially-Aware Spiking Neuron. Based on these, we construct a hierarchical Spiking Discrepancy Transformer. Experimental results demonstrate that our method achieves state-of-the-art performance within the Spiking Neural Networks and exhibits impressive performance compared to Artificial Neural Networks along with a few parameters and significantly lower theoretical energy consumption.

Theory · Probabilistic Methods

Wei Guo, Molei Tao, Yongxin Chen

Given an unnormalized probability density $\pi\propto\mathrm{e}^{-V}$, estimating its normalizing constant $Z=\int_{\mathbb{R}^d}\mathrm{e}^{-V(x)}\mathrm{d}x$ or free energy $F=-\log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning. It is challenging especially in high dimensions or when $\pi$ is multimodal. To mitigate the high variance of conventional importance sampling estimators, annealing-based methods such as Jarzynski equality and annealed importance sampling are commonly adopted, yet their quantitative complexity guarantees remain largely unexplored. We take a first step toward a non-asymptotic analysis of annealed importance sampling. In particular, we derive an oracle complexity of $\widetilde{O}\left(\frac{d\beta^2{\mathcal{A}}^2}{\varepsilon^4}\right)$ for estimating $Z$ within $\varepsilon$ relative error with high probability, where $\beta$ is the smoothness of $V$ and $\mathcal{A}$ denotes the action of a curve of probability measures interpolating $\pi$ and a tractable reference distribution. Our analysis, leveraging Girsanov's theorem and optimal transport, does not explicitly require isoperimetric assumptions on the target distribution. Finally, to tackle the large action of the widely used geometric interpolation, we propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.

Computer Vision · Everything Else

Xiaoshan Wu, Xiaoyang Lyu, Yifei Yu, Bo Wang, Zhongrui Wang, XIAOJUAN QI

Dense semantic segmentation in dynamic environments is fundamentally limited by the low-frame-rate (LFR) nature of standard cameras, which creates critical perceptual gaps between frames. To solve this, we introduce *Anytime Interframe Semantic Segmentation*: a new task for predicting segmentation at any arbitrary time using only a single past RGB frame and a stream of asynchronous event data. This task presents a core challenge: how to robustly propagate dense semantic features using a motion field derived from sparse and often noisy event data, all while mitigating feature degradation in highly dynamic scenes. We propose LiFR-Seg, a novel framework that directly addresses these challenges by propagating deep semantic features through time. The core of our method is an *uncertainty-aware warping process*, guided by an event-driven motion field and its learned, explicit confidence. A *temporal memory attention* module further ensures coherence in dynamic scenarios. We validate our method on the DSEC dataset and a new high-frequency synthetic benchmark (SHF-DSEC) we contribute. Remarkably, our LFR system achieves performance (73.82\% mIoU on DSEC) that is statistically indistinguishable from an HFR upper-bound (within 0.09\%) that has full access to the target frame. % We further demonstrate superior robustness in *highly dynamic* (M3ED-Drone \& Quadruped) and *low-light* (DSEC-Night) scenarios, where our method can even surpass the HFR baseline. We further demonstrate superior robustness across extreme scenarios: in highly dynamic (M3ED) tests, our method closely matches the HFR baseline's performance, while in the low-light (DSEC-Night) evaluation, it even surpasses it. This work presents a new, efficient paradigm for achieving robust, high-frame-rate perception with low-frame-rate hardware.

Optimization · Zero-order and Black-box Optimization

Chao Wang, Licheng Jiao, Lingling Li, Jiaxuan Zhao, Guanchun Wang, Fang Liu, Shuyuan Yang

Handcrafted optimizers become prohibitively inefficient for complex black-box optimization (BBO) tasks. MetaBBO addresses this challenge by meta-learning to automatically configure optimizers for low-level BBO tasks, thereby eliminating heuristic dependencies. However, existing methods typically require extensive handcrafted training tasks to learn meta-strategies that generalize to target tasks, which poses a critical limitation for realistic applications with unknown task distributions. To overcome the issue, we propose the Adaptive meta Black-box Optimization Model (ABOM), which performs online parameter adaptation using solely optimization data from the target task, obviating the need for predefined task distributions. Unlike conventional metaBBO frameworks that decouple meta-training and optimization phases, ABOM introduces a closed-loop adaptive parameter learning mechanism, where parameterized evolutionary operators continuously self-update by leveraging generated populations during optimization. This paradigm shift enables zero-shot optimization: ABOM achieves competitive performance on synthetic BBO benchmarks and realistic unmanned aerial vehicle path planning problems without any handcrafted training tasks. Visualization studies reveal that parameterized evolutionary operators exhibit statistically significant search patterns, including natural selection and genetic recombination.

Social Aspects · Fairness, Equity, Justice and Safety

Yiran HU, Zongyue Xue, Haitao Li, Siyuan Zheng, Qingjing Chen, Shaochun Wang, Xihan Zhang, Ning Zheng, Yun Liu, Qingyao Ai 等

Large Language Models (LLMs) are increasingly used in high-stakes fields, such as law, where their decisions can directly impact people's lives. When LLMs act as judges, the ability to fairly resolve judicial issues is necessary to ensure their trustworthiness. Based on theories of judicial fairness, we construct a comprehensive framework to measure LLM fairness, leading to a selection of 65 labels and 161 corresponding values. We further compile an extensive dataset, JudiFair, comprising 177,100 unique case facts. To achieve robust statistical inference, we develop three evaluation metrics—inconsistency, bias, and imbalanced inaccuracy—and introduce a method to assess the overall fairness of multiple LLMs across various labels. Through experiments with 16 LLMs, we uncover pervasive inconsistency, bias, and imbalanced inaccuracy across models, underscoring severe LLM judicial unfairness. Particularly, LLMs display notably more pronounced biases on demographic labels, with slightly less bias on substance labels compared to procedure ones. Interestingly, increased inconsistency correlates with reduced biases, but more accurate predictions exacerbate biases. While we find that adjusting the temperature parameter can influence LLM fairness, model size, release date, and country of origin do not exhibit significant effects on judicial fairness. Accordingly, we introduce a publicly available toolkit to support future research in evaluating and improving LLM fairness, along with a full technical analysis included as an appendix.

Computer Vision · Image and Video Generation

Shi Zhan Liu, Hao ZHENG, Hang Yu, Jianguo Li

Image personalization enables customizing Text-to-Image models with a few reference images but is plagued by "concept coupling"—the model creating spurious associations between a subject and its context. Existing methods tackle this indirectly, forcing a trade-off between personalization fidelity and text control. This paper is the first to formalize concept coupling as a statistical dependency problem, identifying two root causes: a Denoising Dependence Discrepancy that arises during the generative process, and a Prior Dependence Discrepancy within the learned concept itself. To address this, we introduce ACCORD, a framework with two targeted, plug-and-play regularization losses. The Denoising Decouple Loss minimizes dependency changes across denoising steps, while the Prior Decouple Loss aligns the concept’s relational priors with those of its superclass. Extensive experiments across subject, style, and face personalization demonstrate that ACCORD achieves a superior balance between fidelity and text control, consistently improving upon existing methods.

Theory · Domain Adaptation and Transfer Learning

Wei Chen, Xingyu Guo, Shuang Li, Zhao Zhang, Yan Zhong, Fuzhen Zhuang, deqing wang

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we propose \textbf{ADAlign}, an Adaptive Distribution Alignment framework for GDA. Unlike heuristic methods, ADAlign requires no manual specification of alignment criteria. It automatically identifies the most relevant discrepancies in each transfer and aligns them jointly, capturing the interplay between attributes, structures, and their dependencies. This makes ADAlign flexible, scenario-aware, and robust to diverse and dynamically evolving shifts. To enable this adaptivity, we introduce the Neural Spectral Discrepancy (NSD), a theoretically principled parametric distance that provides a unified view of cross-graph shifts. NSD leverages neural characteristic function in the spectral domain to encode feature-structure dependencies of all orders, while a learnable frequency sampler adaptively emphasizes the most informative spectral components for each task via minimax paradigm. Extensive experiments on 10 datasets and 16 transfer tasks show that ADAlign not only outperforms state-of-the-art baselines but also achieves efficiency gains with lower memory usage and faster training.