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Applications · Time Series

Dongyuan Li, Shun Zheng, Chang XU, Jiang Bian, Renhe Jiang

Time series forecasting has attracted significant attention in the field of AI. Previous works have revealed that the Channel-Independent (CI) strategy improves forecasting performance by modeling each channel individually, but it often suffers from poor generalization and overlooks meaningful inter-channel interactions. Conversely, Channel-Dependent (CD) strategies aggregate all channels, which may introduce irrelevant information and lead to oversmoothing. Despite recent progress, few existing methods offer the flexibility to adaptively balance CI and CD strategies in response to varying channel dependencies. To address this, we propose a generic plugin xCPD, that can adaptively model the channel-patch dependencies from the perspective of graph spectral decomposition. Specifically, xCPD first projects multivariate signals into the frequency domain using a shared graph Fourier basis, and groups patches into low-, mid-, and high-frequency bands based on their spectral energy responses. xCPD then applies a channel-adaptive routing mechanism that dynamically adjusts the degree of inter-channel interaction for each patch, enabling selective activation of frequency-specific experts. This facilitates fine-grained input-aware modeling of smooth trends, local fluctuations, and abrupt transitions. xCPD can be seamlessly integrated on top of existing CI and CD forecasting models, consistently enhancing both accuracy and generalization across benchmarks. The code is available [https://github.com/Clearloveyuan/xCPD].

Deep Learning · Algorithms

Deyu Bo, Songhua Liu, Xinchao Wang

Dataset distillation (DD) has emerged as a promising approach to compress datasets and speed up model training. However, the underlying connections among various DD methods remain largely unexplored. In this paper, we introduce UniDD, a spectral filtering framework that unifies diverse DD objectives. UniDD interprets each DD objective as a specific filter function applied to the eigenvalues of the feature-feature correlation (FFC) matrix to extract certain frequency information of the feature-label correlation (FLC) matrix. In this way, UniDD reveals that the essence of DD fundamentally lies in matching frequency-specific features. Moreover, we characterize the roles of different filters. For example, low-pass filters, \eg, DM and DC, capture blurred patches, while high-pass filters, \eg, MTT and FrePo, prefer to synthesize fine-grained textures and have better diversity. However, existing methods can only learn the sole frequency information as they rely on fixed filter functions throughout distillation. To address this limitation, we further propose Curriculum Frequency Matching (CFM), which gradually adjusts the filter parameter to cover both low- and high-frequency information of the FFC and FLC matrices. Extensive experiments on small-scale datasets, such as CIFAR-10/100, and large-scale ImageNet-1K, demonstrate the superior performance of CFM over existing baselines and validate the practicality of UniDD.

Hongjun Liu, Leyu Zhou, Zijianghao Yang, Chao Yao

For real-world BCI applications, lightweight Electroencephalography (EEG) systems offer the best cost–deployment balance. However, such spatial sparsity of EEG limits spatial fidelity, hurting learning and introducing bias. EEG spatial super-resolution methods aim to recover high-density EEG signals from sparse measurements, yet is often hindered by distribution shift and signal distortion and thus reducing fidelity and usability for EEG analysis and visualization. To overcome these challenges, we introduce SRGDiff, a step-aware residual-guided diffusion model that formulates EEG spatial super-resolution as dynamic conditional generation. Our key idea is to learn a dynamic residual condition from the low-density input that predicts the step-wise temporal and spatial details to add and uses the evolving cue to steer the denoising process toward high density reconstructions. At each denoising step, the proposed residual condition is additively fused with the previous denoiser feature maps, then a step-dependent affine modulation scales and shifts the activation to produce the current features. This iterative procedure dynamically extracts step-wise temporal rhythms and spatial-topographic cues to steer high-density recovery and maintain a fidelity–consistency balance. We adopt a comprehensive evaluation protocol spanning signal-, feature-, and downstream-level metrics across SEED, SEED-IV, and Localize-MI and multiple upsampling scales. SRGDiff achieves consistent gains of up to 40\% over strong baselines, proving its superiority in the task of EEG spatial super-resolution. Moreover, topographic visualizations comparison and substantial EEG-FID gains jointly indicate that our SR EEG mitigates the spatial–spectral shift between low- and high-density recordings. Our code is available at https://github.com/DhrLhj/ICLR2026SRGDiff.

Theory · Reinforcement Learning and Planning

Anand Brahmbhatt, Gon Buzaglo, Sofiia Druchyna, Elad Hazan

We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.

General Machine Learning · Representation Learning

Hangke Sui, Yuqing Wang, Minh Do

Contrastive objectives power state-of-the-art multimodal models, but their training remains slow, relying on long stochastic optimization. We propose a Unified Framework for Efficient Contrastive Alignment via Kernels (UniCon), which spans linear and nonlinear encoders as well as one-to-one and many-to-many alignments. At its core, UniCon introduces the contrastive similarity weight matrix $S(\gamma)$, which enables closed-form global solutions that provably replace minibatch back-propagation with exact updates. Through the lens of reproducing kernel Hilbert spaces (RKHS), UniCon provides a kernelized perspective that unifies contrastive alignment and reveals its connection to spectral methods. To validate the theory, we conduct experiments on synthetic, unimodal, multimodal, and zero-shot tasks, demonstrating that UniCon achieves substantial efficiency gains while preserving generality and strong empirical performance.

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.

Deep Learning · Robustness

Desong Zhang, Jia Hu, Geyong Min

Spiking Neural Networks (SNNs) process information via discrete spikes, enabling them to operate at remarkably low energy levels. However, our experimental observations reveal a striking vulnerability when SNNs are trained using the mainstream method—direct encoding combined with backpropagation through time (BPTT): even a single backward pass on data drawn from a slightly different distribution can lead to catastrophic network collapse. We refer to this phenomenon as the heterogeneous training vulnerability of SNNs. Our theoretical analysis attributes this vulnerability to the repeated inputs inherent in direct encoding and the gradient accumulation characteristic of BPTT, which together produce an exceptional large Hessian spectral radius. To address this challenge, we develop a hyperparameter-free method called Dominant Singular Deflation (DSD). By orthogonally projecting the dominant singular components of gradients, DSD effectively reduces the Hessian spectral radius, thereby preventing SNNs from settling into sharp minima. Extensive experiments demonstrate that DSD not only mitigates the vulnerability of SNNs under heterogeneous training, but also significantly enhances overall robustness compared to key baselines, providing strong support for safer SNNs.

General Machine Learning · Representation Learning

Yisi Luo, Deyu Meng

Separable neural networks (SepNNs) are emerging neural architectures that significantly reduce computational costs by factorizing a multivariate function into linear combinations of univariate functions, benefiting downstream applications such as implicit neural representations (INRs) and physics-informed neural networks (PINNs). However, fundamental theoretical analysis for SepNN, including detailed representation capacity and spectral bias characterization \& alleviation, remains unexplored. This work makes three key contributions to theoretically understanding and improving SepNN. First, using Weierstrass-based approximation and universal approximation theory, we prove that SepNN can approximate any multivariate function with arbitrary precision, confirming its representation completeness. Second, we derive the neural tangent kernel (NTK) regimes for SepNN, showing that the NTK of infinite-width SepNN converges to a deterministic (or random) kernel under infinite (or fixed) decomposition rank, with corresponding convergence and spectral bias characterization. Third, we propose an efficient separable preconditioned gradient descent (SepPGD) for optimizing SepNN, which alleviates the spectral bias of SepNN by provably adjusting its NTK spectrum. The SepPGD enjoys an efficient $\mathcal{O}(nD)$ complexity for $n^D$ training samples, which is much more efficient than previous neural network PGD methods. Extensive experiments for kernel ridge regression, image and surface representation using INRs, and numerical PDEs using PINNs validate the efficiency of SepNN and the effectiveness of SepPGD for alleviating spectral bias.

Theory · Optimization

Ravindran Kannan, Kijun Shin, David Woodruff

We study the Nearest Neighbor Search (NNS) problem in a high-dimensional setting where data originates from a low-dimensional subspace and is corrupted by Gaussian noise. Specifically, we consider a semi-random model where $n$ points from an unknown $k$-dimensional subspace of $\mathbb{R}^d$ ($k \ll d$) are perturbed by zero-mean $d$-dimensional Gaussian noise with variance $\sigma^2$ on each coordinate. Without loss of generality, we may assume the nearest neighbor is at distance $1$ from the query, and that all other points are at distance at least $1+\varepsilon$. We assume we are given only the noisy data and are required to find NN of the uncorrupted data. We prove the following results: 1. For $\sigma \in O(1/k^{1/4})$, we show that simply performing SVD denoises the data; namely, we provably recover accurate NN of uncorrupted data (Theorem 1.1). 2. For $\sigma \gg 1/k^{1/4}$, NN in uncorrupted data is not even {\bf identifiable} from the noisy data in general. This is a matching lower bound on $\sigma$ with the above result, demonstrating the necessity of this threshold for NNS (Lemma 3.1). 3. For $\sigma \gg 1/\sqrt k$, the noise magnitude ($\sigma \sqrt{d}$) is significantly exceeds the inter-point distances in the unperturbed data. Moreover, NN in noisy data is different from NN in the uncorrupted data in general. \end{enumerate} Note that (1) and (3) together imply SVD identifies correct NN in uncorrupted data even in a regime where it is different from NN in noisy data. This was not the case in existing literature (see e.g. (Abdullah et al., 2014)). Another comparison with (Abdullah et al., 2014) is that it requires $\sigma$ to be at least an inverse polynomial in the ambient dimension $d$. The proof of (1) above uses upper bounds on perturbations of singular spaces of matrices as well as concentration and spherical symmetry of Gaussians. We thus give theoretical justification for the performance of spectral methods in practice. We also provide empirical results on real datasets to corroborate our findings.

Optimization · Sampling and Optimization

Konstantinos Emmanouilidis, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Rene Vidal

From adversarial robustness to multi-agent learning, many machine learning tasks can be cast as finite-sum min–max optimization or, more generally, as variational inequality problems (VIPs). Owing to their simplicity and scalability, stochastic gradient methods with constant step size are widely used, despite the fact that they converge only up to a constant term. Among the many heuristics adopted in practice, two classical techniques have recently attracted attention to mitigate this issue: *Random Reshuffling* of data and *Richardson–Romberg extrapolation* across iterates. Random Reshuffling sharpens the mean-squared error (MSE) of the estimated solution, while Richardson-Romberg extrapolation acts orthogonally, providing a second order reduction in its bias. In this work, we show that their composition is strictly better than both, not only maintaining the enhanced MSE guarantees but also yielding an even greater cubic refinement in the bias. To the best of our knowledge, our work provides the first theoretical guarantees for such a synergy in structured non-monotone VIPs. Our analysis proceeds in two steps: (i) we smooth the discrete noise induced by reshuffling and leverage tools from continuous-state Markov chain theory to establish a novel law of large numbers and a central limit theorem for its iterates; and (ii) we employ spectral tensor techniques to prove that extrapolation debiases and sharpens the asymptotic behavior even under the biased gradient oracle induced by reshuffling. Finally, extensive experiments validate our theory, consistently demonstrating substantial speedups in practice.

Deep Learning · Theory

Gabriel Mel

Local loss geometry in machine learning is inherently a two-operator concept. While a single loss is locally characterized by its Hessian spectrum, practical learning depends on both training and test losses, whose joint geometry is determined not only by their spectra but by the alignment of their eigenspaces. We establish general foundations for this two-loss geometry by deriving a universal local fluctuation law: the expected test-loss increment under small training perturbations is a trace combining train and test spectral data with a precise factor quantifying eigenvector overlap. We further prove a transfer law describing how overlaps transform under noise. As a solvable model, we apply these results to ridge regression under arbitrary covariate shift, where operator-valued free probability yields asymptotically exact overlap decompositions that identify overlaps as the natural quantities for specifying shift, and resolve multiple descent: error peaks are governed by eigenspace misalignment rather than Hessian ill-conditioning alone. We then validate the fluctuation law in multilayer perceptrons, develop scalable estimators for overlap functionals based on subspace iteration and kernel polynomial methods, and apply them to a ResNet-20 trained on CIFAR-10, showing that class imbalance reshapes train–test geometry through induced misalignment. Together, these results establish eigenvector overlaps as the fundamental missing ingredient in local loss geometry, providing both theoretical foundations and practical tools for analyzing generalization in modern neural networks.

Optimization · Large Scale, Parallel and Distributed

Muqing Liu, Chongjie Si, Yuheng Jia

Large pre-trained models achieve remarkable success across diverse domains, yet fully fine-tuning incurs prohibitive computational and memory costs. Parameter-efficient fine-tuning (PEFT) has thus become a mainstream paradigm. Among them, Low-Rank Adaptation (LoRA) introduces trainable low-rank matrices and shows strong performance, nevertheless, its fixed-rank design limits flexibility. Dynamic rank allocation methods mitigate this issue by pruning redundant directions; however, they often rely on heuristic, element-level metrics that globally sort rank directions without matrix-wise distinction, and they lack mechanisms to expand capacity in layers requiring additional adaptation. To overcome these limitations, we propose FlexLoRA, an entropy-guided flexible low-rank adaptation framework that (i) evaluates matrix importance via spectral energy entropy, (ii) supports rank pruning and expansion under a global budget, and (iii) employs zero-impact initialization for newly added singular directions to ensure stability. By addressing granularity, flexibility, and stability limitations, FlexLoRA provides a more principled solution for PEFT. Extensive experiments show that FlexLoRA consistently outperforms state-of-the-art baselines across benchmarks.

Theory · Probabilistic Methods

Qiaochu Xu, Zi Yang, Ying Li, Michael Minyi Zhang, Pablo Olmos

Multi-output Gaussian processes (MOGPs) provide a Bayesian framework for modeling non-linear functions with multiple outputs, in which nonstationary kernels are essential for capturing input-dependent variations in observations. However, from a spectral (dual) perspective, existing nonstationary kernels inherit the inflexibility and over-parameterization of their spectral densities due to the restrictive spectral–kernel duality. To overcome this, we establish a generalized spectral–kernel duality that enables fully flexible matrix-valued spectral densities — albeit at the cost of quadratic parameter growth in the number of outputs. To achieve linear scaling while retaining sufficient expressiveness, we propose the multi-output low-rank nonstationary (MO-LRN) kernel: by modeling the spectral density through a low-rank matrix whose rows are independently parameterized by bivariate Gaussian mixtures. Experiments on synthetic and real-world datasets demonstrate that MO-LRN consistently outperforms existing MOGP kernels in regression, missing-data interpolation, and imputation tasks.

Reinforcement Learning · Online

Dongxie Wen, Hanyan Yin, Xiao Zhang, Peng Zhao, Lijun Zhang, Zhewei Wei

Linear bandits have become a cornerstone of online learning and sequential decision-making, providing solid theoretical foundations for balancing exploration and exploitation. Within this domain, matrix sketching serves as a critical component for achieving computational efficiency, especially when confronting high-dimensional problem instances. The sketch-based approaches reduce per-round complexity from $\Omega(d^2)$ to $O(dl)$, where $d$ is the dimension and $l<d$ is the sketch size. However, this computational efficiency comes with a fundamental pitfall: when the streaming matrix exhibits heavy spectral tails, such algorithms can incur vacuous *linear regret*. In this paper, we revisit the regret bounds and algorithmic design for sketch-based linear bandits. Our analysis reveals that inappropriate sketch sizes can lead to substantial spectral error, severely undermining regret guarantees. To overcome this issue, we propose Dyadic Block Sketching, a novel multi-scale matrix sketching approach that dynamically adjusts the sketch size during the learning process. We apply this technique to linear bandits and demonstrate that the new algorithm achieves *sublinear regret* bounds without requiring prior knowledge of the streaming matrix properties. It establishes a general framework for efficient sketch-based linear bandits, which can be integrated with any matrix sketching method that provides covariance guarantees. Comprehensive experimental evaluation demonstrates the superior utility-efficiency trade-off achieved by our approach.

Computer Vision · Vision Models & Multimodal

Peilin Feng, Zhutao Lv, Junyan Ye, Xiaolei Wang, Xinjie Huo, Jinhua Yu, Wanghan Xu, Wenlong Zhang, LEI BAI, Conghui He 等

Earth observation (EO) is essential for understanding the evolving states of the Earth system. Although recent MLLMs have advanced EO research, they still lack the capability to tackle complex tasks that require multi-step reasoning and the use of domain-specific tools. Agent-based methods offer a promising direction, but current attempts remain in their infancy, confined to RGB perception, shallow reasoning, and lacking systematic evaluation protocols. To overcome these limitations, we introduce Earth-Agent, the first agentic framework that unifies RGB and spectral EO data within an MCP-based tool ecosystem, enabling cross-modal, multi-step, and quantitative spatiotemporal reasoning beyond pretrained MLLMs. Earth-Agent supports complex scientific tasks such as geophysical parameter retrieval and quantitative spatiotemporal analysis by dynamically invoking expert tools and models across modalities. To support comprehensive evaluation, we further propose Earth-Bench, a benchmark of 248 expert-curated tasks with 13,729 images, spanning spectrum, products and RGB modalities, and equipped with a dual-level evaluation protocol that assesses both reasoning trajectories and final outcomes. We conduct comprehensive experiments varying different LLM backbones, comparisons with general agent frameworks, and comparisons with MLLMs on remote sensing benchmarks, demonstrating both the effectiveness and potential of Earth-Agent. Earth-Agent establishes a new paradigm for EO analysis, moving the field toward scientifically grounded, next-generation applications of LLMs in Earth observation. More information about Earth-Agent can be found at https://github.com/opendatalab/Earth-Agent

Applications · Language, Speech and Dialog

Zengwei Yao, Wei Kang, Han Zhu, Liyong Guo, Lingxuan Ye, Fangjun Kuang, Weiji Zhuang, Zhaoqing Li, Zhifeng Han, Long Lin 等

Existing dominant methods for audio generation include Generative Adversarial Networks (GANs) and diffusion-based methods like Flow Matching. GANs suffer from slow convergence during training, while diffusion methods require multi-step inference that introduces considerable computational overhead. In this work, we introduce Flow2GAN, a two-stage framework that combines Flow Matching training for learning generative capabilities with GAN fine-tuning for efficient few-step inference. Specifically, given audio's unique properties, we first improve Flow Matching for audio modeling through: 1) reformulating the objective as endpoint estimation, avoiding velocity estimation difficulties when involving empty regions; 2) applying spectral energy-based loss scaling to emphasize perceptually salient quieter regions. Building on these Flow Matching adaptations, we demonstrate that a further stage of lightweight GAN fine-tuning enables us to obtain few-step (e.g., 1/2/4 steps) generators that produce high-quality audio. In addition, we develop a multi-branch network architecture that processes Fourier coefficients at different time-frequency resolutions, which improves the modeling capabilities compared to prior single-resolution designs. Experimental results indicate that our Flow2GAN delivers high-fidelity audio generation from Mel-spectrograms or discrete audio tokens, achieving highly favorable quality-efficiency trade-offs compared to existing state-of-the-art GAN-based and Flow Matching-based methods. Online demo samples are available at \url{https://flow2gan.github.io}, and the source code is released at \url{https://github.com/k2-fsa/Flow2GAN}.

Deep Learning · Theory

Bhavya Vasudeva, Puneesh Deora, Yize Zhao, Vatsal Sharan, Christos Thrampoulidis

The growing adoption of spectrum-aware matrix-valued optimizers such as Muon and Shampoo in deep learning motivates a systematic study of their generalization properties and, in particular, when they might outperform competitive algorithms. We approach this question by introducing appropriate simplifying abstractions as follows: First, we use imbalanced data as a testbed. Second, we study the canonical form of such optimizers, which is Spectral Gradient Descent (SpecGD)—each update step is $\mathbf{U}\mathbf{V}^T$ where $\mathbf{U}\mathbf{\Sigma}\mathbf{ V}^T$ is the truncated SVD of the gradient. Third, within this framework we identify a canonical setting for which we precisely quantify when SpecGD outperforms vanilla Euclidean GD. For a Gaussian mixture data model and both linear and bilinear models, we show that unlike GD, which prioritizes learning dominant principal components of the data first, SpecGD learns all principal components of the data at equal rates. We demonstrate how this translates to a growing gap in class balanced loss favoring SpecGD early in training and further show that the gap remains consistent even when the GD counterpart uses adaptive step-sizes via normalization. By extending the analysis to deep linear models, we show that depth amplifies these effects. We empirically verify our theoretical findings on a variety of imbalanced datasets. Our experiments compare practical variants of spectral methods, like Muon and Shampoo, against their Euclidean counterparts and Adam. The results validate our findings that these spectral optimizers achieve superior generalization by promoting a more balanced learning of the data's underlying components.

Xize Cheng, Chenyuhao Wen, Slytherin Wang, Yongqi Wang, zehan wang, Rongjie Huang, Tao Jin, Zhou Zhao

Video Query Sound Separation (VQSS) aims to isolate target sounds conditioned on visual queries while suppressing off-screen interference—a task central to audiovisual understanding. However, existing methods often fail under conditions of homogeneous interference and overlapping soundtracks, due to limited temporal modeling and weak audiovisual alignment. We propose \textbf{AlignSep}, the first generative VQSS model based on flow matching, designed to address common issues such as spectral holes and incomplete separation. To better capture cross-modal correspondence, we introduce a series of temporal consistency mechanisms that guide the vector field estimator toward learning robust audiovisual alignment, enabling accurate and resilient separation in complex scenes. As a \textit{multi-conditioned generation} task, VQSS presents unique challenges that differ fundamentally from traditional flow matching setups. We provide an in-depth analysis of these differences and their implications for generative modeling. To systematically evaluate performance under realistic and difficult conditions, we further construct \textbf{VGGSound-Hard}, a challenging benchmark composed entirely of separation cases with homogeneous interference and strong reliance on temporal visual cues. Extensive experiments across multiple benchmarks demonstrate that AlignSep achieves state-of-the-art performance both quantitatively and perceptually, validating its practical value for real-world applications. More results and audio examples are available at: \url{https://AlignSep.github.io}.

Chang Li, Kanglei Zhou, Liyuan Wang

Audio is a fundamental modality for analyzing speech, music, and environmental sounds. While pretrained audio models have significantly advanced audio understanding, they remain fragile in real-world scenarios where data distributions evolve over time. In this work, we present the first systematic benchmark for audio continual learning (CL) with pretrained models (PTMs) and provide a comprehensive analysis of its unique challenges. Unlike in the vision domain where parameter-efficient fine-tuning (PEFT) has proven effective for CL, directly applying such strategies to audio leads to poor performance. This is due to a fundamental property of audio backbones: they emphasize low-level spectral details rather than structured semantics, resulting in severe upstream–downstream misalignment. Through extensive empirical analysis, we identify a promising technical route based on analytic classifiers with first-session adaptation (FSA), but also uncover two major limitations: representation saturation in coarse-grained scenarios and representation shifts in fine-grained scenarios. To address these challenges, we propose **PACE**, an innovative method that improves FSA via a regularized analytic classifier and introduces multi-session adaptation through adaptive subspace-orthogonal PEFT for better semantic alignment. Additionally, we design spectrogram-based boundary-aware perturbations to mitigate representation overlap and improve stability. Experiments across six diverse audio CL benchmarks demonstrate that PACE substantially outperforms state-of-the-art baselines, representing a significant step toward robust and scalable audio CL with PTMs.

Reinforcement Learning · Deep RL

Ofir Nabati, Bo Dai, Shie Mannor, Guy Tennenholtz

Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces the Spectral Bellman Method, a novel framework derived from the Inherent Bellman Error (IBE) condition. It aligns representation learning with the fundamental structure of Bellman updates across a space of possible value functions, making it directly suited for value-based RL. Our key insight is a fundamental spectral relationship: under the zero-IBE condition, the transformation of a distribution of value functions by the Bellman operator is intrinsically linked to the feature covariance structure. This connection yields a new, theoretically-grounded objective for learning state-action features that capture this Bellman-aligned covariance, requiring only a simple modification to existing algorithms. We demonstrate that our learned representations enable structured exploration by aligning feature covariance with Bellman dynamics, improving performance in hard-exploration and long-horizon tasks. Our framework naturally extends to multi-step Bellman operators, offering a principled path toward learning more powerful and structurally sound representations for value-based RL.