Research Papers

arXiv:2605.20670v2 Announce Type: replace Abstract: Looped Transformers (LT) have emerged as a powerful architecture by iterating their layers multiple times before decoding the final token. However, pairing them with full attention retains quadratic complexity, making them computationally expensive and slow. We introduce LT2 (Linear-Time Looped Transformers), a family of looped architectures that replace quadratic softmax attention with subquadratic, linear-time attention. We study two variants: LT2-linear with linear attention and LT2-sparse with sparse attention. We find that looping uniquely synergizes with these variants: it enables iterative memory refinement in linear attention and progressively expands the effective receptive field in sparse attention. We formalize these benefits theoretically and demonstrate consistent empirical gains across controlled recall, state-tracking, and language modeling tasks. We then explore LT2-hybrid, which combines different attention variants i

arXiv:2605.22242v2 Announce Type: replace Abstract: Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale Lorenz 1996 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel Bayesian and flow-based approaches. Our results show that ensemble perturbations do not increase the system's long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore t

arXiv:2605.22532v2 Announce Type: replace Abstract: Linear properties are ubiquitous in the representations of language models; however, testing them experimentally remains a challenging task. This work focuses on relational linearity: the hypothesis that, for a fixed relation (e.g., "plays"), the unembedding of an object (e.g., "trumpet") can be predicted from the embedding of its subject (e.g.,"Miles Davis") by a linear map. We present an experimental method to test the formulation of relational linearity by Marconato et al. (2025). Specifically, we introduce a probing method, based on Kullback-Leibler divergence, to evaluate this property and examine its variation across layers and paraphrased relational queries. It is also more efficient than previous work; for example, it avoids the crude Jacobian approximations used in Linear Relational Embeddings by Hernandez et al. (2024). Our findings across four datasets show that relational linearity varies across models, exhibits layer-wise

arXiv:2605.22586v2 Announce Type: replace Abstract: This tutorial develops diffusion models from the viewpoint of differential equations. We begin with the conditional Gaussian forward process and show that this path admits both an ordinary differential equation (ODE) representation and a stochastic differential equation (SDE) representation. Averaging the conditional process over the data distribution then yields marginalized forward ODE and SDE formulations that transport the data distribution $p_0=p_{\mathrm{data}}$ to a Gaussian prior $p_1=\mathcal{N}(0,I)$. We next derive the corresponding reverse-time dynamics, namely the reverse SDE and the reverse probability-flow ODE, both of which are governed by the marginal score $\grad\log p_t(x)$. This leads to a training objective for score estimation and shows that the standard noise-prediction objective is equivalent to score matching up to an additive constant independent of the model parameters. We then discuss sampling methods for t

arXiv:2605.22684v2 Announce Type: replace Abstract: Time Series Foundation Models (TSFMs) have become a new component of the state-of-the-art in general time series forecasting. However, adapting them to specialized classification tasks remains constrained by two interconnected challenges: the quadratic cost of standard attention mechanisms and the inability to disentangle the structural components underlying time series variability. This technical report introduces ChronoVAE-HOPE, a next-generation TSFM that reconciles massive generalization with structured latent representation for time series classification. The core of the proposal is a Variational Autoencoder (VAE) framework built upon the HOPE Block, which replaces quadratic attention with a dual-memory system: Titans modules for dynamic short-term retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. A key architectural novelty is the disentangled latent space, which factorizes repres

arXiv:2011.10331v4 Announce Type: replace-cross Abstract: Multi-view clustering has wide applications in many image processing scenarios. In these scenarios, original image data often contain missing instances and noises, which is ignored by most multi-view clustering methods. However, missing instances may make these methods difficult to use directly and noises will lead to unreliable clustering results. In this paper, we propose a novel Auto-weighted Noisy and Incomplete Multi-view Clustering framework (ANIMC) via a soft auto-weighted strategy and a doubly soft regular regression model. Firstly, by designing adaptive semi-regularized nonnegative matrix factorization (adaptive semi-RNMF), the soft auto-weighted strategy assigns a proper weight to each view and adds a soft boundary to balance the influence of noises and incompleteness. Secondly, by proposing{\theta}-norm, the doubly soft regularized regression model adjusts the sparsity of our model by choosing different{\theta}. Compa

arXiv:2306.14853v5 Announce Type: replace-cross Abstract: In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within ${\mathcal{O}}(\epsilon^{-2})$ oracle calls. However, the HVP oracle may be inaccessible or expensive in practice. Kwon et al. (ICML 2023) addressed this issue by proposing a first-order method that can achieve the same goal at a slower rate of $\tilde{\mathcal{O}}(\epsilon^{-3})$. In this paper, we incorporate a two-time-scale update to improve their method to achieve the near-optimal $\tilde {\mathcal{O}}(\epsilon^{-2})$ first-order oracle complexity. Our analysis is highly extensible. In the stochastic setting, our algorithm can achieve the stochastic first-order oracle complexity of $\tilde {\mathcal{O}}(\epsilon^{-4})$ and $\tilde {\mathcal{O}}(\epsilon^{-6})$ when the stochastic noises are only in the up

arXiv:2310.01285v2 Announce Type: replace-cross Abstract: Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to classify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of the Wasserstein k-means clustering algorithm applied to synthetic one-dimensional time series data. We extend the previous work by studying, in detail, the dynamics of the clustering algorithm and how varying the hyperparameters impacts the performance over different random initialisations. We compute simple metrics that we find to be useful in identifying high-quality clusterings. We then extend the technique of Wasserstein k-means clustering to multidimensional time series data by approximating the multidimensional Wasserstein distance as a sliced Wasserstein distance, resulting in a method we call 'sliced Wasserstein k-means (sWk-means) clustering'. We apply the sWk-means clustering method

arXiv:2310.04981v2 Announce Type: replace-cross Abstract: Vision-language models (VLMs) transform environment percepts into vision-language semantics interpretable by LLMs. However, completing complex tasks often requires reasoning about information beyond what is currently perceived. We propose latent compositional semantic embeddings z* as a principled learning-based knowledge representation for queryable spatio-semantic memories. We mathematically prove that z* can always be found, and that the optimal z* is the centroid for any set Z. We derive a probabilistic bound for estimating separability of related and unrelated semantics. We prove that z* is discoverable from visual appearance and singular descriptions by iterative gradient descent. We experimentally verify our findings on four embedding spaces including CLIP and SBERT. Our results show that z* can represent up to 10 semantics encoded by SBERT, and up to 100 semantics for ideal uniformly distributed high-dimensional embeddin

arXiv:2401.01160v3 Announce Type: replace-cross Abstract: We investigate a framework for train-free MRI segmentation based on Topological Data Analysis. The pipeline proceeds in three steps, first identifying the whole object to segment via automatic thresholding, then detecting a distinctive subset whose topology is known in advance, and finally deducing the various components of the segmentation. A key ingredient is the extraction of approximate representative cycles from persistence diagrams, which provides an interpretable link between persistent features and anatomical components. To clarify the method's scope, we make the underlying topological and intensity assumptions explicit, quantify when they hold on real data, and analyze typical failure modes. We evaluate the approach on glioblastoma and on fetal cortical plate segmentation, with comparisons to unsupervised and deep-learning references. By operating without large annotated datasets, the method is well suited to scarce-dat

arXiv:2402.08726v2 Announce Type: replace-cross Abstract: We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value of the sum of single-qubit observables over all the qubits. First, we prove that the probability distribution of the function generated by the untrained network with randomly initialized parameters converges in distribution to a Gaussian process whenever each measured qubit is correlated only with few other measured qubits. Then, we analytically characterize the training of the network via gradient descent with square loss on supervised learning problems. We prove that, as long as the network is not affected by barren plateaus, the trained network can perfectly fit the training set and that the probability distribution of the function generated after training still converges in distribution to a Gaussian process. Finally, we consider the statistical no

arXiv:2404.08073v3 Announce Type: replace-cross Abstract: Bregman proximal-type algorithms (BPs), such as mirror descent, have become popular tools in machine learning and data science for exploiting problem structures through non-Euclidean geometries. In this paper, we show that BPs can get trapped near a class of non-stationary points, which we term \emph{spurious stationary points}. Such stagnation can persist for any finite number of iterations if the gradient of the Bregman kernel is not Lipschitz continuous, even in convex problems. The root cause lies in a fundamental contrast in descent behavior between Euclidean and Bregman geometries: While Euclidean gradient descent ensures sufficient decrease near any non-stationary point, BPs may exhibit arbitrarily slow decrease around spurious stationary points. As a result, commonly used Bregman-based stationarity measure, such as relative change in terms of Bregman divergence, can vanish near spurious stationary points. This may mislea

arXiv:2406.04374v2 Announce Type: replace-cross Abstract: Recommender systems play a crucial role in internet economies by connecting users with relevant products. However, designing effective recommender systems faces the key challenges: the exploration-exploitation tradeoff in securing incentive to explore new products against user's self-interested preferences. While prior work addresses Bayesian Incentive Compatibility (BIC) in fixed-design linear bandits (Sellke & Slivkins, 2023), we tackle the challenge of stochastic user covariates sampled online. Unlike standard black-box reductions (Mansour et al., 2020), our two-stage framework exploits the linear reward structure to achieve sublinear regret while satisfying incentive constraints. To address it, we propose a two-stage algorithm that integrates incentivized exploration with any efficient plug-in offline learning algorithms. In the first stage, it explores products while maintaining incentive compatibility to gather optimal sam

arXiv:2409.03777v3 Announce Type: replace-cross Abstract: Deep convolutional neural networks (CNNs) have achieved impressive performance in many computer vision tasks. However, their large model sizes require heavy computational resources, making pruning redundant filters from existing pre-trained CNNs an essential task in developing efficient models for resource-constrained devices. Whole-network filter pruning algorithms prune varying fractions of filters from each layer, hence providing greater flexibility. Current whole-network pruning methods are either computationally expensive due to the need to calculate the loss for each pruned filter using a training dataset, or use various heuristic / learned criteria for determining the pruning fractions for each layer. This paper proposes a two-level hierarchical approach for whole-network filter pruning which is efficient and uses the classification loss as the final criterion. The lower-level algorithm (called filter-pruning) uses a spar

arXiv:2410.10652v4 Announce Type: replace-cross Abstract: Cells in multicellular organisms coordinate to form structural and functional niches. With spatial transcriptomics (ST) enabling gene expression profiling in spatial contexts, it has been revealed that spatial niches serve as cohesive and recurrent units in physiological and pathological processes. These observations suggest universal tissue organization principles encoded by conserved niche patterns, and call for a query-based niche analytical paradigm beyond current computational tools. In this work, we defined the niche-query task, which is to identify similar niches across ST samples given a niche of interest (NOI). We further developed QueST, a specialized method for solving this task. QueST models each niche as a subgraph, uses contrastive learning to learn discriminative niche embeddings, and incorporates adversarial training to mitigate batch effects. In simulations and benchmark datasets, QueST outperformed existing met