Multiscale

We introduce "Courant", a Perceiver-based encoder-processor-decoder surrogate model that has latent features exhibiting adaptive specialization and local support in the physical space, enabling functionality akin to an adaptive hp-refinement scheme, an attribute that is highly desirable in traditional numerical solvers and scientific machine learning broadly. The proposed architecture combines a shared random Fourier feature coordinate embedding, state-adapted latent queries, and a light-weight decoder. Courant is trained end-to-end with steady or transient simulation data and only a standard L_2 prediction loss in the physical space, achieving competitive accuracy on benchmarks. We demonstrate that Courant's inductive biases yield latents that are interpretable by design: they develop multiscale geometric specialization in the simulation domain and track coherent structures in the time-dependent case, acting analogously to time-evolving spatial basis functions and allowing for decoding a compact, geometry-anchored, partition-of-unity-like decomposition of the simulated field.

Electricity load peak forecasting (ELPF), simultaneously predicting peak timing and intensity, is a prerequisite for effective grid scheduling and risk management. However, existing methods face three limitations. First, they adopt a two-stage predict-then-locate paradigm, which severs the link between temporal localization and intensity regression. Second, they still struggle with the multi-scale representation conflict, leading to peak misjudgment and timing misalignment. Third, the lack of explicit peak timing context during intensity regression causes intensity smoothing because predictions are dominated by global smoothing trends. To address these limitations, we propose PeakFocus, a unified framework for ELPF. (i) A Unified Peak-Aware Pipeline (UPAP) utilizes a triple hybrid loss to jointly supervise temporal localization and intensity regression, alongside a tolerance-based evaluation protocol. (ii) A Multi-Scale Mixing Peak Locator (MSM-PL) exploits coarse-grained features to mitigate peak misjudgment caused by local fluctuations, and injects them into fine-grained features via a cascade mechanism to resolve timing misalignment. (iii) A Location-Aware Decoder (LAD) injects peak timing context into the intensity regression process, providing explicit guidance to counteract intensity smoothing and improve peak intensity estimation. Extensive experiments on the public Electricity (ELC) dataset and our industrial-scale World Large-scale Electricity Load (WLEL) dataset show that PeakFocus outperforms baselines in both timing precision and intensity estimation.

Image super-resolution (SR) aims to reconstruct high-quality, high-resolution (HR) images from low-resolution (LR) inputs and plays a critical role in various downstream applications. Despite recent advancements, balancing reconstruction fidelity and computational efficiency remains a fundamental challenge, particularly in resource-constrained scenarios. While existing lightweight methods attempt to expand receptive fields, many of them either incur substantial computational overhead, naively scale up kernel sizes, or lack mechanisms for coherent multi-scale integration, limiting their overall effectiveness and scalability. To address these limitations, we propose EchoSR, an efficient context-harnessing framework for lightweight image super-resolution, which unifies multi-scale receptive field modeling and hierarchical context fusion. EchoSR decouples feature learning into disentangled local, multi-scale, and global modeling stages through an efficient context-harnessing strategy, and further promotes seamless cross-scale integration via a cross-scale overlapping fusion mechanism. Extensive experiments have shown that EchoSR consistently outperforms state-of-the-art lightweight super-resolution methods across multiple benchmarks, while also achieving a faster speed $(\sim 2\times)$. The source code is available at https://github.com/funnyWang-Echoes/EchoSR.

Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets.

We present MSCoT, a multi-scale, coarse-to-fine model for test-time human motion synthesis and control. Unlike recent approaches that rely on multiple iterative denoising/token-prediction steps, or modules tailored for specific control signals, MSCoT discretizes motion into a multi-scale hierarchical representation and predicts the entire token sequence at each temporal scale in a coarse-to-fine fashion. Building on this coarse-to-fine paradigm, we propose an efficient multi-scale token guidance strategy that overcomes the challenge of discrete sampling and steers the token distribution towards the control goals, allowing for fast and flexible control. To address the limitations of a discrete codebook, a lightweight token refiner further adds continuous residuals to the discrete token embeddings and allows differentiable test-time refinement optimization to ensure precise alignment with the control objectives. MSCoT is able to produce quality motions, consistent with the control constraints, while offering substantially faster sampling than diffusion-based approaches. Experiments on popular benchmarks demonstrate state-of-the-art controllable text-to-motion generation performance of MSCoT over existing baselines, with better motion quality (48% FID improvement), higher control accuracy (-61% avg error), and $10 \times$ faster inference speed on HumanML3D.

Accurate precipitation nowcasting over extended horizons (0-3 hours) is essential for disaster mitigation and operational decision-making, yet remains a critical challenge in the field. Existing deterministic approaches are predominantly constrained to shorter prediction windows (0-2 hours), exhibiting severe performance degradation beyond 90 minutes owing to their inherent difficulty in capturing long-range spatiotemporal dependencies from radar-derived observations. To address these fundamental limitations, we propose MambaRain, a novel multi-scale encoder-decoder architecture that synergistically integrates Mamba's linear-complexity long-range temporal modeling with self-attention mechanisms for explicit spatial correlation capture. The core innovation lies in a hybrid design paradigm wherein Mamba blocks leverage selective state space mechanisms to model global temporal dynamics across extended sequences with computational efficiency, while self-attention modules explicitly characterize spatial correlations within precipitation fields - a capability inherently absent in Mamba's sequential processing paradigm. This complementary synergy enables comprehensive spatiotemporal representation learning, effectively extending the viable forecasting horizon to 2-3 hours with substantial accuracy improvements. Furthermore, we introduce a spectral loss formulation to mitigate blurring artifacts characteristic of chaotic precipitation systems, thereby preserving fine-scale motion details critical for nowcasting accuracy. Experimental validation demonstrates that MambaRain substantially outperforms existing deterministic methodologies in 0-3 hour nowcasting tasks, with particularly pronounced performance gains in the challenging 2-3 hour prediction range.

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of randomly initialized curves to blindly compete for pixel-level error reduction. This disordered optimization leads to topology collapse, where macroscopic structures are distorted by internal high-frequency noise, resulting in a redundant and uneditable "polygon soup" that limits practical editability. To address this limitation, we propose Vector Scaffolding, a novel hierarchical optimization framework that shifts from flat pixel-matching to structured topological construction tailored for vector graphics. By identifying a key cause of topology collapse as the mathematical imbalance between area and boundary gradients, we introduce Interior Gradient Aggregation to stabilize the learning dynamics of multi-scale curve mixtures. Upon this stabilized landscape, we employ Progressive Stratification and Rapid Inflation Scheduling to progressively densify vector primitives with extremely high learning rates ($\times 50$). Experiments demonstrate that our approach accelerates optimization by $2.5\times$ while simultaneously improving PSNR by up to 1.4 dB over the previous state of the art.

The accurate classification of benign and malignant pulmonary nodules in CT scans is critical for early lung cancer screening, yet remains challenging due to the multi-scale and heterogeneous nature of pulmonary nodules. While deep learning offers potential for auxiliary diagnosis, most existing models act as "black boxes", lacking the transparency and explainability required for trustworthy clinical integration. To address this issue, we propose M3Net, a novel 3D network for pulmonary nodule classification inspired by the hierarchical diagnostic workflow of radiologists, which integrates multi-scale contextual information from fine-grained structures to global anatomical relationships. Our framework constructs a progressive multi-scale input, from fine-grained nodule structures to local semantics and global spatial relationships. M3Net employs scale-specific encoders and ensures cross-scale semantic consistency through latent space projection and mutual information maximization. Extensive experiments on the public LIDC-IDRI dataset and a self-collected clinical dataset (USTC-FHLN) demonstrate that our method achieves state-of-the-art performance, with accuracies of 86.96% and 84.24% respectively, outperforming the best baseline by 3.26% and 2.17%. The results validate that M3Net provides a more robust and clinically relevant solution for pulmonary nodule classification. The code is available at https://github.com/jylEcho/M3-Net.

Learning latent representations that capture both semantic and spatial information is central to efficient spatio-semantic reasoning. However, many existing approaches rely on implicit latent structures combined with dense feature maps or task-specific heads, limiting computational efficiency and flexibility. We propose WorldComp2D, a novel lightweight representation learning framework that explicitly structures latent space geometry according to object identity and spatial proximity using multiscale local receptive fields. This framework consists of (i) a proximity-dependent encoder that maps a given observation into a spatio-semantic latent space and (ii) a localizer that infers the coordinates of objects in the input from the resulting spatio-semantic representation. Using facial landmark localization as a proof-of-concept, we show that, compared to SoTA lightweight models, WorldComp2D reduces the numbers of parameters and FLOPs by up to 4.0X and 2.2X, respectively, while maintaining real-time performance on CPU. These results demonstrate that explicitly structured latent spaces provide an efficient and general foundation for spatio-semantic reasoning. This framework is open-sourced at https://github.com/JinSeongmin/WorldComp2D.

Cardiovascular stability estimation from wearable photoplethysmography (PPG) requires a principled nonlinear framework, yet major gaps persist in heuristic parameter selection and evaluation protocols that inflate reported performance. We introduce a Stability-Constrained Cardiovascular Stability Index (SCSI) grounded in Cardiac Stability Theory and validate it across 176,742 segments from four heterogeneous PPG datasets at three temporal scales. Cross-dataset analysis demonstrates a large Kruskal-Wallis effect size (eta2 = 0.351, p < 0.001), strong cross-scale consistency (kappa > 0.97), and significant correlation with respiratory rate across 53 ICU records (Spearman r = 0.346, p = 0.011). We identify three evaluation artifacts that inflate heuristic AUC from a true baseline of 0.573 to 0.752: segment-level cross-validation leakage, test-set normalization leakage, and pooled-AUC overweighting that conceals per-patient failure. Correcting these artifacts and applying Bayesian optimization over 15 joint parameters yields SCSI with cross-validation AUC of 0.720. On 18 held-out records, SCSI achieves pooled AUC of 0.757 (95% CI: 0.686-0.828) and negative predictive value of 0.966 for tachypnea screening, while per-record AUC of 0.497 +/- 0.207 is disclosed for transparency. External validation on 42 elective-surgery records yields AUC of 0.621, confirming cross-population generalization. Ablation analysis identifies the nonlinear complexity module as the dominant component. A sparse three-component architecture is proposed as the minimal deployable configuration. The corrected protocol provides a reproducible benchmark for future wearable cardiovascular stability indices.

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a single trajectory of the slow component, while the fast dynamics remain unobserved, making statistical learning challenging. Approaches based on partial differential equations (PDE), such as Fokker-Planck formulations, aim to characterize the evolution of probability densities, typically requiring dense space-time data or grid-based solvers. In contrast, we adopt a trajectory-based perspective and develop a data-driven framework for learning effective stochastic dynamics from a single observed path. We model the dynamics by coupled multiscale stochastic differential equations (SDEs) and first obtain a principled model reduction through stochastic averaging. Unlike generic model reduction techniques such as PCA, this respects the dynamical structure of the original system and explicitly incorporates the interaction between slow and fast scales. A central challenge, however, is that the reduced model depends on the invariant distribution of the fast process, which is a solution to an intractable and often unknown PDE. We introduce a novel learning framework that parameterizes the invariant distribution using normalizing flows, enabling expressive density modeling in the latent fast-variable space. The flow is trained end-to-end by optimizing a penalized likelihood objective induced by the reduced stochastic dynamics. Furthermore, we develop a Bayesian variational inference procedure for uncertainty quantification, employing a second normalizing flow to approximate the posterior distribution over model parameters. This yields a scalable approach to capturing epistemic uncertainty in multiscale systems.

This paper investigates robust representation learning in offline goal-conditioned reinforcement learning (GCRL). Particularly in sparse reward scenarios, learning representations that align state and goal latents is a challenge that frequently culminates in representation divergence where the encoder drifts toward a low-dimensional, goal-agnostic subspace that destabilizes policy learning. We address this issue by showing that an agent must acquire a fundamental understanding of its environment across multiple scales, from local physical dynamics to long-horizon goal-directed structure. Building on this insight, we propose Ms.PR, a framework that leverages multi-scale predictive supervision to enforce goal-directed alignment within the latent space. We demonstrate that Ms.PR leads to improved representation quality and strong performance on both vision and state-based tasks. Furthermore, we show that our approach is exceptionally resilient under realistic, challenging data regimes, maintaining state-of-the-art performance across a wide variety of tasks, trajectory stitching scenarios, and extreme noise conditions.

Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity. To mitigate this measure-induced bias, we propose M$^3$ (Multi-scale Morton Measure), a scalable framework that balances training measures by partitioning space according to physical variation and allocating supervision across multiple scales. Applied to three industrial-scale datasets with diverse discretizations, M$^3$ consistently improves predictions in the continuous physical domain, achieving up to 4.7$\times$ lower error in large-scale volumetric cases. These gains persist under aggressive subsampling (160M $\rightarrow$ 16M $\rightarrow$ 1.6M points), where M$^3$-trained models outperform those trained on higher-resolution data, reducing physics-weighted relative $L_2$ error by 3--4$\times$ and the corresponding MSE by up to 13$\times$. These results highlight data distribution as a key factor in operator learning and position M$^3$ as a scalable, data-efficient approach for physically consistent modeling. Code is available at https://github.com/PhysDataRefine/M3.

Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale refinements that continue beyond the levels directly observed. We introduce classification fields: infinite-depth hierarchical cluster structures on $\mathbb{R}^d$ generated by a local parent-to-child refinement rule. A classification field generator maps each parent centre to an ordered, bounded, and separated tuple of child residuals. Together with a root and a scale factor, this rule recursively generates cluster centres, Voronoi cells, and a metric DAG encoding the hierarchy. Given only a finite prefix of such a hierarchy, we learn a classification field predictor that approximates the generator and can be rolled out to unseen depths. We prove exponential truncation convergence in the completed cell metric and ReLU realizability with width $O(\varepsilon^{-γ})$ and depth $\widetilde O(\varepsilon^{-3γ/2})$, where $γ=\log K/(-\log s)$, up to finite-window aspect-ratio factors. The approximation holds at the level of the induced compact metric structures, measured in the completed cell-metric Hausdorff distance. Experimental validation on matched CFG-generated hierarchies, IFS fractals, and image-induced recursive clustering hierarchies shows that learned predictors preserve ordered child slots, unordered geometry, and hierarchy-level path metrics under recursive rollout. These results support the claim that finite hierarchical observations can reveal local refinement rules capable of generating substantially deeper classification fields.

DNA language model aims to decipher the regulatory grammar and semantic of genomes by capturing long range dependencies in DNA sequences. Existing methods emphasize long range token interactions but often ignore the interplay between local motifs and global dependencies. In this paper, we propose Wisteria, a genomic language model that integrates multi scale feature learning within a unified framework for DNA sequence. Specifically, Wisteria augments the Mamba based architecture with gated dilated convolutions to capture local motifs and regulatory patterns, while gated multilayer perceptrons refine global dependencies. We further introduce a Fourier based attention mechanism to support frequency domain modeling, periodic extension and length generalization. Across four experimental settings with both short and long range dependencies, Wisteria demonstrates strong performance on downstream benchmarks against competitive DNA language model baselines. These results indicate that Wisteria effectively unifies local and global dependency modeling for multi scale genomic sequence analysis.

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating accuracy and computational cost, which can be misleading since architectures exhibit different accuracy-cost scaling as width and depth vary. This issue is particularly relevant for U-Net-type encoder-decoder models, widely used for multi-scale gas, fluid, and plasma dynamics due to their ability to represent features across spatial scales. A U-Net constructs a multi-resolution representation via an encoder that progressively reduces spatial resolution, followed by a decoder that restores it for prediction. Skip connections link corresponding encoder and decoder features, preserving fine-scale information and improving optimization. In practice, U-Net width is routinely tuned, while depth is typically kept fixed (a set number of down/up-sampling stages with few convolutions per stage), limiting systematic exploration of depth for improving the accuracy-cost trade-off. We address this limitation by increasing effective depth through stacking multiple encoder-decoder "waves" in series, with skip connections both within and across waves to enable progressive cross-scale refinement. We call this architecture a Deep Wave Network (DW-Net). Training data, optimization, and schedules are kept identical across models. Instead of evaluating single configurations, we train multiple width variants of each architecture and compare accuracy vs. GPU time Pareto fronts. Across several 2D and 3D flow benchmarks, DW-Net models consistently improve the Pareto frontier over single-wave U-Nets, achieving higher accuracy at matched cost or similar accuracy at reduced cost, and reaching low-error regimes with up to 3x less training time under identical training settings.

Detecting anomalies from 3D point clouds has received increasing attention in the field of computer vision, with some group-based or point-based methods achieving impressive results in recent years. However, learning accurate point-wise representations for 3D anomaly detection faces great challenges due to the large scale and sparsity of point clouds. In this study, a surface-based method is proposed for 3D anomaly detection, which learns a discriminative signed distance function using multi-scale level-of-detail features. We first present a Noisy Points Generation (NPG) module to generate different types of noise, thereby facilitating the learning of discriminative features by exposing abnormal points. Then, we introduce a Multi-scale Level-of-detail Feature (MLF) module to capture multi-scale information from a point cloud, which provides both fine-grained local and coarse-grained global feature information. Finally, we design an Implicit Surface Discrimination (ISD) module that leverages the extracted multi-scale features to learn an implicit surface representation of point clouds, which effectively trains a signed distance function to distinguish between abnormal and normal points. Experimental results demonstrate that the proposed method achieves an average object-level AUROC of 92.1% and 85.9% on the Anomaly-ShapeNet and Real3D-AD datasets, outperforming the current best approach by 2.1% and 3.6%, respectively. Codes are available at https://anonymous.4open.science/r/DLF-3AD-DA61.

Long-term time series forecasting requires models that simultaneously capture rapid oscillations, medium-range periodicities, and slowly evolving macro-trends from a fixed look-back window. Existing lightweight MLP-based models typically operate on a single temporal resolution, limiting their ability to explicitly model patterns at multiple scales. We propose MSMixer, a channel-independent multi-scale MLP architecture that addresses this limitation through three complementary innovations: (i) three parallel scale branches at down-sample factors {1x, 4x, 16x} with independent MLP blocks, (ii) a learnable softmax gate that dynamically weighs branch outputs, and (iii) a DLinear complementary shortcut that provides full-window trend and seasonality context. MSMixer contains only 112K parameters at H=96 and runs at O(T) complexity. Evaluated on four ETT benchmarks with standard chronological splits and three random seeds, MSMixer achieves the lowest average MSE (0.357) among lightweight models, outperforming DLinear (0.386, -7.4%) and NLinear (0.365, -2.1%), winning 12 of 16 configurations. Against five Transformer-based baselines from the literature, MSMixer achieves best or second-best MSE in 9 of 16 configurations while using 5x fewer parameters than PatchTST. Ablation and sensitivity analyses confirm the complementary contributions of the multi-scale branches and the DLinear shortcut.

Representational collapse, where embeddings become anisotropic and lose multi-scale structure, can erode downstream performance long before performance metrics react. We propose an online, topology-aware monitor for evolving neural representations that couples Modular Morse Homology Maintenance (MMHM) with a composite Collapse Index (CI). Instead of rebuilding complexes each epoch, we apply sparse edits at a fixed scale and maintain a discrete Morse matching, yielding fast, incremental updates. Across LLM fine-tuning and temporal KGE training, CI provides a low-latency early-warning signal suitable for in-training interventions. Code and experimental scripts will be released publicly

In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from microscopic to macroscopic physics, making it a challenging multi-task problem to solve over all ranges simultaneously. Solving tasks in different asymptotic regions often encounter gradient conflicts, which can lead to the failure of multi-task learning. To address this challenge, we explicitly encode a hidden representation of these parameters, ensuring that the corresponding solving tasks are serialized for simultaneous training. Furthermore, to mitigate gradient conflicts, we segment the prediction results to construct task losses and introduce a novel gradient alignment metric to ensure a positive dot product between the final update and each loss-specific gradient. This metric maintains consistent optimization rates for all task losses and dynamically adjusts gradient magnitudes based on conflict levels. Moreover, we provide a mathematical proof demonstrating the convergence of the HRGrad method, which is evaluated across a range of challenging asymptotic-preserving neural networks (APNNs) scenarios. We conduct an extensive set of experiments encompassing the Bhatnagar-Gross-Krook (BGK) equation and the linear transport equation in all ranges of Knudsen number. Our results indicate that HRGrad effectively overcomes the `failure modes' of APNNs in these problems.

Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that structural similarity at a fixed resolution is sufficient. The role of spatial scale in deep-feature similarity modeling thus remains insufficiently understood. In this letter, we isolate spatial scale as an independent factor using a minimal multiscale extension of DeepSSIM, referred to as Deep Structural Similarity with Multiscale Representation (MSDS). The proposed framework decouples deep feature representation from cross-scale integration by computing DeepSSIM independently across pyramid levels and fusing the resulting scores with a lightweight set of learnable global weights. Experiments on multiple benchmark datasets demonstrate consistent and statistically significant improvements over the single-scale baseline, while introducing negligible additional complexity. The results empirically confirm spatial scale as a non-negligible factor in deep perceptual similarity, isolated here via a minimal testbed.

Microscopy-based phenotypic profiling is scalable for drug discovery but lacks the mechanistic depth of transcriptomics, which remains costly and scarce. Existing multimodal approaches either use images to support other modalities or naively align representations by sample identity, ignoring cell-type and dose variations in weakly paired data-limiting generalization to unseen interventions. In this paper, we introduce an intervention-aware distillation framework that leverages perturbational transcriptomics to guide image representation learning. A transcriptome-conditioned teacher integrates gene expression and intervention metadata to produce soft distributions over a chemistry-aware codebook organized by drug similarity. The teacher employs a fine-tuned single-cell foundation model to encode cell-type context and disentangle dose effects. An image-only student learns to predict these distributions from microscopy alone, distilling mechanistic knowledge while operating independently at test time. This design emphasizes intervention semantics rather than identity alignment and explicitly handles dose and cell-type mismatches. We provide theoretical guarantees showing that transcriptomic guidance tightens the risk bound for image-based prediction. On Cell Painting and RxRx datasets paired with L1000, our method significantly improves one-shot transfer to unseen interventions and drug-target gene discovery compared to self-supervised and alignment baselines.

Query-based 3D object detection methods using multi-view images often struggle to efficiently leverage dynamic multi-scale information, e.g., the relationship between the object features and the geometric of the queries are not sufficiently learned, directly exploring the multi-scale spatiotemporal features will pay too many costs. To address these challenges, we propose CAM3DNet, a novel sparse query-based framework which combines three new modules, composite query (CQ), adaptive self-attention (ASA), and multi-scale hybrid sampling (MSHS). First, the core idea in the CQ module is a multi-scale projection strategy to transform 2D queries into 3D space. Second, the ASA module learns the interactions between the spatiotemporal multi-scale queries. Third, the MSHS module uses the deformable attention mechanism to sample multi-scale object information by considering multi-scales queries, pyramid feature maps, and 2D-camera prior knowledge. The entire model employs a backbone network and a feature pyramid network (FPN) as the encoder, then introduces a YOLOX and a DepthNet as a ROI_Head to produce CQ, and repeatedly utilizes ASA and MSHS as the decoder to gain detection features. Extensive experiments on the nuScenes, Waymo, and Argoverse benchmark datasets demonstrate the effectiveness of our CAM3DNet, and most existing camera-based 3D object detection methods are outperformed. Besides, we make comprehensive ablation studies to check the individual effect of CQ, ASA, and MSHS, as well as their cost of space and computation complexity.

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework for representing images, audio, video, 3D geometry, and beyond as continuous functions of their coordinates. This functional viewpoint enables signal operations such as differentiation to be carried out analytically through automatic differentiation rather than through discrete approximations. In this article, we examine the evolution of INRs from a signal processing perspective, emphasizing spectral behavior, sampling theory, and multiscale representation. We trace the progression from standard coordinate based networks, which exhibit a spectral bias toward low frequency components, to more advanced designs that reshape the approximation space through specialized activations, including periodic, localized, and adaptive functions. We also discuss structured representations, such as hierarchical decompositions and hash grid encodings, that improve spatial adaptivity and computational efficiency. We further highlight the utility of INRs across a broad range of applications, including inverse problems in medical and radar imaging, compression, and 3D scene representation. By interpreting INRs as learned signal models whose approximation spaces adapt to the underlying data, this article clarifies the field's core conceptual developments and outlines open challenges in theoretical stability, weight space interpretability, and large scale generalization.

Alzheimer's disease (AD) confirmation often relies on positron emission tomography (PET) or cerebrospinal fluid (CSF) analysis, which are costly and invasive. Consequently, structural MRI biomarkers such as cortical thickness (CT) are widely used for non-invasive AD screening. Multiscale structural mapping (MSSM) was recently proposed to integrate gray-white matter contrasts (GWCs) with CT from a single T1-weighted MRI (T1w) scan. Building on this framework, we propose MSSM+, together with surface supervertex mapping (SSVM) and a Supervertex Vision Transformer (SV-ViT). 3D T1w images from individuals with AD and cognitively normal (CN) controls were analyzed. MSSM+ extends MSSM by incorporating sulcal depth and cortical curvature at the vertex level. SSVM partitions the cortical surface into supervertices (surface patches) that effectively represent inter- and intra-regional spatial relationships. SV-ViT is a Vision Transformer architecture operating on these supervertices, enabling anatomically informed learning from surface mesh representations. Compared with MSSM, MSSM+ identified more spatially extensive and statistically significant group differences between AD and CN. In AD vs. CN classification, MSSM+ achieved a 3%p higher area under the precision-recall curve than MSSM. Vendor-specific analyses further demonstrated reduced signal variability and consistently improved classification performance across MR manufacturers relative to CT, GWCs, and MSSM. These findings suggest that MSSM+ combined with SV-ViT is a promising MRI-based imaging marker for AD detection prior to CSF/PET confirmation.

Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure. Neighbor embedding methods such as t-SNE and UMAP prioritize local similarity preservation but do not explicitly constrain global organization, whereas standard spectral methods such as Laplacian Eigenmaps capture smooth, coarse-scale graph structure but offer limited flexibility to depict finer local structure. Second, the flexibility of nonlinear DR methods often comes at the cost of analytical transparency. Many methods do not explicitly reveal how high-dimensional structure produces patterns in the embedding. We introduce SDMP (Spectral Decomposition for Multiscale Projection), a nonlinear DR framework built on an explicit spectral decomposition. In this formulation, each embedding dimension is expressed as a weighted combination of Laplacian eigenvectors derived from a neighborhood graph, with the weights learned via a UMAP-style cross-entropy objective. By progressively expanding the spectral subspace to capture increasingly fine graph structure, SDMP produces a sequence of embeddings, making the evolving balance between global organization and local detail explicit, controllable, and inspectable. The explicit decomposition also reveals which spectral scales shape the overall embedding and how individual eigenvectors influence point positions. Quantitative evaluations on synthetic, image, and single-cell data show competitive local and global structure preservation, while case studies illustrate how the decomposition supports interpretation of clusters and developmental trajectories across spectral scales.

Modeling multiscale patterns is crucial for long-term time series forecasting (TSF). However, redundancy and noise in time series, together with semantic gaps between non-adjacent scales, make the efficient alignment and integration of multi-scale temporal dependencies challenging. To address this, we propose SEMixer, a lightweight multiscale model designed for long-term TSF. SEMixer features two key components: a Random Attention Mechanism (RAM) and a Multiscale Progressive Mixing Chain (MPMC). RAM captures diverse time-patch interactions during training and aggregates them via dropout ensemble at inference, enhancing patch-level semantics and enabling MLP-Mixer to better model multi-scale dependencies. MPMC further stacks RAM and MLP-Mixer in a memory-efficient manner, achieving more effective temporal mixing. It addresses semantic gaps across scales and facilitates better multiscale modeling and forecasting performance. We not only validate the effectiveness of SEMixer on 10 public datasets, but also on the \textit{2025 CCF AlOps Challenge} based on 21GB real wireless network data, where SEMixer achieves third place. The code is available at the link https://github.com/Meteor-Stars/SEMixer.

Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to $k$-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.

Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales. Despite recent advances leveraging different decomposition operations and novel architectures based on CNN, MLP or Transformer, existing methods still struggle with static decomposition strategies, fragmented dependency modeling, and inflexible fusion mechanisms, limiting their ability to model intricate temporal dependencies. To explicitly solve the mentioned three problems respectively, we propose a novel Dynamic Multi-Scale Coordination Framework (DMSC) with Multi-Scale Patch Decomposition block (EMPD), Triad Interaction Block (TIB) and Adaptive Scale Routing MoE block (ASR-MoE). Specifically, EMPD is designed as a built-in component to dynamically segment sequences into hierarchical patches with exponentially scaled granularities, eliminating predefined scale constraints through input-adaptive patch adjustment. TIB then jointly models intra-patch, inter-patch, and cross-variable dependencies within each layer's decomposed representations. EMPD and TIB are jointly integrated into layers forming a multi-layer progressive cascade architecture, where coarse-grained representations from earlier layers adaptively guide fine-grained feature extraction in subsequent layers via gated pathways. And ASR-MoE dynamically fuses multi-scale predictions by leveraging specialized global and local experts with temporal-aware weighting. Comprehensive experiments on thirteen real-world benchmarks demonstrate that DMSC consistently maintains state-of-the-art (SOTA) performance and superior computational efficiency for TSF tasks. Code is available at https://github.com/1327679995/DMSC.

Small-object detection in Unmanned Aerial Vehicle (UAV) imagery requires preserving weak local evidence while using broader context to separate tiny foreground targets from cluttered backgrounds. Existing multi-scale fusion methods improve feature aggregation, but they often add computation or blur fine details during repeated cross-scale fusion. The central challenge is to balance low-SNR target preservation, clutter suppression, and efficient cross-scale context exchange. To address this challenge, we propose the Multi-scale Global-detail Feature Integration Strategy (MGDFIS), a neck-level feature-fusion strategy that couples global context exchange, local-detail recovery, and pixel-level foreground-background recalibration. MGDFIS integrates three coordinated modules: FusionLock-TSS Attention for stabilizing spectral-spatial responses, Global-detail Integration for combining long-range mixing with local detail capture, and Dynamic Pixel Attention for reweighting compact foreground regions. On the controlled VisDrone setting, YOLO26m + MGDFIS improves AP50:95 from 25.7 to 30.2 and AP50 from 37.2 to 44.2 over the YOLO26m baseline, with 96.1 GFLOPs. Additional dataset-specific evaluations report 38.9 AP50 and 21.9 AP50:95 on UAVDT and 97.4 AP50 on CARPK. The code is available at: https://github.com/JackBaixue/MGDFIS.

In real-world applications of image recognition tasks, such as human pose estimation, cameras often capture objects, like human bodies, at low resolutions. This scenario poses a challenge in extracting and leveraging multi-scale features, which is often essential for precise inference. To address this challenge, we propose a new attention mechanism, named cascaded multi-scale attention (CMSA), tailored for use in CNN-ViT hybrid architectures, to handle low-resolution inputs effectively. The design of CMSA enables the extraction and seamless integration of features across various scales without necessitating the downsampling of the input image or feature maps. This is achieved through a novel combination of grouped multi-head self-attention mechanisms with window-based local attention and cascaded fusion of multi-scale features over different scales. This architecture allows for the effective handling of features across different scales, enhancing the model's ability to perform tasks such as human pose estimation, head pose estimation, and more with low-resolution images. Our experimental results show that the proposed method outperforms existing state-of-the-art methods in these areas with fewer parameters, showcasing its potential for broad application in real-world scenarios where capturing high-resolution images is not feasible. Code is available at https://github.com/xyongLu/CMSA.