Recent success in contrastive learning has sparked growing interest in more effectively leveraging multiple augmented views of an instance. While prior methods incorporate multiple views at the loss or feature level, they primarily capture pairwise relationships and fail to model the joint structure across all views. In this work, we propose a divergence-based similarity function (DSF) that explicitly captures the joint structure by representing each set of augmented views as a distribution and measuring similarity as the divergence between distributions. Extensive experiments demonstrate that DSF consistently improves performance across various tasks, including kNN classification and linear evaluation, while also offering greater efficiency compared to other multi-view methods. Furthermore, we establish a theoretical connection between DSF and cosine similarity, and show that, unlike cosine similarity, DSF operates effectively without requiring a temperature hyperparameter.

Wafer probing is a critical inspection stage in semiconductor manufacturing, where the electrical behavior of on-wafer circuits is evaluated prior to packaging. Most existing wafer anomaly detection approaches have primarily relied on image-based inspection, while recent time-series–based models such as SwinProbeFormer have focused on detecting over-gain anomalies in probing signals. In contrast, undergain anomalies have received relatively little attention due to their subtle deviation from normal probing behavior, despite their significant impact on probing efficiency and test-cell throughput. In this paper, we propose M-WAD, a multimodal wafer anomaly detection framework that jointly leverages time-series signals, data-specific visual representations, and textual prompts to effectively detect undergain anomalies during wafer probing. M-WAD introduces a domain-aware residual image generation strategy that amplifies subtle motion degradations and enables robust multimodal representation learning. Extensive experimental results on real-world wafer probing datasets demonstrate that the proposed approach achieves state-of-the-art performance in undergain anomaly detection and consistently outperforms existing methods, including models tailored for wafer probing. These results highlight the effectiveness of multimodal learning for capturing subtle probing anomalies and its potential for practical deployment in industrial wafer testing environments.

Abstract. This paper proposes a theoretical framework for analyzing modified incomplete LU (MILU) preconditioners for coefficient matrices that are symmetric positive definite M-matrices. Considering a generalized MILU preconditioner on a weighted undirected graph with self-loops, we extend its applicability beyond matrices derived from Poisson equation solvers on uniform grids with compact stencils. A major contribution is a novel measure, the localized estimator of condition number (LECN), which quantifies the condition number locally at each vertex of the graph. We prove that the maximum value of the LECN provides an upper bound for the condition number of the MILU-preconditioned system, offering an estimation of the condition number using only local measurements. This localized approach significantly simplifies the condition number estimation and provides a powerful tool for analyzing the MILU preconditioner applied to previously unexplored matrix structures. To demonstrate the usability of LECN analysis, we present three cases: (1) a revisit of existing results of MILU preconditioners on uniform grids, (2) analysis of high-order implicit finite difference schemes on wide stencils, and (3) analysis of variable coefficient Poisson equations on hierarchical adaptive grids such as quadtree and octree. For the third case, we also validate LECN analysis numerically on a quadtree.

Multivariate long-term time series forecasting (LTSF) supports critical applications such as traffic-flow management, solar-power scheduling, and electricity-transformer monitoring. The existing LTSF paradigms follow a three-stage pipeline of embedding, backbone refinement, and long-horizon prediction. However, the behaviors of individual backbone layers remain underexplored. We introduce layer sensitivity, a gradient-based metric inspired by GradCAM and effective receptive field theory, which quantifies both positive and negative contributions of each time point to a layer's latent features. Applying this metric to a three-layer MLP backbone reveals depth-specific specialization in modeling temporal dynamics in the input sequence. Motivated by these insights, we propose MoDEx, a lightweight Mixture of Depth-specific Experts, which replaces complex backbones with depth-specific MLP experts. MoDEx achieves state-of-the-art accuracy on seven real-world benchmarks, ranking first in 78 percent of cases, while using significantly fewer parameters and computational resources. It also integrates seamlessly into transformer variants, consistently boosting their performance and demonstrating robust generalizability as an efficient and high-performance LTSF framework.

Building reliable low-dimensional representations of fluid flows is central to data-driven modeling, control, and design, yet it remains unclear when modern local feature encoders offer advantages over classical global decompositions within a fixed configuration. Here, we compare a Galilean-invariant local descriptor field that encodes each grid point from a small neighborhood using relative geometric and physical differences and advances descriptors with a lightweight pointwise latent dynamics model, against baselines: a raw patch autoencoder, local principal component analysis, a global convolutional autoencoder, and global proper orthogonal decomposition (POD). We benchmark two-dimensional incompressible flows spanning an analytic Taylor-Green vortex, lid-driven cavity flows at Re = 100 and 500, and channel Poiseuille flow. Under a common protocol with matched training budgets, we evaluate one-step field error and physics-aware metrics beyond mean-squared error, including vorticity and divergence errors, a Galilean invariance diagnostic, one-step latent prediction error, and multi-step full-field rollouts obtained by iterating the learned latent dynamics. On self-dataset evaluation, global POD achieves near-oracle one-step accuracy, explained by rapid energy saturation in POD diagnostics. Among learned models, the descriptor is competitive in one-step prediction while consistently reducing divergence and latent dynamics errors relative to global convolutional compression. Rollout evaluation highlights stability trade-offs under iteration, underscoring that one-step accuracy alone is insufficient to characterize dynamical usability. These results quantify practical trade-offs between global modal and local descriptor-based encodings under a reproducible benchmark and provide a physics-aware baseline for future descriptor designs in computational fluid dynamics.

Text-to-Image (T2I) diffusion models enable high quality open ended synthesis, but practical use requires suppressing unsafe generations while preserving behavior on benign prompts. We study this tension relative to the frozen generator, using its prompt conditioned distribution as the preservation reference. Since T2I safety is commonly evaluated by bounded risk scores on generated images, total variation (TV) bounds how much expected risk can change from this reference. We call this fixed reference constraint the Safety-Prompt Alignment Tradeoff (SPAT): reducing expected unsafety requires prompt conditioned distributional deviation. To make this deviation selective and adjustable, we define the tau safe set as prompts whose reference risk is at most tau, and cast intervention as projection toward nearby prompts in this set. We propose Selective Prompt prOjecTion (SPOT), an inference time framework that approximates this projection without retraining the generator or learning a category specific rewriter. SPOT uses an LLM to rank candidate rewrites and a safeguard VLM to accept generated images under the same tau. Across four datasets and three diffusion backbones, SPOT achieves relative inappropriate (IP) score reductions from 14.2

Self-supervised learning (SSL) in computer vision has advanced through joint-embedding methods that learn representations invariant to semantic transformations between image pairs. However, although geometric transformations such as rotation are semantically invariant, learning rotation-invariant representations remains challenging due to the inherently rotation-equivariant nature of object images. Previous methods attempted to improve rotation robustness via equivariant learning, yet a clear performance gap persists between non-rotated and rotated samples. To address these limitations, we propose GIE (Guiding Invariance with Equivariance), a framework that forms rotation-invariant representations guided by the rotation-equivariant structure of images. GIE employs group-equivariant convolutional networks to produce strictly rotation-equivariant feature maps. An equivariance-guided orientation-alignment step then transforms equivariant features into invariant embeddings while preserving discriminative information. This eliminates the need for repeated inferences required in canonicalization, enabling computationally efficient and scalable training within standard SSL frameworks. Experimental results show that across multiple SSL frameworks—including SimCLR, SimSiam, and MoCo v2—GIE significantly improves robustness on rotated data. Notably, it yields up to a 7% gain over the base p4-equivariant CNN and up to a 24% gain over standard ResNet backbones. These results demonstrate the effectiveness of GIE in learning robust, rotation-invariant representations.

The Convolutional Neural Network (CNN) is one of the most prominent neural network architectures in deep learning. Despite its widespread adoption, our understanding of its universal approximation properties has been limited due to its intricate nature. CNNs inherently function as tensor-to-tensor mappings, preserving the spatial structure of input data. However, limited research has explored the universal approximation properties of fully convolutional neural networks as arbitrary continuous tensor-to-tensor functions. In this study, we demonstrate that CNNs, when utilizing zero padding, can approximate arbitrary continuous functions in cases where both the input and output values exhibit the same spatial shape. Additionally, we determine the minimum depth of the neural network required for approximation and substantiate its optimality. We also verify that deep, narrow CNNs possess the UAP as tensor-to-tensor functions. The results encompass a wide range of activation functions, and our research covers CNNs of all dimensions.

Reference-based super-resolution (RefSR) aims to enhance low-resolution (LR) imagery by leveraging auxiliary reference observations. While effective under controlled settings, most existing RefSR methods implicitly assume that reference images are clean or geometrically consistent with the target input. In real-world remote sensing systems, however, reference observations are frequently degraded by sensor noise, atmospheric blur, and geometric inconsistencies caused by different viewing angles and acquisition times. Moreover, due to the inherent resolution gap between LR and reference images, strict spectral consistency is difficult to guarantee in practice. These factors substantially reduce the reliability of reference cues and limit the applicability of RefSR in multisensor satellite imaging scenarios. To address these challenges, we propose spectral fusion super-resolution (SFSR), a diffusion-based RefSR framework designed to operate robustly under degraded reference conditions. At its core, SFSR introduces the spectral swin cross-attention module (S2CAM), which enables frequency-aware reference utilization and integrates the refined reference features as conditional guidance within the reverse diffusion process. By explicitly redistributing spectral components and suppressing unreliable high-frequency responses introduced by noise, SFSR enables stable and effective use of reference information that conventional RefSR methods struggle to exploit. Extensive experiments on synthetic and benchmark satellite datasets demonstrate that SFSR consistently outperforms state-of-the-art RefSR approaches in terms of peak signal-to-noise ratio (PSNR), similarity index measure (SSIM), and perceptual metrics while maintaining high visual fidelity under severe degradation. In addition, evaluations on downstream tasks such as object detection and semantic segmentation show that SFSR leads to clear performance improvements, confirming its robustness and practical value for real-world multisensor remote sensing applications.

Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions selected by reconstruction and Riemann solvers. Here we introduce an operator-level formulation in which conservative dynamics is realized as an exact discrete interaction rule on a quantized state space. The update is defined by an antisymmetric integer-transfer operator, which enforces conservation exactly at the arithmetic level and eliminates round-off drift from the primitive evolution . For scalar laws, monotone order-preserving transfers select admissible shock structures within the primitive update, rather than through flux reconstruction. Numerical experiments show that the interaction rule preserves high-frequency transport near the Nyquist limit and maintains sharply localized discontinuities in Burgers dynamics. The same construction extends to multidimensional problems and systems of conservation laws through oriented, vector-valued integer transfers. These results indicate that conservative dynamics admits an exact discrete realization in which both invariance and entropy selection are encoded at the operator level, rather than arising from approximate flux cancellation.

Deepfake technologies pose increasing threats to facial privacy and identity security, motivating proactive defenses that protect facial images before misuse. Although adversarial perturbations generated by projected gradient descent (PGD) can disrupt the identity representations used by face-swapping models, their visual quality is degraded by two characteristics: perturbations are distributed broadly over the image, including identity-insensitive regions, and they contain visually salient high-frequency components. We analyze these spatial and spectral inefficiencies through identity-sensitivity estimation and the singular-value decomposition (SVD) of PGD perturbations. Our analysis shows that later singular components contain a disproportionate amount of high-frequency energy, while the leading components preserve most of the perturbation energy and defense utility. Based on these observations, we propose SRAP, which combines per-channel truncated SVD refinement with an identity-importance mask at every optimization step. The SVD refinement suppresses high-rank, high-frequency residuals, while the mask restricts perturbations to locations that strongly influence identity representations. Experiments on CelebA-HQ and VGGFace2-HQ demonstrate that SRAP substantially improves protected-image fidelity across all reported metrics while maintaining competitive identity-disruption performance, yielding a favorable trade-off between face-swap defense and visual imperceptibility.

Conservative dynamics are typically computed as floating-point approximations to continuum differential operators, which can obscure conservation through rounding and discretisation artefacts. Here we instead formulate conservative evolution directly as quantised interaction rules acting on countable states. The resulting Fast Quantised Numerical Method (FQNM) executes dynamics through antisymmetric integer transfer, with physical fields appearing only after reconstruction. In high-frequency transport, the method remains accurate deep into the Nyquist regime where a standard high-order floating-point baseline deteriorates. In nonlinear shock formation, it preserves grid-level structure and remains robust to cell drifting while maintaining exact discrete conservation. These results show that conservative dynamics can be executed directly through discrete interaction rules, with continuum behaviour emerging only as a reconstruction of underlying quantised states.

Text-to-image (T2I) generation model has made significant advancements, resulting in high-quality images aligned with an input prompt. However, despite T2I generation's ability to generate fine-grained images, it still faces challenges in accurately generating images when the input prompt contains complex concepts, especially human pose. In this paper, we propose PointT2I, a framework that effectively generates images that accurately correspond to the human pose described in the prompt by using a large language model (LLM). PointT2I consists of three components: Keypoint generation, Image generation, and Feedback system. The keypoint generation uses an LLM to directly generate keypoints corresponding to a human pose, solely based on the input prompt, without external references. Subsequently, the image generation produces images based on both the text prompt and the generated keypoints to accurately reflect the target pose. To refine the outputs of the preceding stages, we incorporate an LLM-based feedback system that assesses the semantic consistency between the generated contents and the given prompts. Our framework is the first approach to leveraging LLM for keypoints-guided image generation without any fine-tuning, producing accurate pose-aligned images based solely on textual prompts.

Despite remarkable advances in image generation, existing diffusion models struggle to capture diverse cultural aesthetics. While Low-Rank Adaptation (LoRA) enables efficient fine-tuning, conventional approaches lack semantic awareness. They apply uniform adaptations across all features, leading to suboptimal cultural representation. To address these limitations, we introduce K-StyleLoRA, a novel framework that leverages CLIP's cross-modal capabilities for cultural image generation. Our approach introduces two key contributions. First, CLIP-Guided Information Gating dynamically modulates LoRA adaptations based on cultural relevance scores, selectively enhancing relevant features while suppressing irrelevant ones. Second, Cultural Semantic Loss provides additional semantic guidance by optimizing CLIP-based similarity to cultural concepts. Extensive experiments on Korean traditional culture show superior cultural fidelity while maintaining generation quality and diversity. In particular, K-StyleLoRA demonstrates exceptional cultural transfer capability on generic prompts that require implicit cultural understanding. Our method achieves a Cultural Similarity Score of 0.274, representing a 9.6% improvement over the vanilla SDXL baseline (0.250). Our framework establishes semantic-aware adaptation as a powerful paradigm for cultural representation. This scalable approach can be extended to diverse cultural contexts and generation tasks beyond Korean aesthetics.

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma motion through ideal MHD equations. Solving these hyperbolic PDEs requires sophisticated numerical methods, presenting computational challenges due to complex structures and high costs. Recent advances introduce neural operators like the Fourier Neural Operator (FNO) as surrogate models for traditional numerical analysis. This study proposes a modified Flux Neural Operator (Flux NO) model to approximate the numerical flux of ideal MHD, offering a novel approach with enhanced generalization capabilities and significant computational efficiency. Our methodology adapts the Flux NO to process each physical quantity individually and incorporates loss functions ensuring total variation diminishing (TVD) property and divergence freeness for numerical stability. The proposed method achieves superior generalization beyond sampled distributions compared to existing neural operators and demonstrates computation speeds 25 times faster than the reference numerical scheme.

In this paper, we propose the neural shortest path (NSP), a vector-valued implicit neural representation (INR) that approximates a distance function and its gradient. The key feature of NSP is to learn the exact shortest path (ESP), which directs an arbitrary point to its nearest point on the target surface. The NSP is decomposed into its magnitude and direction, and a variable splitting method is used that each decomposed component approximates a distance function and its gradient, respectively. Unlike to existing methods of learning the distance function itself, the NSP ensures the simultaneous recovery of the distance function and its gradient. We mathematically prove that the decomposed representation of NSP guarantees the convergence of the magnitude of NSP in the H^1 norm. Furthermore, we devise a novel loss function that enforces the property of ESP, demonstrating that its global minimum is the ESP. We evaluate the performance of the NSP through comprehensive experiments on diverse datasets, validating its capacity to reconstruct high-quality surfaces with the robustness to noise and data sparsity. The numerical results show substantial improvements over state-of-the-art methods, highlighting the importance of learning the ESP, the product of distance function and its gradient, for representing a wide variety of complex surfaces.

With the rapid advancement of Artificial Intelligence (AI) and computing technologies, improving semiconductor yield and detecting defective wafers before packaging has become increasingly important. However, anomaly detection during wafer probing remains challenging due to issues such as probe-to-wafer misalignment, pad scratches, and electrical noise from friction. To address these challenges, we introduce SwinProbeFormer, a model specifically designed to detect overgain anomalies in wafer prober equipment using dynamic probe sensor data collected during the wafer probing process. Built on the Swin Transformer architecture, SwinProbeFormer leverages window-based attention and cyclic shifts to enhance spatial-temporal learning while maintaining computational efficiency. Experimental results show that SwinProbeFormer outperforms the vanilla Transformer encoder used in AnomalyBERT, achieving the highest F1 scores among baseline models. It also demonstrates strong generalization across diverse production lots, highlighting its robustness and adaptability for practical deployment in wafer probing environments.

Self-supervised learning (SSL) has made significant progress through joint-embedding methods that learn in-variant representations across transformed views. However, achieving robustness to image rotations remains challenging, as naively incorporating rotation augmentations often degrades performance. Inspired by cognitive studies on human mental rotation, we propose FRTAlign, an SSL framework with feature-level alignment that explicitly mitigates rotation-induced shifts in the representation space. FRTAlign introduces a unified module that learns rotation-equivariant feature transformations and combines them with a lightweight rotation predictor to produce human-inspired rotation-invariant representations. This design enables the model to preserve performance on non-rotated samples while significantly improving robustness to rotated inputs. Through extensive experiments on STL10, Ima-geNet100, and EMNIST, we demonstrate that FRTAlign consistently outperforms baselines in both standard and rotated settings. Further analysis reveals that our method mitigates distributional shifts caused by rotation and is robust to architectural and hyperparameter variations.

We introduce Multimodal Matching based on Valence and Arousal (MMVA), a tri-modal encoder framework designed to capture emotional content across images, music, and musical captions. To support this framework, we expand the Image-Music-Emotion-Matching-Net (IMEMNet) dataset, creating IMEMNet-C which includes 24,756 images and 25,944 music clips with corresponding musical captions. We employ multimodal matching scores based on the continuous valence (emotional positivity) and arousal (emotional intensity) values. This continuous matching score allows for random sampling of image-music pairs during training by computing similarity scores from the valence-arousal values across different modalities. Consequently, the proposed approach achieves state-of-the-art performance in valence-arousal prediction tasks. Furthermore, the framework demonstrates its efficacy in various zeroshot tasks, highlighting the potential of valence and arousal predictions in downstream applications.