Riemannian and Symplectic Geometry for Hierarchical Text-Driven Place Recognition

Text-to-point-cloud localization enables robots to understand spatial positions through natural language descriptions, which is crucial for human-robot collaboration in applications such as autonomous driving and last-mile delivery. However, existing methods employ pooled global descriptors for similarity retrieval, which suffer from severe information loss and fail to capture discriminative scene structures. To address these issues, we propose SympLoc, a novel coarse-to-fine localization framework with multi-level alignment in the coarse stage. Different from previous methods that rely solely on global descriptors, our coarse stage consists of three complementary alignment levels: 1) Instance-level alignment establishes direct correspondence between individual object instances in point clouds and textual hints through Riemannian self-attention in hyperbolic space; 2) Relation-level alignment explicitly models pairwise spatial relationships between objects using the Information-Symplectic Relation Encoder (ISRE), which reformulates relation features through Fisher-Rao metric and Hamiltonian dynamics for uncertainty-aware geometrically consistent propagation; 3) Global-level alignment synthesizes discriminative global descriptors via the Spectral Manifold Transform (SMT) that extracts structural invariants through graph spectral analysis. This hierarchical alignment strategy progressively captures fine-grained to coarse-grained scene semantics, enabling robust cross-modal retrieval. Extensive experiments on the KITTI360Pose dataset demonstrate that SympLoc achieves a 19% improvement in Top-1 recall@10m compared to existing state-of-the-art approaches.

Conditional Diffusion-Based Point Cloud Imaging for UAV Position and Attitude Sensing

This paper studies an unmanned aerial vehicle (UAV) position and attitude sensing problem, where a base station equipped with an antenna array transmits signals to a predetermined potential flight region of a flying UAV, and exploits the reflected echoes for wireless imaging. The UAV is represented by an electromagnetic point cloud in this region that contains its spatial information and electromagnetic properties (EPs), enabling the unified extraction of UAV position, attitude, and shape from the reconstructed point cloud. To accomplish this task, we develop a generative UAV sensing approach. The position and signal-to-noise ratio embedding are adopted to assist the UAV features extraction from the estimated sensing channel under the measurement noise and channel variations. Guided by the obtained features, a conditional diffusion model is utilized to generate the point cloud. The simulation results demonstrate that the reconstructed point clouds via the proposed approach present higher fidelity compared to the competing schemes, thereby enabling a more accurate capture of the UAV attitude and shape information, as well as a more precise position estimation.

AnnoRetrieve: Efficient Structured Retrieval for Unstructured Document Analysis

Unstructured documents dominate enterprise and web data, but their lack of explicit organization hinders precise information retrieval. Current mainstream retrieval methods, especially embedding-based vector search, rely on coarse-grained semantic similarity, incurring high computational cost and frequent LLM calls for post-processing. To address this critical issue, we propose AnnoRetrieve, a novel retrieval paradigm that shifts from embeddings to structured annotations, enabling precise, annotation-driven semantic retrieval. Our system replaces expensive vector comparisons with lightweight structured queries over automatically induced schemas, dramatically reducing LLM usage and overall cost. The system integrates two synergistic core innovations: SchemaBoot, which automatically generates document annotation schemas via multi-granularity pattern discovery and constraint-based optimization, laying a foundation for annotation-driven retrieval and eliminating manual schema design, and Structured Semantic Retrieval (SSR), the core retrieval engine, which unifies semantic understanding with structured query execution; by leveraging the annotated structure instead of vector embeddings, SSR achieves precise semantic matching, seamlessly completing attribute-value extraction, table generation, and progressive SQL-based reasoning without relying on LLM interventions. This annotation-driven paradigm overcomes the limitations of traditional vector-based methods with coarse-grained matching and heavy LLM dependency and graph-based methods with high computational overhead. Experiments on three real-world datasets confirm that AnnoRetrieve significantly lowers LLM call frequency and retrieval cost while maintaining high accuracy. AnnoRetrieve establishes a new paradigm for cost-effective, precise, and scalable document analysis through intelligent structuring.

ContextClaim: A Context-Driven Paradigm for Verifiable Claim Detection

Verifiable claim detection asks whether a claim expresses a factual statement that can, in principle, be assessed against external evidence. As an early filtering stage in automated fact-checking, it plays an important role in reducing the burden on downstream verification components. However, existing approaches to claim detection, whether based on check-worthiness or verifiability, rely solely on the claim text itself. This is a notable limitation for verifiable claim detection in particular, where determining whether a claim is checkable may benefit from knowing what entities and events it refers to and whether relevant information exists to support verification. Inspired by the established role of evidence retrieval in later-stage claim verification, we propose Context-Driven Claim Detection (ContextClaim), a paradigm that advances retrieval to the detection stage. ContextClaim extracts entity mentions from the input claim, retrieves relevant information from Wikipedia as a structured knowledge source, and employs large language models to produce concise contextual summaries for downstream classification. We evaluate ContextClaim on two datasets covering different topics and text genres, the CheckThat! 2022 COVID-19 Twitter dataset and the PoliClaim political debate dataset, across encoder-only and decoder-only models under fine-tuning, zero-shot, and few-shot settings. Results show that context augmentation can improve verifiable claim detection, although its effectiveness varies across domains, model architectures, and learning settings. Through component analysis, human evaluation, and error analysis, we further examine when and why the retrieved context contributes to more reliable verifiability judgments.

Hybrid Quantum-Classical AI for Industrial Defect Classification in Welding Images

Hybrid quantum-classical machine learning offers a promising direction for advancing automated quality control in industrial settings. In this study, we investigate two hybrid quantum-classical approaches for classifying defects in aluminium TIG welding images and benchmarking their performance against a conventional deep learning model. A convolutional neural network is used to extract compact and informative feature vectors from weld images, effectively reducing the higher-dimensional pixel space to a lower-dimensional feature space. Our first quantum approach encodes these features into quantum states using a parameterized quantum feature map composed of rotation and entangling gates. We compute a quantum kernel matrix from the inner products of these states, defining a linear system in a higher-dimensional Hilbert space corresponding to the support vector machine (SVM) optimization problem and solving it using a Variational Quantum Linear Solver (VQLS). We also examine the effect of the quantum kernel condition number on classification performance. In our second method, we apply angle encoding to the extracted features in a variational quantum circuit and use a classical optimizer for model training. Both quantum models are tested on binary and multiclass classification tasks and the performance is compared with the classical CNN model. Our results show that while the CNN model demonstrates robust performance, hybrid quantum-classical models perform competitively. This highlights the potential of hybrid quantum-classical approaches for near-term real-world applications in industrial defect detection and quality assurance.

The Rashomon Effect for Visualizing High-Dimensional Data

Dimension reduction (DR) is inherently non-unique: multiple embeddings can preserve the structure of high-dimensional data equally well while differing in layout or geometry. In this paper, we formally define the Rashomon set for DR -- the collection of `good' embedding -- and show how embracing this multiplicity leads to more powerful and trustworthy representations. Specifically, we pursue three goals. First, we introduce PCA-informed alignment to steer embeddings toward principal components, making axes interpretable without distorting local neighborhoods. Second, we design concept-alignment regularization that aligns an embedding dimension with external knowledge, such as class labels or user-defined concepts. Third, we propose a method to extract common knowledge across the Rashomon set by identifying trustworthy and persistent nearest-neighbor relationships, which we use to construct refined embeddings with improved local structure while preserving global relationships. By moving beyond a single embedding and leveraging the Rashomon set, we provide a flexible framework for building interpretable, robust, and goal-aligned visualizations.

ColorFLUX: A Structure-Color Decoupling Framework for Old Photo Colorization

Old photos preserve invaluable historical memories, making their restoration and colorization highly desirable. While existing restoration models can address some degradation issues like denoising and scratch removal, they often struggle with accurate colorization. This limitation arises from the unique degradation inherent in old photos, such as faded brightness and altered color hues, which are different from modern photo distributions, creating a substantial domain gap during colorization. In this paper, we propose a novel old photo colorization framework based on the generative diffusion model FLUX. Our approach introduces a structure-color decoupling strategy that separates structure preservation from color restoration, enabling accurate colorization of old photos while maintaining structural consistency. We further enhance the model with a progressive Direct Preference Optimization (Pro-DPO) strategy, which allows the model to learn subtle color preferences through coarse-to-fine transitions in color augmentation. Additionally, we address the limitations of text-based prompts by introducing visual semantic prompts, which extract fine-grained semantic information directly from old photos, helping to eliminate the color bias inherent in old photos. Experimental results on both synthetic and real datasets demonstrate that our approach outperforms existing state-of-the-art colorization methods, including closed-source commercial models, producing high-quality and vivid colorization.

Information-Theoretic Limits of Safety Verification for Self-Improving Systems

Can a safety gate permit unbounded beneficial self-modification while maintaining bounded cumulative risk? We formalize this question through dual conditions -- requiring sum delta_n < infinity (bounded risk) and sum TPR_n = infinity (unbounded utility) -- and establish a theory of their (in)compatibility. Classification impossibility (Theorem 1): For power-law risk schedules delta_n = O(n^{-p}) with p > 1, any classifier-based gate under overlapping safe/unsafe distributions satisfies TPR_n <= C_alpha * delta_n^beta via Holder's inequality, forcing sum TPR_n < infinity. This impossibility is exponent-optimal (Theorem 3). A second independent proof via the NP counting method (Theorem 4) yields a 13% tighter bound without Holder's inequality. Universal finite-horizon ceiling (Theorem 5): For any summable risk schedule, the exact maximum achievable classifier utility is U*(N, B) = N * TPR_NP(B/N), growing as exp(O(sqrt(log N))) -- subpolynomial. At N = 10^6 with budget B = 1.0, a classifier extracts at most U* ~ 87 versus a verifier's ~500,000. Verification escape (Theorem 2): A Lipschitz ball verifier achieves delta = 0 with TPR > 0, escaping the impossibility. Formal Lipschitz bounds for pre-LayerNorm transformers under LoRA enable LLM-scale verification. The separation is strict. We validate on GPT-2 (d_LoRA = 147,456): conditional delta = 0 with TPR = 0.352. Comprehensive empirical validation is in the companion paper [D2].

Rethinking Representations for Cross-Domain Infrared Small Target Detection: A Generalizable Perspective from the Frequency Domain

The accurate target-background separation in infrared small target detection (IRSTD) highly depends on the discriminability of extracted representations. However, most existing methods are confined to domain-consistent settings, while overlooking whether such discriminability can generalize to unseen domains. In practice, distribution shifts between training and testing data are inevitable due to variations in observational conditions and environmental factors. Meanwhile, the intrinsic indistinctiveness of infrared small targets aggravates overfitting to domain-specific patterns. Consequently, the detection performance of models trained on source domains can be severely degraded when deployed in unseen domains. To address this challenge, we propose a spatial-spectral collaborative perception network (S$^2$CPNet) for cross-domain IRSTD. Moving beyond conventional spatial learning pipelines, we rethink IRSTD representations from a frequency perspective and reveal inconsistencies in spectral phase as the primary manifestation of domain discrepancies. Based on this insight, we develop a phase rectification module (PRM) to derive generalizable target awareness. Then, we employ an orthogonal attention mechanism (OAM) in skip connections to preserve positional information while refining informative representations. Moreover, the bias toward domain-specific patterns is further mitigated through selective style recomposition (SSR). Extensive experiments have been conducted on three IRSTD datasets, and the proposed method consistently achieves state-of-the-art performance under diverse cross-domain settings.

ROMAN: A Multiscale Routing Operator for Convolutional Time Series Models

We introduce ROMAN (ROuting Multiscale representAtioN), a deterministic operator for time series that maps temporal scale and coarse temporal position into an explicit channel structure while reducing sequence length. ROMAN builds an anti-aliased multiscale pyramid, extracts fixed-length windows from each scale, and stacks them as pseudochannels, yielding a compact representation on which standard convolutional classifiers can operate. In this way, ROMAN provides a simple mechanism to control the inductive bias of downstream models: it can reduce temporal invariance, make temporal pooling implicitly coarse-position-aware, and expose multiscale interactions through channel mixing, while often improving computational efficiency by shortening the processed time axis. We formally analyze the ROMAN operator and then evaluate it in two complementary ways by measuring its impact as a preprocessing step for four representative convolutional classifiers: MiniRocket, MultiRocket, a standard CNN-based classifier, and a fully convolutional network (FCN) classifier. First, we design synthetic time series classification tasks that isolate coarse position awareness, long-range correlation, multiscale interaction, and full positional invariance, showing that ROMAN behaves consistently with its intended mechanism and is most useful when class information depends on temporal structure that standard pooled convolution tends to suppress. Second, we benchmark the same models with and without ROMAN on long-sequence subsets of the UCR and UEA archives, showing that ROMAN provides a practically useful alternative representation whose effect on accuracy is task-dependent, but whose effect on efficiency is often favorable. Code is available at https://github.com/gon-uri/ROMAN