Kolmogorov-Arnold Networks (KANs) relocate learnable nonlinearities from nodes to edges, demonstrating remarkable capabilities in scientific machine learning and interpretable modeling. However, current KAN implementations suffer from fundamental inefficiencies due to redundancy in high-dimensional spline parameter spaces, where numerous distinct parameterisations yield functionally equivalent behaviors. This redundancy manifests as a "nuisance space" in the model's Jacobian, leading to susceptibility to overfitting and poor generalization. We introduce Projective Kolmogorov-Arnold Networks (P-KANs), a novel training framework that guides edge function discovery towards interpretable functional representations through entropy-minimisation techniques from signal analysis and sparse dictionary learning. Rather than constraining functions to predetermined spaces, our approach maintains spline space flexibility while introducing "gravitational" terms that encourage convergence towards optimal functional representations. Our key insight recognizes that optimal representations can be identified through entropy analysis of projection coefficients, compressing edge functions to lower-parameter projective spaces (Fourier, Chebyshev, Bessel). P-KANs demonstrate superior performance across multiple domains, achieving up to 80% parameter reduction while maintaining representational capacity, significantly improved robustness to noise compared to standard KANs, and successful application to industrial automated fiber placement prediction. Our approach enables automatic discovery of mixed functional representations where different edges converge to different optimal spaces, providing both compression benefits and enhanced interpretability for scientific machine learning applications.

Dialectal data are characterized by linguistic variation that appears small to humans but has a significant impact on the performance of models. This dialect gap has been related to various factors (e.g., data size, economic and social factors) whose impact, however, turns out to be inconsistent. In this work, we investigate factors impacting the model performance more directly: we correlate Tokenization Parity (TP) and Information Parity (IP), as measures of representational biases in pre-trained multilingual models, with the downstream performance. We compare state-of-the-art decoder-only LLMs with encoder-based models across three tasks: dialect classification, topic classification, and extractive question answering, controlling for varying scripts (Latin vs. non-Latin) and resource availability (high vs. low). Our analysis reveals that TP is a better predictor of the performance on tasks reliant on syntactic and morphological cues (e.g., extractive QA), while IP better predicts performance in semantic tasks (e.g., topic classification). Complementary analyses, including tokenizer behavior, vocabulary coverage, and qualitative insights, reveal that the language support claims of LLMs often might mask deeper mismatches at the script or token level.

The reliability of secure graphic verification, a key anti-counterfeiting tool, is undermined by poor image acquisition on smartphones. Uncontrolled user captures of these high-entropy patterns cause high false rejection rates, creating a significant'reliability gap'. T o bridge this gap, we depart from traditional perceptual IQA and introduce a framework that predictively estimates a frame's utility for the downstream verification task. W e propose a lightweight model to predict a quality score for a video frame, determining its suitability for a resource-intensive oracle model. Our framework is validated using re-contextualized FNMR and ISRR metrics on a large-scale dataset of 32,000+ images from 105 smartphones. Furthermore, a novel cross-domain analysis on graphics from different industrial printing presses reveals a key finding: a lightweight probe on a frozen, ImageNet-pretrained network generalizes better to an unseen printing technology than a fully fine-tuned model. This provides a key insight for real-world generalization: for domain shifts from physical manufacturing, a frozen general-purpose backbone can be more robust than full fine-tuning, which can overfit to source-domain artifacts.

Traditional object detection methods face performance degradation challenges in complex scenarios such as low-light conditions and heavy occlusions due to a lack of high-level semantic understanding. To address this, this paper proposes an adaptive guidance-based semantic enhancement edge-cloud collaborative object detection method leveraging Multimodal Large Language Models (MLLM), achieving an effective balance between accuracy and efficiency. Specifically, the method first employs instruction fine-tuning to enable the MLLM to generate structured scene descriptions. It then designs an adaptive mapping mechanism that dynamically converts semantic information into parameter adjustment signals for edge detectors, achieving real-time semantic enhancement. Within an edge-cloud collaborative inference framework, the system automatically selects between invoking cloud-based semantic guidance or directly outputting edge detection results based on confidence scores. Experiments demonstrate that the proposed method effectively enhances detection accuracy and efficiency in complex scenes. Specifically, it can reduce latency by over 79% and computational cost by 70% in low-light and highly occluded scenes while maintaining accuracy.

Sobolev training, which integrates target derivatives into the loss functions, has been shown to accelerate convergence and improve generalization compared to conventional $L^2$ training. However, the underlying mechanisms of this training method remain only partially understood. In this work, we present the first rigorous theoretical framework proving that Sobolev training accelerates the convergence of Rectified Linear Unit (ReLU) networks. Under a student-teacher framework with Gaussian inputs and shallow architectures, we derive exact formulas for population gradients and Hessians, and quantify the improvements in conditioning of the loss landscape and gradient-flow convergence rates. Extensive numerical experiments validate our theoretical findings and show that the benefits of Sobolev training extend to modern deep learning tasks.

Accurate text recognition for historical documents can greatly advance the study and preservation of cultural heritage. Existing vision-language models (VLMs), however, are designed for modern, standardized texts and are not equipped to read the diverse languages and scripts, irregular layouts, and frequent degradation found in historical materials. This paper presents CHURRO, a 3B-parameter open-weight VLM specialized for historical text recognition. The model is trained on CHURRO-DS, the largest historical text recognition dataset to date. CHURRO-DS unifies 155 historical corpora comprising 99,491 pages, spanning 22 centuries of textual heritage across 46 language clusters, including historical variants and dead languages. We evaluate several open-weight and closed VLMs and optical character recognition (OCR) systems on CHURRO-DS and find that CHURRO outperforms all other VLMs. On the CHURRO-DS test set, CHURRO achieves 82.3% (printed) and 70.1% (handwritten) normalized Levenshtein similarity, surpassing the second-best model, Gemini 2.5 Pro, by 1.4% and 6.5%, respectively, while being 15.5 times more cost-effective. By releasing the model and dataset, we aim to enable community-driven research to improve the readability of historical texts and accelerate scholarship.

Positional encoding is essential for supplementing transformer with positional information of tokens. Existing positional encoding methods demand predefined token/feature order, rendering them unsuitable for real-world data with non-sequential yet causally-related features. To address this limitation, we propose CAPE, a novel method that identifies underlying causal structure over non-sequential features as a weighted directed acyclic graph (DAG) using generalized structural equation modeling. The DAG is then embedded in hyperbolic space where its geometric structure is well-preserved using a hyperboloid model-based approach that effectively captures two important causal graph properties (causal strength & causal specificity). This step yields causality-aware positional encodings for the features, which are converted into their rotary form for integrating with transformer's self-attention mechanism. Theoretical analysis reveals that CAPE-generated rotary positional encodings possess three valuable properties for enhanced self-attention, including causal distance-induced attenuation, causal generality-induced attenuation, and robustness to positional disturbances. We evaluate CAPE over both synthetic and real-word datasets, empirically demonstrating its theoretical properties and effectiveness in enhancing transformer for data with non-sequential features. Our code is available at https://github.com/Catchxu/CAPE.

Recent speech-LLMs have shown impressive performance in tasks like transcription and translation, yet they remain limited in understanding the paralinguistic aspects of speech crucial for social and emotional intelligence. We propose CP-Bench, a benchmark for evaluating speech-LLMs on contextual paralinguistic reasoning the integration of verbal content with non-verbal cues like emotion and prosody. The benchmark includes two curated question answering (QA) datasets requiring both linguistic and empathetic understanding. We evaluate state-of-the-art speech-LLMs from both open and closed-source models and perform a comprehensive analysis across different question types. The top two models were further analyzed under temperature tuning to understand its effect on this task. Our benchmark reveals a key gap in existing evaluations and offers insights into building more context-aware and emotionally intelligent speech-capable LLMs.

The rapid advancement of generative AI has democratized access to powerful tools such as Text-to-Image models. However, to generate high-quality images, users must still craft detailed prompts specifying scene, style, and context-often through multiple rounds of refinement. We propose PromptSculptor, a novel multi-agent framework that automates this iterative prompt optimization process. Our system decomposes the task into four specialized agents that work collaboratively to transform a short, vague user prompt into a comprehensive, refined prompt. By leveraging Chain-of-Thought reasoning, our framework effectively infers hidden context and enriches scene and background details. To iteratively refine the prompt, a self-evaluation agent aligns the modified prompt with the original input, while a feedback-tuning agent incorporates user feedback for further refinement. Experimental results demonstrate that PromptSculptor significantly enhances output quality and reduces the number of iterations needed for user satisfaction. Moreover, its model-agnostic design allows seamless integration with various T2I models, paving the way for industrial applications.

Code Large Language Models (Code LLMs) have opened a new era in programming with their impressive capabilities. However, recent research has revealed critical limitations in their ability to reason about runtime behavior and understand the actual functionality of programs, which poses significant challenges for their post-training and practical deployment. Specifically, Code LLMs encounter two principal issues: (1) a lack of proficiency in reasoning about program execution behavior, as they struggle to interpret what programs actually do during runtime, and (2) the inconsistent and fragmented representation of semantic information, such as execution traces, across existing methods, which hinders their ability to generalize and reason effectively. These challenges underscore the necessity for more systematic approaches to enhance the reasoning capabilities of Code LLMs. To address these issues, we introduce a generic framework to support integrating semantic information~(e.g., execution trace) to code task-relevant prompts, and conduct a comprehensive study to explore the role of semantic information in enhancing the reasoning ability of Code LLMs accordingly. Specifically, we focus on investigating the usefulness of trace-based semantic information in boosting supervised fine-tuning~(SFT) and post-phase inference of Code LLMs. The experimental results surprisingly disagree with previous works and demonstrate that semantic information has limited usefulness for SFT and test time scaling of Code LLM.