TrustGeoGen: Scalable and Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Stochastic Gradient Descent in Non-Convex Problems: Asymptotic Convergence with Relaxed Step-Size via Stopping Time Methods

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of step-size schemes are frequently employed, yet existing convergence results remain limited and often rely on strong assumptions. This paper bridges this gap by introducing a novel analytical framework based on a stopping-time method, enabling asymptotic convergence analysis of SGD under more relaxed step-size conditions and weaker assumptions. In the non-convex setting, we prove the almost sure convergence of SGD iterates for step-sizes $ \{ \epsilon_t \}_{t \geq 1} $ satisfying $\sum_{t=1}^{+\infty} \epsilon_t = +\infty$ and $\sum_{t=1}^{+\infty} \epsilon_t^p < +\infty$ for some $p > 2$. Compared with previous studies, our analysis eliminates the global Lipschitz continuity assumption on the loss function and relaxes the boundedness requirements for higher-order moments of stochastic gradients. Building upon the almost sure convergence results, we further establish $L_2$ convergence. These significantly relaxed assumptions make our theoretical results more general, thereby enhancing their applicability in practical scenarios.

Object Placement for Anything

Object placement aims to determine the appropriate placement (\emph{e.g.}, location and size) of a foreground object when placing it on the background image. Most previous works are limited by small-scale labeled dataset, which hinders the real-world application of object placement. In this work, we devise a semi-supervised framework which can exploit large-scale unlabeled dataset to promote the generalization ability of discriminative object placement models. The discriminative models predict the rationality label for each foreground placement given a foreground-background pair. To better leverage the labeled data, under the semi-supervised framework, we further propose to transfer the knowledge of rationality variation, \emph{i.e.}, whether the change of foreground placement would result in the change of rationality label, from labeled data to unlabeled data. Extensive experiments demonstrate that our framework can effectively enhance the generalization ability of discriminative object placement models.

Efficient Tuning of Large Language Models for Knowledge-Grounded Dialogue Generation

Large language models (LLMs) demonstrate remarkable text comprehension and generation capabilities but often lack the ability to utilize up-to-date or domain-specific knowledge not included in their training data. To address this gap, we introduce KEDiT, an efficient method for fine-tuning LLMs for knowledge-grounded dialogue generation. KEDiT operates in two main phases: first, it employs an information bottleneck to compress retrieved knowledge into learnable parameters, retaining essential information while minimizing computational overhead. Second, a lightweight knowledge-aware adapter integrates these compressed knowledge vectors into the LLM during fine-tuning, updating less than 2\% of the model parameters. The experimental results on the Wizard of Wikipedia and a newly constructed PubMed-Dialog dataset demonstrate that KEDiT excels in generating contextually relevant and informative responses, outperforming competitive baselines in automatic, LLM-based, and human evaluations. This approach effectively combines the strengths of pretrained LLMs with the adaptability needed for incorporating dynamic knowledge, presenting a scalable solution for fields such as medicine.

OmniCaptioner: One Captioner to Rule Them All

We propose OmniCaptioner, a versatile visual captioning framework for generating fine-grained textual descriptions across a wide variety of visual domains. Unlike prior methods limited to specific image types (e.g., natural images or geometric visuals), our framework provides a unified solution for captioning natural images, visual text (e.g., posters, UIs, textbooks), and structured visuals (e.g., documents, tables, charts). By converting low-level pixel information into semantically rich textual representations, our framework bridges the gap between visual and textual modalities. Our results highlight three key advantages: (i) Enhanced Visual Reasoning with LLMs, where long-context captions of visual modalities empower LLMs, particularly the DeepSeek-R1 series, to reason effectively in multimodal scenarios; (ii) Improved Image Generation, where detailed captions improve tasks like text-to-image generation and image transformation; and (iii) Efficient Supervised Fine-Tuning (SFT), which enables faster convergence with less data. We believe the versatility and adaptability of OmniCaptioner can offer a new perspective for bridging the gap between language and visual modalities.

Computational Efficient Informative Nonignorable Matrix Completion: A Row- and Column-Wise Matrix U-Statistic Pseudo-Likelihood Approach

In this study, we establish a unified framework to deal with the high dimensional matrix completion problem under flexible nonignorable missing mechanisms. Although the matrix completion problem has attracted much attention over the years, there are very sparse works that consider the nonignorable missing mechanism. To address this problem, we derive a row- and column-wise matrix U-statistics type loss function, with the nuclear norm for regularization. A singular value proximal gradient algorithm is developed to solve the proposed optimization problem. We prove the non-asymptotic upper bound of the estimation error's Frobenius norm and show the performance of our method through numerical simulations and real data analysis.

Multi-Dimensional AGV Path Planning in 3D Warehouses Using Ant Colony Optimization and Advanced Neural Networks

Within modern warehouse scenarios, the rapid expansion of e-commerce and increasingly complex, multi-level storage environments have exposed the limitations of traditional AGV (Automated Guided Vehicle) path planning methods--often reliant on static 2D models and expert-tuned heuristics that struggle to handle dynamic traffic and congestion. Addressing these limitations, this paper introduces a novel AGV path planning approach for 3D warehouse environments that leverages a hybrid framework combining ACO (Ant Colony Optimization) with deep learning models, called NAHACO (Neural Adaptive Heuristic Ant Colony Optimization). NAHACO integrates three key innovations: first, an innovative heuristic algorithm for 3D warehouse cargo modeling using multidimensional tensors, which addresses the challenge of achieving superior heuristic accuracy; second, integration of a congestion-aware loss function within the ACO framework to adjust path costs based on traffic and capacity constraints, called CARL (Congestion-Aware Reinforce Loss), enabling dynamic heuristic calibration for optimizing ACO-based path planning; and third, an adaptive attention mechanism that captures multi-scale spatial features, thereby addressing dynamic heuristic calibration for further optimization of ACO-based path planning and AGV navigation. NAHACO significantly boosts path planning efficiency, yielding faster computation times and superior performance over both vanilla and state-of-the-art methods, while automatically adapting to warehouse constraints for real-time optimization. NAHACO outperforms state-of-the-art methods, lowering the total cost by up to 24.7% on TSP benchmarks. In warehouse tests, NAHACO cuts cost by up to 41.5% and congestion by up to 56.1% compared to previous methods.

LeX-Art: Rethinking Text Generation via Scalable High-Quality Data Synthesis

We introduce LeX-Art, a comprehensive suite for high-quality text-image synthesis that systematically bridges the gap between prompt expressiveness and text rendering fidelity. Our approach follows a data-centric paradigm, constructing a high-quality data synthesis pipeline based on Deepseek-R1 to curate LeX-10K, a dataset of 10K high-resolution, aesthetically refined 1024$\times$1024 images. Beyond dataset construction, we develop LeX-Enhancer, a robust prompt enrichment model, and train two text-to-image models, LeX-FLUX and LeX-Lumina, achieving state-of-the-art text rendering performance. To systematically evaluate visual text generation, we introduce LeX-Bench, a benchmark that assesses fidelity, aesthetics, and alignment, complemented by Pairwise Normalized Edit Distance (PNED), a novel metric for robust text accuracy evaluation. Experiments demonstrate significant improvements, with LeX-Lumina achieving a 79.81% PNED gain on CreateBench, and LeX-FLUX outperforming baselines in color (+3.18%), positional (+4.45%), and font accuracy (+3.81%). Our codes, models, datasets, and demo are publicly available.

Lumina-Image 2.0: A Unified and Efficient Image Generative Framework

We introduce Lumina-Image 2.0, an advanced text-to-image generation framework that achieves significant progress compared to previous work, Lumina-Next. Lumina-Image 2.0 is built upon two key principles: (1) Unification - it adopts a unified architecture (Unified Next-DiT) that treats text and image tokens as a joint sequence, enabling natural cross-modal interactions and allowing seamless task expansion. Besides, since high-quality captioners can provide semantically well-aligned text-image training pairs, we introduce a unified captioning system, Unified Captioner (UniCap), specifically designed for T2I generation tasks. UniCap excels at generating comprehensive and accurate captions, accelerating convergence and enhancing prompt adherence. (2) Efficiency - to improve the efficiency of our proposed model, we develop multi-stage progressive training strategies and introduce inference acceleration techniques without compromising image quality. Extensive evaluations on academic benchmarks and public text-to-image arenas show that Lumina-Image 2.0 delivers strong performances even with only 2.6B parameters, highlighting its scalability and design efficiency. We have released our training details, code, and models at https://github.com/Alpha-VLLM/Lumina-Image-2.0.

BACE-RUL: A Bi-directional Adversarial Network with Covariate Encoding for Machine Remaining Useful Life Prediction

Prognostic and Health Management (PHM) are crucial ways to avoid unnecessary maintenance for Cyber-Physical Systems (CPS) and improve system reliability. Predicting the Remaining Useful Life (RUL) is one of the most challenging tasks for PHM. Existing methods require prior knowledge about the system, contrived assumptions, or temporal mining to model the life cycles of machine equipment/devices, resulting in diminished accuracy and limited applicability in real-world scenarios. This paper proposes a Bi-directional Adversarial network with Covariate Encoding for machine Remaining Useful Life (BACE-RUL) prediction, which only adopts sensor measurements from the current life cycle to predict RUL rather than relying on previous consecutive cycle recordings. The current sensor measurements of mechanical devices are encoded to a conditional space to better understand the implicit inner mechanical status. The predictor is trained as a conditional generative network with the encoded sensor measurements as its conditions. Various experiments on several real-world datasets, including the turbofan aircraft engine dataset and the dataset collected from degradation experiments of Li-Ion battery cells, show that the proposed model is a general framework and outperforms state-of-the-art methods.