GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning

We present GLM-4.1V-Thinking, a vision-language model (VLM) designed to advance general-purpose multimodal understanding and reasoning. In this report, we share our key findings in the development of the reasoning-centric training framework. We first develop a capable vision foundation model with significant potential through large-scale pre-training, which arguably sets the upper bound for the final performance. We then propose Reinforcement Learning with Curriculum Sampling (RLCS) to unlock the full potential of the model, leading to comprehensive capability enhancement across a diverse range of tasks, including STEM problem solving, video understanding, content recognition, coding, grounding, GUI-based agents, and long document understanding. We open-source GLM-4.1V-9B-Thinking, which achieves state-of-the-art performance among models of comparable size. In a comprehensive evaluation across 28 public benchmarks, our model outperforms Qwen2.5-VL-7B on nearly all tasks and achieves comparable or even superior performance on 18 benchmarks relative to the significantly larger Qwen2.5-VL-72B. Notably, GLM-4.1V-9B-Thinking also demonstrates competitive or superior performance compared to closed-source models such as GPT-4o on challenging tasks including long document understanding and STEM reasoning, further underscoring its strong capabilities. Code, models and more information are released at https://github.com/THUDM/GLM-4.1V-Thinking.

Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model multi-dimensional data, offer a promising framework for this problem. This paper introduces the quaternion nuclear norm over the Frobenius norm (QNOF) as a novel nonconvex approximation for the rank of quaternion matrices. QNOF is parameter-free and scale-invariant. Utilizing quaternion singular value decomposition, we prove that solving the QNOF can be simplified to solving the singular value $L_1/L_2$ problem. Additionally, we extend the QNOF to robust quaternion matrix completion, employing the alternating direction multiplier method to derive solutions that guarantee weak convergence under mild conditions. Extensive numerical experiments validate the proposed model's superiority, consistently outperforming state-of-the-art quaternion methods.

A Rule Based Solution to Co-reference Resolution in Clinical Text

Objective: The aim of this study was to build an effective co-reference resolution system tailored for the biomedical domain. Materials and Methods: Experiment materials used in this study is provided by the 2011 i2b2 Natural Language Processing Challenge. The 2011 i2b2 challenge involves coreference resolution in medical documents. Concept mentions have been annotated in clinical texts, and the mentions that co-refer in each document are to be linked by coreference chains. Normally, there are two ways of constructing a system to automatically discover co-referent links. One is to manually build rules for co-reference resolution, and the other category of approaches is to use machine learning systems to learn automatically from training datasets and then perform the resolution task on testing datasets. Results: Experiments show the existing co-reference resolution systems are able to find some of the co-referent links, and our rule based system performs well finding the majority of the co-referent links. Our system achieved 89.6% overall performance on multiple medical datasets. Conclusion: The experiment results show that manually crafted rules based on observation of training data is a valid way to accomplish high performance in this coreference resolution task for the critical biomedical domain.

Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

Joint PET-MRI Reconstruction with Diffusion Stochastic Differential Model

PET suffers from a low signal-to-noise ratio. Meanwhile, the k-space data acquisition process in MRI is time-consuming by PET-MRI systems. We aim to accelerate MRI and improve PET image quality. This paper proposed a novel joint reconstruction model by diffusion stochastic differential equations based on learning the joint probability distribution of PET and MRI. Compare the results underscore the qualitative and quantitative improvements our model brings to PET and MRI reconstruction, surpassing the current state-of-the-art methodologies. Joint PET-MRI reconstruction is a challenge in the PET-MRI system. This studies focused on the relationship extends beyond edges. In this study, PET is generated from MRI by learning joint probability distribution as the relationship.

Joint Diffusion: Mutual Consistency-Driven Diffusion Model for PET-MRI Co-Reconstruction

Positron Emission Tomography and Magnetic Resonance Imaging (PET-MRI) systems can obtain functional and anatomical scans. PET suffers from a low signal-to-noise ratio. Meanwhile, the k-space data acquisition process in MRI is time-consuming. The study aims to accelerate MRI and enhance PET image quality. Conventional approaches involve the separate reconstruction of each modality within PET-MRI systems. However, there exists complementary information among multi-modal images. The complementary information can contribute to image reconstruction. In this study, we propose a novel PET-MRI joint reconstruction model employing a mutual consistency-driven diffusion mode, namely MC-Diffusion. MC-Diffusion learns the joint probability distribution of PET and MRI for utilizing complementary information. We conducted a series of contrast experiments about LPLS, Joint ISAT-net and MC-Diffusion by the ADNI dataset. The results underscore the qualitative and quantitative improvements achieved by MC-Diffusion, surpassing the state-of-the-art method.

A Region of Interest Focused Triple UNet Architecture for Skin Lesion Segmentation

Skin lesion segmentation is of great significance for skin lesion analysis and subsequent treatment. It is still a challenging task due to the irregular and fuzzy lesion borders, and diversity of skin lesions. In this paper, we propose Triple-UNet to automatically segment skin lesions. It is an organic combination of three UNet architectures with suitable modules. In order to concatenate the first and second sub-networks more effectively, we design a region of interest enhancement module (ROIE). The ROIE enhances the target object region of the image by using the predicted score map of the first UNet. The features learned by the first UNet and the enhanced image help the second UNet obtain a better score map. Finally, the results are fine-tuned by the third UNet. We evaluate our algorithm on a publicly available dataset of skin lesion segmentation. Experiments show that Triple-UNet outperforms the state-of-the-art on skin lesion segmentation.

Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI

Recently, regularization model-driven deep learning (DL) has gained significant attention due to its ability to leverage the potent representational capabilities of DL while retaining the theoretical guarantees of regularization models. However, most of these methods are tailored for supervised learning scenarios that necessitate fully sampled labels, which can pose challenges in practical MRI applications. To tackle this challenge, we propose a self-supervised DL approach for accelerated MRI that is theoretically guaranteed and does not rely on fully sampled labels. Specifically, we achieve neural network structure regularization by exploiting the inherent structural low-rankness of the $k$-space data. Simultaneously, we constrain the network structure to resemble a nonexpansive mapping, ensuring the network's convergence to a fixed point. Thanks to this well-defined network structure, this fixed point can completely reconstruct the missing $k$-space data based on matrix completion theory, even in situations where full-sampled labels are unavailable. Experiments validate the effectiveness of our proposed method and demonstrate its superiority over existing self-supervised approaches and traditional regularization methods, achieving performance comparable to that of supervised learning methods in certain scenarios.

Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and robustness. In response, we introduce Convex Latent-Optimized Adversarial Regularizers (CLEAR), a novel and interpretable data-driven paradigm. CLEAR represents a fusion of deep learning (DL) and variational regularization. Specifically, we employ a latent optimization technique to adversarially train an input convex neural network, and its set of minima can fully represent the real data manifold. We utilize it as a convex regularizer to formulate a CLEAR-informed variational regularization model that guides the solution of the imaging inverse problem on the real data manifold. Leveraging its inherent convexity, we have established the convergence of the projected subgradient descent algorithm for the CLEAR-informed regularization model. This convergence guarantees the attainment of a unique solution to the imaging inverse problem, subject to certain assumptions. Furthermore, we have demonstrated the robustness of our CLEAR-informed model, explicitly showcasing its capacity to achieve stable reconstruction even in the presence of measurement interference. Finally, we illustrate the superiority of our approach using MRI reconstruction as an example. Our method consistently outperforms conventional data-driven techniques and traditional regularization approaches, excelling in both reconstruction quality and robustness.

Synthesizing PET images from High-field and Ultra-high-field MR images Using Joint Diffusion Attention Model

MRI and PET are crucial diagnostic tools for brain diseases, as they provide complementary information on brain structure and function. However, PET scanning is costly and involves radioactive exposure, resulting in a lack of PET. Moreover, simultaneous PET and MRI at ultra-high-field are currently hardly infeasible. Ultra-high-field imaging has unquestionably proven valuable in both clinical and academic settings, especially in the field of cognitive neuroimaging. These motivate us to propose a method for synthetic PET from high-filed MRI and ultra-high-field MRI. From a statistical perspective, the joint probability distribution (JPD) is the most direct and fundamental means of portraying the correlation between PET and MRI. This paper proposes a novel joint diffusion attention model which has the joint probability distribution and attention strategy, named JDAM. JDAM has a diffusion process and a sampling process. The diffusion process involves the gradual diffusion of PET to Gaussian noise by adding Gaussian noise, while MRI remains fixed. JPD of MRI and noise-added PET was learned in the diffusion process. The sampling process is a predictor-corrector. PET images were generated from MRI by JPD of MRI and noise-added PET. The predictor is a reverse diffusion process and the corrector is Langevin dynamics. Experimental results on the public Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that the proposed method outperforms state-of-the-art CycleGAN for high-field MRI (3T MRI). Finally, synthetic PET images from the ultra-high-field (5T MRI and 7T MRI) be attempted, providing a possibility for ultra-high-field PET-MRI imaging.