Multimodal Mathematical Reasoning with Diverse Solving Perspective

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.

SafePTR: Token-Level Jailbreak Defense in Multimodal LLMs via Prune-then-Restore Mechanism

By incorporating visual inputs, Multimodal Large Language Models (MLLMs) extend LLMs to support visual reasoning. However, this integration also introduces new vulnerabilities, making MLLMs susceptible to multimodal jailbreak attacks and hindering their safe deployment.Existing defense methods, including Image-to-Text Translation, Safe Prompting, and Multimodal Safety Tuning, attempt to address this by aligning multimodal inputs with LLMs' built-in safeguards.Yet, they fall short in uncovering root causes of multimodal vulnerabilities, particularly how harmful multimodal tokens trigger jailbreak in MLLMs? Consequently, they remain vulnerable to text-driven multimodal jailbreaks, often exhibiting overdefensive behaviors and imposing heavy training overhead.To bridge this gap, we present an comprehensive analysis of where, how and which harmful multimodal tokens bypass safeguards in MLLMs. Surprisingly, we find that less than 1% tokens in early-middle layers are responsible for inducing unsafe behaviors, highlighting the potential of precisely removing a small subset of harmful tokens, without requiring safety tuning, can still effectively improve safety against jailbreaks. Motivated by this, we propose Safe Prune-then-Restore (SafePTR), an training-free defense framework that selectively prunes harmful tokens at vulnerable layers while restoring benign features at subsequent layers.Without incurring additional computational overhead, SafePTR significantly enhances the safety of MLLMs while preserving efficiency. Extensive evaluations across three MLLMs and five benchmarks demonstrate SafePTR's state-of-the-art performance in mitigating jailbreak risks without compromising utility.

Rethinking Range-View LiDAR Segmentation in Adverse Weather

LiDAR segmentation has emerged as an important task to enrich multimedia experiences and analysis. Range-view-based methods have gained popularity due to their high computational efficiency and compatibility with real-time deployment. However, their generalized performance under adverse weather conditions remains underexplored, limiting their reliability in real-world environments. In this work, we identify and analyze the unique challenges that affect the generalization of range-view LiDAR segmentation in severe weather. To address these challenges, we propose a modular and lightweight framework that enhances robustness without altering the core architecture of existing models. Our method reformulates the initial stem block of standard range-view networks into two branches to process geometric attributes and reflectance intensity separately. Specifically, a Geometric Abnormality Suppression (GAS) module reduces the influence of weather-induced spatial noise, and a Reflectance Distortion Calibration (RDC) module corrects reflectance distortions through memory-guided adaptive instance normalization. The processed features are then fused and passed to the original segmentation pipeline. Extensive experiments on different benchmarks and baseline models demonstrate that our approach significantly improves generalization to adverse weather with minimal inference overhead, offering a practical and effective solution for real-world LiDAR segmentation.

Truth in the Few: High-Value Data Selection for Efficient Multi-Modal Reasoning

While multi-modal large language models (MLLMs) have made significant progress in complex reasoning tasks via reinforcement learning, it is commonly believed that extensive training data is necessary for improving multi-modal reasoning ability, inevitably leading to data redundancy and substantial computational costs. However, can smaller high-value datasets match or outperform full corpora for multi-modal reasoning in MLLMs? In this work, we challenge this assumption through a key observation: meaningful multi-modal reasoning is triggered by only a sparse subset of training samples, termed cognitive samples, whereas the majority contribute marginally. Building on this insight, we propose a novel data selection paradigm termed Reasoning Activation Potential (RAP), which identifies cognitive samples by estimating each sample's potential to stimulate genuine multi-modal reasoning by two complementary estimators: 1) Causal Discrepancy Estimator (CDE) based on the potential outcome model principle, eliminates samples that overly rely on language priors by comparing outputs between multi-modal and text-only inputs; 2) Attention Confidence Estimator (ACE), which exploits token-level self-attention to discard samples dominated by irrelevant but over-emphasized tokens in intermediate reasoning stages. Moreover, we introduce a Difficulty-aware Replacement Module (DRM) to substitute trivial instances with cognitively challenging ones, thereby ensuring complexity for robust multi-modal reasoning. Experiments on six datasets show that our RAP method consistently achieves superior performance using only 9.3% of the training data, while reducing computational costs by over 43%. Our code is available at https://github.com/Leo-ssl/RAP.

InSpire: Vision-Language-Action Models with Intrinsic Spatial Reasoning

Leveraging pretrained Vision-Language Models (VLMs) to map language instruction and visual observations to raw low-level actions, Vision-Language-Action models (VLAs) hold great promise for achieving general-purpose robotic systems. Despite their advancements, existing VLAs tend to spuriously correlate task-irrelevant visual features with actions, limiting their generalization capacity beyond the training data. To tackle this challenge, we propose Intrinsic Spatial Reasoning (InSpire), a simple yet effective approach that mitigates the adverse effects of spurious correlations by boosting the spatial reasoning ability of VLAs. Specifically, InSpire redirects the VLA's attention to task-relevant factors by prepending the question "In which direction is the [object] relative to the robot?" to the language instruction and aligning the answer "right/left/up/down/front/back/grasped" and predicted actions with the ground-truth. Notably, InSpire can be used as a plugin to enhance existing autoregressive VLAs, requiring no extra training data or interaction with other large models. Extensive experimental results in both simulation and real-world environments demonstrate the effectiveness and flexibility of our approach. Our code, pretrained models and demos are publicly available at: https://Koorye.github.io/proj/Inspire.

Policy Contrastive Decoding for Robotic Foundation Models

Robotic foundation models, or generalist robot policies, hold immense potential to enable flexible, general-purpose and dexterous robotic systems. Despite their advancements, our empirical experiments reveal that existing robot policies are prone to learning spurious correlations from pre-training trajectories, adversely affecting their generalization capabilities beyond the training data. To tackle this, we propose a novel Policy Contrastive Decoding (PCD) approach, which redirects the robot policy's focus toward object-relevant visual clues by contrasting action probability distributions derived from original and object-masked visual inputs. As a training-free method, our PCD can be used as a plugin to improve different types of robot policies without needing to finetune or access model weights. We conduct extensive experiments on top of three open-source robot policies, including the autoregressive policy OpenVLA and the diffusion-based policies Octo and $\pi_0$. The obtained results in both simulation and real-world environments prove PCD's flexibility and effectiveness, e.g., PCD enhances the state-of-the-art policy $\pi_0$ by 8% in the simulation environment and by 108% in the real-world environment. Code and demos are publicly available at: https://Koorye.github.io/proj/PCD.

Towards Generalized and Training-Free Text-Guided Semantic Manipulation

Text-guided semantic manipulation refers to semantically editing an image generated from a source prompt to match a target prompt, enabling the desired semantic changes (e.g., addition, removal, and style transfer) while preserving irrelevant contents. With the powerful generative capabilities of the diffusion model, the task has shown the potential to generate high-fidelity visual content. Nevertheless, existing methods either typically require time-consuming fine-tuning (inefficient), fail to accomplish multiple semantic manipulations (poorly extensible), and/or lack support for different modality tasks (limited generalizability). Upon further investigation, we find that the geometric properties of noises in the diffusion model are strongly correlated with the semantic changes. Motivated by this, we propose a novel $\textit{GTF}$ for text-guided semantic manipulation, which has the following attractive capabilities: 1) $\textbf{Generalized}$: our $\textit{GTF}$ supports multiple semantic manipulations (e.g., addition, removal, and style transfer) and can be seamlessly integrated into all diffusion-based methods (i.e., Plug-and-play) across different modalities (i.e., modality-agnostic); and 2) $\textbf{Training-free}$: $\textit{GTF}$ produces high-fidelity results via simply controlling the geometric relationship between noises without tuning or optimization. Our extensive experiments demonstrate the efficacy of our approach, highlighting its potential to advance the state-of-the-art in semantics manipulation.

Syzygy of Thoughts: Improving LLM CoT with the Minimal Free Resolution

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Exploring Kernel Transformations for Implicit Neural Representations

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image representation, with pixel coordinates as input and pixel values as output. In contrast to prior works focusing on investigating the effect of the model's inside components (activation function, for instance), this work pioneers the exploration of the effect of kernel transformation of input/output while keeping the model itself unchanged. A byproduct of our findings is a simple yet effective method that combines scale and shift to significantly boost INR with negligible computation overhead. Moreover, we present two perspectives, depth and normalization, to interpret the performance benefits caused by scale and shift transformation. Overall, our work provides a new avenue for future works to understand and improve INR through the lens of kernel transformation.

Attention Hijackers: Detect and Disentangle Attention Hijacking in LVLMs for Hallucination Mitigation

Despite their success, Large Vision-Language Models (LVLMs) remain vulnerable to hallucinations. While existing studies attribute the cause of hallucinations to insufficient visual attention to image tokens, our findings indicate that hallucinations also arise from interference from instruction tokens during decoding. Intuitively, certain instruction tokens continuously distort LVLMs' visual perception during decoding, hijacking their visual attention toward less discriminative visual regions. This distortion prevents them integrating broader contextual information from images, ultimately leading to hallucinations. We term this phenomenon 'Attention Hijacking', where disruptive instruction tokens act as 'Attention Hijackers'. To address this, we propose a novel, training-free strategy namely Attention HIjackers Detection and Disentanglement (AID), designed to isolate the influence of Hijackers, enabling LVLMs to rely on their context-aware intrinsic attention map. Specifically, AID consists of three components: First, Attention Hijackers Detection identifies Attention Hijackers by calculating instruction-driven visual salience. Next, Attention Disentanglement mechanism is proposed to mask the visual attention of these identified Hijackers, and thereby mitigate their disruptive influence on subsequent tokens. Finally, Re-Disentanglement recalculates the balance between instruction-driven and image-driven visual salience to avoid over-masking effects. Extensive experiments demonstrate that AID significantly reduces hallucination across various LVLMs on several benchmarks.