Recent advancements in large language models (LLMs) underscore the need for more comprehensive evaluation methods to accurately assess their reasoning capabilities. Existing benchmarks are often domain-specific and thus cannot fully capture an LLM's general reasoning potential. To address this limitation, we introduce the Knowledge Orthogonal Reasoning Gymnasium (KORGym)1, a dynamic evaluation platform inspired by KOR-Bench [1] and Gymnasium [2]. KORGym offers over fifty games in either textual or visual formats and supports interactive, multi-turn assessments with reinforcement learning scenarios. Using KORGym, we conduct extensive experiments on 19 LLMs and 8 VLMs, revealing consistent reasoning patterns within model families and demonstrating the superior performance of closed-source models. Further analysis examines the effects of modality, reasoning strategies, reinforcement learning techniques, and response length on model performance. We expect KORGym to become a valuable resource for advancing LLM reasoning research and developing evaluation methodologies suited to complex, interactive environments.

Math reasoning has been one crucial ability of large language models (LLMs), where significant advancements have been achieved in recent years. However, most efforts focus on LLMs by curating high-quality annotation data and intricate training (or inference) paradigms, while the math reasoning performance of multimodal LLMs (MLLMs) remains lagging behind. Since the MLLM typically consists of an LLM and a vision block, we wonder: Can MLLMs directly absorb math reasoning abilities from off-the-shelf math LLMs without tuning? Recent model-merging approaches may offer insights into this question. However, they overlook the alignment between the MLLM and LLM, where we find that there is a large gap between their parameter spaces, resulting in lower performance. Our empirical evidence reveals two key factors behind this issue: the identification of crucial reasoning-associated layers in the model and the mitigation of the gaps in parameter space. Based on the empirical insights, we propose IP-Merging that first Identifies the reasoning-associated parameters in both MLLM and Math LLM, then Projects them into the subspace of MLLM, aiming to maintain the alignment, and finally merges parameters in this subspace. IP-Merging is a tuning-free approach since parameters are directly adjusted. Extensive experiments demonstrate that our IP-Merging method can enhance the math reasoning ability of MLLMs directly from Math LLMs without compromising their other capabilities.

Despite the impressive performance of large language models (LLMs), the process of endowing them with new capabilities--such as mathematical reasoning-- remains largely empirical and opaque. A critical open question is whether reasoning abilities stem from the entire model, specific modules, or are merely artifacts of overfitting. In this work, we hypothesize that the reasoning capabilities in welltrained LLMs are primarily attributed to the output projection module (o_proj) in the Transformer's multi-head self-attention (MHSA) module. To support this hypothesis, we introduce Stethoscope for Networks (SfN), a suite of diagnostic tools designed to probe and analyze the internal behaviors of LLMs. Using SfN, we provide both circumstantial and empirical evidence suggesting that o_proj plays a central role in enabling reasoning, whereas other modules contribute more to fluent dialogue. These findings offer a new perspective on LLM interpretability and open avenues for more targeted training strategies, potentially enabling more efficient and specialized LLMs.

Tabular reasoning requires complex, multi-step information extraction and logical inference, such as aggregation, comparison, or calculation over tabular data. While recent advances have leveraged large language models (LLMs) for reasoning over structured text tables, such high-quality textual representations are often unavailable in real-world settings, where tables typically appear as images. In this paper, we tackle the task of tabular reasoning directly from table images. Our core strategy is to leverage privileged structured information--specifically, the ground-truth structured table data available during training but inaccessible at test time--to enhance multimodal large language models (MLLMs). The key challenges lie in: accurately aligning visual representations with the structured information, particularly mapping the visual evidence to logical steps; and effectively transferring the reasoning skills learned during training to the MLLM for visual inference. To address these, we introduce TURBO (TabUlar Reasoning with Bridged infOrmation), a new framework for multimodal tabular reasoning using privileged information. TURBO benefits from a structure-aware reasoning trace generator based on DeepSeek-R1, which contributes to high-quality modality-bridged information. On this basis, TURBO repeatedly generates and selects advantageous reasoning traces, further enhancing the model's tabular reasoning ability. Experimental results demonstrate that, with limited (9k) data, TURBO achieves state-of-the-art performance (+7.2% vs. previous SOTA) across multiple datasets.

Large Reasoning Models (LRMs) have become powerful tools for complex problem solving, but their structured reasoning pathways can lead to unsafe outputs when exposed to harmful prompts. Existing safety alignment methods reduce harmful outputs but can degrade reasoning depth, leading to significant trade-offs in complex, multi-step tasks, and remain vulnerable to sophisticated jailbreak attacks. To address this, we introduce SAFEPATH, a lightweight alignment method that fine-tunes LRMs to emit a short, 8-token Safety Primer at the start of their reasoning, in response to harmful prompts, while leaving the rest of the reasoning process unsupervised. Empirical results across multiple benchmarks indicate that SAFEPATH effectively reduces harmful outputs while maintaining reasoning performance. Specifically, SAFEPATH reduces harmful responses by up to 90.0% and blocks 83.3% of jailbreak attempts in the DeepSeek-R1-Distill-Llama-8B model, while requiring 295.9x less compute than Direct Refusal and 314.1x less than SafeChain. We further introduce a zero-shot variant that requires no finetuning. In addition, we provide a comprehensive analysis of how existing methods in LLMs generalize, or fail, when applied to reasoning-centric models, revealing critical gaps and new directions for safer AI. We release model and code at https://ai-isl.github.io/safepath.

Recent language models exhibit strong reasoning capabilities, yet the influence of long-context capacity on reasoning remains underexplored. In this work, we hypothesize that current limitations in reasoning stem, in part, from insufficient long-context capacity, motivated by empirical observations such as i) higher context window length often leads to stronger reasoning performance, and ii) failed reasoning cases resemble failed long-context cases. To test this hypothesis, we examine whether enhancing a model's long-context ability before Supervised Fine-Tuning (SFT) leads to improved reasoning performance. Specifically, we compared models with identical architectures and fine-tuning data but varying levels of long-context capacity. Our results reveal a consistent trend: models with stronger long-context capacity achieve significantly higher accuracy on reasoning benchmarks after SFT. Notably, these gains persist even on tasks with short input lengths, indicating that long-context training offers generalizable benefits for reasoning performance. These findings suggest that long-context modeling is not just essential for processing lengthy inputs, but also serves as a critical foundation for reasoning. We advocate for treating long-context capacity as a first-class objective in the design of future language models.

Visual Reasoning (AVR) entails discerning latent patterns in visual data and inferring underlying rules. Existing solutions often lack scalability and adaptability, as deep architectures tend to overfit training data, and static neural networks fail to dynamically capture diverse rules. To tackle the challenges, we propose a Dynamic and Scalable Reasoning Framework (DSRF) that greatly enhances the reasoning ability by widening the network instead of deepening it, and dynamically adjusting the reasoning network to better fit novel samples instead of a static network. Specifically, we design a Multi-View Reasoning Pyramid (MVRP) to capture complex rules through layered reasoning to focus features at each view on distinct combinations of attributes, widening the reasoning network to cover more attribute combinations analogous to complex reasoning rules. Additionally, we propose a Dynamic Domain-Contrast Prediction (DDCP) block to handle varying task-specific relationships dynamically by introducing a Gram matrix to model feature distributions, and a gate matrix to capture subtle domain differences between context and target features. Extensive experiments on six AVR tasks demonstrate DSRF's superior performance, achieving state-of-the-art results under various settings. Code is available here: https://github.com/UNNCRoxLi/DSRF.

Multimodal Audio-Language Models (ALMs) can understand and reason over both audio and text. Typically, reasoning performance correlates with model size, with the best results achieved by models exceeding 8 billion parameters. However, no prior work has explored enabling small audio-language models to perform reasoning tasks, despite the potential applications for edge devices. To address this gap, we introduce Mellow, a small Audio-Language Model specifically designed for reasoning. Mellow achieves state-of-the-art performance among existing small audio-language models and surpasses several larger models in reasoning capabilities. For instance, Mellow scores 52.11 on MMAU, comparable to SoTAQwen2 Audio (which scores 52.5) while using 50 times fewer parameters and being trained on 60 times less data (audio hrs).

Long chain-of-thought (LongCoT) has emerged as a powerful reasoning paradigm for enabling large language models (LLMs) to solve complex tasks through a systematic and thorough thinking phase. Although supervised fine-tuning (SFT) on high-quality LongCoT traces has proven effective to activate LongCoT abilities, we find that models trained in this way tend to overfit problem-specific knowledge and heuristics, leading to degraded out-of-distribution performance. To address this issue, we propose a Decoupled LongCoT Fine-Tuning (DLoFT) algorithm, which enables the model to learn generalizable LongCoT reasoning abilities while preventing overfitting to the reasoning content with problem-specific information. The key idea is to decouple the gradient into two orthogonal components: 1) a paradigm-relevant gradient corresponding to the general LongCoT paradigm and 2) a content-relevant gradient reflecting the problem-specific information, where only the former gradient is used to update model parameters. Specifically, by leveraging the unique two-phase composition (thinking and solution) of the LongCoT response, our gradient decoupling mechanism isolates the content-relevant gradient via a projection operation and separates the paradigm-relevant gradient through orthogonalization. Our DLoFT ensures the model concentrate on internalizing the LongCoT paradigm rather than memorizing problem-specific knowledge and heuristics. Extensive experiments demonstrate that our DLoFT significantly improves the generalization behavior of LongCoT abilities compared to SFT while maintaining strong in-distribution performance.

Improving the reasoning capabilities of large language models (LLMs) has attracted considerable interest. Recent approaches primarily focus on improving the reasoning process to yield a more precise final answer.