Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose Hint-Engineering, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRMCI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning.

Tokenization is the process of encoding strings into tokens of a fixed vocabulary size, and is widely utilized in Natural Language Processing applications. The leading tokenization algorithm today is Byte-Pair Encoding (BPE), which formulates the tokenization problem as a compression problem and tackles it by performing sequences of merges. In this work, we formulate tokenization as an optimization objective, show that it is NP-hard via a simple reduction from vertex cover, and propose a polynomial-time greedy algorithm GREEDTOK. Our formulation naturally relaxes to the well-studied weighted maximum coverage problem which has a simple (1 1/e)-approximation algorithm GREEDWMC. Through empirical evaluations on real-world corpora, we show that GREEDTOK outperforms BPE and UNIGRAM on compression and achieves a covering score comparable to GREEDWMC.

Reinforcement learning (RL) has become the dominant paradigm for improving the performance of language models on complex reasoning tasks. Despite the substantial empirical gains demonstrated by RL-based training methods like GRPO, a granular understanding of why and how RL enhances performance is still lacking. To bridge this gap, we introduce SPARKLE, a fine-grained analytic framework to dissect the effects of RL across three key dimensions: (1) plan following and execution, (2) knowledge integration, and (3) chain of subproblems. Using this framework, we gain insights beyond mere accuracy.

In this work, we address the task of table image to LaTeX code generation, with the goal of automating the reconstruction of high-quality, publication-ready tables from visual inputs. A central challenge of this task lies in accurately handling complex tables--those with large sizes, deeply nested structures, and semantically rich or irregular cell content--where existing methods often fail. We begin with a comprehensive analysis, identifying key challenges and highlighting the limitations of current evaluation protocols. To overcome these issues, we propose a reinforced multimodal large language model (MLLM) framework, where a pre-trained MLLM is fine-tuned on a large-scale table-to-LaTeX dataset. To further improve generation quality, we introduce a dual-reward reinforcement learning strategy based on Group Relative Policy Optimization (GRPO). Unlike standard approaches that optimize purely over text outputs, our method incorporates both a structure-level reward on LaTeX code and a visual fidelity reward computed from rendered outputs, enabling direct optimization of the visual output quality. We adopt a hybrid evaluation protocol combining TEDS-Structure and CW-SSIM, and show that our method achieves state-of-the-art performance, particularly on structurally complex tables, demonstrating the effectiveness and robustness of our approach.

Vision-Language models (VLMs) show impressive abilities to answer questions on visual inputs (e.g., counting objects in an image), yet demonstrate higher accuracies when performing an analogous task on text (e.g., counting words in a text). We investigate this accuracy gap by identifying and comparing the circuits--the task-specific computational sub-graphs--in different modalities. We show that while circuits are largely disjoint between modalities, they implement relatively similar functionalities: the differences lie primarily in processing modality-specific data positions (an image or a text sequence). Zooming in on the image data representations, we observe they become aligned with the higher-performing analogous textual representations only towards later layers, too late in processing to effectively influence subsequent positions. To overcome this, we patch the representations of visual data tokens from later layers back into earlier layers. In experiments with multiple tasks and models, this simple intervention closes a third of the performance gap between the modalities, on average.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term rank axes. We define a model as rankable for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings.

Large vision-language models (LVMs) extend large language models (LLMs) with visual mation.

A.1 Details of Dimension Design We argue that multi-dimensional evaluation is significant to visual caption evaluation and is more comprehensive than previous work. So how to choose proper dimensions? We refer to existing VQA benchmarks [62, 63, 64, 65] and visual generation benchmarks [31, 32, 33]. VQA benchmarks usually design various types of questions to include multi-dimensional evaluation and analysis of MLLMs. For instance, MMBench [64] defines 20 ability dimensions, including attribute recognition, attribute comparison, action recognition, spatial relationship, physical property, OCR, object localization, image style, image scene, identity reasoning, etc. MVBench [64] covers 20 challenging video tasks including action, object, position, count, scene, pose, attribute, character, cognition, etc. Due to the flexible design of questions, VQA benchmarks can be naturally built with comprehensive dimensions. Different from the VQA task, the visual caption task does not require specific questions, but inspects the alignment of visual and textual information. Visual generation is the inverse task of visual captioning, as it requires models to generate specific visual content based on detailed textual descriptions. GenEval [31] designs 6 different tasks to evaluate text-to-image alignment, including single object, two object, counting, colors, position, and attribute binding. VBench [32] comprises 16 dimensions, including subject consistency, background consistency, object class, human action, color, spatial relationship, scene, style, etc. We follow their explored dimensions to design proper dimensions for visual captioning. Finally, we design 6 views, covering object, global, text, camera, temporal, and knowledge. The object-related view includes object category, object color, object 1 number, and spatial relation, the global-related view includes scene and style, the text-related view evaluates the OCR capability of captions, the camera-related view covers the camera angle and movement, the temporal-related view contains action and event, and we also design a view to evaluate the knowledge of MLLMs, i.e., character identification. We believe these dimensions contribute to a comprehensive visual caption benchmarking.

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Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly--producing correct answers without explicitly verbalizing intermediate steps--but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a threestage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.