ConvexBench: Can LLMs Recognize Convex Functions?

Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with convexity. We introduce \cb, a scalable and mechanically verifiable benchmark for testing \textit{whether LLMs can identify the convexity of a symbolic objective under deep functional composition.} Experiments on frontier LLMs reveal a sharp compositional reasoning gap: performance degrades rapidly with increasing depth, dropping from an F1-score of $1.0$ at depth $2$ to approximately $0.2$ at depth $100$. Inspection of models' reasoning traces indicates two failure modes: \textit{parsing failure} and \textit{lazy reasoning}. To address these limitations, we propose an agentic divide-and-conquer framework that (i) offloads parsing to an external tool to construct an abstract syntax tree (AST) and (ii) enforces recursive reasoning over each intermediate sub-expression with focused context. This framework reliably mitigates deep-composition failures, achieving substantial performance improvement at large depths (e.g., F1-Score $= 1.0$ at depth $100$).

CausalEmbed: Auto-Regressive Multi-Vector Generation in Latent Space for Visual Document Embedding

Although Multimodal Large Language Models (MLLMs) have shown remarkable potential in Visual Document Retrieval (VDR) through generating high-quality multi-vector embeddings, the substantial storage overhead caused by representing a page with thousands of visual tokens limits their practicality in real-world applications. To address this challenge, we propose an auto-regressive generation approach, CausalEmbed, for constructing multi-vector embeddings. By incorporating iterative margin loss during contrastive training, CausalEmbed encourages the embedding models to learn compact and well-structured representations. Our method enables efficient VDR tasks using only dozens of visual tokens, achieving a 30-155x reduction in token count while maintaining highly competitive performance across various backbones and benchmarks. Theoretical analysis and empirical results demonstrate the unique advantages of auto-regressive embedding generation in terms of training efficiency and scalability at test time. As a result, CausalEmbed introduces a flexible test-time scaling strategy for multi-vector VDR representations and sheds light on the generative paradigm within multimodal document retrieval.

Preconditioning Benefits of Spectral Orthogonalization in Muon

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of gradient orthogonalization -- remain poorly understood, with very few works providing end-to-end analyses that rigorously explain its advantages in concrete applications. We take a step by studying the effectiveness of a simplified variant of Muon through two case studies: matrix factorization, and in-context learning of linear transformers. For both problems, we prove that simplified Muon converges linearly with iteration complexities independent of the relevant condition number, provably outperforming gradient descent and Adam. Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior. Our theory formalizes the preconditioning effect induced by spectral orthogonalization, offering insight into Muon's effectiveness in these matrix optimization problems and potentially beyond.

XLinear: A Lightweight and Accurate MLP-Based Model for Long-Term Time Series Forecasting with Exogenous Inputs

Despite the prevalent assumption of uniform variable importance in long-term time series forecasting models, real world applications often exhibit asymmetric causal relationships and varying data acquisition costs. Specifically, cost-effective exogenous data (e.g., local weather) can unilaterally influence dynamics of endogenous variables, such as lake surface temperature. Exploiting these links enables more effective forecasts when exogenous inputs are readily available. Transformer-based models capture long-range dependencies but incur high computation and suffer from permutation invariance. Patch-based variants improve efficiency yet can miss local temporal patterns. To efficiently exploit informative signals across both the temporal dimension and relevant exogenous variables, this study proposes XLinear, a lightweight time series forecasting model built upon MultiLayer Perceptrons (MLPs). XLinear uses a global token derived from an endogenous variable as a pivotal hub for interacting with exogenous variables, and employs MLPs with sigmoid activation to extract both temporal patterns and variate-wise dependencies. Its prediction head then integrates these signals to forecast the endogenous series. We evaluate XLinear on seven standard benchmarks and five real-world datasets with exogenous inputs. Compared with state-of-the-art models, XLinear delivers superior accuracy and efficiency for both multivariate forecasts and univariate forecasts influenced by exogenous inputs.

A Visual Semantic Adaptive Watermark grounded by Prefix-Tuning for Large Vision-Language Model

Watermarking has emerged as a pivotal solution for content traceability and intellectual property protection in Large Vision-Language Models (LVLMs). However, vision-agnostic watermarks introduce visually irrelevant tokens and disrupt visual grounding by enforcing indiscriminate pseudo-random biases, while some semantic-aware methods incur prohibitive inference latency due to rejection sampling. In this paper, we propose the VIsual Semantic Adaptive Watermark (VISA-Mark), a novel framework that embeds detectable signals while strictly preserving visual fidelity. Our approach employs a lightweight, efficiently trained prefix-tuner to extract dynamic Visual-Evidence Weights, which quantify the evidentiary support for candidate tokens based on the visual input. These weights guide an adaptive vocabulary partitioning and logits perturbation mechanism, concentrating watermark strength specifically on visually-supported tokens. By actively aligning the watermark with visual evidence, VISA-Mark effectively maintains visual fidelity. Empirical results confirm that VISA-Mark outperforms conventional methods with a 7.8% improvement in visual consistency (Chair-I) and superior semantic fidelity. The framework maintains highly competitive detection accuracy (96.88% AUC) and robust attack resilience (99.3%) without sacrificing inference efficiency, effectively establishing a new standard for reliability-preserving multimodal watermarking.

Open-Source Multimodal Moxin Models with Moxin-VLM and Moxin-VLA

Recently, Large Language Models (LLMs) have undergone a significant transformation, marked by a rapid rise in both their popularity and capabilities. Leading this evolution are proprietary LLMs like GPT-4 and GPT-o1, which have captured widespread attention in the AI community due to their remarkable performance and versatility. Simultaneously, open-source LLMs, such as LLaMA and Mistral, have made great contributions to the ever-increasing popularity of LLMs due to the ease to customize and deploy the models across diverse applications. Moxin 7B is introduced as a fully open-source LLM developed in accordance with the Model Openness Framework, which moves beyond the simple sharing of model weights to embrace complete transparency in training, datasets, and implementation detail, thus fostering a more inclusive and collaborative research environment that can sustain a healthy open-source ecosystem. To further equip Moxin with various capabilities in different tasks, we develop three variants based on Moxin, including Moxin-VLM, Moxin-VLA, and Moxin-Chinese, which target the vision-language, vision-language-action, and Chinese capabilities, respectively. Experiments show that our models achieve superior performance in various evaluations. We adopt open-source framework and open data for the training. We release our models, along with the available data and code to derive these models.

Transformers Provably Learn Chain-of-Thought Reasoning with Length Generalization

The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned reasoning patterns to solve harder tasks with longer chain-of-thought (CoT). In this work, we present a theoretical analysis of transformers learning on synthetic state-tracking tasks with gradient descent. We mathematically prove how the algebraic structure of state-tracking problems governs the degree of extrapolation of the learned CoT. Specifically, our theory characterizes the length generalization of transformers through the mechanism of attention concentration, linking the retrieval robustness of the attention layer to the state-tracking task structure of long-context reasoning. Moreover, for transformers with limited reasoning length, we prove that a recursive self-training scheme can progressively extend the range of solvable problem lengths. To our knowledge, we provide the first optimization guarantee that constant-depth transformers provably learn $\mathsf{NC}^1$-complete problems with CoT, significantly going beyond prior art confined in $\mathsf{TC}^0$, unless the widely held conjecture $\mathsf{TC}^0 \neq \mathsf{NC}^1$ fails. Finally, we present a broad set of experiments supporting our theoretical results, confirming the length generalization behaviors and the mechanism of attention concentration.

Multi-head Transformers Provably Learn Symbolic Multi-step Reasoning via Gradient Descent

Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a theoretical standpoint. This work investigates how transformers learn to solve symbolic multi-step reasoning problems through chain-of-thought processes, focusing on path-finding in trees. We analyze two intertwined tasks: a backward reasoning task, where the model outputs a path from a goal node to the root, and a more complex forward reasoning task, where the model implements two-stage reasoning by first identifying the goal-to-root path and then reversing it to produce the root-to-goal path. Our theoretical analysis, grounded in the dynamics of gradient descent, shows that trained one-layer transformers can provably solve both tasks with generalization guarantees to unseen trees. In particular, our multi-phase training dynamics for forward reasoning elucidate how different attention heads learn to specialize and coordinate autonomously to solve the two subtasks in a single autoregressive path. These results provide a mechanistic explanation of how trained transformers can implement sequential algorithmic procedures. Moreover, they offer insights into the emergence of reasoning abilities, suggesting that when tasks are structured to take intermediate chain-of-thought steps, even shallow multi-head transformers can effectively solve problems that would otherwise require deeper architectures.

MedMKEB: A Comprehensive Knowledge Editing Benchmark for Medical Multimodal Large Language Models

Recent advances in multimodal large language models (MLLMs) have significantly improved medical AI, enabling it to unify the understanding of visual and textual information. However, as medical knowledge continues to evolve, it is critical to allow these models to efficiently update outdated or incorrect information without retraining from scratch. Although textual knowledge editing has been widely studied, there is still a lack of systematic benchmarks for multimodal medical knowledge editing involving image and text modalities. To fill this gap, we present MedMKEB, the first comprehensive benchmark designed to evaluate the reliability, generality, locality, portability, and robustness of knowledge editing in medical multimodal large language models. MedMKEB is built on a high-quality medical visual question-answering dataset and enriched with carefully constructed editing tasks, including counterfactual correction, semantic generalization, knowledge transfer, and adversarial robustness. We incorporate human expert validation to ensure the accuracy and reliability of the benchmark. Extensive single editing and sequential editing experiments on state-of-the-art general and medical MLLMs demonstrate the limitations of existing knowledge-based editing approaches in medicine, highlighting the need to develop specialized editing strategies. MedMKEB will serve as a standard benchmark to promote the development of trustworthy and efficient medical knowledge editing algorithms.

NEARL-CLIP: Interacted Query Adaptation with Orthogonal Regularization for Medical Vision-Language Understanding

Computer-aided medical image analysis is crucial for disease diagnosis and treatment planning, yet limited annotated datasets restrict medical-specific model development. While vision-language models (VLMs) like CLIP offer strong generalization capabilities, their direct application to medical imaging analysis is impeded by a significant domain gap. Existing approaches to bridge this gap, including prompt learning and one-way modality interaction techniques, typically focus on introducing domain knowledge to a single modality. Although this may offer performance gains, it often causes modality misalignment, thereby failing to unlock the full potential of VLMs. In this paper, we propose \textbf{NEARL-CLIP} (i\underline{N}teracted qu\underline{E}ry \underline{A}daptation with o\underline{R}thogona\underline{L} Regularization), a novel cross-modality interaction VLM-based framework that contains two contributions: (1) Unified Synergy Embedding Transformer (USEformer), which dynamically generates cross-modality queries to promote interaction between modalities, thus fostering the mutual enrichment and enhancement of multi-modal medical domain knowledge; (2) Orthogonal Cross-Attention Adapter (OCA). OCA introduces an orthogonality technique to decouple the new knowledge from USEformer into two distinct components: the truly novel information and the incremental knowledge. By isolating the learning process from the interference of incremental knowledge, OCA enables a more focused acquisition of new information, thereby further facilitating modality interaction and unleashing the capability of VLMs. Notably, NEARL-CLIP achieves these two contributions in a parameter-efficient style, which only introduces \textbf{1.46M} learnable parameters.