arXiv:2603.08291v1 Announce Type: new Abstract: Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems that involve both textual and visual modalities. However, current models still face significant challenges in real-world visual math tasks. They often misinterpret diagrams, fail to align mathematical symbols with visual evidence, and produce inconsistent reasoning steps. Moreover, existing evaluations mainly focus on checking final answers rather than verifying the correctness or executability of each intermediate step. To address these limitations, a growing body of recent research addresses these issues by integrating structured perception, explicit alignment, and verifiable reasoning within unified frameworks. To establish a clear roadmap for understanding and comparing different MMR approaches, we systematically study them around four fundamental questions: (1) What to extract from multimodal inputs, (2) How to represent and align textual and visual information, (3) How to perform the reasoning, and (4) How to evaluate the correctness of the overall reasoning process. Finally, we discuss open challenges and offer perspectives on promising directions for future research.

arXiv:2402.15751v2 Announce Type: replace-cross Abstract: While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO) optimizers, recently proposed to address this issue, only require forward passes during training, making them more memory-friendly. However, compared with exact gradients, ZO-based gradients usually exhibit an estimation error, which can significantly hurt the optimization process, leading to slower convergence and suboptimal solutions. In addition, we find that the estimation error will hurt more when adding to large weights instead of small weights. Based on this observation, this paper introduces Sparse MeZO, a novel memory-efficient zeroth-order optimization approach that applies ZO only to a carefully chosen subset of parameters. We propose a simple yet effective parameter selection scheme that yields significant performance gains with Sparse-MeZO. Additionally, we develop a memory-optimized implementation for sparse masking, ensuring the algorithm requires only inference-level memory consumption, allowing Sparse-MeZO to fine-tune LLaMA-30b on a single A100 GPU. Experimental results illustrate that Sparse-MeZO consistently improves both performance and convergence speed over MeZO without any overhead. For example, it achieves a 9\% absolute accuracy improvement and 3.5x speedup over MeZO on the RTE task. Code is available at https://github.com/NUS-HPC-AI-Lab/SparseMeZO.