Translating natural language to First-Order Logic (NL2FOL) is crucial for logic-based reasoning, but most existing models and benchmarks focus on English, leaving cross-lingual generalization underexplored. In this study, we present the first comprehensive investigation of cross-lingual robustness in NL2FOL. To support this, we introduce Multi-MALLS, the first multilingual benchmark for NL2FOL, which extends the widely-used MALLS dataset with high-quality translations into multiple languages. Using Multi-MALLS, we observe that state-of-the-art models experience a significant performance drop when applied to non-English inputs, highlighting the lack of robustness. To address this, we propose MA-FOL, a multi-agent framework that improves generalization without requiring any training on target languages. By decomposing the task into three modules, a language-agnostic structure generator, a language-specific predicate combiner, and a refinement component, MA-FOL achieves robust zero-shot generalization across diverse linguistic inputs. Additionally, we show that traditional evaluation metrics, such as Exact Match, often fail to assess semantic correctness. To remedy this, we introduce large language models (LLMs)-Judged Semantic Equivalence (SE), a new metric that leverages LLMs to evaluate whether generated formulas preserve the intended meaning. Extensive experiments demonstrate that MA-FOL outperforms strong baselines on Multi-MALLS, without any multilingual fine-tuning. The SE metric further reveals semantic correctness that traditional metrics miss. Overall, our work provides a benchmark to test robustness of NL2FOL, a framework to improve it, and a metric to evaluate it more effectively.

Low-Rank Adaptation (LoRA) has become a widely adopted parameter-efficient fine-tuning method for large language models, with its effectiveness largely influenced by the allocation of ranks and scaling factors, as well as initialization. Existing LoRA variants typically address only one of these factors, often at the cost of increased training complexity or reduced practical efficiency.In this work, we present Task-aware Low-Rank Adaptation (TLoRA), a unified framework that jointly optimizes initialization and resource allocation at the outset of training. TLoRA introduces a data-driven initialization strategy that aligns the LoRA A matrix with task-relevant subspaces by performing singular value decomposition on the product of pre-trained weights and input activation covariance. After this, the A matrix is frozen, and only the B matrix is trained. Furthermore, TLoRA employs a sensitivity-based importance metric to adaptively allocate ranks and scaling factors across layers under a fixed parameter budget.We conduct extensive experiments that demonstrate TLoRA consistently performs excellently across various tasks, including natural language understanding, commonsense reasoning, math reasoning, code generation, and chat generation, while significantly reducing the number of trainable parameters. Our code are available at https://github.com/Rambo-Yi/TLora/tree/main