SepSeq: A Training-Free Framework for Long Numerical Sequence Processing in LLMs

While transformer-based Large Language Models (LLMs) theoretically support massive context windows, they suffer from severe performance degradation when processing long numerical sequences. We attribute this failure to the attention dispersion in the Softmax mechanism, which prevents the model from concentrating attention. To overcome this, we propose Separate Sequence (SepSeq), a training-free, plug-and-play framework to mitigate dispersion by strategically inserting separator tokens. Mechanistically, we demonstrate that separator tokens act as an attention sink, recalibrating attention to focus on local segments while preserving global context. Extensive evaluations on 9 widely-adopted LLMs confirm the effectiveness of our approach: SepSeq yields an average relative accuracy improvement of 35.6% across diverse domains while reducing total inference token consumption by 16.4% on average.

LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To make problem formulating and solving automated, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of way suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.