- Updated: August 24, 2026
- 3 min read
Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection
Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization
Recent advances in Large Language Models (LLMs) open new perspectives for automation in optimization, yet little is known about whether their internal representations capture problem structure or algorithmic behavior. This article provides a comprehensive, SEO‑optimized overview of the research presented in arXiv:2512.13374v2, highlighting key findings, methodology, and implications for the field.
Abstract
Recent advances in Large Language Models (LLMs) open new perspectives for automation in optimization, yet little is known about whether their internal representations capture problem structure or algorithmic behavior. We investigate whether representations learned by frozen, open-weight LLMs for combinatorial optimization instances can support downstream decision tasks. The goal is not to replace exact feature extractors or to propose a new algorithm, but to assess whether such representations are reusable for feature recovery and algorithm selection. Our methodology combines direct querying, which tests explicit feature extraction, with probing analyses of whether this information is implicitly encoded in the hidden layers. The probing framework is further extended to a per‑instance algorithm selection task. Experiments span four benchmark problems, three instance representations, and five open‑weight models from 3B to 120B parameters across the Llama instruct and GPT reasoning families, including a chain‑of‑thought study on Llama models. Results show a limited ability to recover features explicitly, particularly those requiring structured computation, while part of this information remains implicitly encoded in the hidden states. A consistent gap separates implicit encoding from explicit retrieval. Model scale attenuates this gap, whereas the effect of chain‑of‑thought prompting depends strongly on model size, and in all cases the gap remains open. Reasoning‑oriented models also tend to abstain more when reliable computation is not possible. Notably, the predictive power of LLM hidden‑layer representations is comparable to traditional feature extraction across all five models, indicating they can act as effective surrogate descriptors for downstream optimization tasks.
Key Insights
- LLM hidden‑layer representations can serve as surrogate descriptors for combinatorial optimization tasks.
- Explicit feature extraction from LLMs remains limited, especially for structured computations.
- Model scale reduces the gap between implicit encoding and explicit retrieval.
- Chain‑of‑thought prompting benefits larger models but does not close the encoding gap.
- Reasoning‑oriented models exhibit higher abstention rates when faced with uncertain computations.
For a deeper dive into the methodology, experimental setup, and detailed results, read the full paper on arXiv.
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Andrii Bidochko
CTO UBOS
Andrii Bidochko is an AI entrepreneur and researcher focused on AI agents, reinforcement learning, and autonomous systems. He writes about the technologies shaping the future of machine intelligence, from frontier models and agent architectures to real-world AI applications.