The standard practice in Large Language Models (LLMs) is to base predictions on final-layer representations. However, intermediate layers encode complementary task-relevant signals, and the optimal layer is task-dependent, making single-layer usage inherently suboptimal. In this work, we introduce Inter-Layer Structural Encoders (ILSE), a powerful and parameter-efficient post-training framework that learns to aggregate representations from all layers of a frozen LLM through structured inter-layer interactions. Central to ILSE is the Cayley-Encoder, a mathematically grounded module based on expander Cayley graphs that enables efficient and effective inter-layer information propagation. We evaluate ILSE on 13 classification and semantic similarity tasks across 9 pre-trained LLMs ranging from 14M to 8B parameters. ILSE consistently outperforms strong baselines, achieving up to 44% improvements in accuracy and 25% in similarity, while introducing at most 0.1% additional parameters relative to the base LLM size. Furthermore, ILSE is highly data-efficient in few-shot regimes and enables small LLMs to match or exceed the performance of substantially larger models. Notably, it also outperforms LoRA-based fine-tuning despite operating on frozen representations.

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