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The standard practice in Large Language Models (LLMs) is to base predictions on the final-layer token representations. Recent studies, however, show that intermediate layers encode substantial information, which may contain more task-relevant features than the final-layer representations alone. Importantly, it was shown that for different tasks, different layers may be optimal. In this work we introduce Inter-Layer Structural Encoders (ILSE), a powerful structural approach to learn one effective representation from the LLM's internal layer representations all together. Central to ILSE is Cayley-Encoder, a mathematically grounded geometric encoder that leverages expander Cayley graphs for efficient inter-layer information propagation. We evaluate ILSE across 13 classification and semantic similarity tasks with 9 pre-trained LLMs ranging from 14 million to 8 billion parameters. ILSE consistently outperforms baselines and existing approaches, achieving up to 44% improvement in accuracy and 25% in similarity metrics. We further show that ILSE is data-efficient in few-shot regimes and can make small LLMs competitive with substantially larger models.