Large Language Models (LLMs) encode vast amounts of knowledge in their massive parameters, which is accessible to locate, trace, and analyze. Despite advances in neural interpretability, it is still not clear how to transfer knowledge in a fine-grained manner, namely parametric knowledge transfer (PKT). A key problem is enabling effective and efficient knowledge transfer across LLMs of different scales, which is essential for achieving greater flexibility and broader applicability in transferring knowledge between LLMs. Due to neural incompatibility, referring to the architectural and parametric differences between LLMs of varying scales, existing methods that directly reuse layer parameters are severely limited. In this paper, we identify the semantic alignment in latent space as the fundamental prerequisite for LLM cross-scale knowledge transfer. Instead of directly using the layer parameters, our approach takes activations as the medium of layer-wise knowledge transfer. Leveraging the semantics in latent space, our approach is simple and outperforms prior work, better aligning model behaviors across varying scales. Evaluations on four benchmarks demonstrate the efficacy of our method. Further analysis reveals the key factors easing cross-scale knowledge transfer and provides insights into the nature of latent semantic alignment.

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