Large language models (LLMs) have shown remarkable performances across a wide range of tasks. However, the mechanisms by which these models encode tasks of varying complexities remain poorly understood. In this paper, we explore the hypothesis that LLMs process concepts of varying complexities in different layers, introducing the idea of “Concept Depth” to suggest that more complex concepts are typically acquired in deeper layers. Specifically, we categorize concepts based on their level of abstraction, defining them in the order of increasing complexity within factual, emotional, and inferential tasks. We conduct extensive probing experiments using layer-wise representations across various LLM families (Gemma, LLaMA, Qwen) on various datasets spanning the three domains of tasks. Our findings reveal that models could efficiently conduct probing for simpler tasks in shallow layers, and more complex tasks typically necessitate deeper layers for accurate understanding. Additionally, we examine how external factors, such as adding noise to the input and quantizing the model weights, might affect layer-wise representations. Our findings suggest that these factors can impede the development of a conceptual understanding of LLMs until deeper layers are explored. We hope that our proposed concept and experimental insights will enhance the understanding of the mechanisms underlying LLMs. Our codes are available at https://github.com/Luckfort/CD.

Prompt-based learning is vulnerable to backdoor attacks. Existing backdoor attacks against prompt-based models consider injecting backdoors into the entire embedding layers or word embedding vectors. Such attacks can be easily affected by retraining on downstream tasks and with different prompting strategies, limiting the transferability of backdoor attacks. In this work, we propose transferable backdoor attacks against prompt-based models, called NOTABLE, which is independent of downstream tasks and prompting strategies. Specifically, NOTABLE injects backdoors into the encoders of PLMs by utilizing an adaptive verbalizer to bind triggers to specific words (i.e., anchors). It activates the backdoor by pasting input with triggers to reach adversary-desired anchors, achieving independence from downstream tasks and prompting strategies. We conduct experiments on six NLP tasks, three popular models, and three prompting strategies. Empirical results show that NOTABLE achieves superior attack performance (i.e., attack success rate over 90% on all the datasets), and outperforms two state-of-the-art baselines. Evaluations on three defenses show the robustness of NOTABLE. Our code can be found at https://github.com/RU-System-Software-and-Security/Notable.