S4.2 Training Table S2 presents architectures.

Graphs are commonly used in machine learning to model relationships between instances. Consider the task of predicting the political preferences of users in a social network; to solve this task one should consider, both, the features of each individual user and the relationships between them. However, oftentimes one is not interested in the label of a single instance but rather in the distribution of labels over a set of instances; e.g., when predicting the political preferences of users, the overall prevalence of a given opinion might be of higher interest than the opinion of a specific person. This label prevalence estimation task is commonly referred to as quantification learning (QL). Current QL methods for tabular data are typically based on the so-called prior probability shift (PPS) assumption which states that the label-conditional instance distributions should remain equal across the training and test data. In the graph setting, PPS generally does not hold if the shift between training and test data is structural, i.e., if the training data comes from a different region of the graph than the test data. To address such structural shifts, an importance sampling variant of the popular adjusted count quantification approach has previously been proposed. In this work, we extend the idea of structural importance sampling to the state-of-the-art KDEy quantification approach. We show that our proposed method adapts to structural shifts and outperforms standard quantification approaches.

SVs and SIs, various methods have been proposed that exploit structural assumptions or yield probabilistic estimates given limited resources.

Consequently, if the parameterization is not rich enough, then it may not be possible to represent the distribution ratios accurately, and when using rich function approximators (such as neural networks) then the optimization procedure may get stuck in sub-optimal saddle points.

System Instructions (SIs), or system prompts, are pivotal for guiding Large Language Models (LLMs) but manual crafting is resource-intensive and often suboptimal. Existing automated methods frequently generate non-human-readable "soft prompts," sacrificing interpretability. This paper introduces SI-Agent, a novel agentic framework designed to automatically generate and iteratively refine human-readable SIs through a feedback-driven loop. SI-Agent employs three collaborating agents: an Instructor Agent, an Instruction Follower Agent (target LLM), and a Feedback/Reward Agent evaluating task performance and optionally SI readability. The framework utilizes iterative cycles where feedback guides the Instructor's refinement strategy (e.g., LLM-based editing, evolutionary algorithms). We detail the framework's architecture, agent roles, the iterative refinement process, and contrast it with existing methods. We present experimental results validating SI-Agent's effectiveness, focusing on metrics for task performance, SI readability, and efficiency. Our findings indicate that SI-Agent generates effective, readable SIs, offering a favorable trade-off between performance and interpretability compared to baselines. Potential implications include democratizing LLM customization and enhancing model transparency. Challenges related to computational cost and feedback reliability are acknowledged.