Existing summarizers for memory systems are typically optimized for human-facing criteria such as faithfulness, which misaligns with their true objective: preserving the evidence needed to support future queries. We show that conditioning summarization on query-answer pairs substantially improves answer quality, and that this utility-aware behavior is transferable across queries. Motivated by these findings, we propose MemSuit, a self-distillation framework in which a teacher summarizer, conditioned on observed query-answer pairs, produces utility-aware memory entries that a student learns to reproduce from the raw conversation alone. To prevent collateral erasure where conditioning on a single query-answer pair discards evidence relevant to other plausible queries, the teacher decomposes each block into multiple self-contained entries that preserve distinct query-relevant facets as independently retrievable units. To align the retriever with the compact, fact-dense style of teacher entries, we further fine-tune the embedding model with a contrastive objective supervised by teacher entries. Across a diverse suite of conversational query types, MemSuit consistently outperforms state-of-the-art baselines, confirming the value of grounding memory in downstream utility.

The capability of in-context learning (ICL) enables large language models (LLMs) to perform novel tasks without parameter updates by conditioning on a few input-output examples. However, collecting high-quality examples for new or challenging tasks can be costly and labor-intensive. In this work, we propose a cost-efficient two-stage pipeline that reduces reliance on LLMs for data labeling. Our approach first leverages readily available cross-task examples to prompt an LLM and pseudo-label a small set of target task instances. We then introduce a graph-based label propagation method that spreads label information to the remaining target examples without additional LLM queries. The resulting fully pseudo-labeled dataset is used to construct in-task demonstrations for ICL. This pipeline combines the flexibility of cross-task supervision with the scalability of LLM-free propagation. Experiments across five tasks demonstrate that our method achieves strong performance while lowering labeling costs.