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.

Large Language Models (LLMs) fine-tuning technologies have achieved remarkable results. However, traditional LLM fine-tuning approaches face significant challenges: they require large Floating Point(FP) computation, raising privacy concerns when handling sensitive data, and are impractical for resource-constrained edge devices. While Parameter-Efficient Fine-Tuning (PEFT) techniques reduce trainable parameters, their reliance on floating-point arithmetic creates fundamental incompatibilities with edge hardware. In this work, we introduce a novel framework for on-device LLM fine-tuning that eliminates the need for floating-point operations in both inference and training, named GSQ-Tuning. At its core is the Group-Shared Exponents Integer format, which efficiently represents model parameters in integer format using shared exponents among parameter groups. When combined with LoRA-like adapters, this enables fully integer-based fine-tuning that is both memory and compute efficient. We demonstrate that our approach achieves accuracy comparable to FP16-based fine-tuning while significantly reducing memory usage ( 50%). Moreover, compared to FP8, at comparable performance levels, our method can reduce 5x power consumption and 11x chip area, making large-scale model adaptation feasible on edge devices.