Significant challenges remain in AI-driven educational systems in balancing privacy preservation with accurate cognitive diagnosis. To overcome this, we propose a federated inference framework in which several commercial LLM APIs collaborate without requiring access to raw student data or proprietary model internals. Using multiple federated entities, such as LLaMA-3.3-70B, GPT-4o-mini, and Claude-3-Haiku, our framework builds upon a heterogeneous multi-LLM architecture. The predictions generated by these entities are combined with epsilon-local differential privacy by adding Laplace noise locally to each entity's prediction output before aggregation, while residual-based aggregation mitigates model heterogeneity. Our approach is predicated on an honest-but-curious trust paradigm in which API providers are presumed not to abuse submitted queries, and our differential privacy mechanism shields the published diagnostic results from external inference. We conduct rigorous privacy-utility analysis showing strong privacy guarantees with minimal accuracy loss, and extensive real-world evaluations across three educational benchmarks confirm the framework's practical usability and cross-domain generalizability.
Text summarization is deceptively difficult. While condensing information seems straightforward, real-world enterprise summarization of support tickets, legal documents, incident reports, and more, demands strict adherence to domain-specific guidelines, output formats, and organizational conventions. Crafting prompts that reliably satisfy these constraints is labor-intensive, requiring significant human expertise and continuous maintenance as requirements evolve. Existing automated prompt optimization methods reduce this burden through Large Language Model (LLM) critique-driven refinement, yet remain limited by static prompts that cannot adapt to the diversity of summary applications. We propose Multi-LLM Iterative Data-Adaptive Summarization (MIDAS), a multi-LLM framework that extends this paradigm with data-driven pattern learning and use-case-specific personalization, enabling automatic adaptation to different summarization requirements without manual prompt engineering. Applied to enterprise customer ticket summarization across five output formats, MIDAS achieves the strongest overall performance against state-of-the-art critique-driven optimization frameworks such as CriSPO and ZERA, improving ROUGE-1 by up to 11.0%, ROUGE-2 by up to 18.2%, and ROUGE-L by up to 8.0%, while consistently improving BERTScore F1 across all formats and output types. We additionally demonstrate cross-model and cross-domain generalization through multi-LLM configurations and finance-domain summarization benchmarks.