Bounded State in an Infinite Horizon: Proactive Hierarchical Memory for Ad-Hoc Recall over Streaming Dialogues

Real-world dialogue usually unfolds as an infinite stream. It thus requires bounded-state memory mechanisms to operate within an infinite horizon. However, existing read-then-think memory is fundamentally misaligned with this setting, as it cannot support ad-hoc memory recall while streams unfold. To explore this challenge, we introduce \textbf{STEM-Bench}, the first benchmark for \textbf{ST}reaming \textbf{E}valuation of \textbf{M}emory. It comprises over 14K QA pairs in dialogue streams that assess perception fidelity, temporal reasoning, and global awareness under infinite-horizon constraints. The preliminary analysis on STEM-Bench indicates a critical \textit{fidelity-efficiency dilemma}: retrieval-based methods use fragment context, while full-context models incur unbounded latency. To resolve this, we propose \textbf{ProStream}, a proactive hierarchical memory framework for streaming dialogues. It enables ad-hoc memory recall on demand by reasoning over continuous streams with multi-granular distillation. Moreover, it employs Adaptive Spatiotemporal Optimization to dynamically optimize retention based on expected utility. It enables a bounded knowledge state for lower inference latency without sacrificing reasoning fidelity. Experiments show that ProStream outperforms baselines in both accuracy and efficiency.