Memory systems are becoming a core component of LLM agents, but constructing and maintaining memory remains expensive because it relies on repeated calls to large proprietary language models. This cost creates a major barrier to deploying memory-enhanced agents at scale. In this paper, we present Pseudo Self-Distillation (PSD), a framework that enables small language models (SLMs) to construct hierarchical memory representations by distilling behavior from a strong black-box oracle through a multi-stage training pipeline. Standard distillation methods require access to teacher logits or hidden states, which closed models do not expose. Unlike conventional self-distillation settings, where supervision is derived from a model's own predictions, sampled rollouts, or aggregated outputs, PSD enables a single-model distillation setup while channeling external oracle knowledge through the prompt. PSD uses a single small model in two roles: a teacher that sees a privileged prompt containing the oracle's answer as reference context, and a student that sees only the task prompt. The student learns to reproduce the teacher's output distribution, absorbing oracle-guided behavior into its own weights without accessing the oracle's internals. On LoCoMo, PSD-trained Qwen3-0.6B, 1.7B, and 4B match or exceed GPT-4.1-mini on downstream retrieval at a fraction of the deployment cost, with off-policy PSD achieving the strongest results across most conditions. We further show that this memory-construction capability transfers out-of-distribution to LongMemEval, despite the students being trained exclusively on LoCoMo with no exposure to LongMemEval data.

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