External memory in long-horizon language agents is often treated as a frozen world model: it gets judged by task success or token cost. This work argues that the missing object is the shape of memory use. Under finite context and repeated retrieval, memory tends to concentrate on a small core of states, leaving rare ones in a heavy tail. That is where prediction errors accumulate.

The authors ran a conservative tail audit. The concentration is reproducible but policy-dependent. A random-walk agent produces retrieval artifacts compatible with a log-normal distribution, while semantic LLM policies produce the strongest core-tail traces compatible with a truncated power law. In other words, the exact tail shape is not a fixed property of the model; it changes with the way the agent explores and retrieves.

From this audit comes Coreโ€“Tail World Model (CTWM), a rank-based memory controller. The core idea is to allocate the prompt budget with a single exponent ฯ„, keep a summarized tail, and give priority to the core. On Synthetic Graph World, CTWM preserves full state and transition coverage, reduces prompt tokens by 5.9%, and lowers bottom-half tail prediction error by 13.6% relative to a graph-memory baseline. On ALFWorld the token savings are consistent; on LongMemEval the reduction reaches 24.48% at aggregate accuracy parity.

These numbers say more than a simple efficiency gain. They challenge the idea that an agent's external memory is a neutral store. If context budget is scarce, every prompt slot is an allocated resource. Treating rare states as a tail to summarizeโ€”rather than ignoring them or including them in fullโ€”is a design choice with measurable effects.

For teams evaluating on-premise or self-hosted deployments, the result has immediate value. Lighter prompts reduce per-call computational load and, in turn, memory and compute requirements. It is not only a matter of TCO: the heavy tail becomes an operational signal. If a controller can maintain coverage of rare states with fewer tokens, the marginal cost of a long-horizon agent changes. AI-RADAR has an /llm-onpremise area covering the trade-offs between context, memory, and latency.

The structural point is that memory management is no longer an accessory to inference. Until recently, the problem seemed solvable by enlarging the context window or adding storage. This work suggests that the shape of the retrieval distribution is a first-order control variable: it is not just a diagnostic of behavior, but a way to govern it.

Benchmarks that measure only aggregate success and cost miss rare failure modes. An agent can look solid overall and fail precisely in the least frequent states, where prediction error is highest. Teams that adopt tail audits get a signal to allocate budget more effectively; those that keep optimizing for the average risk tuning a system that degrades asymmetrically.