Memory Is Communication: The Frontier Between Remembering and Signaling

Long-horizon language agents must operate under limited runtime memory, yet existing memory mechanisms often organize experience around descriptive criteria such as relevance, salience, or summary quality. For an agent, however, memory is valuable not because it faithfully describes the past, but because it preserves the distinctions between histories that must remain separated under a fixed budget to support good decisions. We cast this as a decision-centric rate-distortion problem, measuring memory quality by the loss in achievable decision quality induced by compression. This yields an exact forgetting boundary for what can be safely forgotten, and a memory-distortion frontier characterizing the optimal tradeoff between memory budget and decision quality. Motivated by this decision-centric view of memory, we propose DeMem, an online memory learner that refines its partition only when data certify that a shared state would induce decision conflict, and prove near-minimax regret guarantees. On both controlled synthetic diagnostics and long-horizon conversational benchmarks, DeMem yields consistent gains under the same runtime budget, supporting the principle that memory should preserve the distinctions that matter for decisions, not descriptions.

Memory enables language agents to carry useful distinctions from past experience into future decisions. Its value depends on which distinctions survive, whether a bounded agent can use them, and what can be recovered or revised as demands evolve. We develop a decision-theoretic framework that follows this value from raw history through persistent state, operational use, and costly recovery and revision. Original and retained value are expressed in units of avoided task loss; risk-cost frontiers describe attainable recovery and preservation across uses. Unknown demand yields value profiles, while interactive feedback changes the distribution of future work. A cost-aware simulation condition and five minimal counterexamples expose the roles of information timing, retrieval access, component interaction, feedback and demand uncertainty. In particular, a pointer with zero mutual information about the answer can still reduce the cost of exact recovery. Diagnostics on LoCoMo, a two-project update task and longitudinal cases exhibit failures of preservation, use and measurement. At fixed retrieved evidence, a saved ledger changes subsequent answers; at fixed agent outputs, an evaluator revision changes scores. The framework connects these distinctions to operational risk bounds and testable principles for allocating memory, preserving recovery options and revising evidence dependencies.

Rate-limited multi-agent teams raise three questions the emergent-communication literature has answered only empirically: what an optimal message should encode, what compression costs over a horizon, and when a learned protocol is unique enough for a teammate to read. We answer them for rate-limited Dec-POMDPs, then measure how far reinforcement learning falls short of the optimum. Our theorems fix what is achievable independently of any learner, so a gap between an engineered and a learned sender at the same bit budget is an optimization fact, not an information-theoretic one. We instantiate this on three MuJoCo arenas spanning zero, partial and rigid physical coupling, charging every condition exactly 2 bits per decision, and create the discriminating regime by closing a physical side channel within one arena, holding bodies, task and reward fixed. Communication value is governed by coupling: under rigid coupling through a shared object, no channel beats silence (+0.001 +/- 0.001, p = 0.982, n = 25), since proprioception already carries that information; without coupling, every condition solves the task; under partial coupling, the engineered 2-bit sender reaches an interquartile mean of 1.000 but the learned one reaches 0.482, indistinguishable from silence (p = 0.400, n = 25). With a shared alphabet, bandwidth cannot explain the gap. Warm-starting from an engineered receiver localizes the failure: the same channel reaches 0.857 versus 0.562 cold-started (p < 0.001), so it is neither representational nor one of maintenance; reinforcement learning fails to discover the protocol. Cross-play shows learned protocols are individually meaningful but mutually unintelligible: self-play 0.980 collapses to 0.144 across seeds, and our best constructed alignment leaves at least 77% of that gap. All headline results use 25 seeds per arena and seven published baselines at matched rate.