🤖 AI Summary
This study addresses the challenge of achieving optimal estimation of dynamic latent variables from asynchronous, irregularly timed observations in a decentralized agent network lacking shared clocks, common models, or retrainable weights. The work establishes, for the first time, that under fixed-weight bases, optimal estimation necessitates two conditions—adaptive timescale modulation and observation-gap awareness—and that this requirement is independent of network capacity. To fulfill both criteria, the authors propose a multi-timescale modeling framework grounded in continuous-time liquid networks, integrating adaptive filtering with gap-sensitive mechanisms. Empirical results demonstrate that the proposed architecture simultaneously satisfies both theoretical conditions and attains optimal estimation performance, whereas LSTM-based approaches or conventional continuous-time filters meet only one of the two requirements.
📝 Abstract
A mesh of sovereign agents has no center: no shared clock, no shared model, and no coordinator to gather data or retrain. Its competence rests on each agent folding the projections its peers emit into a single internal state, online, from observations that arrive at irregular, unscheduled times, on a substrate whose weights it cannot retrain. Any one of these constraints is tractable on its own; folding optimally under all three at once is not. We ask what such a substrate must be, and prove two necessary conditions from one model of a self-evolving latent observed at irregular, exogenous times. Because the latent changes, its optimal estimator is time-varying: an adaptive timescale is necessary, and every fixed-gain filter is strictly suboptimal. And because arrivals are clock-free, the optimal estimate depends on the elapsed gap between them, which no gap-blind network recovers at any width or depth. This second condition is capacity-independent: scale cannot substitute for the missing dependence. The two conditions intersect in the continuous-time liquid class. An LSTM satisfies the first, a fixed continuous-time filter the second, and a multi-timescale liquid network both. Synthetic experiments confirm each: the network attains the timescale, and the separation is computed exactly. The characterization is necessary, not sufficient, and binds fixed-weight substrates: a network free to retrain reaches the class by other means. Proved per agent, the necessity binds every agent of a mesh, a structural condition on mesh intelligence.