On the Necessity of a Liquid Substrate for Mesh Intelligence
A preprint proves that in a mesh of sovereign agents without central coordination, the substrate for each agent must belong to the continuous-time liquid class to optimally process irregular, asynchronous observations. Two necessary conditions are identified: an adaptive timescale and sensitivity to elapsed inter-arrival times, which scale cannot compensate.
[2606.28413] On the Necessity of a Liquid Substrate for Mesh Intelligence
[Submitted on 25 Jun 2026]
Title:On the Necessity of a Liquid Substrate for Mesh Intelligence
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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.
Comments: 14 pages, 3 figures
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA)
Cite as: arXiv:2606.28413 [cs.LG]
(or arXiv:2606.28413v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.28413
arXiv-issued DOI via DataCite
Submission history
From: Hongwei Xu [view email] [v1] Thu, 25 Jun 2026 08:42:26 UTC (211 KB)
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