arXiv subjects

Galen J. Wilkerson

Publications and source records attributed to Galen J. Wilkerson.

4 recordsLinked to original sources

arXiv2026

A mechanism for collective foraging: percolating recruitment cascades coupled to a maximum-entropy field

Foraging recruitment is a contagion: an agent that finds a resource triggers a linear-threshold cascade, the model built for rumour and adoption spread on social networks, now embedded in space. Because activation is degree-normalized, the same rule that spreads the cascade also stifles it as neighbourhoods crowd, so the swarm aggregates on a resource and then releases to explore again. The cascade runs on the communication network, but acting on it moves agents in physical space, and that motion rewires the network: network and space are one coupled system, and this feedback, not any tuning, makes the coordination self-limiting. Because recruitment chains along the graph rather than reaching near neighbours alone, whether a discovery stays local or spans the swarm is a question of percolation. The swarm holds itself in a cascade window that is locally near-critical though globally subcritical, a self-organized, self-limiting drive-release cycle, sandpile-like but non-conservative. Nothing is tuned, yet behaviours that foraging biology documents separately emerge together: recruitment to discoveries, marginal-value patch-leaving, and Levy search with a switch to local exploitation. These follow from one least-committal principle, the resource field and the search both as maximum entropy, with Levy search matched to the field's sparsity and recruitment to its clustering, so active-matter order and optimal foraging appear as one system seen in two domains. The gains are real but conditional: up to 7.6x the harvest of solitary search when resources are sparse and clustered, shrinking to nothing when search is already easy. That sparse, clustered field is also the generic one, because resources almost inevitably aggregate, so one untuned rule should recur widely.

physics.soc-ph↗

arXiv2026

Self-organizing reinforcement learning: a learner-free swarm approaches the explore-exploit optimum

The explore/exploit trade-off is the core problem of reinforcement learning (RL). We show that a minimal foraging swarm approaches its optimum - the ideal-free / Nash allocation of a multi-agent resource-sharing game (an equilibrium, not a return maximum) - with no learner and no reward signal. Agents explore by heavy-tailed (Levy) flights, recruit neighbours to a discovery through a threshold cascade on their proximity network, and disperse as a patch crowds; this cascade cycle balances exploration and exploitation and drives foragers toward the ideal free distribution. The swarm attains the shape of this optimum (committed foragers track richness with slope 0.94) but not its exact equilibrium - it stays measurably exploitable - reaching it dynamically (~150 steps) through the coupling of recruitment to movement: remove the coupling and matching collapses (0.94 -> 0.08). The RL sits at the level of the problem and the allocation reached, not the micro-rule: no step evaluates payoff (reward-free by construction, though the crowd signal is informationally tied to payoff), and the swarm reaches the allocation without learning it (quality plateaus and re-settles after resources move, no cumulative gain). Against a trained baseline the comparison is two-sided: in an easier, disembodied game a learner is more precise, while in the same embodied environment the reward-free swarm reaches ~65% of a validated oracle ceiling at zero training and leads until trained PPO and centralised-critic (CTDE) learners overtake it (~74-75%, 16 seeds, all above the swarm mean) after ~4,000 of 15,000 training steps - its advantage is in budget, not asymptote. In this one setting we read it not as beating RL but as a strong zero-shot, reward-free operating point: a demonstration that the self-organizing physics of a minimal swarm can carry a collective close to the optimum RL seeks, with none of RL's machinery.

cs.LG↗

arXiv2026

Functional Percolation: Criticality of Form and Function

Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and analyze how connectivity governs realizable input-output transformations under cascade dynamics. Using Erdos-Renyi networks as a minimal ensemble, we examine structural, functional, and information-theoretic observables as functions of mean degree. We find that the emergence of the giant connected component coincides with a sharp transition in realizable information processing: complex input-output response functions become accessible, functional diversity increases rapidly, output entropy rises, and directed information flow, quantified by transfer entropy, extends beyond local neighborhoods. We term this coincidence of structural, functional, and informational transitions functional percolation, referring to a sharp expansion of the space of realizable input-output functions at the percolation threshold. Near criticality, networks exhibit a Pareto-optimal tradeoff between functional complexity and diversity, suggesting that percolation criticality may provide a general organizing principle of information processing capacity in systems with local interactions and propagating influences.

physics.soc-ph↗

arXiv2026

Crossing the Functional Desert: Cascade-Driven Assembly and Feasibility Transitions in Early Life

The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a "functional desert" in which accumulation is dynamically unsupported. Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems. Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation. This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times. The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone.

physics.soc-ph↗