From Microscopic Capability to Collective Function: An Evidential Ladder and Reducibility Audit for Interacting Units

As active and physical-learning systems acquire sensing, memory, communication, internal regulation, and learning, richer microscopic architectures increasingly produce different macroscopic behavior. The central inferential problem is not whether such mechanisms can change collective dynamics, but what level of claim the evidence supports. We formulate a cumulative evidential ladder for claims of a new useful collective capability: (I) microscopic mechanism availability; (II) a causal collective dynamical effect under matched intervention; (III) response-class expansion relative to an adversarially optimized lower architecture under a hard capability budget; (IV) positive task-specific value after explicit cost accounting; and (V) collective irreducibility relative to a stated family of reducible alternatives. The evidence types are heterogeneous—interventional, set-theoretic, decision-theoretic, and causal—but the composite claim becomes stronger as criteria accumulate. We operationalize the framework through a reducibility audit combining expressive null models, matched resources, information-preserving shuffles, explicit reductions, held-out evaluation, and stopping rules. A Vicsek-type calibration shows that verdicts depend on the reducer family: local alignment sustains O(1) polarization while a matched independent-persistent null decays approximately as N^-0.46, yet a global-broadcast reducer also sustains O(1) polarization and therefore closes any stronger locality-specific irreducibility claim for that observable. Two worked audit examples then show why stronger claims can be reduced, downgraded, or remain unresolved. A state-matched anticipation assay reduces, under its stated low-dimensional predictive objective, to a single-controller problem. An interaction-only mechanical stiffness-reallocation gate is highly topology-sensitive: across 24 held-out network realizations the pre-specified mean comparison is statistically inconclusive, and a post-hoc ratio sensitivity check can reverse the nominal sign without yielding a stable network-level advantage. We position the framework as a domain-specific synthesis of null-model reasoning, functional reducibility, causal-emergence ideas, and active/physical-learning methodology rather than as a universal theory or certificate of emergence.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.22026877
Primary Topic
Neural Networks and Reservoir Computing
Type
preprint
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preprint

From Microscopic Capability to Collective Function: An Evidential Ladder and Reducibility Audit for Interacting Units

Kai Wang
Zenodo (CERN European Organization for Nuclear Research)
Neural Networks and Reservoir Computing
preprint

From Microscopic Capability to Collective Function: An Evidential Ladder and Reducibility Audit for Interacting Units

Kai Wang
preprint en

Abstract

As active and physical-learning systems acquire sensing, memory, communication, internal regulation, and learning, richer microscopic architectures increasingly produce different macroscopic behavior. The central inferential problem is not whether such mechanisms can change collective dynamics, but what level of claim the evidence supports. We formulate a cumulative evidential ladder for claims of a new useful collective capability: (I) microscopic mechanism availability; (II) a causal collective dynamical effect under matched intervention; (III) response-class expansion relative to an adversarially optimized lower architecture under a hard capability budget; (IV) positive task-specific value after explicit cost accounting; and (V) collective irreducibility relative to a stated family of reducible alternatives. The evidence types are heterogeneous—interventional, set-theoretic, decision-theoretic, and causal—but the composite claim becomes stronger as criteria accumulate. We operationalize the framework through a reducibility audit combining expressive null models, matched resources, information-preserving shuffles, explicit reductions, held-out evaluation, and stopping rules. A Vicsek-type calibration shows that verdicts depend on the reducer family: local alignment sustains O(1) polarization while a matched independent-persistent null decays approximately as N^-0.46, yet a global-broadcast reducer also sustains O(1) polarization and therefore closes any stronger locality-specific irreducibility claim for that observable. Two worked audit examples then show why stronger claims can be reduced, downgraded, or remain unresolved. A state-matched anticipation assay reduces, under its stated low-dimensional predictive objective, to a single-controller problem. An interaction-only mechanical stiffness-reallocation gate is highly topology-sensitive: across 24 held-out network realizations the pre-specified mean comparison is statistically inconclusive, and a post-hoc ratio sensitivity check can reverse the nominal sign without yielding a stable network-level advantage. We position the framework as a domain-specific synthesis of null-model reasoning, functional reducibility, causal-emergence ideas, and active/physical-learning methodology rather than as a universal theory or certificate of emergence.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Neural Networks and Reservoir Computing
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