Key result
Adaptive Kuramoto networks inevitably collapse into rigid monolithic synchronization under standard Hebbian rules; however, an entropy-window sliding mode controller prevents this by sign-switching plasticity, preserving structural diversity and preventing systemic failure.
Edited by Sergey Dzhumaev, an author
Why the study?
In adaptive swarms, Hebbian rules promote coherence but risk rigid lockstep. General Coherent Field Theory (G-CFT) requires systems to stay within an "entropy window" to function. We address the lack of control mechanisms for this constraint. Our analysis shows standard rules fail: positive feedback inevitably drives the order parameter R → 1, causing a "monolithic collapse" where functional complexity is lost. This work proves this inevitability and introduces a Sliding Mode Controller (SMC) to enforce the entropy window, preventing freezing and ensuring the network remains adaptable.
Edited by Sergey Dzhumaev, an author
Answers are grounded in this paper and cite their sources.
Author’s note
This paper addresses a critical failure mode in adaptive networks—systems where connections strengthen based on success (Hebbian learning). While often beneficial, we prove mathematically that this rule generically drives networks to a "monolithic collapse": a rigid, fully synchronized state where diversity vanishes and the system loses adaptability. This is relevant not just for physics, but for neural ensembles, power grids, and swarm intelligence. What readers often get wrong: They assume local fixes (like simple weight decay or capping) can prevent this collapse. Our simulations show these naive remedies fail because the positive feedback loop is structural. The solution: We introduce a Sliding Mode Controller (SMC) based on an "entropy window." Instead of micromanaging pairs, it monitors global coherence. If the network becomes too rigid (synchronized), the controller flips the learning rule to anti-Hebbian, effectively "cooling" the system. This preserves a healthy, multi-cluster structure. It’s a mechanism for maintaining the balance between order and chaos in self-organizing systems.
Sergey Dzhumaev, an author of this paper
No takes yet. Share an insight, caveat, or question.
Introduces a framework for decision making amidst conflicting data, suggesting new analysis approaches.
10.5281/zenodo.19812700 In engineering, management, and analytical systems, decision making often occursunder structural conflict—when input data are incomplete, internally contradictory, ordistorted. Classical probabilistic approaches treat such situations as a problem of aggregatingindependent factors. When signals conflict, these methods typically yield diffuse,poorly interpretable, and unstable results.This paper introduces an approach that represents the decision process as a coherentlandscape formed by interacting factors. In this model, probability is not an estimate of ahypothesis’s truth but rather a distribution of attention among alternatives, determinedby the degree of internal consistency of the corresponding factor configurations. In otherwords, the question shifts from “how true is an alternative?” to “how structurally does itcapture the attention of the decision-making system or agent?”Crucially, “attention” here is not a metaphor but an operationally defined quantity.The distribution P(s) is normalized,Ps P(s) = 1, and can be interpreted as an allocationof computational resources, confidence, or processing priorities among alternatives. Themodel thus provides an explicit mechanism for redistributing a limited computationalbudget toward the most coherent factor configurations.We introduce the concept of a Heuristic Decision Field (HDF), where each alternativecorresponds to a point in decision space, and its “height” is determined by the coherenceof the input signals. To quantitatively describe the landscape structure, we use entropy,peak sharpness, and a decision threshold layer.This approach does not claim to be a complete theory of decision making. Rather,it offers a general conceptual framework that reinterprets choice under conflicting factorsand can serve as a foundation for further research in multi-criteria selection, analysisof contradictory requirements, and engineering methods for conflict resolution, includingproblems akin to TRIZ.
Sergey Dzhumaev (2026) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: