⚡ electrical engineering

Defining Decentralization: An Ontological Perspective

This paper addresses the "Decentralization Problem" by introducing a graph-based ontology that formally defines decentralization as a relational and subject-specific property distinct from mere distribution, accompanied by novel metrics and a browser-based tool to enable consistent, domain-independent analysis of heterogeneous systems like federated learning and blockchain.

Original authors: Jakub Kacper Szeląg, Aydin Abadi, Mohammad Naseri

Published 2026-08-11

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Jakub Kacper Szeląg, Aydin Abadi, Mohammad Naseri

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Great "Who's in Charge?" Confusion

Imagine you are trying to describe a city. You might say it is "spread out" because the houses are far apart, or you might say it is "decentralized" because no single mayor controls every streetlight. In the world of computer science, these two words—distribution and decentralization—have been getting mixed up for decades. Distribution is like a pizza delivery: the toppings are scattered across the whole pie, but they all belong to the same pizza. Decentralization is more like a neighborhood where everyone has their own garden, and no single person holds the keys to all the gates.

For a long time, scientists and engineers have used these terms to build everything from secure internet networks to artificial intelligence that learns together. But here is the problem: everyone agrees that "decentralization" is a good thing because it makes systems harder to hack, more private, and more resilient. Yet, no one actually agrees on what it is. Is a system decentralized if the data is on many computers, even if one boss computer tells them what to do? Or does it have to be a free-for-all where no one is in charge? This confusion is like trying to build a house without a blueprint; you might end up with a structure that looks like a home but collapses when the wind blows. As we start building smarter AI and more complex digital networks, figuring out the exact definition of "decentralized" isn't just a word game—it's the difference between a system that survives a crisis and one that falls apart.

The Paper's Big Idea: A Map for the Chaos

This paper, titled "Defining Decentralization: An Ontological Perspective," acts like a detective trying to solve the mystery of what "decentralization" really means. The authors, researchers from Newcastle University and Flower Labs, argue that the current way we talk about decentralization is messy and often wrong. They point out that people often confuse distribution (where things are physically placed) with decentralization (how things are connected and who controls them).

To fix this, the team built a new "map" called an ontology. Think of an ontology as a super-precise dictionary that doesn't just define words, but explains how the things those words describe fit together in the real world. Instead of just counting how many computers are in a network (a method the paper says is too simple), they created a system that looks at the relationships between the parts. They treat a computer system like a graph, where computers are dots and the cables connecting them are lines.

The paper's main finding is that you cannot simply say a whole system is "decentralized" or "centralized." Instead, a system can be decentralized in some ways and centralized in others. For example, in a popular type of AI training called Federated Learning, the data might be scattered across many phones (decentralized), but a single server might still tell them all what to do (centralized). The authors' new map can spot this difference. They prove that a system can be partially decentralized, meaning some parts are free and others are controlled, rather than forcing a "yes or no" answer.

The New Tools: "Void Tolerance" and "Imperviousness"

To measure this new, more complex idea of decentralization, the authors invented two playful but powerful tools: Void Tolerance and Imperviousness.

Imagine the network is a web of friends passing notes.

Void Tolerance asks: "If one friend suddenly disappears, does the whole group stop talking?" If the group splits into two isolated islands because one person left, the system has low Void Tolerance. If the group keeps chatting even after someone leaves, it has high Void Tolerance. This measures how well the system survives missing pieces.
Imperviousness asks: "How many phone lines do we have to cut to stop a specific person from talking to the group?" If you only need to cut one wire to silence a person, they are not very protected. If you have to cut a dozen wires, they are highly impervious. This measures how hard it is to break the system's connections.

The authors tested their map on two very different real-world examples: Federated Learning (where AI learns from private data on many devices) and Blockchain (the technology behind cryptocurrencies).

In their simulations, they showed that old ways of measuring decentralization often got it wrong. For instance, a blockchain network might look "decentralized" because it has many computers, but if all those computers are controlled by one company, the new map reveals it is actually centralized in terms of control. Conversely, a system might look "centralized" because of a boss computer, but if the data and training happen on many different devices, the map shows it is actually decentralized in those specific areas.

The paper concludes that by using this new graph-based map and these two new metrics, we can finally compare different systems fairly. We can say, "This AI system is more decentralized in its data storage but less decentralized in its decision-making," rather than just guessing. The authors built a browser-based tool that lets anyone draw a network and instantly see these scores, proving that their definition works across different types of technology.

What the Paper Says It Is Not

It is important to know what this paper doesn't claim. The authors are very clear that their map only looks at the structure of the connections (the graph). It does not measure how fast the system is, how much money it costs, or how fair the rules are. They also admit that their new "Void Tolerance" and "Imperviousness" numbers are specific formulas they created for this study; they are not universal constants of nature like gravity. The paper suggests that these numbers are useful for comparison, but they are not the final, perfect answer to every problem. They also note that their definition doesn't account for who owns the computers (like if one company owns all the servers), only how the computers are connected.

The Takeaway

In short, this paper suggests that we need to stop treating "decentralization" as a simple switch that is either on or off. Instead, it is a multi-dimensional property, like a color that can be a mix of red and blue. By using a new mathematical map and two fresh ways to measure resilience, the authors provide a clearer, more honest way to understand how our digital world is built. They show that a system can be a mix of bossy and free, and that understanding that mix is the key to building better, safer technology for the future.

Technical Summary: Defining Decentralization: An Ontological Perspective

Problem Statement
The paper identifies a critical gap in computer science literature termed the "Decentralization Problem." Despite decentralization being a foundational concept in security, distributed computing, AI, and IoT, there is no universally accepted, transferable definition applicable across different communication systems. Current literature suffers from four primary issues:

Definitional Ambiguity: Decentralization is often defined through examples or domain-specific heuristics (e.g., blockchain) rather than a formal, context-independent definition.
Conceptual Confusion: The terms "decentralization" and "distribution" are frequently conflated. While distribution refers to the physical or logical placement of components, decentralization concerns the relational structure and dependencies between entities.
Lack of Structural Formalism: Existing approaches often rely on node-centric metrics (e.g., participant counts, ownership concentration) that ignore the relational topology and communication paths between entities.
Absence of Transferable Quantification: Current metrics are typically tied to specific architectures (like blockchain) and cannot consistently compare heterogeneous systems (e.g., Federated Learning vs. Peer-to-Peer networks).

This ambiguity leads to inconsistent system analysis, where identical architectures may be labeled "centralized" in one context (e.g., structural graph topology) and "decentralized" in another (e.g., data locality), hindering rigorous formal reasoning and protocol design.

Methodology
The authors propose a solution grounded in graph-based ontology, treating decentralization as a structural, relational, and subject-specific property. The methodology is structured into four layers:

Ontological Layer: The framework establishes a formal commitment to graph-theoretic realism. A system is modeled as a non-empty graph $G=(V, E)$ . The ontology introduces three primitive concepts: System, Topology, and Subject (a context-relative projection, such as data storage or consensus authority). It defines Projection Particulars to link a system, a topology, and a specific subject.
Logical Layer: Using formal semantics and Description Logic, the authors define decentralization based on multiplicity rather than mere placement.
- Decentralization is defined by the function $\delta(p_u)$ , representing the number of distinct realization particulars for a subject $u$ . If $\delta(p_u) > 1$ , the subject is decentralized; if $\delta(p_u) = 1$ , it is centralized.
- Distribution is defined by the function $\lambda(p_u)$ , representing the number of distinct vertices supporting those realizations. A subject is distributed if $\lambda(p_u) > 1$ .
- Crucially, the framework proves that a subject can be decentralized ( $\delta > 1$ ) but undistributed ( $\lambda = 1$ ) if multiple realizations co-locate on a single vertex, formally separating the two concepts.
Modeling Layer: This layer maps the abstract ontology to concrete computational representations (e.g., adjacency matrices, edge lists), allowing for the calculation of subject support sets and realization counts.
Analytical Layer: To quantify the degree of decentralization beyond binary classification, the authors introduce two novel, subject-specific metrics:
- Void Tolerance ( $T_L$ ): Measures vertex-focused resilience by assessing how many vertices, if removed, would isolate a portion of the subject-induced subgraph.
- Imperviousness ( $I_L$ ): Measures edge-focused resilience by calculating the minimum number of edge deletions required to isolate a subject-specific vertex.
- These metrics generate a decentralization vector $\vec{d}_u = [T_L, I_L]$ for each subject, allowing for multidimensional comparison.

Key Contributions

Formal Separation of Concepts: The paper provides the first rigorous semantic distinction between decentralization (relational multiplicity) and distribution (spatial dispersion), resolving a long-standing ambiguity in the literature.
Graph-Based Ontology: It introduces a domain-independent ontology that defines decentralization as a structural property of interacting computational entities, supporting multi-dimensional evaluation (e.g., a system can be decentralized regarding data but centralized regarding aggregation authority).
Novel Analytical Metrics: The introduction of Void Tolerance and Imperviousness allows for the quantification of structural and functional resilience, moving beyond scalar measures like the Nakamoto coefficient or Gini index.
Implementation and Validation: The framework is implemented as a browser-based application supporting interactive modeling and automated classification. It is validated on heterogeneous real-world systems, specifically Federated Learning (comparing vanilla star-topology vs. fully decentralized aggregation) and Blockchain architectures (comparing permissioned setups with different consensus and ledger replication strategies).

Results
The application of the framework to Federated Learning and Blockchain systems demonstrates that:

Consistency: The ontology produces consistent classifications where existing definitions yield contradictory results. For instance, it correctly identifies "Vanilla Federated Learning" as Partially Decentralized (decentralized data/training, centralized aggregation) rather than fully decentralized.
Granularity: The vector-based metrics reveal structural vulnerabilities that scalar metrics miss. For example, in a blockchain topology, the framework can distinguish between a consensus authority that is centralized (single node) versus one that is decentralized but structurally fragile (multiple nodes but high connectivity dependency).
Transferability: The same topological graph can yield different decentralization profiles depending on how subjects (e.g., consensus, ledger, transactions) are realized, proving that decentralization is a property of the subject-topology relationship, not just the graph structure itself.

Significance and Claims
The paper claims to provide a domain-independent foundation for analyzing decentralization. By treating decentralization as a formal, relational property rather than an informal or application-specific label, the framework enables:

Comparability: Direct comparison of fundamentally different architectures (e.g., AI pipelines vs. distributed ledgers) using a unified formal language.
Rigorous Reasoning: The ability to perform formal reasoning about system properties, distinguishing between structural robustness and mere component dispersion.
Bridging Formal and Informal: The ontology bridges the gap between informal design intuition and formal verification, allowing analysts to specify context-dependent subjects (e.g., "data privacy") while maintaining decidable, formal semantics.

The authors position this work not as a final, immutable truth, but as a necessary step to correct the "collective amnesia" regarding the relational aspect of decentralization in modern literature, which has largely reverted to node-centric analysis since the rise of blockchain. The framework acknowledges limitations, such as its focus on structural snapshots rather than dynamic behavior and its exclusion of socio-economic factors like ownership, but asserts that it successfully establishes a transferable, formal baseline for the concept.