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Virgil Griffith

Publications and source records attributed to Virgil Griffith.

14 recordsLinked to original sources
arXiv2026

Quantifying Spacetime Integration across a Partition with Synergy

In service to the mathematical underpinnings of the Information Integration Theory of Consciousness (IIT), we introduce four principled measures of integration based on the partial information decomposition framework. We compare our measures to current IIT practice in simple deterministic networks. Our measures are the first IIT-related state-dependent integration measures to naturally obey standard info-theoretic lower and upper bounds. Matching IIT4, the four measures are non-Shannon, but outside IIT they work just as well as standard Shannon-based measures of irreducibility in discrete dynamical systems.

cs.IT↗
arXiv2020

The darkweb: a social network anomaly

We analyse the darkweb and find its structure is unusual. For example, $ \sim 87 \%$ of darkweb sites \emph{never} link to another site. To call the darkweb a "web" is thus a misnomer -- it's better described as a set of largely isolated dark silos. As we show through a detailed comparison to the World Wide Web (www), this siloed structure is highly dissimilar to other social networks and indicates the social behavior of darkweb users is much different to that of www users. We show a generalized preferential attachment model can partially explain the strange topology of the darkweb, but an understanding of the anomalous behavior of its users remains out of reach. Our results are relevant to network scientists, social scientists, and other researchers interested in the social interactions of large numbers of agents.

physics.soc-ph↗
arXiv2019

Casper the Friendly Finality Gadget

We introduce Casper, a proof of stake-based finality system which overlays an existing proof of work blockchain. Casper is a partial consensus mechanism combining proof of stake algorithm research and Byzantine fault tolerant consensus theory. We introduce our system, prove some desirable features, and show defenses against long range revisions and catastrophic crashes. The Casper overlay provides almost any proof of work chain with additional protections against block reversions.

cs.CR↗
arXiv2017

Graph Theoretic Properties of the Darkweb

We collect and analyze the darkweb (a.k.a. the "onionweb") hyperlink graph. We find properties highly dissimilar to the well-studied world wide web hyperlink graph; for example, our analysis finds that >87% of darkweb sites never link to another site. We compare our results to prior work on world-wide-web and speculate about reasons for their differences. We conclude that in the term "darkweb", the word "web" is a connectivity misnomer. Instead, it is more accurate to view the darkweb as a set of largely isolated dark silos.

cs.CR↗
arXiv2015

Synergy, Redundancy and Common Information

We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between "redundant information" and the more familiar information-theoretic notions of "common information". Our main contribution is an impossibility result. We show that for independent predictor random variables, any common information based measure of redundancy cannot induce a nonnegative decomposition of the total mutual information. Interestingly, this entails that any reasonable measure of redundant information cannot be derived by optimization over a single random variable.

cs.IT↗
arXiv2015

Intersection Information based on Common Randomness

The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts, such as synergy. Here, we introduce an intersection information measure based on the Gács-Körner common random variable that is the first to satisfy the coveted target monotonicity property. Our measure is imperfect, too, and we suggest directions for improvement.

cs.IT↗
arXiv2014

Quantifying Redundant Information in Predicting a Target Random Variable

This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a measure, and propose new measures with some desirable properties.

cs.IT↗
arXiv2014

A Principled Infotheoretic ϕ-like Measure

Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $ϕ$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we pinpoint three concerns about $ϕ$ and propose a revised measure, $ψ$, which addresses them. Our measure $ψ$ is rigorously grounded in Partial Information Decomposition and is faster to compute than $ϕ$.

cs.IT↗
arXiv2014

Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory

In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would necessitate continuous damage to existing memories, we propose it is more natural to frame consciousness as a lossless integrative process and provide a formalization of this idea using algorithmic information theory. We prove that complete lossless integration requires noncomputable functions. This result implies that if unitary consciousness exists, it cannot be modelled computationally.

cs.IT↗
arXiv2014

Quantifying synergistic mutual information

Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel synergy measure defined as the difference between the whole and the union of its parts. We apply all four measures against a suite of binary circuits to demonstrate that our measure alone quantifies the intuitive concept of synergy across all examples. We show that for our measure of synergy that independent predictors can have positive redundant information.

cs.IT↗
arXiv2013

Irreducibility is Minimum Synergy Among Parts

For readers already familiar with Partial Information Decomposition (PID), we show that PID's definition of synergy enables quantifying at least four different notions of irreducibility. First, we show four common notions of "parts" give rise to a spectrum of four distinct measures of irreducibility. Second, we introduce a nonnegative expression based on PID for each notion of irreducibility. Third, we delineate these four notions of irreducibility with exemplary binary circuits. This work will become more useful once the complexity community has converged on a palatable $\operatorname{I}_{\cap}$ or $\operatorname{I}_{\cup}$ measure.

cs.IT↗
arXiv2011

Passive and Driven Trends in the Evolution of Complexity

The nature and source of evolutionary trends in complexity is difficult to assess from the fossil record, and the driven vs. passive nature of such trends has been debated for decades. There are also questions about how effectively artificial life software can evolve increasing levels of complexity. We extend our previous work demonstrating an evolutionary increase in an information theoretic measure of neural complexity in an artificial life system (Polyworld), and introduce a new technique for distinguishing driven from passive trends in complexity. Our experiments show that evolution can and does select for complexity increases in a driven fashion, in some circumstances, but under other conditions it can also select for complexity stability. It is suggested that the evolution of complexity is entirely driven---just not in a single direction---at the scale of species. This leaves open the question of evolutionary trends at larger scales.

cs.NE↗
arXiv2011

Ideal Free Distribution in Agents with Evolved Neural Architectures

We investigate the matching of agents to resources in a computational ecology configured to present heterogeneous resource patches to evolving, neurally controlled agents. We repeatedly find a nearly optimal, ideal free distribution (IFD) of agents to resources. Deviations from IFD are shown to be consistent with models of human foraging behaviors, and possibly driven by spatial constraints and maximum foraging rates. The lack of any model parameters addressing agent foraging or clustering behaviors and the biological verisimilitude of our agent control systems differentiates these results from simpler models and suggests the possibility of exploring the underlying mechanisms by which optimal foraging emerges.

q-bio.PE↗