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Quantifying Synergistic Information


Griffith, Virgil (2014) Quantifying Synergistic Information. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZS2T-XQ55.


Within the microcosm of information theory, I explore what it means for a system to be functionally irreducible. This is operationalized as quantifying the extent to which cooperative or "synergistic" effects enable random variables X1, ... , Xn to predict (have mutual information about) a single target random variable Y . In Chapter 1, we introduce the problem with some emblematic examples. In Chapter 2, we show how six different measures from the existing literature fail to quantify this notion of synergistic mutual information. In Chapter 3 we take a step towards a measure of synergy which yields the first nontrivial lowerbound on synergistic mutual information. In Chapter 4, we find that synergy is but the weakest notion of a broader concept of irreducibility. In Chapter 5, we apply our results from Chapters 3 and 4 towards grounding Giulio Tononi’s ambitious φ measure which attempts to quantify the magnitude of consciousness experience.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:information theory, synergy, consciousness, irreducibility
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computation and Neural Systems
Awards:Demetriades-Tsafka-Kokkalis Prize in Entrepreneurship or Related Fields, 2009
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Koch, Christof
Group:Koch Laboratory (KLAB)
Thesis Committee:
  • Perona, Pietro (chair)
  • Koch, Christof
  • Ho, Tracey C.
  • Beck, James L.
  • Bruck, Jehoshua
Defense Date:2 December 2013
Non-Caltech Author Email:i (AT)
Additional Information:Those interested in reading my thesis are encouraged to instead read the papers on They cover the same material in more "bite-size chunks".
Funding AgencyGrant Number
DOE CSGF (Department of Energy Computational Science Graduate Fellowship)UNSPECIFIED
Department of Homeland Security Graduate FellowshipUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
Record Number:CaltechTHESIS:12132013-161604752
Persistent URL:
Related URLs:
URLURL TypeDescription Synergistic Mutual Information - Adapted for ch. 2 and 3 is Minimum Synergy Among Parts - Adapted for ch. 4 Information based on Common Randomness - Adapted for ch. 3 Principled Infotheoretic φ-like Measure - Adapted for ch. 5
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8041
Deposited By: Virgil Griffith
Deposited On:27 Feb 2014 19:55
Last Modified:07 Jun 2023 17:21

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