Pith. sign in

REVIEW 3 cited by

Synergy, Redundancy and Common Information

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1509.03706 v1 pith:IBZJPX7C submitted 2015-09-12 cs.IT math.IT

Pradeep Kr. Banerjee , Virgil Griffith This is my paper · ORCID
classification cs.ITmath.IT
keywords informationrandomcommonredundantcannotmeasuremutualpredictor
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Novel Approach to the Partial Information Decomposition

    cs.IT 2019-08 accept novelty 7.0 of 10

    A Blackwell-order-based definition of redundancy yields a new multivariate PID measure that satisfies natural axioms and is operationally grounded, while its union dual reduces to an existing measure.

  2. The mathematical landscape of partial information decomposition: A comprehensive review of properties and measures

    cs.IT 2026-03 conditional novelty 6.0 of 10

    A comprehensive survey plus new theorems systematically comparing PID redundancy measures and their axioms, with a Z3-checked map of property implications and incompatibilities.

  3. Dissipation alters modes of information encoding in small quantum reservoirs near criticality

    quant-ph 2024-12 conditional novelty 6.0 of 10

    In a two-oscillator quantum reservoir, near the critical coupling J=|Δ|, information encoding switches from redundant to synergistic, with synergy aiding short-term and dissipation aiding longer-term memory.

Pith tools