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In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is…

Neurons and Cognition · Quantitative Biology 2015-10-07 Michael Wibral , Viola Priesemann , Jim W. Kay , Joseph T. Lizier , William A. Phillips

Distributed computation in artificial life and complex systems is often described in terms of component operations on information: information storage, transfer and modification. Information modification remains poorly described however,…

Information Theory · Computer Science 2013-10-10 Joseph T. Lizier , Benjamin Flecker , Paul L. Williams

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more…

Information Theory · Computer Science 2017-07-14 Robin A. A. Ince

In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information…

Information Theory · Computer Science 2024-04-03 Jesse Milzman

The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…

Data Analysis, Statistics and Probability · Physics 2024-09-23 Chiara Barà , Yuri Antonacci , Marta Iovino , Ivan Lazic , Luca Faes

Partial Information Decomposition (PID) seeks to disentangle how information about a target variable is distributed across multiple sources, separating redundant, unique, and synergistic contributions. Despite extensive theoretical…

Information Theory · Computer Science 2025-12-19 Philip Hendrik Matthias , Abdullah Makkeh , Michael Wibral , Aaron J. Gutknecht

The information that two random variables $Y$, $Z$ contain about a third random variable $X$ can have aspects of shared information (contained in both $Y$ and $Z$), of complementary information (only available from $(Y,Z)$ together) and of…

Information Theory · Computer Science 2015-03-05 Johannes Rauh , Nils Bertschinger , Eckehard Olbrich , Jürgen Jost

How can the information that a set ${X_{1},...,X_{n}}$ of random variables contains about another random variable $S$ be decomposed? To what extent do different subgroups provide the same, i.e. shared or redundant, information, carry unique…

Information Theory · Computer Science 2014-06-18 Nils Bertschinger , Johannes Rauh , Eckehard Olbrich , Jürgen Jost

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate…

Machine Learning · Statistics 2026-05-06 Mingzhe Yang , Shuo Wang , Jiang Zhang

Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…

Data Analysis, Statistics and Probability · Physics 2023-06-07 Steven J. van Enk

Information processing in neural systems can be described and analysed at multiple spatiotemporal scales. Generally, information at lower levels is more fine-grained and can be coarse-grained in higher levels. However, information processed…

Neurons and Cognition · Quantitative Biology 2020-07-21 Acer Y. C. Chang , Martin Biehl , Yen Yu , Ryota Kanai

What are the distinct ways in which a set of predictor variables can provide information about a target variable? When does a variable provide unique information, when do variables share redundant information, and when do variables combine…

Information Theory · Computer Science 2018-05-04 Conor Finn , Joseph T Lizier

Partial Information Decomposition (PID) represents multivariate mutual information via antichain-lattice that aims to specify which source groups can recover which informational components of a target. For three or more sources, widely…

Information Theory · Computer Science 2026-04-15 Aobo Lyu , Andrew Clark , Netanel Raviv

Cross-modal Knowledge Distillation has demonstrated promising performance on paired modalities with strong semantic connections, referred to as Symmetric Cross-modal Knowledge Distillation (SCKD). However, implementing SCKD becomes…

Computer Vision and Pattern Recognition · Computer Science 2025-11-13 Riling Wei , Kelu Yao , Chuanguang Yang , Jin Wang , Zhuoyan Gao , Chao Li

To characterize the complex higher-order interactions among variables within a system, this study introduces a novel framework, termed System Information Decomposition (SID), aimed at decomposing the information entropy of variables into…

Information Theory · Computer Science 2024-11-12 Aobo Lyu , Bing Yuan , Ou Deng , Mingzhe Yang , Jiang Zhang

Cognitive diagnosis is a fundamental and critical task in learning assessment, which aims to infer students' proficiency on knowledge concepts from their response logs. Current works assume each knowledge concept will certainly be tested…

Artificial Intelligence · Computer Science 2024-10-21 Miao Zhang , Ziming Wang , Runtian Xing , Kui Xiao , Zhifei Li , Yan Zhang , Chang Tang

The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific…

Neurons and Cognition · Quantitative Biology 2022-01-26 Pedro A. M. Mediano , Fernando E. Rosas , Juan Carlos Farah , Murray Shanahan , Daniel Bor , Adam B. Barrett

For multiple scientific endeavors it is common to measure a phenomenon of interest in more than one ways. We make observations of objects from several different perspectives in space, at different points in time; we may also measure…

Machine Learning · Computer Science 2024-08-29 George A. Kevrekidis , Eleni D. Koronaki , Yannis G. Kevrekidis

We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion.…

Artificial Intelligence · Computer Science 2025-09-22 Abel Jansma

This review presents recent and older results on elementary quantitative and qualitative aspects of consciousness and cognition and tackles the question "What is consciousness?" conjointly from biological, neuroscience-cognitive, physical…

Neurons and Cognition · Quantitative Biology 2018-07-17 Pierre Baudot