This brief note considers the problem of estimating temporal synergy and integrated information in dyadic dynamical processes. One of the standard estimators of dynamic synergy is based on the minimal mutual information between sets of elements, however, despite it's increasingly widespread use, the mathematical features of this redundancy function have largely gone unexplored. Here, we show that it has two previously unrecognized limitations: it cannot disambiguate between truly integrated systems and disintegrated systems with first-order autocorrelation. Second, paradoxically, there are some systems that become more synergistic when dis-integrated (as long as first-order autocorrelations are preserved). In these systems, integrated information can decrease while synergy simultaneously increases. We derive conditions under which this occurs and discuss the implications of these findings for past and future work in applied fields such as neuroscience.
This article introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric capable of characterising synergy- and redundancy-dominated systems. We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we use…
The decomposition of channel information into synergies of different order is an open, active problem in the theory of complex systems. Most approaches to the problem are based on information theory, and propose decompositions of mutual information between inputs and outputs in se\-veral ways, none of which is generally accepted yet. We propose a new point of view on the topic. We model a multi-input channel as a Markov kernel. We can project the channel onto a series of exponential families which form a hierarchical structure. This is carried out with tools from information geometry, in a way…
Quantifying synergy among stochastic variables is an important open problem in information theory. Information synergy occurs when multiple sources together predict an outcome variable better than the sum of single-source predictions. It is an essential phenomenon in biology such as in neuronal networks and cellular regulatory processes, where different information flows integrate to produce a single response, but also in social cooperation processes as well as in statistical inference tasks in machine learning. Here we propose a metric of synergistic entropy and synergistic information from f…
Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.…
Is reduction always a good scientific strategy? Does it always lead to a gain in information? The very existence of the special sciences above and beyond physics seems to hint no. Previous research has shown that dimension reduction (macroscales) can increase the dependency between elements of a system (a phenomenon called "causal emergence"). However, this has been shown only for specific measures like effective information or integrated information. Here, we provide an umbrella mathematical framework for emergence based on information conversion. Specifically, we show evidence that a macrosc…
We offer a new approach to the information decomposition problem in information theory: given a 'target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative terms that quantify the contributions of each random variable, not only individually but also in combination? We derive our composition from cooperative game theory. It can be seen as assigning a "fair share" of the mutual information to each combination of the source variables. Our decomposition is based on a different lattice from the usual 'partial infor…
Dependency, Compression, and Synergy: A Unified Information-Theoretic View of Multimodal Learning
School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics（西南财经大学计算机与人工智能学院）；Beijing Humanoid Robot Innovation Center (X-Humanoid)（北京人形机器人创新中心（X-Humanoid））；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Electronic Science and Technology of China（电子科技大学）
Tsinghua University（清华大学）；Huawei Technologies Co. Ltd.（华为技术有限公司）；Université de Paris（巴黎大学）
Information transfer between coupled stochastic dynamics, measured by transfer entropy and information flow, is suggested as a physical process underlying the causal relation of systems. While information transfer analysis has booming applications in both science and engineering fields, critical mysteries about its foundations remain unsolved. Fundamental yet difficult questions concern how information transfer and causal relation originate, what they depend on, how they differ from each other, and if they are created by a unified and general quantity. These questions essentially determine the…
The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these mechanisms by identifying synergistic, redundant, and unique contributions to the mutual information between one and several variables. While many works have studied aspects of PID for Gaussian and discrete distributions, the case of general continuous distributions is still uncharted territory. In this work we present a method for estimating the unique infor…
In dynamical systems, local interactions between dynamical units generate correlations which are stored and transmitted throughout the system, generating the macroscopic behavior. However a framework to quantify and study this at the microscopic scale is missing. Here we propose an 'information processing' framework based on Shannon mutual information quantities between the initial and future states. We apply it to the 256 elementary cellular automata (ECA), which are the simplest possible dynamical systems exhibiting behaviors ranging from simple to complex. Our main finding for ECA is that o…
