Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2402.08135

A scalable, synergy-first backbone decomposition of higher-order structures in complex systems

Thomas F. Varley
View original source ↗Read source document ↗Export metadata ↓

Abstract

Since its introduction in 2011, the partial information decomposition (PID) has triggered an explosion of interest in the field of multivariate information theory and the study of emergent, higher-order ("synergistic") interactions in complex systems. Despite its power, however, the PID has a number of limitations that restrict its general applicability: it scales poorly with system size and the standard approach to decomposition hinges on a definition of "redundancy", leaving synergy only vaguely defined as "that information not redundant." Other heuristic measures, such as the O-information, have been introduced, although these measures typically only provided a summary statistic of redundancy/synergy dominance, rather than direct insight into the synergy itself. To address this issue, we present an alternative decomposition that is synergy-first, scales much more gracefully than the PID, and has a straightforward interpretation. Our approach defines synergy as that information in a set that would be lost following the minimally invasive perturbation on any single element. By generalizing this idea to sets of elements, we construct a totally ordered "backbone" of partial synergy atoms that sweeps systems scales. Our approach starts with entropy, but can be generalized to the Kullback-Leibler divergence, and by extension, to the total correlation and the single-target mutual information. Finally, we show that this approach can be used to decompose higher-order interactions beyond just information theory: we demonstrate this by showing how synergistic combinations of pairwise edges in a complex network supports signal communicability and global integration. We conclude by discussing how this perspective on synergistic structure (information-based or otherwise) can deepen our understanding of part-whole relationships in complex systems.

Explore related subjects

cs.ITmath.ITstat.OT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thomas F. Varley. 2024-02-13. A scalable, synergy-first backbone decomposition of higher-order structures in complex systems. https://arxiv.org/abs/2402.08135

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Radiance-Field Guided Pretraining: Scaling Localization Models with Unlabeled Wireless Signals

Radio frequency (RF)-based indoor localization offers significant promise for applications such as indoor navigation, augmented reality, and pervasive computing. While deep learning has greatly enhanced localization accuracy and robustness, existing localization models still face major challenges in cross-scene generalization due to their reliance on scene-specific labeled data. To address this, we introduce Radiance-Field Reinforced Pretraining (RFRP). This novel self-supervised pretraining framework couples a large localization model (LM) with a neural radio-frequency radiance field (RF-NeRF) in an asymmetrical autoencoder architecture. In this design, the LM encodes received RF spectra into latent, position-relevant representations, while the RF-NeRF decodes them to reconstruct the original spectra. This alignment between input and output enables effective representation learning using large-scale, unlabeled RF data, which can be collected continuously with minimal effort. To this end, we collected RF samples at 7,327,321 positions across 100 diverse scenes using four common wireless technologies--RFID, BLE, WiFi, and IIoT. Data from 75 scenes were used for training, and the remaining 25 for evaluation. Experimental results show that the RFRP-pretrained LM reduces localization error by over 40% compared to non-pretrained models and by 21% compared to those pretrained using supervised learning.

cs.IT↗
arXiv2026

Uniform Recovery of Structured Signals from Nonlinear Observations: Improved Error Rates

Consider the recovery of structured signals from nonlinear observations. Under Gaussian matrix and a large class of unknown nonlinear link functions, Plan and Vershynin (2016) showed that generalized Lasso achieves accurate nonuniform recovery of a fixed signal. More recently, Genzel and Stollenwerk (2023) showed that generalized Lasso is indeed capable of accurately recovering all structured signals. However, in some canonical settings with discontinuous link functions, their uniform recovery error rate is essentially slower than the nonuniform one. Specifically, in the recovery of $n$-dimensional $k$-sparse vectors from $m$ measurements, generalized Lasso with a perfectly tuned $\ell_1$ constraint achieves nonuniform error rate $ O(\sqrt{k\log(en/k)/m})$, while the uniform error rate of Genzel and Stollenwerk is no faster than $O((k\log(en/k)/m)^{1/4})$. In this paper, we narrow this gap by establishing improved uniform recovery guarantees under piecewise Lipschitz link functions with well-separated jump discontinuities. We analyze a projected gradient descent (PGD) algorithm whose projection can be onto a convex set or a cone, and our results for the PGD with a convex set are also valid for the generalized Lasso. In sparse recovery, the improved uniform error rates match the nonuniform rate $O(\sqrt{k\log(en/k)/m})$ up to logarithmic factors. Under the sign link function, we further show that iterative hard thresholding (a specific instance of the PGD) achieves uniform recovery error rate $O(\sqrt{k\log(en/k)/m})$, matching the nonuniform rate up to a universal constant. Technically, the uniform guarantees for the PGD are obtained by showing that the gradient maps satisfy the restricted approximate invertibility condition uniformly over all signals. We demonstrate that this is a general approach to uniform recovery under nonlinear observations.

cs.IT↗
arXiv2026

Recursive overlap Bernoulli distributions and an entropy concavity conjecture

We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.

cs.IT↗