Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2008.09535

Bits and Pieces: Understanding Information Decomposition from Part-whole Relationships and Formal Logic

Aaron J. Gutknecht·Michael Wibral·Abdullah Makkeh
View original source ↗Read source document ↗Export metadata ↓

Abstract

Partial information decomposition (PID) seeks to decompose the multivariate mutual information that a set of source variables contains about a target variable into basic pieces, the so called "atoms of information". Each atom describes a distinct way in which the sources may contain information about the target. In this paper we show, first, that the entire theory of partial information decomposition can be derived from considerations of elementary parthood relationships between information contributions. This way of approaching the problem has the advantage of directly characterizing the atoms of information, instead of taking an indirect approach via the concept of redundancy. Secondly, we describe several intriguing links between PID and formal logic. In particular, we show how to define a measure of PID based on the information provided by certain statements about source realizations. Furthermore, we show how the mathematical lattice structure underlying PID theory can be translated into an isomorphic structure of logical statements with a particularly simple ordering relation: logical implication. The conclusion to be drawn from these considerations is that there are three isomorphic "worlds" of partial information decomposition, i.e. three equivalent ways to mathematically describe the decomposition of the information carried by a set of sources about a target: the world of parthood relationships, the world of logical statements, and the world of antichains that was utilized by Williams and Beer in their original exposition of PID theory. We additionally show how the parthood perspective provides a systematic way to answer a type of question that has been much discussed in the PID field: whether a partial information decomposition can be uniquely determined based on concepts other than redundant information.

Explore related subjects

cs.AIcs.ITmath.ITmath.LOq-bio.NC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Aaron J. Gutknecht, Michael Wibral, Abdullah Makkeh. 2022-03-07. Bits and Pieces: Understanding Information Decomposition from Part-whole Relationships and Formal Logic. https://doi.org/10.1098/rspa.2021.0110

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

KEEP EXPLORING

Related papers

arXiv2026

Memory-Free Continual Learning with Null Space Adaptation for Zero-Shot Vision-Language Models

Pre-trained vision-language models (VLMs), such as CLIP, have demonstrated remarkable zero-shot generalization, enabling deployment in a wide range of real-world tasks without additional task-specific training. However, in real deployment scenarios with evolving environments or emerging classes, these models inevitably face distributional shifts and novel tasks. In such contexts, static zero-shot capabilities are insufficient, and there is a growing need for continual learning methods that allow models to adapt over time while avoiding catastrophic forgetting. We introduce NuSA-CL (Null Space Adaptation for Continual Learning), a lightweight memory-free continual learning framework designed to address this challenge. NuSA-CL employs low-rank adaptation and constrains task-specific weight updates to lie within an approximate null space of the model's current parameters. This strategy minimizes interference with previously acquired knowledge, effectively preserving the zero-shot capabilities of the original model. Unlike methods relying on replay buffers or costly distillation, NuSA-CL imposes minimal computational and memory overhead, making it practical for deployment in resource-constrained, real-world continual learning environments. Experiments show that our framework not only effectively preserves zero-shot transfer capabilities but also achieves highly competitive performance on continual learning benchmarks. These results position NuSA-CL as a practical and scalable solution for continually evolving zero-shot VLMs in real-world applications.

cs.AI↗
arXiv2026

VeRA: Renewing Reasoning Benchmarks with Executable Specifications

Reasoning benchmarks need renewal along two axes: freshness and headroom. VeRA makes both executable and auditable by turning each item into a task family: a natural-language template, an input generator, and a deterministic answer program. VeRA-E draws fresh instances within a family; VeRA-H modifies the family toward harder tasks; and VeRA-H Pro selects one judge-ranked candidate from up to five validated proposals per seed. Execution checks, seed anchoring, answer discrimination, and independent human solving validate specifications and items. Accepted programs generate further labeled instances through local computation. Across 16 models, AIME-2024 accuracy decreases from 84.46% on seeds to 70.25% on VeRA-E variants, exposing a gap between fixed-item success and fresh-instance robustness. On AIME-2024-II, the human-audited VeRA-H Pro release lowers accuracy from 84.91% to 58.57%. Across the three hardening sources, H Pro has lower mean accuracy than H. On AMO-Bench, both releases average higher accuracy than the seeds under the evaluated budget. Initial auditing accepts 75.4% of hardened candidates; targeted repair raises usable yield to 95.1%. Executable families thus support repeatable benchmark renewal, with validation improving task quality and selection shaping the delivered challenge.

cs.AI↗
arXiv2026

When can we trust untrusted monitoring? A safety case sketch across collusion strategies

AIs are increasingly being deployed with greater autonomy and capabilities, which increases the risk that a misaligned AI may be able to cause catastrophic harm. Untrusted monitoring -- using one untrusted model to oversee another -- is one approach to reducing risk. Justifying the safety of an untrusted monitoring deployment is challenging because developers cannot safely deploy a misaligned model to test their protocol directly. In this paper, we develop upon existing methods for rigorously demonstrating safety based on pre-deployment testing. We relax assumptions that previous AI control research made about the collusion strategies a misaligned AI might use to subvert untrusted monitoring. We develop a taxonomy covering passive self-recognition, causal collusion (hiding pre-shared signals), acausal collusion (hiding signals via Schelling points), and combined strategies. We create a safety case sketch to clearly present our argument, explicitly state our assumptions, and highlight unsolved challenges. We identify conditions under which passive self-recognition could be a more effective collusion strategy than those studied previously. Our work builds towards more robust evaluations of untrusted monitoring.

cs.AI↗