Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.18522 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908895129108480 |
|---|---|
| author | Bohm, Clifford Ragusa, Vincent R. Hintze, Arend Ofria, Charles Dolson, Emily Adami, Christoph |
| author_facet | Bohm, Clifford Ragusa, Vincent R. Hintze, Arend Ofria, Charles Dolson, Emily Adami, Christoph |
| contents | A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate a system's intrinsic functional logic with statistical artifacts of limited data. As a result, distinct systems can yield identical observations, rendering information decomposition fundamentally underdetermined and obscuring true higher-order interactions.
We introduce Functional Information Decomposition (FID), both a computational and theoretical framework, which defines informational components with respect to a system's complete input-output mapping, thereby addressing a core cross-scale inference problem: determining how information carried by individual components combines to shape system-level behavior. When the mapping is fully specified, FID provides a unique decomposition into independent and synergistic contributions. Crucially, given only partial observations, FID characterizes the entire space of consistent decompositions by sampling compatible functions, making inferential limits explicit. A complementary geometric perspective clarifies the structural origin of informational components.
We demonstrate FID's interdisciplinary utility on canonical logical functions, Conway's Game of Life, and gene-expression-based prediction of cancer drug response, and provide an open-source implementation. By separating functional architecture from observational distribution, FID offers a principled foundation for analyzing multivariate dependence in both fully and partially observed complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Information Decomposition: A First-Principles Approach to Analyzing Functional Relationships Bohm, Clifford Ragusa, Vincent R. Hintze, Arend Ofria, Charles Dolson, Emily Adami, Christoph Information Theory A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate a system's intrinsic functional logic with statistical artifacts of limited data. As a result, distinct systems can yield identical observations, rendering information decomposition fundamentally underdetermined and obscuring true higher-order interactions. We introduce Functional Information Decomposition (FID), both a computational and theoretical framework, which defines informational components with respect to a system's complete input-output mapping, thereby addressing a core cross-scale inference problem: determining how information carried by individual components combines to shape system-level behavior. When the mapping is fully specified, FID provides a unique decomposition into independent and synergistic contributions. Crucially, given only partial observations, FID characterizes the entire space of consistent decompositions by sampling compatible functions, making inferential limits explicit. A complementary geometric perspective clarifies the structural origin of informational components. We demonstrate FID's interdisciplinary utility on canonical logical functions, Conway's Game of Life, and gene-expression-based prediction of cancer drug response, and provide an open-source implementation. By separating functional architecture from observational distribution, FID offers a principled foundation for analyzing multivariate dependence in both fully and partially observed complex systems. |
| title | Functional Information Decomposition: A First-Principles Approach to Analyzing Functional Relationships |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.18522 |