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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.15266 |
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| _version_ | 1866914334124277760 |
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| author | Padilla, Pablo López-Corona, Oliver Ramírez-Carrillo, Elvia Sánchez, Ariadne Hernández |
| author_facet | Padilla, Pablo López-Corona, Oliver Ramírez-Carrillo, Elvia Sánchez, Ariadne Hernández |
| contents | Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $, which quantifies the net informational gain from contrasting explained variance $p$ with unexplained novelty $(1 - p)$. This function is strictly concave on $(0,1)$ and reaches its unique maximum at $ p^* \approx 0.882$, revealing a regime where confidence is high but the residual uncertainty carries a disproportionate potential for surprise.
Independently of this maximum, imposing a self-similarity condition between known, unknown and total information, $p : (1-p) = 1 : p$, leads to the golden-ratio reciprocal $p = 1/φ\approx 0.618$, where $ φ$ is the golden ratio. We interpret this value not as the maximizer of $f$, but as a structurally privileged \emph{partition} in which known and unknown are proportionally nested across scales.
Embedding this dual structure into a Compute-Inference-Model-Action (CIMA) loop yields a dynamic process that maintains the system near a critical regime where prediction and surprise coexist. At this edge, neuronal dynamics exhibit power-law structure and maximal dynamic range, while the system's response to perturbations becomes convex at the level of its payoff function-fulfilling the formal definition of antifragility. We suggest that the golden-ratio partition is not merely a mathematical artifact, but a candidate design principle linking prediction, surprise, criticality, and antifragile adaptation across scales and domains, while the maximum of $f$ identifies the point of greatest informational vulnerability to being wrong. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_15266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A golden-ratio partition of information and the balance between prediction and surprise: a neuro-cognitive route to antifragility Padilla, Pablo López-Corona, Oliver Ramírez-Carrillo, Elvia Sánchez, Ariadne Hernández Dynamical Systems Neurons and Cognition 94D99 Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $, which quantifies the net informational gain from contrasting explained variance $p$ with unexplained novelty $(1 - p)$. This function is strictly concave on $(0,1)$ and reaches its unique maximum at $ p^* \approx 0.882$, revealing a regime where confidence is high but the residual uncertainty carries a disproportionate potential for surprise. Independently of this maximum, imposing a self-similarity condition between known, unknown and total information, $p : (1-p) = 1 : p$, leads to the golden-ratio reciprocal $p = 1/φ\approx 0.618$, where $ φ$ is the golden ratio. We interpret this value not as the maximizer of $f$, but as a structurally privileged \emph{partition} in which known and unknown are proportionally nested across scales. Embedding this dual structure into a Compute-Inference-Model-Action (CIMA) loop yields a dynamic process that maintains the system near a critical regime where prediction and surprise coexist. At this edge, neuronal dynamics exhibit power-law structure and maximal dynamic range, while the system's response to perturbations becomes convex at the level of its payoff function-fulfilling the formal definition of antifragility. We suggest that the golden-ratio partition is not merely a mathematical artifact, but a candidate design principle linking prediction, surprise, criticality, and antifragile adaptation across scales and domains, while the maximum of $f$ identifies the point of greatest informational vulnerability to being wrong. |
| title | A golden-ratio partition of information and the balance between prediction and surprise: a neuro-cognitive route to antifragility |
| topic | Dynamical Systems Neurons and Cognition 94D99 |
| url | https://arxiv.org/abs/2602.15266 |