New risk-aware information theory challenges Shannon's 75-year-old framework

Hamidou Tembine's new paper, "Risk-Aware Information Theory," published on arXiv, overhauls the mathematical foundation of information theory by replacing the traditional expectation operator with expectiles—statistics that weight tail risks differently. This shift produces expectile entropy, divergence, and mutual information that behave in ways impossible under Shannon's risk-neutral framework. For example, under risk-seeking preferences, the divergence can become negative, a result that classical theory cannot produce. The framework also shows that mutual information in a risk-aware sense can deviate fundamentally from its Shannon counterpart, meaning that communication limits must account for the risk attitudes of the agents involved.

Tembine extends the theory to multiuser systems, where it naturally induces a mean-field-type game theory of information exchange. In this setting, achievable rate regions become endogenous to heterogeneous risk-sensitivity indices, meaning that optimal transmission strategies depend not just on channel conditions but on each user's tolerance for extreme outcomes. The paper argues that traditional Shannon information is insufficient to quantify the extreme risks that drive advanced machine intelligence, such as in large language models or autonomous driving. This establishes a mathematical foundation for risk-aware communication, collective intelligence, and safe AI systems that can account for tail events.