Papers for
data fusion engineers
Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.
Limitations found for splitting information when some sources are known
Partial Information Decomposition When Some Sources Are Known: A Source Chain Rule and a No-Go Theorem
Abstract: Partial information decomposition (PID) splits the information that several sources carry about a target into atoms, distinguished by which collections of sources give access to them. We ask how such a decomposition should behave when some of the sources are already known. The access structure of the atoms suggests one answer: discard the atoms that the known sources provide and regroup the rest according to which further sources unlock them. The classical construction of conditional information suggests another: recompute the decomposition under the conditional distributions and average. We show that the two answers agree, atom by atom, exactly when redundant information obeys a source chain rule, an analogue of the chain rule of mutual information: when the same sources are added to several collections, the enlarged collections share everything the added sources provide and, beyond that, exactly what the original collections share once the added sources are known. The rule divides established measures of redundant information, so that adopting or rejecting it genuinely narrows the choice of measure. Our main result is a no-go theorem: for three or more sources, the source chain rule and local positivity, the requirement that all atoms be nonnegative, cannot hold together in any PID.
Bayesian reasoning explains how agents show signs of intelligence
Bayesian Intelligence from the Outside
Abstract: Inferring intelligence from observable behavior is a foundational challenge in artificial intelligence. We develop a theory of Bayesian intelligence for agents such as language models. Each prompt induces a possibly imperfect internal experiment; the agent updates a full-support prior by Bayes' rule and faithfully reports its posterior over the possible answers to the question. Repetitions draw fresh, independent outcomes from the same unobserved experiment at one fixed state. We show that the agent's behavior admits this explanation if and only if its reports are not fully contradictory, i.e., some state remains possible under every report across all prompts. Report frequencies and the sizes of positive probabilities impose no further restrictions. We further propose and characterize the behavioral implications of an intelligence order that makes the behavior of two agents consistent with one agent having access to a more informative experiment: there should exist a coupling of report distributions such that the more informative agent's report excludes every answer excluded by its counterpart. Finally, we show the difficulty of aggregating coarse reports from intelligent agents: unless the agent reports a belief about the complete state of the world, the optimal aggregation can assign arbitrary weights to states that have not been excluded. These results provide a basis for understanding when agents' behavior is intelligent and highlight the difficulty of rejecting Bayesian rationality.