Log-Ratio Propagation
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Related Articles from SNS
Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data
Announce Type: cross Abstract: Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation.
Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models
Announce Type: replace Abstract: Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships: \[ \log \tilde q_t(i) = \alpha_t \left( \log...