[Google AI Overview (operator default of 2026-10-01); signed out and incognito (operator default of 2026-10-14). One turn. The operator's message of 2026-10-18 11:34 EDT gives sixteen: one attachment and fifteen inline pastes separated by '$'. Inline links masked; sources below the answer as pasted.] [QUERENT] "relevance-preserving compression" [ANSWER] Relevance-preserving compression is a data compression framework that focuses on discarding information irrelevant to a specific task or target variable while retaining everything necessary to predict or understand it. Unlike traditional compression—which prioritizes either exact reconstruction (lossless) or broad visual/auditory fidelity (lossy)—relevance-preserving approaches optimize for a defined downstream objective. Core Concepts & Frameworks • The Information Bottleneck (IB): This is the formal mathematical framework for relevance-preserving compression. Given an input X and a target variable of interest Y, the goal is to find a compressed representation Z that minimizes the mutual information I(X; Z) (compressing the data as much as possible) while maximizing the mutual information I(Z; Y) (retaining all relevant clues about the target). • Predictive Information Bottleneck (PIB): A temporal variant where a model compresses historical data (\(X_{\le t}\)) in a way that preserves only the features necessary to predict future states (\(Z_{t+\Delta }\)). • Coding for Machines: A major real-world paradigm of this technique. Instead of compressing an image so it looks clean to a human eye, the data is heavily compressed around features critical for automated algorithms, such as Optical Character Recognition (OCR) or object detection. Key Applications 1. AI & Multimodal LLMs: Used in prompt and context compression. Systems like PReM (Preserve and Refresh Memory) dynamically decide which context segments to compress or prune based on what is relevant to the model's immediate reasoning steps. 2. Scientific Data (Quantity-of-Interest): Instead of preserving the raw floating-point precision of every node in a climate or physics simulation, QoI-preserving lossy compression maps error tolerances strictly to desired outputs (like regional averages or isolines), allowing up to 4× higher compression ratios without losing vital scientific conclusions. 3. Biological Evolution: The concept also explains how neural plasticity works. Biological sensory systems continuously act as information bottlenecks, compressing massive environmental stimuli to preserve only what is behaviorally relevant for survival (e.g., recognizing a predator's cue). Are you looking at this from a machine learning perspective (like Information Bottleneck models), or are you trying to apply it to a specific type of data (like text, images, or scientific datasets)? [SOURCES] arXiv.org Information Preservation Does Not Imply Predictive-Contribution ... - arXiv Oct 7, 2026 — The information bottleneck formulates relevance-preserving compression [3] . Williams and Beer introduced PID to separate redundant, unique ...