Given data from a general metric space, one of the standard machine learning pipelines is to first embed the data into a Euclidean space and subsequently apply out of the box machine learning algorithms to analyze the data. The quality of such an embedding is typically described in terms of a distortion measure. In this paper, we show that many of the existing distortion measures behave in an undesired way, when considered from a machine learning point of view. We investigate desirable properties of distortion measures and formally prove that most of the existing measures fail to satisfy these properties. These theoretical findings are supported by simulations, which for example demonstrate that existing distortion measures are not robust to noise or outliers and cannot serve as good indicators for classification accuracy. As an alternative, we suggest a new measure of distortion, called $\sigma$-distortion. We can show both in theory and in experiments that it satisfies all desirable properties and is a better candidate to evaluate distortion in the context of machine learning.

From a theoretical computer science point of view, many aspects of distance preservation of emed-dings are well understood.

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination.

How does that provide hints on the generator's design and compare to the flourishing but almost exclusively experimental

Given data from a general metric space, one of the standard machine learning pipelines is to first embed the data into a Euclidean space and subsequently apply out of the box machine learning algorithms to analyze the data. The quality of such an embedding is typically described in terms of a distortion measure. In this paper, we show that many of the existing distortion measures behave in an undesired way, when considered from a machine learning point of view. We investigate desirable properties of distortion measures and formally prove that most of the existing measures fail to satisfy these properties. These theoretical findings are supported by simulations, which for example demonstrate that existing distortion measures are not robust to noise or outliers and cannot serve as good indicators for classification accuracy. As an alternative, we suggest a new measure of distortion, called $\sigma$-distortion. We can show both in theory and in experiments that it satisfies all desirable properties and is a better candidate to evaluate distortion in the context of machine learning.

From a theoretical computer science point of view, many aspects of distance preservation of emed-dings are well understood.

Dimensionality reduction plays a central role in real world applications for Machine Learning, among many fields.

The development of 6G wireless systems is taking place alongside the development of increasingly intelligent wireless devices and network nodes. The changing technological landscape is motivating a rethinking of classical Shannon information theory that emphasizes semantic and task-oriented paradigms. In this paper, we study a prediction-powered communication setting, in which devices, equipped with artificial intelligence (AI)-based predictors, communicate under zero-delay constraints with strict distortion guarantees. Two classes of distortion measures are considered: (i) outage-based metrics, suitable for tasks tolerating occasional packet losses, such as real-time control or monitoring; and (ii) bounded distortion metrics, relevant to semantic-rich tasks like text or video transmission. We propose two zero-delay compression algorithms leveraging online conformal prediction to provide per-sequence guarantees on the distortion of reconstructed sequences over error-free and packet-erasure channels with feedback. For erasure channels, we introduce a doubly-adaptive conformal update to compensate for channel-induced errors and derive sufficient conditions on erasure statistics to ensure distortion constraints. Experiments on semantic text compression validate the approach, showing significant bit rate reductions while strictly meeting distortion guarantees compared to state-of-the-art prediction-powered compression methods.

SUMMARY When points in one metric space are embedded into another (eg. This paper is a systematic study of distortion measures. It formally defines several desired properties of a distortion measure, and compares existing distortion measures from the lens of those formal definitions and by simulations on synthetic data. Based on these, the pros and cons of each measure are discussed, and a new notion of distortion is suggested. COMMENTS The systematic study of desirable properties of distortion is solid and in my view constitutes the main strength of this submission.

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.