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In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. Here, we investigate quantum Doeblin coefficients as a generalization of the classical concept. In particular, we define various new quantum Doeblin coefficients, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. We also develop various interpretations of two of the quantum Doeblin coefficients, including representations as minimal singlet fractions, exclusion values, reverse max-mutual and oveloH informations, reverse robustnesses, and hypothesis testing reverse mutual and oveloH informations. Our interpretations of quantum Doeblin coefficients as either entanglement-assisted or unassisted exclusion values are particularly appealing, indicating that they are proportional to the best possible error probabilities one could achieve in state-exclusion tasks by making use of the channel. We also outline various applications of quantum Doeblin coefficients, ranging from limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus), on error mitigation protocols, on the sample complexity of noisy quantum hypothesis testing, on the fairness of noisy quantum models, and on mixing times of time-varying channels. All of these applications make use of the fact that quantum Doeblin coefficients appear in upper bounds on various trace-distance contraction coefficients of a channel. Furthermore, in all of these applications, our analysis using Doeblin coefficients provides improvements of various kinds over contributions from prior literature, both in terms of generality and being efficiently computable.

Artificial Intelligence (AI) has achieved new levels of performance and spread in public usage with the rise of deep neural networks (DNNs). Initially inspired by human neurons and their connections, NNs have become the foundation of AI models for many advanced architectures. However, some of the most integral processes in the human brain, particularly neurogenesis and neuroplasticity in addition to the more spread neuroapoptosis have largely been ignored in DNN architecture design. Instead, contemporary AI development predominantly focuses on constructing advanced frameworks, such as large language models, which retain a static structure of neural connections during training and inference. In this light, we explore how neurogenesis, neuroapoptosis, and neuroplasticity can inspire future AI advances. Specifically, we examine analogous activities in artificial NNs, introducing the concepts of ``dropin'' for neurogenesis and revisiting ``dropout'' and structural pruning for neuroapoptosis. We additionally suggest neuroplasticity combining the two for future large NNs in ``life-long learning'' settings following the biological inspiration. We conclude by advocating for greater research efforts in this interdisciplinary domain and identifying promising directions for future exploration.

Stein Variational Gradient Descent (SVGD) is a popular particle-based variational inference algorithm with impressive empirical performance across various domains. Although the population (i.e, infinite-particle) limit dynamics of SVGD is well characterized, its behavior in the finite-particle regime is far less understood. To this end, our work introduces the notion of virtual particles to develop novel stochastic approximations of population-limit SVGD dynamics in the space of probability measures, that are exactly realizable using finite particles.

Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and ground-truths. Ensemble learning, as a powerful machine learning technique, aims to address these deviations by combining the predictions of multiple base models. Most existing works adopt ensemble learning during the design of restoration models, while only limited research focuses on the inference-stage ensemble of pre-trained restoration models. Regression-based methods fail to enable efficient inference, leading researchers in academia and industry to prefer averaging as their choice for post-training ensemble.

Note: Additional visualizations of our experiments can be found here: https://sites.google. AI-assisted teaching of motor control tasks can provide significant benefits such as more reliable teaching to individual students with different abilities (e.g. by leveraging more granular information about student actions), adaptability to any type of motor task or expert agent, and improved safety by reducing burden on human teachers for safety-critical tasks. However, we emphasize that our approach is solely meant to assist human teaching, as there exist many important aspects of human instruction that would be challenging to replace, including providing inspiration and motivation, in depth knowledge of human physical limitations, and an awareness of the broader context of a specific motor control task. Further risks of our approach, and avenues to address them, include: Bias of the expert agent. The suitability of the skills we use for teaching relies on how diverse the set of demonstrations from an expert is.