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Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of…

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The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

Diffusion Transformers have achieved state-of-the-art performance in class-conditional and multimodal generation, yet the structure of their learned conditional embeddings remains poorly understood. In this work, we present the first…

Identifying beneficial tasks to transfer from is a critical step toward successful intermediate-task transfer learning. In this work, we experiment with 130 source-target task combinations and demonstrate that the transfer performance…

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

It is interesting and challenging to study double-ended queues with First-Come-First-Match discipline under customers' impatient behavior and non-Poisson inputs. The system stability can be guaranteed by the customers' impatient behavior,…

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The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…

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Constituting highly informative network embeddings is an important tool for network analysis. It encodes network topology, along with other useful side information, into low-dimensional node-based feature representations that can be…

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…

Transformer architectures are typically described in algorithmic and statistical terms, leaving their internal mechanics without a familiar structural language for researchers trained in physical theories. To bridge this gap, we develop a…