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Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…
We propose Network Automatic Relevance Determination (NARD), an extension of ARD for linearly probabilistic models, to simultaneously model sparse relationships between inputs $X \in \mathbb R^{d \times N}$ and outputs $Y \in \mathbb R^{m…
Side information is being used extensively to improve the effectiveness of sequential recommendation models. It is said to help capture the transition patterns among items. Most previous work on sequential recommendation that uses side…
Distributed Image Compression (DIC) is crucial for multi-view transmission, especially when operating at extremely low bitrates (< 0.1 bpp). Its core challenge is effectively utilizing side information to achieve high-quality reconstruction…
Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…
We propose uncommon self-knowledge (USK) as a candidate criterion for consciousness: synergistic information a system carries about itself that exists only in the joint of its subsystems and is destroyed by decomposition. Drawing on…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…
Multimodal image alignment is the process of finding spatial correspondences between images formed by different imaging techniques or under different conditions, to facilitate heterogeneous data fusion and correlative analysis. The…
Recently, \textit{diffusion history inference} has become an emerging research topic due to its great benefits for various applications, whose purpose is to reconstruct the missing histories of information diffusion traces according to…
In the era of artificial intelligence (AI), Transformer demonstrates its performance across various applications. The excessive amount of parameters incurs high latency and energy overhead when processed in the von Neumann architecture.…
Generative Recommendation (GR) has recently transitioned from atomic item-indexing to Semantic ID (SID)-based frameworks to capture intrinsic item relationships and enhance generalization. However, the adoption of high-granularity SIDs…
Machine unlearning in neural information retrieval (IR) systems requires removing specific data whilst maintaining model performance. Applying existing machine unlearning methods to IR may compromise retrieval effectiveness or inadvertently…
Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
We propose a new solution to the blind source separation problem that factors mixed time-series signals into a sum of spatiotemporal modes, with the constraint that the temporal components are intrinsic mode functions (IMF's). The key…
Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…