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Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…
The work fluctuation theorem (FT) is a symmetry connecting the moment generating functions (MGFs) of the work extracted in a given process and in its time-reversed counterpart. We show that, equivalently, the FT for work in isolated quantum…
This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three…
Graph condensation (GC) has become a vital strategy for scaling Graph Neural Networks by compressing massive datasets into small, synthetic node sets. While current GC methods effectively maintain predictive accuracy, they are primarily…
This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by…
A framework of M-estimation based fuzzy C-means clustering (MFCM) algorithm is proposed with iterative reweighted least squares (IRLS) algorithm, and penalty constraint and kernelization extensions of MFCM algorithms are also developed.…
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes…
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…
A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…
Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…
In high energy physics experiments, calorimetric data reconstruction requires a suitable clustering technique in order to obtain accurate information about the shower characteristics such as position of the shower and energy deposition.…
Fuzzy clustering has become a widely used data mining technique and plays an important role in grouping, traversing and selectively using data for user specified applications. The deterministic Fuzzy C-Means (FCM) algorithm may result in…
Federated Graph Learning (FGL) enables collaborative learning over distributed graph data, yet existing approaches largely rely on a closed-world assumption, limiting their applicability in dynamic environments where novel categories…
Identification of the causal relationship between multivariate time series is a ubiquitous problem in data science. Granger causality measure (GCM) and conditional Granger causality measure (cGCM) are widely used statistical methods for…
Taking into account that Rold\'an et al.'s ample spectrum contractions have managed to extend and unify more than ten distinct families of contractive mappings in the setting of metric spaces, in this manuscript we present a first study on…
Leveraging Large Language Models (LLMs) for Knowledge Graph Completion (KGC) is promising but hindered by a fundamental granularity mismatch. LLMs operate on fragmented token sequences, whereas entities are the fundamental units in…
State-of-the-art federated learning methods can perform far worse than their centralized counterparts when clients have dissimilar data distributions. For neural networks, even when centralized SGD easily finds a solution that is…
In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects'…
We propose a novel framework to study asynchronous federated learning optimization with delays in gradient updates. Our theoretical framework extends the standard FedAvg aggregation scheme by introducing stochastic aggregation weights to…
Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: Training the network exclusively on a…