相关论文: Predicting the von Neumann Entanglement Entropy Us…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…

Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…

Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under…

Maximum likelihood estimation of energy-based models is a challenging problem due to the intractability of the log-likelihood gradient. In this work, we propose learning both the energy function and an amortized approximate sampling…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…

We study the effect of the choice of embedding geometry on the entropy of random geometric graph ensembles with soft connection functions. First we show that when the connection range is small, the entropy is dependent only on the dimension…

Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…

The von Neumann entanglement entropy of exact valence-bond ground states is studied in two frustrated one-dimensional spin chains: the spin-1/2 Majumdar-Ghosh (MG) model and the spin-3/2 J1-J2-J3 chain in its fully dimerized (FD) and…

This paper presents novel methods for parameter identification in electrical grids with small numbers of spatially distributed measuring devices, which is an issue for distribution system operators managing aged and not properly mapped…

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…

When humans learn a new concept, they might ignore examples that they cannot make sense of at first, and only later focus on such examples, when they are more useful for learning. We propose incorporating this idea of tunable sensitivity…

We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…

This paper studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in…

Several distributed frameworks have been developed to scale Graph Neural Networks (GNNs) on billion-size graphs. On several benchmarks, we observe that the graph partitions generated by these frameworks have heterogeneous data distributions…

Multitude of deep learning models have been proposed for node classification in graphs. However, they tend to perform poorly under labeled-data scarcity. Although Few-shot learning for graphs has been introduced to overcome this problem,…

Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole…

Graph neural networks (GNNs) extend convolutional neural networks (CNNs) to graph-based data. A question that arises is how much performance improvement does the underlying graph structure in the GNN provide over the CNN (that ignores this…

We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…