Related papers: A renormalization-group inspired lattice-based fra…

Complex systems with many degrees of freedom are typically intractable, but some of their behaviors may admit simpler effective descriptions. The question of when such effective descriptions are possible remains open. The paradigmatic…

Latent feature representation methods play an important role in the dimension reduction and statistical modeling of high-dimensional complex data objects. However, existing approaches to assess the quality of these methods often rely on…

We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states.…

It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\phi,t]$ and the scale-dependent full effective action $\Gamma[\Phi,t]$ --in…

Large neural networks have proved remarkably effective in modern deep learning practice, even in the overparametrized regime where the number of active parameters is large relative to the sample size. This contradicts the classical…

In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and…

Recurrent neural networks with a gating mechanism such as an LSTM or GRU are powerful tools to model sequential data. In the mechanism, a forget gate, which was introduced to control information flow in a hidden state in the RNN, has…

Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into…

Linear modeling is ubiquitous, but performance can suffer when the model is misspecified. We have recently demonstrated that latent groupings in the levels of categorical predictors can complicate inference in a variety of fields including…

We propose a modification of the Nightingale renormalization group for lattice spin and gauge models by combining it with the cluster decimation approximation. Essential ingredients of our approach are: 1) exact calculation of the partition…

We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry. Our framework unifies the Linear Representation Hypothesis with…

In this paper, we are concerned with the generalization performance of non-parametric estimation for pairwise learning. Most of the existing work requires the hypothesis space to be convex or a VC-class, and the loss to be convex. However,…

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate…

There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…

Reinforcement Learning (RL) has proven to be a powerful tool for combinatorial optimization (CO) problems due to its ability to learn heuristics that can generalize across problem instances. However, integrating knowledge that will steer…

Group Re-identification (G-ReID) faces greater complexity than individual Re-identification (ReID) due to challenges like mutual occlusion, dynamic member interactions, and evolving group structures. Prior graph-based approaches have aimed…

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…