Related papers: Dimension Correction for Hierarchical Latent Class…

Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed…

Large language model-generated code (LLMgCode) has become increasingly common in software development. So far LLMgCode has more quality issues than human-authored code (HaCode). It is common for LLMgCode to mix with HaCode in a code change,…

Lack of diversity in data collection has caused significant failures in machine learning (ML) applications. While ML developers perform post-collection interventions, these are time intensive and rarely comprehensive. Thus, new methods to…

With the increase of the nonlinearity and dimension, it is difficult for the present popular metamodeling techniques to construct reliable metamodels. To address this problem, Convolutional Neural Network (CNN) is introduced to construct a…

Gradient-based methods for instance-based explanation for large language models (LLMs) are hindered by the immense dimensionality of model gradients. In practice, influence estimation is restricted to a subset of model parameters to make…

Causal representation learning (CRL) models aim to transform high-dimensional data into a latent space, enabling interventions to generate counterfactual samples or modify existing data based on the causal relationships among latent…

We introduce a novel capacity measure 2sED for statistical models based on the effective dimension. The new quantity provably bounds the generalization error under mild assumptions on the model. Furthermore, simulations on standard data…

Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…

Large Language Models (LLMs) have become a milestone in the field of artificial intelligence and natural language processing. However, their large-scale deployment remains constrained by the need for significant computational resources.…

Heteroscedasticity is common in real world applications and is often handled by incorporating case weights into a modeling procedure. Intuitively, models fitted with different weight schemes would have a different level of complexity…

As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because…

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…

Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of…

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…

The ability of Large Language Models (LLMs) to use external tools unlocks powerful real-world interactions, making rigorous evaluation essential. However, current benchmarks primarily report final accuracy, revealing what models can do but…

Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…

Neuroscience models commonly have a high number of degrees of freedom and only specific regions within the parameter space are able to produce dynamics of interest. This makes the development of tools and strategies to efficiently find…

A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like…