Related papers: Error-in-variables modelling for operator learning

Recent advances in the literature have demonstrated that standard supervised learning algorithms are ill-suited for problems with endogenous explanatory variables. To correct for the endogeneity bias, many variants of nonparameteric…

As one of the most popular generative models, Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. However, when the decoder network is sufficiently expressive, VAE may lead…

We introduce a Noise-based prior Learning (NoL) approach for training neural networks that are intrinsically robust to adversarial attacks. We find that the implicit generative modeling of random noise with the same loss function used…

Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control…

Auto-encoding Variational Bayes (AEVB) is a powerful and general algorithm for fitting latent variable models (a promising direction for unsupervised learning), and is well-known for training the Variational Auto-Encoder (VAE). In this…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solution of partial differential equations (PDEs), and are used in…

Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…

Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational…

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Accurate analysis of microscopy images is hindered by the presence of noise. This noise is usually signal-dependent and often additionally correlated along rows or columns of pixels. Current self- and unsupervised denoisers can address…

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…

Analyzing large-scale text corpora is a core challenge in machine learning, crucial for tasks like identifying undesirable model behaviors or biases in training data. Current methods often rely on costly LLM-based techniques (e.g.…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

Steering has emerged as a promising approach in controlling large language models (LLMs) without modifying model parameters. However, most existing steering methods rely on large-scale datasets to learn clear behavioral information, which…

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial…

In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…

Large Audio Language Models (LALMs) have been widely applied in real-time scenarios, such as in-car assistants and online meeting comprehension. In practice, audio inputs are often corrupted by device and environmental noise, leading to…

Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more…