Related papers: Machine learning Calabi-Yau metrics

Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical…

In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to…

We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz…

There is a growing trend toward AI systems interacting with humans to revolutionize a range of application domains such as healthcare and transportation. However, unsafe human-machine interaction can lead to catastrophic failures. We…

Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in…

Recent advances in cancer research largely rely on new developments in microscopic or molecular profiling techniques offering high level of detail with respect to either spatial or molecular features, but usually not both. Here, we present…

Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of…

Estimates of predictive uncertainty are important for accurate model-based planning and reinforcement learning. However, predictive uncertainties---especially ones derived from modern deep learning systems---can be inaccurate and impose a…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

We develop tools of Bayesian inference on the moduli space of Calabi--Yau (CY) manifolds. We sample from the invariant Weil--Petersson (WP) measure using Markov Chain Monte Carlo and normalising flows on \Kahler moduli space with dimension…

Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…

Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

Predicting the outcome of liquid droplet collisions is an extensively studied phenomenon but the current physics based models for predicting the outcomes are poor (accuracy $\approx 43\%$). The key weakness of these models is their limited…

We present herein a new approach based on the simultaneous application of the deep learning and statistical physics methods to solve the combinatorial optimization problems. The recent modern advanced techniques, such as an artificial…

We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal…

This paper introduces a novel method for optimizing learning rates in machine learning. A previously unrecognized proportionality between learning rates and dataset sizes is discovered, providing valuable insights into how dataset scale…

Machine learning and deep learning methods have become essential for computer-assisted prediction in medicine, with a growing number of applications also in the field of mammography. Typically these algorithms are trained for a specific…

Motivated by the study of collapsing Calabi-Yau threefolds with a Lefschetz K3 fibration, we construct a complete Calabi-Yau metric on $\mathbb{C}^3$ with maximal volume growth, which in the appropriate scale is expected to model the…

In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the…