Topology in dynamical Lattice QCD simulations

Lattice simulations of Quantum Chromodynamics (QCD), the quantum field theory which describes the interaction between quarks and gluons, have reached a point were contact to experimental data can be made. The underlying mechanisms, like chiral symmetry breaking or the confinement of quarks, are however still not understood. This thesis focuses on topological structures in the QCD vacuum. Those are not only mathematically interesting but also closely related to chiral symmetry and confinement. We consider methods to identify these objects in lattice QCD simulations. Based on this, we explore the structures resulting from different discretizations and investigate the effect of a very strong electromagnetic field on the QCD vacuum

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry in different fermion actions. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to vanish in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10 %. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for this specific observable related to topology, both among themselves and compared to overlap fermions.Comment: 7 pages, talk presented at The XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi

Better Uncertainty Calibration via Proper Scores for Classification and Beyond

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the reliability of probabilistic predictions but their estimators are usually biased and inconsistent. In this work, we introduce the framework of proper calibration errors, which relates every calibration error to a proper score and provides a respective upper bound with optimal estimation properties. This relationship can be used to reliably quantify the model calibration improvement. We theoretically and empirically demonstrate the shortcomings of commonly used estimators compared to our approach. Due to the wide applicability of proper scores, this gives a natural extension of recalibration beyond classification.Comment: Accepted at NeurIPS 202

Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work well for in-domain samples, these estimates are unreliable under domain drift and restricted to classification. Alternatively, proper scores can be used for most predictive tasks but a bias-variance decomposition for model uncertainty does not exist in the current literature. In this work we introduce a general bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We discover how exponential families and the classification log-likelihood are special cases and provide novel formulations. Surprisingly, we can express the classification case purely in the logit space. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions. Further, we demonstrate how different approximations of the instance-level Bregman Information allow reliable out-of-distribution detection for all degrees of domain drift.Comment: Accepted at AISTATS 202

A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Models

Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of uncertainty estimation is commonly solved in an ad-hoc manner and task dependent. For example, natural language approaches cannot be transferred to image generation. In this paper we introduce the first bias-variance-covariance decomposition for kernel scores and their associated entropy. We propose unbiased and consistent estimators for each quantity which only require generated samples but not the underlying model itself. As an application, we offer a generalization evaluation of diffusion models and discover how mode collapse of minority groups is a contrary phenomenon to overfitting. Further, we demonstrate that variance and predictive kernel entropy are viable measures of uncertainty for image, audio, and language generation. Specifically, our approach for uncertainty estimation is more predictive of performance on CoQA and TriviaQA question answering datasets than existing baselines and can also be applied to closed-source models.Comment: Preprin

Spreading the word or reducing the term spread? Assessing spillovers from euro area monetary policy

As a consequence of asset purchases by the European Central Bank (ECB), longer-term yields in the euro area decline, and spreads between euro area long-term yields narrow. To assess spillovers of these recent financial developments, we use a Bayesian variant of the global vector autoregressive (BGVAR) model with stochastic volatility and propose a novel mixture of zero impact and sign restrictions that we impose on the cross-section of the data. Both shocks generate positive and significant spillovers to industrial production in Central, Eastern and Southeastern Europe (CESEE) and other non-euro area EU member states. These effects are transmitted via the financial channel (mainly through interest rates and equity prices) and outweigh costs of appreciation pressure on local currencies vis-á-vis the euro (trade channel). While these results represent general trends, we also find evidence for both cross-country heterogeneity of effects within the euro area and region-specific spillovers thereof.Series: Department of Economics Working Paper Serie

Auf den Spuren des „Chamer Stadtschlosses“. Vom landesherrlichen Sitz zum Brauereigebäude

Ein bauhistorischer Aufsatz, herausgegeben von der Regionalgruppe Cham des "Historischen Vereins für Oberpfalz und Regensburg