937 research outputs found
Symmetries of Riemann surfaces and magnetic monopoles
This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bringâs curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bringâs curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions
Coverage-based Example Selection for In-Context Learning
In-context learning (ICL), the ability of large language models to perform
novel tasks by conditioning on a prompt with a few task examples, requires
demonstrations that are informative about the test instance. The standard
approach of independently selecting the most similar examples selects redundant
demonstrations while overlooking important information. This work proposes a
framework for assessing the informativeness of demonstrations based on their
coverage of salient aspects (e.g., reasoning patterns) of the test input. Using
this framework, we show that contextual token embeddings effectively capture
these salient aspects, and their recall measured using BERTScore-Recall (BSR)
yields a reliable measure of informativeness. Further, we extend recall metrics
like BSR to propose their set versions to find maximally informative sets of
demonstrations. On 6 complex compositional generation tasks and 7 diverse LLMs,
we show that Set-BSR outperforms the standard similarity-based approach by up
to 16% on average and, despite being learning-free, often surpasses methods
that leverage task or LLM-specific training
The Embodied Reader and Experiential Death: Emerging Readership for âBrooksianâ Fiction
Narratives being the cornerstone of societal development will never go out of fashion. The act of reading will naturally be a part of highly developed cognitive beings. In this paper, the ideal reader is replaced by the embodied reader. The neurocognitive implications of the narratee will be analysed to uncover the fact that reading is quite similar to using a VR headset to play video games. The reason behind a good book being a favourite pastime for many is due to the ability of fiction to be experiential. Understanding fiction as a catalyst for neural engagement and triggering sensory-motor neural movement will be used to understand the true nature of the reading community. In addition to this close-up analysis of the embodied reader, the psychological response of such a reader when coming across a text that highlights the theme of death will also be analysed using the findings of terror management theory (TMT). 
Policy Space Diversity for Non-Transitive Games
Policy-Space Response Oracles (PSRO) is an influential algorithm framework
for approximating a Nash Equilibrium (NE) in multi-agent non-transitive games.
Many previous studies have been trying to promote policy diversity in PSRO. A
major weakness in existing diversity metrics is that a more diverse (according
to their diversity metrics) population does not necessarily mean (as we proved
in the paper) a better approximation to a NE. To alleviate this problem, we
propose a new diversity metric, the improvement of which guarantees a better
approximation to a NE. Meanwhile, we develop a practical and well-justified
method to optimize our diversity metric using only state-action samples. By
incorporating our diversity regularization into the best response solving in
PSRO, we obtain a new PSRO variant, Policy Space Diversity PSRO (PSD-PSRO). We
present the convergence property of PSD-PSRO. Empirically, extensive
experiments on various games demonstrate that PSD-PSRO is more effective in
producing significantly less exploitable policies than state-of-the-art PSRO
variants
Determinantal Beam Search
Beam search is a go-to strategy for decoding neural sequence models. The
algorithm can naturally be viewed as a subset optimization problem, albeit one
where the corresponding set function does not reflect interactions between
candidates. Empirically, this leads to sets often exhibiting high overlap,
e.g., strings may differ by only a single word. Yet in use-cases that call for
multiple solutions, a diverse or representative set is often desired. To
address this issue, we propose a reformulation of beam search, which we call
determinantal beam search. Determinantal beam search has a natural relationship
to determinantal point processes (DPPs), models over sets that inherently
encode intra-set interactions. By posing iterations in beam search as a series
of subdeterminant maximization problems, we can turn the algorithm into a
diverse subset selection process. In a case study, we use the string
subsequence kernel to explicitly encourage n-gram coverage in text generated
from a sequence model. We observe that our algorithm offers competitive
performance against other diverse set generation strategies in the context of
language generation, while providing a more general approach to optimizing for
diversity
Decision-making with gaussian processes: sampling strategies and monte carlo methods
We study Gaussian processes and their application to decision-making in the real world. We begin by reviewing the foundations of Bayesian decision theory and show how these ideas give rise to methods such as Bayesian optimization. We investigate practical techniques for carrying out these strategies, with an emphasis on estimating and maximizing acquisition functions. Finally, we introduce pathwise approaches to conditioning Gaussian processes and demonstrate key benefits for representing random variables in this manner.Open Acces
The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry
The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations
Learning from Invalid Data: On Constraint Satisfaction in Generative Models
Generative models have demonstrated impressive results in vision, language,
and speech. However, even with massive datasets, they struggle with precision,
generating physically invalid or factually incorrect data. This is particularly
problematic when the generated data must satisfy constraints, for example, to
meet product specifications in engineering design or to adhere to the laws of
physics in a natural scene. To improve precision while preserving diversity and
fidelity, we propose a novel training mechanism that leverages datasets of
constraint-violating data points, which we consider invalid. Our approach
minimizes the divergence between the generative distribution and the valid
prior while maximizing the divergence with the invalid distribution. We
demonstrate how generative models like GANs and DDPMs that we augment to train
with invalid data vastly outperform their standard counterparts which solely
train on valid data points. For example, our training procedure generates up to
98 % fewer invalid samples on 2D densities, improves connectivity and stability
four-fold on a stacking block problem, and improves constraint satisfaction by
15 % on a structural topology optimization benchmark in engineering design. We
also analyze how the quality of the invalid data affects the learning procedure
and the generalization properties of models. Finally, we demonstrate
significant improvements in sample efficiency, showing that a tenfold increase
in valid samples leads to a negligible difference in constraint satisfaction,
while less than 10 % invalid samples lead to a tenfold improvement. Our
proposed mechanism offers a promising solution for improving precision in
generative models while preserving diversity and fidelity, particularly in
domains where constraint satisfaction is critical and data is limited, such as
engineering design, robotics, and medicine
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