arXiv subjects

Matthias Weissenbacher

Publications and source records attributed to Matthias Weissenbacher.

16 recordsLinked to original sources

arXiv2024

SiT: Symmetry-Invariant Transformers for Generalisation in Reinforcement Learning

An open challenge in reinforcement learning (RL) is the effective deployment of a trained policy to new or slightly different situations as well as semantically-similar environments. We introduce Symmetry-Invariant Transformer (SiT), a scalable vision transformer (ViT) that leverages both local and global data patterns in a self-supervised manner to improve generalisation. Central to our approach is Graph Symmetric Attention, which refines the traditional self-attention mechanism to preserve graph symmetries, resulting in invariant and equivariant latent representations. We showcase SiT's superior generalization over ViTs on MiniGrid and Procgen RL benchmarks, and its sample efficiency on Atari 100k and CIFAR10.

cs.LG↗

arXiv2022

Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics

Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current algorithms over-fit to the training dataset and as a consequence perform poorly when deployed to out-of-distribution generalizations of the environment. We aim to address these limitations by learning a Koopman latent representation which allows us to infer symmetries of the system's underlying dynamic. The latter is then utilized to extend the otherwise static offline dataset during training; this constitutes a novel data augmentation framework which reflects the system's dynamic and is thus to be interpreted as an exploration of the environments phase space. To obtain the symmetries we employ Koopman theory in which nonlinear dynamics are represented in terms of a linear operator acting on the space of measurement functions of the system and thus symmetries of the dynamics may be inferred directly. We provide novel theoretical results on the existence and nature of symmetries relevant for control systems such as reinforcement learning settings. Moreover, we empirically evaluate our method on several benchmark offline reinforcement learning tasks and datasets including D4RL, Metaworld and Robosuite and find that by using our framework we consistently improve the state-of-the-art of model-free Q-learning methods.

cs.LG↗

arXiv2021

A Quadratic Actor Network for Model-Free Reinforcement Learning

In this work we discuss the incorporation of quadratic neurons into policy networks in the context of model-free actor-critic reinforcement learning. Quadratic neurons admit an explicit quadratic function approximation in contrast to conventional approaches where the the non-linearity is induced by the activation functions. We perform empiric experiments on several MuJoCo continuous control tasks and find that when quadratic neurons are added to MLP policy networks those outperform the baseline MLP whilst admitting a smaller number of parameters. The top returned reward is in average increased by $5.8\%$ while being about $21\%$ more sample efficient. Moreover, it can maintain its advantage against added action and observation noise.

cs.LG↗

arXiv2020

On $α'$-effects from $D$-branes in $4d \; \mathcal{N} = 1$

In this work we study type IIB Calabi-Yau orientifold compactifications in the presence of space-time filling D7-branes and O7-planes. In particular, we conclude that $α'^2 g_s$-corrections to their DBI actions lead to a modification of the four-dimensional $\mathcal{N}=1$ Kähler potential and coordinates. We focus on the one-modulus case of the geometric background i.e. $h^{1,1}=1$ where we find that the $α'^2 g_s$-correction is of topological nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau orientifold which is wrapped by the D7-branes and O7-plane. This is in agreement with our previous F-theory analysis and provides further evidence for a potential breaking of the no-scale structure at order $α'^2 g_s$. Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss $α'$-corrections from other D$p$-branes.

hep-th↗

arXiv2020

Temporally Folded Convolutional Neural Networks for Sequence Forecasting

In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions $D=1,2$ is considered democratically as the input of a spatiotemporal $(D+1)$-dimensional convolutional neural network. Latter then reduces the data stream from $D +1 \to D$ dimensions followed by an incriminator cell which uses this information to forecast the subsequent time step. We empirically compare this strategy to convolutional LSTM's and LSTM's on their performance on the sequential MNIST and the JSB chorals dataset, respectively. We conclude that temporally folded convolutional neural networks (TFC's) may outperform the conventional recurrent strategies.

cs.LG↗

arXiv2019

F-theory Vacua and $α'$-Corrections

In this work we analyze F-theory and Type IIB orientifold compactifications to study $α'$-corrections to the four-dimensional, $\mathcal{N} = 1$ effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the $G^ 2 R^3$ and $(\nabla G)^2R^2$-sector in eleven-dimensions relevant in Calabi--Yau fourfold reductions. We suggest that the three-dimensional, $\mathcal{N}=2$ Kähler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi--Yau fourfold. The divisor integral Ansatz for the Kähler potential and Kähler coordinates may be lifted to four-dimensional, $\mathcal{N} = 1$ F-theory vacua. We identify a novel correction to the Kähler potential and coordinates at order $ α'^2$, which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of $D7$-branes and $O7$-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel $α'$-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.

hep-th↗

arXiv2019

$\large{α'}$-Corrections and de Sitter Vacua - a Mirage?

In this work we analyze the role of $α'$-corrections to type IIB orientifold compactifications in Kähler moduli stabilization and inflation. In particular, we propose a model independent scenario to achieve non-supersymmetric Minkowski and de Sitter vacua for geometric backgrounds with positive Euler-characteristic and generic number of Kähler moduli. The vacua are obtained by a tuning of the flux superpotential. Moreover, in the one-modulus case we argue for a mechanisms to achieve model independent slow-roll.

hep-th↗

arXiv2017

One-modulus Calabi-Yau fourfold reductions with higher-derivative terms

In this note we consider M-theory compactified on a warped Calabi-Yau fourfold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kahler modulus and determine the resulting three-dimensional Kahler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property.

hep-th↗

arXiv2017

Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kahler structure of the compact space and the form-field background are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kahler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kahler modulus case is presented for both Type II theories and M-theory.

hep-th↗

arXiv2016

The Euler characteristic correction to the Kaehler potential - revisited

We confirm the leading $α'^3$ correction to the 4d, $\mathcal N = 1$ Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the $α'^3$-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an $SU(3)$ structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multiplied by a non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified background we derive the $α'^3$-corrected kinetic terms for the dilaton and the Kähler deformations of the internal Calabi-Yau threefold for arbitrary $h^{1,1}$. We analyze these kinetic terms in the 4d, $\mathcal N = 2$ un-orientifolded theory, confirming the expected correction to the Kähler moduli space prepotential, as well as in the 4d, $\mathcal N = 1$ orientifolded theory, thus determining the corrections to the Kähler potential and Kähler coordinates.

hep-th↗

arXiv2016

On four-derivative terms in IIB Calabi-Yau orientifold reductions

We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational $α'^3$-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of $O3/O7$-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inflation.

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arXiv2015

The effective action of warped M-theory reductions with higher-derivative terms - Part II

We study the three-dimensional effective action obtained by reducing eleven-dimensional supergravity with higher-derivative terms on a background solution including a warp-factor, an eight-dimensional compact manifold, and fluxes. The dynamical fields are Kähler deformations and vectors from the M-theory three-form. We show that the potential is only induced by fluxes and the naive contributions obtained from higher-curvature terms on a Calabi-Yau background vanish once the back-reaction to the full solution is taken into account. For the resulting three-dimensional action we analyse the Kähler potential and complex coordinates and show compatibility with N=2 supersymmetry. We argue that the higher-order result is also compatible with a no-scale condition. We find that the complex coordinates should be formulated as divisor integrals for which a non-trivial interplay between the warp-factor terms and the higher-curvature terms allow a derivation of the moduli space metric. This leads us to discuss higher-derivative corrections to the M5-brane action.

hep-th↗

arXiv2014

The effective action of warped M-theory reductions with higher derivative terms - Part I

M-theory accessed via eleven-dimensional supergravity admits globally consistent warped solutions with eight-dimensional compact spaces if background fluxes and higher derivative terms are considered. The internal background is conformally Kähler with vanishing first Chern class. We perturb these solutions including a finite number of Kähler deformations of the metric and vector deformations of the M-theory three-form. Special emphasis is given to the field-dependence of the warp-factor and the higher-derivative terms. We show that the three-dimensional two-derivative effective action takes a surprisingly simple form in terms of a single higher-curvature building block due to numerous non-trivial cancellations. Both the ansatz and the effective action admit a moduli dependent scaling symmetry of the internal metric. Furthermore, we find that the required departure from Ricci-flatness and harmonicity of the zero-mode eigenforms does not alter the effective theory.

hep-th↗

arXiv2014

On M-theory fourfold vacua with higher curvature terms

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kahler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions.

hep-th↗

arXiv2013

From M-theory higher curvature terms to α' corrections in F-theory

We perform a Kaluza-Klein reduction of eleven-dimensional supergravity on a Calabi-Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional N=2 effective action. We focus on the effective Einstein-Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kahler potential and complex coordinates. The classical expressions for the Kahler coordinates are non-trivially modified, while the functional form of the Kahler potential is shown to be uncorrected. For elliptically fibered Calabi-Yau fourfolds the corrections can be uplifted to a four-dimensional F-theory compactification. We argue that also the four-dimensional N=1 Kahler coordinates receive non-trivial corrections. We find a simple expression for the induced corrections for different Abelian and non-Abelian seven-brane configurations by scanning over many Calabi-Yau fourfolds with resolved singularities. The interpretation of this expression leads us to conjecture that the higher-curvature corrections correspond to α'^2 corrections that arise from open strings at the self-intersection of seven-branes.

hep-th↗

arXiv2013

On α' corrections in N=1 F-theory compactifications

We consider N=1 F-theory and Type IIB orientifold compactifications and derive new α' corrections to the four-dimensional effective action. They originate from higher derivative corrections to eleven-dimensional supergravity and survive the M-theory to F-theory limit. We find a correction to the Kahler moduli depending on a non-trivial intersection curve of seven-branes. We also analyze a four-dimensional higher curvature correction.

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