arXiv subjects

Florian Wolf

Publications and source records attributed to Florian Wolf.

13 recordsLinked to original sources

arXiv2026

Expressivity In Multimodal Contrastive Learning

Contrastive learning has become a cornerstone of modern representation learning, powering CLIP-style models that underpin text-to-image generation, vision-language models, and retrieval across a rapidly growing range of modalities. Despite this empirical success, the expressive power of these architectures remains poorly understood. To gain insight, we study expressivity by adopting a population-level, density-estimation viewpoint: each architecture comprises a parameterized set of densities whose parameters may be chosen to approximate the joint distribution of the modalities. This isolates a question of pure representational capacity: which joint distributions can a given contrastive family of parameterizations approximate to arbitrary accuracy? We show that expressivity is sharply architecture-dependent. For two modalities, the simple two-tower CLIP architecture is a universal approximator. A natural generalization of CLIP, widely used in practice when three or more modalities are present, is based on a loss found by summing over all pairwise similarities. This provably cannot represent arbitrary joint distributions, although we prove that it remains expressive enough to match all pairwise conditionals. Motivated by this gap, we propose Hadamard-CLIP, which adds a single learned weight vector on top of the existing encoders and restores universal approximation of the joint for any number of modalities while preserving CLIP's fast, precomputable-embedding retrieval.

stat.ML↗

arXiv2026

Global Optimality for Constrained Exploration via Penalty Regularization

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood, real-world exploration is often constrained by safety, resource, or imitation requirements. This constrained setting is particularly challenging because entropy maximization lacks additive structure, rendering Bellman-equation-based methods inapplicable. Moreover, scalable approaches require policy parameterization, inducing non-convexity in both the objective and the constraints. To our knowledge, the only prior model-free policy-gradient approach for this setting under general policy parameterization is due to Ying et al. (2025). Unfortunately, their guarantees are limited to weak regret and ergodic averages, which do not imply that the final output is a single deployable policy that is near-optimal and nearly feasible. In this work we take a different approach to this problem, and propose Policy Gradient Penalty (PGP) method, a single-loop policy-space method that enforces general convex occupancy-measure constraints via quadratic-penalty regularization. PGP constructs pseudo-rewards that yield gradient estimates of the penalized objective, subsequently exploiting the classical Policy Gradient Theorem. We further establish the regularity of the penalized objective, providing the smoothness properties needed to justify the convergence of PGP. Leveraging hidden convexity and strong duality, we then establish global last-iterate convergence guarantees, attaining an $\epsilon$-optimal constrained entropy value with $\epsilon$ bounded constraint violation despite policy-induced non-convexity. We validate PGP through ablations on a grid-world benchmark and further demonstrate scalability on two challenging continuous-control tasks.

cs.LG↗

arXiv2025

Global Solutions to Non-Convex Functional Constrained Problems with Hidden Convexity

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and reinforcement learning, such problems possess hidden convexity, meaning they can be reformulated as convex programs via a nonlinear invertible transformation. Typically such transformations are implicit or unknown, making the direct link with the convex program impossible. On the other hand, (sub-)gradients with respect to the original variables are often accessible or can be easily estimated, which motivates algorithms that operate directly in the original (non-convex) problem space using standard (sub-)gradient oracles. In this work, we develop the first algorithms to provably solve such non-convex problems to global minima. First, using a modified inexact proximal point method, we establish global last-iterate convergence guarantees with $\widetilde{\mathcal{O}}(\varepsilon^{-3})$ oracle complexity in non-smooth setting. For smooth problems, we propose a new bundle-level type method based on linearly constrained quadratic subproblems, improving the oracle complexity to $\widetilde{\mathcal{O}}(\varepsilon^{-1})$. Surprisingly, despite non-convexity, our methodology does not require any constraint qualifications, can handle hidden convex equality constraints, and achieves complexities matching those for solving unconstrained hidden convex optimization.

math.OC↗

arXiv2025

On the Energy Distribution of the Galactic Center Excess' Sources

The Galactic Center Excess (GCE) may yet herald the discovery of annihilating dark matter. Weighing against that conclusion are analyses showing evidence for dim point sources within the spatial structure of the emission. Due to technical limitations these analyses are purely spatial with all spectral information that could disentangle the excess from astrophysical backgrounds discarded. Here, we demonstrate that a neural network simulation-based inference approach can jointly analyze the spatial and spectra data. The addition is profound: energy information drives the putative point sources to be significantly dimmer, indicating either the GCE is truly diffuse in nature or made of an exceptionally large number of sources. Quantitatively, for our best fit background model, the excess is essentially consistent with Poisson emission as predicted by dark matter. If due to point sources, our median prediction is $\mathcal{O}(10^5)$ sources, or more than 35,000 at 90\% confidence, both orders of magnitude larger than the hundreds preferred by earlier point-source analyses of the GCE, although variations allowed by background systematics could reduce the required number of sources by roughly an order of magnitude.

astro-ph.HE↗

arXiv2024

Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems

Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement Learning (RL), particularly Deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these issues, we propose a data-efficient, interpretable, and scalable Dyna-style Model-Based RL framework for PDE control, combining the Sparse Identification of Nonlinear Dynamics with Control (SINDy-C) algorithm and an autoencoder (AE) framework for the sake of dimensionality reduction of PDE states and actions. This novel approach enables fast rollouts, reducing the need for extensive environment interactions, and provides an interpretable latent space representation of the PDE forward dynamics. We validate our method on two PDE problems describing fluid flows - namely, the 1D Burgers equation and 2D Navier-Stokes equations - comparing it against a model-free baseline, and carrying out an extensive analysis of the learned dynamics.

cs.LG↗

arXiv2024

A deep learning framework for jointly extracting spectra and source-count distributions in astronomy

Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to statistically characterize populations of point sources too dim to be individually detected. As the properties of a single dim source will be poorly constrained, instead one commonly studies the population as a whole, inferring a source-count distribution (SCD) that describes the number density of sources as a function of their brightness. Statistical and machine learning methods for recovering SCDs exist; however, they typically entirely neglect spectral information associated with the energy distribution of the flux. We present a deep learning framework able to jointly reconstruct the spectra of different emission components and the SCD of point-source populations. In a proof-of-concept example, we show that our method accurately extracts even complex-shaped spectra and SCDs from simulated maps.

astro-ph.IM↗

arXiv2023

Tracking Control for a Spherical Pendulum via Curriculum Reinforcement Learning

Reinforcement Learning (RL) allows learning non-trivial robot control laws purely from data. However, many successful applications of RL have relied on ad-hoc regularizations, such as hand-crafted curricula, to regularize the learning performance. In this paper, we pair a recent algorithm for automatically building curricula with RL on massively parallelized simulations to learn a tracking controller for a spherical pendulum on a robotic arm via RL. Through an improved optimization scheme that better respects the non-Euclidean task structure, we allow the method to reliably generate curricula of trajectories to be tracked, resulting in faster and more robust learning compared to an RL baseline that does not exploit this form of structured learning. The learned policy matches the performance of an optimal control baseline on the real system, demonstrating the potential of curriculum RL to jointly learn state estimation and control for non-linear tracking tasks.

cs.LG↗

arXiv2021

Knowledge Generation -- Variational Bayes on Knowledge Graphs

This thesis is a proof of concept for the potential of Variational Auto-Encoder (VAE) on representation learning of real-world Knowledge Graphs (KG). Inspired by successful approaches to the generation of molecular graphs, we evaluate the capabilities of our model, the Relational Graph Variational Auto-Encoder (RGVAE). The impact of the modular hyperparameter choices, encoding through graph convolutions, graph matching and latent space prior, is compared. The RGVAE is first evaluated on link prediction. The mean reciprocal rank (MRR) scores on the two datasets FB15K-237 and WN18RR are compared to the embedding-based model DistMult. A variational DistMult and a RGVAE without latent space prior constraint are implemented as control models. The results show that between different settings, the RGVAE with relaxed latent space, scores highest on both datasets, yet does not outperform the DistMult. Further, we investigate the latent space in a twofold experiment: first, linear interpolation between the latent representation of two triples, then the exploration of each latent dimension in a $95\%$ confidence interval. Both interpolations show that the RGVAE learns to reconstruct the adjacency matrix but fails to disentangle. For the last experiment we introduce a new validation method for the FB15K-237 data set. The relation type-constrains of generated triples are filtered and matched with entity types. The observed rate of valid generated triples is insignificantly higher than the random threshold. All generated and valid triples are unseen. A comparison between different latent space priors, using the $δ$-VAE method, reveals a decoder collapse. Finally we analyze the limiting factors of our approach compared to molecule generation and propose solutions for the decoder collapse and successful representation learning of multi-relational KGs.

cs.LG↗

arXiv2018

The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces

The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined version of this conjecture says that this range is of the order of the naturally built in scale, namely the Planck scale. It is investigated whether the Refined Swampland Distance Conjecture is consistent with proper field distances arising in the well understood moduli spaces of Calabi-Yau compactification. Investigating in particular the non-geometric phases of Kahler moduli spaces of dimension $h^{11}\in\{1,2,101\}$, we always found proper field distances that are smaller than the Planck-length.

hep-th↗

arXiv2017

Challenges for Moduli Stabilization and String Cosmology near the Conifold

This brief article reviews a recently proposed scenario of moduli stabilization constructed in the vicinity of a conifold locus in the complex structure moduli space. We discuss typical features of moduli stabilization due to the logarithmic structure of the periods over the Calabi-Yau threefold. Integrating out heavy moduli implies exponential terms in the superpotential very reminiscent of non-perturbative contributions. Ultimately, these terms can lead to an alignment of axions potentially realizing large-field inflation. Our goal is to investigate common issues appearing for moduli stabilization near the conifold and subsequent applications to string cosmology. Even though this setup needs to be understood as a toy model, a closer look at the validity of the effective theories reveals characteristic obstacles, which are likely to occur in more serious scenarios as well.

hep-th↗

arXiv2017

The Swampland Conjecture and F-term Axion Monodromy Inflation

We continue the investigation of F-term axion monodromy inflation in string theory, while seriously taking the issue of moduli stabilization into account. For a number of closed and open string models, we show that they suffer from serious control issues once one is trying to realize trans-Planckian field excursions. More precisely, the flux tuning required to delay the logarithmic scaling of the field distance to a trans-Planckian value cannot be done without leaving the regime where the employed effective supergravity theory is under control. Our findings are consistent with the axionic extension of the Refined Swampland Conjecture, stating that in quantum gravity the effective theory breaks down for a field excursion beyond the Planck scale. Our analysis suggests that models of F-term axion monodromy inflation with a tensor-to-scalar ratio $r\ge O(10^{-3})$ cannot be parametrically controlled.

hep-th↗

arXiv2016

String Moduli Stabilization at the Conifold

We study moduli stabilization for type IIB orientifolds compactified on Calabi-Yau threefolds in the region close to conifold singularities in the complex structure moduli space. The form of the periods implies new phenomena like exponential mass hierarchies even in the regime of negligible warping. Integrating out the heavy conic complex structure modulus leads to an effective flux induced potential for the axio-dilaton and the remaining complex structure moduli containing exponentially suppressed terms that imitate non-perturbative effects. It is shown that this scenario can be naturally combined with the large volume scenario so that all moduli are dynamically stabilized in the dilute flux regime. As an application of this moduli stabilization scheme, a string inspired model of aligned inflation is designed that features a parametrically controlled hierarchy of mass scales.

hep-th↗

arXiv2015

A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory

Tree-level moduli stabilization via geometric and non-geometric fluxes in type IIB orientifolds on Calabi-Yau manifolds is investigated. The focus is on stable non-supersymmetric minima, where all moduli are fixed except for some massless axions. The scenario includes the purely axionic orientifold-odd moduli. A set of vacua allowing for parametric control over the moduli vacuum expectation values and their masses is presented, featuring a specific scaling with the fluxes. Uplift mechanisms and supersymmetry breaking soft masses on MSSM-like D7-branes are discussed as well. This scenario provides a complete effective framework for realizing the idea of F-term axion monodromy inflation in string theory. It is argued that, with all masses close to the Planck and GUT scales, one is confronted with working at the threshold of controlling all mass hierarchies.

hep-th↗