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George Pappas

Publications and source records attributed to George Pappas.

At least 37 records · Page 2Linked to original sources
arXiv2025

SMBH shadows: gravity fingerprints revealed by spectral line background radiation

SMBHs at the centers of galaxies, illuminated by their accretion disks, can reveal valuable information on BH spacetimes via their shadows, which can be used for strong-gravity tests. However, the continuum emission from their highly turbulent hot plasma is expected to be strongly time-varying and with very inhomogeneous brightness. This can mask important SMBH-related effects, like the appearance of the light-ring, rendering them ineffective as probes of strong gravitational lensing physics. Besides being an inhomogeneous and strongly time-varying ''illuminator'', the hot plasma emission extends all the way to the ISCO. This then leads to the superposition of the strongly-lensed radiation from the area of the light-ring to the continuum emission from the ISCO, effectively making gravitational lensing physics hard to separate from accretion disk Astrophysics. These problems could be overcome if one utilizes the spectral line radiation field emanating from the cooler parts of the extended accretion disk, the so-called BLR, and especially its expected neutral phase, as a more distant, but still adequately strong SMBH illuminator, typically found at $r\sim (10^2-10^4)\, R_s$. This kind of illumination can provide a cleaner image of the light-ring region, and thus allow more information on the spacetime geometry around the SMBH to be obtained. Here, we examine some of the benefits of such an illumination in discerning strong-gravity physics near SMBHs and their observability. We expand on the fact that such emission can provide a smoking gun signal of lensing, in the form of an Einstein ring. To first order, the imaging of the Einstein ring and its spectroscopic signature can facilitate the measurement of the SMBH mass, while the second order effects associated with the light-ring can constrain the SMBH spin, and even identify deviations from the Kerr spacetime.

gr-qc↗
arXiv2025

Modelling Gaia photometry signals of dark halos

We use the framework of microlensing to show that observations of binary systems, such as those made by {\it Gaia}, combined with follow-up weak lensing measurements, can provide a means to probe halos of exotic matter, possibly clumped around compact objects such as black holes. This could potentially cover a broad range of physical scenarios - from dark matter mini-halos to black holes with bosonic configurations around them, known as hair. In a dark halo-regular star binary system, assuming that light can freely propagate through the halo of the exotic matter, the companion star will produce characteristic, sizable lensing signatures due to the lens's potential deviating from a point mass gravitational potential. The signature of the multiple images, the magnification and the light-curve could be the smoking gun of such a dark halo structure. We discuss how the precise observations of the {\it Gaia} survey offer an opportunity to search for new, yet undiscovered fundamental fields interacting gravitationally with baryons.

astro-ph.CO↗
arXiv2025

Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

stat.ML↗
arXiv2025

Adversarial Reasoning at Jailbreaking Time

As large language models (LLMs) are becoming more capable and widespread, the study of their failure cases is becoming increasingly important. Recent advances in standardizing, measuring, and scaling test-time compute suggest new methodologies for optimizing models to achieve high performance on hard tasks. In this paper, we apply these advances to the task of model jailbreaking: eliciting harmful responses from aligned LLMs. We develop an adversarial reasoning approach to automatic jailbreaking that leverages a loss signal to guide the test-time compute, achieving SOTA attack success rates against many aligned LLMs, even those that aim to trade inference-time compute for adversarial robustness. Our approach introduces a new paradigm in understanding LLM vulnerabilities, laying the foundation for the development of more robust and trustworthy AI systems.

cs.LG↗
arXiv2025

Deep Equivariant Multi-Agent Control Barrier Functions

With multi-agent systems increasingly deployed autonomously at scale in complex environments, ensuring safety of the data-driven policies is critical. Control Barrier Functions have emerged as an effective tool for enforcing safety constraints, yet existing learning-based methods often lack in scalability, generalization and sampling efficiency as they overlook inherent geometric structures of the system. To address this gap, we introduce symmetries-infused distributed Control Barrier Functions, enforcing the satisfaction of intrinsic symmetries on learnable graph-based safety certificates. We theoretically motivate the need for equivariant parametrization of CBFs and policies, and propose a simple, yet efficient and adaptable methodology for constructing such equivariant group-modular networks via the compatible group actions. This approach encodes safety constraints in a distributed data-efficient manner, enabling zero-shot generalization to larger and denser swarms. Through extensive simulations on multi-robot navigation tasks, we demonstrate that our method outperforms state-of-the-art baselines in terms of safety, scalability, and task success rates, highlighting the importance of embedding symmetries in safe distributed neural policies.

eess.SY↗
arXiv2025

Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores: tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query only setting, where prediction sets must be constructed solely from finite queries to a black box generative model, introducing a new trade off between coverage, test time query budget, and informativeness. We introduce Conformal Prediction with Query Oracle (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets. Remarkably, both are rooted in the classical missing mass problem in statistics. Specifically, the optimal query policy depends on the rate of decay, or the derivative, of the missing mass, for which we develop a novel estimator. Meanwhile, the optimal mapping hinges on the missing mass itself, which we estimate using Good Turing estimators. We then turn our focus to implementing our method for language models, where outputs are vast, variable, and often under specified. Fine grained experiments on three real world open ended tasks and two LLMs, show CPQ applicability to any black box LLM and highlight: (1) individual contribution of each principle to CPQ performance, and (2) CPQ ability to yield significantly more informative prediction sets than existing conformal methods for language uncertainty quantification.

cs.LG↗
arXiv2025

Symmetries-enhanced Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning has emerged as a powerful framework for enabling agents to learn complex, coordinated behaviors but faces persistent challenges regarding its generalization, scalability and sample efficiency. Recent advancements have sought to alleviate those issues by embedding intrinsic symmetries of the systems in the policy. Yet, most dynamical systems exhibit little to no symmetries to exploit. This paper presents a novel framework for embedding extrinsic symmetries in multi-agent system dynamics that enables the use of symmetry-enhanced methods to address systems with insufficient intrinsic symmetries, expanding the scope of equivariant learning to a wide variety of MARL problems. Central to our framework is the Group Equivariant Graphormer, a group-modular architecture specifically designed for distributed swarming tasks. Extensive experiments on a swarm of symmetry-breaking quadrotors validate the effectiveness of our approach, showcasing its potential for improved generalization and zero-shot scalability. Our method achieves significant reductions in collision rates and enhances task success rates across a diverse range of scenarios and varying swarm sizes.

cs.RO↗
arXiv2025

Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents

A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions in ways that can usefully inform downstream action. This interface between prediction uncertainty and decision-making is especially important in risk-sensitive domains, such as medicine. In this paper, we develop decision-theoretic foundations that connect uncertainty quantification using prediction sets with risk-averse decision-making. Specifically, we answer three fundamental questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. Answering these questions naturally leads to an algorithm, Risk-Averse Calibration (RAC), which follows a provably optimal design for deriving action policies from predictions. RAC is designed to be both practical-capable of leveraging the quality of predictions in a black-box manner to enhance downstream utility-and safe-adhering to a user-defined risk threshold and optimizing the corresponding risk quantile of the user's downstream utility. Finally, we experimentally demonstrate the significant advantages of RAC in applications such as medical diagnosis and recommendation systems. Specifically, we show that RAC achieves a substantially improved trade-off between safety and utility, offering higher utility compared to existing methods while maintaining the safety guarantee.

cs.LG↗
arXiv2024

Length Optimization in Conformal Prediction

Conditional validity and length efficiency are two crucial aspects of conformal prediction (CP). Conditional validity ensures accurate uncertainty quantification for data subpopulations, while proper length efficiency ensures that the prediction sets remain informative. Despite significant efforts to address each of these issues individually, a principled framework that reconciles these two objectives has been missing in the CP literature. In this paper, we develop Conformal Prediction with Length-Optimization (CPL) - a novel and practical framework that constructs prediction sets with (near-) optimal length while ensuring conditional validity under various classes of covariate shifts, including the key cases of marginal and group-conditional coverage. In the infinite sample regime, we provide strong duality results which indicate that CPL achieves conditional validity and length optimality. In the finite sample regime, we show that CPL constructs conditionally valid prediction sets. Our extensive empirical evaluations demonstrate the superior prediction set size performance of CPL compared to state-of-the-art methods across diverse real-world and synthetic datasets in classification, regression, and large language model-based multiple choice question answering. An Implementation of our algorithm can be accessed at the following link: https://github.com/shayankiyani98/CP.

stat.ML↗
arXiv2024

STLGame: Signal Temporal Logic Games in Adversarial Multi-Agent Systems

We study how to synthesize a robust and safe policy for autonomous systems under signal temporal logic (STL) tasks in adversarial settings against unknown dynamic agents. To ensure the worst-case STL satisfaction, we propose STLGame, a framework that models the multi-agent system as a two-player zero-sum game, where the ego agents try to maximize the STL satisfaction and other agents minimize it. STLGame aims to find a Nash equilibrium policy profile, which is the best case in terms of robustness against unseen opponent policies, by using the fictitious self-play (FSP) framework. FSP iteratively converges to a Nash profile, even in games set in continuous state-action spaces. We propose a gradient-based method with differentiable STL formulas, which is crucial in continuous settings to approximate the best responses at each iteration of FSP. We show this key aspect experimentally by comparing with reinforcement learning-based methods to find the best response. Experiments on two standard dynamical system benchmarks, Ackermann steering vehicles and autonomous drones, demonstrate that our converged policy is almost unexploitable and robust to various unseen opponents' policies. All code and additional experimental results can be found on our project website: https://sites.google.com/view/stlgame

cs.RO↗
arXiv2024

Fractal signatures of non-Kerr spacetimes in the shadow of light-ring bifurcations

Light-ring bifurcations that can occur for prolate non-Kerr compact objects can leave an indelible signature on SMBH shadows as a fractal sequence of eyebrow-like formations. These fractal features are the result of two properties of these spacetimes. The first is that they allow for multiple escapes for the photons (throats in the effective potential of photon geodesic motion). The second is that photon geodesics can resonate between different generalized light-rings related to the escapes, called fundamental photon orbits, that lead photons to alternate between the different exits either towards the compact object or infinity. The resulting fractal structures of the shadow seem to be a generic feature of prolate non-Kerr objects that may be observable in (accretion-disk)-illuminated compact objects, especially along equatorial lines of sight, but the best orientation depends on the specific parameters. Such fractal features if observed in the shadows of singular supermassive black holes at the centers of galaxies, would be smoking gun signals of non-Kerr compact objects.

gr-qc↗
arXiv2024

Explicitly Encoding Structural Symmetry is Key to Length Generalization in Arithmetic Tasks

Despite the success of Transformers on language understanding, code generation, and logical reasoning, they still fail to generalize over length on basic arithmetic tasks such as addition and multiplication. A major reason behind this failure is the vast difference in structure between numbers and text; For example, the numbers are typically parsed from right to left, and there is a correspondence between digits at the same position across different numbers. In contrast, for text, such symmetries are quite unnatural. In this work, we propose to encode these semantics explicitly into the model via modified number formatting and custom positional encodings. Empirically, our method allows a Transformer trained on numbers with at most 5-digits for addition and multiplication to generalize up to 50-digit numbers, without using additional data for longer sequences. We further demonstrate that traditional absolute positional encodings (APE) fail to generalize to longer sequences, even when trained with augmented data that captures task symmetries. To elucidate the importance of explicitly encoding structure, we prove that explicit incorporation of structure via positional encodings is necessary for out-of-distribution generalization. Finally, we pinpoint other challenges inherent to length generalization beyond capturing symmetries, in particular complexity of the underlying task, and propose changes in the training distribution to address them.

cs.LG↗
arXiv2024

Conformal Prediction with Learned Features

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research has considered relaxations of full conditional guarantees, relying on some predefined uncertainty structures. Departing from this line of thinking, we propose Partition Learning Conformal Prediction (PLCP), a framework to improve conditional validity of prediction sets through learning uncertainty-guided features from the calibration data. We implement PLCP efficiently with alternating gradient descent, utilizing off-the-shelf machine learning models. We further analyze PLCP theoretically and provide conditional guarantees for infinite and finite sample sizes. Finally, our experimental results over four real-world and synthetic datasets show the superior performance of PLCP compared to state-of-the-art methods in terms of coverage and length in both classification and regression scenarios.

cs.LG↗
arXiv2024

Optimal Scene Graph Planning with Large Language Model Guidance

Recent advances in metric, semantic, and topological mapping have equipped autonomous robots with semantic concept grounding capabilities to interpret natural language tasks. This work aims to leverage these new capabilities with an efficient task planning algorithm for hierarchical metric-semantic models. We consider a scene graph representation of the environment and utilize a large language model (LLM) to convert a natural language task into a linear temporal logic (LTL) automaton. Our main contribution is to enable optimal hierarchical LTL planning with LLM guidance over scene graphs. To achieve efficiency, we construct a hierarchical planning domain that captures the attributes and connectivity of the scene graph and the task automaton, and provide semantic guidance via an LLM heuristic function. To guarantee optimality, we design an LTL heuristic function that is provably consistent and supplements the potentially inadmissible LLM guidance in multi-heuristic planning. We demonstrate efficient planning of complex natural language tasks in scene graphs of virtualized real environments.

cs.RO↗
arXiv2023

Navigation with shadow prices to optimize multi-commodity flow rates

We propose a method for providing communication network infrastructure in autonomous multi-agent teams. In particular, we consider a set of communication agents that are placed alongside regular agents from the system in order to improve the rate of information transfer between the latter. In order to find the optimal positions to place such agents, we define a flexible performance function that adapts to network requirements for different systems. We provide an algorithm based on shadow prices of a related convex optimization problem in order to drive the configuration of the complete system towards a local maximum. We apply our method to three different performance functions associated with three practical scenarios in which we show both the performance of the algorithm and the flexibility it allows for optimizing different network requirements.

math.OC↗
arXiv2023

Universal Relations for rapidly rotating neutron stars using supervised machine-learning techniques

As some of the most compact stellar objects in the universe, neutron stars are unique cosmic laboratories. The study of neutron stars provides an ideal theoretical testbed for investigating both physics at supra-nuclear densities as well as fundamental physics. Their global astrophysical properties however depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. In recent years, a lot of work has revealed the existence of universal relations between stellar quantities that are insensitive to the equation of state. At the same time, the fields of multimessenger astronomy and machine learning have both advanced significantly. As such, there has been a confluence of research into their combination and the field is growing. In this paper, we develop universal relations for rapidly rotating neutron stars, by using supervised machine learning methods, thus proposing a new way of discovering and validating such relations. The analysis is performed for tabulated hadronic, hyperonic, and hybrid EoS-ensembles that obey the multimessenger constraints and cover a wide range of stiffnesses. The relations discussed could provide an accurate tool to constrain the equation of state of nuclear matter when measurements of the relevant observables become available.

astro-ph.HE↗
arXiv2023

Toward Certified Robustness Against Real-World Distribution Shifts

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts. To do so, we bridge the gap between hand-crafted specifications and realistic deployment settings by proposing a novel neural-symbolic verification framework, in which we train a generative model to learn perturbations from data and define specifications with respect to the output of the learned model. A unique challenge arising from this setting is that existing verifiers cannot tightly approximate sigmoid activations, which are fundamental to many state-of-the-art generative models. To address this challenge, we propose a general meta-algorithm for handling sigmoid activations which leverages classical notions of counter-example-guided abstraction refinement. The key idea is to "lazily" refine the abstraction of sigmoid functions to exclude spurious counter-examples found in the previous abstraction, thus guaranteeing progress in the verification process while keeping the state-space small. Experiments on the MNIST and CIFAR-10 datasets show that our framework significantly outperforms existing methods on a range of challenging distribution shifts.

cs.LG↗
arXiv2023

Is a black hole shadow a reliable test of the no-hair theorem?

Capturing the image of the shadow cast by the event horizon of an illuminated black hole is, at the most basic level, an experiment of extreme light deflection in a strongly curved spacetime. As such, the properties of an imaged shadow can be used to probe the general relativistic Kerr nature of astrophysical black holes. As an example of this prospect, it is commonly asserted that a shadow can test the validity of the theory's famous `no hair theorem' for the black hole's mass and spin multipole moments. In this paper, we assess this statement by calculating the shadow's equatorial radius in spacetimes with an arbitrary multipolar structure and within a slow rotation approximation. We find that when moments higher than the quadrupole are taken into account, the shadow acquires a high degree of degeneracy as a function of the deviation from the Kerr multipole moments. The results of our analysis suggest that dark objects with strongly non-Kerr multipolar structure could nevertheless produce a Kerr-like shadow with its characteristic quasi-circular shape.

gr-qc↗