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Sep 17

On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter sigma > 0. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be O(sigma)-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as O(sigma)-approximation of the original BO, we propose first-order algorithms that find an epsilon-stationary solution by optimizing the penalty formulation with sigma = O(epsilon). When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an epsilon-stationary point of the penalty function, using in total O(epsilon^{-3}) and O(epsilon^{-7}) accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with O(1) samples per iteration, and achieves the improved oracle-complexity of O(epsilon^{-3}) and O(epsilon^{-5}), respectively.

  • 4 authors
·
Sep 4, 2023

How Vulnerable Are AI Agents to Indirect Prompt Injections? Insights from a Large-Scale Public Competition

LLM based agents are increasingly deployed in high stakes settings where they process external data sources such as emails, documents, and code repositories. This creates exposure to indirect prompt injection attacks, where adversarial instructions embedded in external content manipulate agent behavior without user awareness. A critical but underexplored dimension of this threat is concealment: since users tend to observe only an agent's final response, an attack can conceal its existence by presenting no clue of compromise in the final user facing response while successfully executing harmful actions. This leaves users unaware of the manipulation and likely to accept harmful outcomes as legitimate. We present findings from a large scale public red teaming competition evaluating this dual objective across three agent settings: tool calling, coding, and computer use. The competition attracted 464 participants who submitted 272000 attack attempts against 13 frontier models, yielding 8648 successful attacks across 41 scenarios. All models proved vulnerable, with attack success rates ranging from 0.5% (Claude Opus 4.5) to 8.5% (Gemini 2.5 Pro). We identify universal attack strategies that transfer across 21 of 41 behaviors and multiple model families, suggesting fundamental weaknesses in instruction following architectures. Capability and robustness showed weak correlation, with Gemini 2.5 Pro exhibiting both high capability and high vulnerability. To address benchmark saturation and obsoleteness, we will endeavor to deliver quarterly updates through continued red teaming competitions. We open source the competition environment for use in evaluations, along with 95 successful attacks against Qwen that did not transfer to any closed source model. We share model-specific attack data with respective frontier labs and the full dataset with the UK AISI and US CAISI to support robustness research.

sureheremarv Gray Swan
·
Mar 16

IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 39 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation of mathematical reasoning capabilities by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can succeed at the more accessible research-level questions, but still encounter significant difficulties on more challenging problems. Quantitatively, Grok-4 achieves the highest accuracy of 52% on final-answer subproblems, while GPT-5 obtains the best performance for proof generation, achieving a fully correct solution for 22% of problems. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

  • 33 authors
·
Sep 30, 2025

Security Challenges in AI Agent Deployment: Insights from a Large Scale Public Competition

Recent advances have enabled LLM-powered AI agents to autonomously execute complex tasks by combining language model reasoning with tools, memory, and web access. But can these systems be trusted to follow deployment policies in realistic environments, especially under attack? To investigate, we ran the largest public red-teaming competition to date, targeting 22 frontier AI agents across 44 realistic deployment scenarios. Participants submitted 1.8 million prompt-injection attacks, with over 60,000 successfully eliciting policy violations such as unauthorized data access, illicit financial actions, and regulatory noncompliance. We use these results to build the Agent Red Teaming (ART) benchmark - a curated set of high-impact attacks - and evaluate it across 19 state-of-the-art models. Nearly all agents exhibit policy violations for most behaviors within 10-100 queries, with high attack transferability across models and tasks. Importantly, we find limited correlation between agent robustness and model size, capability, or inference-time compute, suggesting that additional defenses are needed against adversarial misuse. Our findings highlight critical and persistent vulnerabilities in today's AI agents. By releasing the ART benchmark and accompanying evaluation framework, we aim to support more rigorous security assessment and drive progress toward safer agent deployment.

  • 17 authors
·
Jul 28, 2025

The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions. In the current paper, we suggest to analyze the neural signal processing in DANNs from the point of view of homogeneous chaos theory as known from polynomial chaos expansion (PCE). From the PCE perspective, the (linear) response on each node of a DANN could be seen as a 1^{st} degree multi-variate polynomial of single neurons from the previous layer, i.e. linear weighted sum of monomials. From this point of view, the conventional DANN structure relies implicitly (but erroneously) on a Gaussian distribution of neural signals. Additionally, this view revels that by design DANNs do not necessarily fulfill any orthogonality or orthonormality condition for a majority of data-driven applications. Therefore, the prevailing handling of neural signals in DANNs could lead to redundant representation as any neural signal could contain some partial information from other neural signals. To tackle that challenge, we suggest to employ the data-driven generalization of PCE theory known as arbitrary polynomial chaos (aPC) to construct a corresponding multi-variate orthonormal representations on each node of a DANN to obtain Deep arbitrary polynomial chaos neural networks.

  • 6 authors
·
Jun 26, 2023

Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole

The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the star's radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this paper we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2's orbit. Owing to its highly elliptical orbit (e = 0.88), S2's SP is mainly a kink between the pre-and post-pericentre directions of motion ~ +- 1 year around pericentre passage, relative to the corresponding Kepler orbit. The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2's position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states ('flares') of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter f_SP for the SP (f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, del phi = 12' per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f_SP = 1.10 +- 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2's orbit cannot exceed ~ 0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M_sun.

  • 56 authors
·
Apr 14, 2020

Radii, masses, and transit-timing variations of the three-planet system orbiting the naked-eye star TOI-396

TOI-396 is an F6V star (Vapprox6.4) orbited by three transiting planets. The orbital periods of the two innermost planets are close to the 5:3 commensurability (P_b sim3.6 d and P_c sim6.0 d). To measure the masses of the three planets, refine their radii, and investigate whether planets b and c are in MMR, we carried out HARPS RV observations and retrieved photometric data from TESS. We extracted the RVs via a skew-normal fit onto the HARPS CCFs and performed an MCMC joint analysis of the Doppler measurements and transit photometry, while employing the breakpoint method to remove stellar activity from the RV time series. We also performed a thorough TTV dynamical analysis of the system. Our analysis confirms that the three planets have similar sizes: R_b=2.004_{-0.047}^{+0.045}R_{oplus}; R_c=1.979_{-0.051}^{+0.054}R_{oplus}; R_d=2.001_{-0.064}^{+0.063}R_{oplus}. For the first time, we have determined the RV masses for TOI-396b and d: M_b=3.55_{-0.96}^{+0.94}M_{oplus} (rho_b=2.44_{-0.68}^{+0.69} g cm^{-3}) and M_d=7.1pm1.6M_{oplus} (rho_d=4.9_{-1.1}^{+1.2} g cm^{-3}). Our results suggest a quite unusual system architecture, with the outermost planet being the densest. The Doppler reflex motion induced by TOI-396c remains undetected in our RV time series, likely due to the proximity of P_c to the star's rotation period (P_{rot}=6.7pm1.3 d). We also discovered that TOI-396b and c display significant TTVs. While the TTV dynamical analysis returns a formally precise mass for TOI-396c (M_{c,dyn}=2.24^{+0.13}_{-0.67}M_{oplus}), the result might not be accurate owing to the poor sampling of the TTV phase. We also conclude that TOI-396b and c are close to but out of the 5:3 MMR. Our numerical simulation suggests TTV semi-amplitudes of up to 5 hours over a temporal baseline of sim5.2 years.

  • 41 authors
·
Nov 22, 2024

ExoMiner++ on TESS with Transfer Learning from Kepler: Transit Classification and Vetting Catalog for 2-min Data

We present ExoMiner++, an enhanced deep learning model that builds on the success of ExoMiner to improve transit signal classification in 2-minute TESS data. ExoMiner++ incorporates additional diagnostic inputs, including periodogram, flux trend, difference image, unfolded flux, and spacecraft attitude control data, all of which are crucial for effectively distinguishing transit signals from more challenging sources of false positives. To further enhance performance, we leverage transfer learning from high-quality labeled data from the Kepler space telescope, mitigating the impact of TESS's noisier and more ambiguous labels. ExoMiner++ achieves high accuracy across various classification and ranking metrics, significantly narrowing the search space for follow-up investigations to confirm new planets. To serve the exoplanet community, we introduce new TESS catalogs containing ExoMiner++ classifications and confidence scores for each transit signal. Among the 147,568 unlabeled TCEs, ExoMiner++ identifies 7,330 as planet candidates, with the remainder classified as false positives. These 7,330 planet candidates correspond to 1,868 existing TESS Objects of Interest (TOIs), 69 Community TESS Objects of Interest (CTOIs), and 50 newly introduced CTOIs. 1,797 out of the 2,506 TOIs previously labeled as planet candidates in ExoFOP are classified as planet candidates by ExoMiner++. This reduction in plausible candidates combined with the excellent ranking quality of ExoMiner++ allows the follow-up efforts to be focused on the most likely candidates, increasing the overall planet yield.

  • 29 authors
·
Feb 13, 2025

The Chandra Source Catalog

The Chandra Source Catalog (CSC) is a general purpose virtual X-ray astrophysics facility that provides access to a carefully selected set of generally useful quantities for individual X-ray sources, and is designed to satisfy the needs of a broad-based group of scientists, including those who may be less familiar with astronomical data analysis in the X-ray regime. The first release of the CSC includes information about 94,676 distinct X-ray sources detected in a subset of public ACIS imaging observations from roughly the first eight years of the Chandra mission. This release of the catalog includes point and compact sources with observed spatial extents <~ 30''. The catalog (1) provides access to the best estimates of the X-ray source properties for detected sources, with good scientific fidelity, and directly supports scientific analysis using the individual source data; (2) facilitates analysis of a wide range of statistical properties for classes of X-ray sources; and (3) provides efficient access to calibrated observational data and ancillary data products for individual X-ray sources, so that users can perform detailed further analysis using existing tools. The catalog includes real X-ray sources detected with flux estimates that are at least 3 times their estimated 1 sigma uncertainties in at least one energy band, while maintaining the number of spurious sources at a level of <~ 1 false source per field for a 100 ks observation. For each detected source, the CSC provides commonly tabulated quantities, including source position, extent, multi-band fluxes, hardness ratios, and variability statistics, derived from the observations in which the source is detected. In addition to these traditional catalog elements, for each X-ray source the CSC includes an extensive set of file-based data products that can be manipulated interactively.

  • 39 authors
·
May 25, 2010