We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density $p^\star$, the goal is to construct an estimator $\widehat{p}$ such that $\mathrm{KL}(p^\star,\widehat{p})$ is small with high probability. We consider two fundamental settings involving a finite dictionary of densities: (i) model aggregation, where $p^\star$ belongs to the dictionary, and (ii) convex aggregation (mixture density estimation), where $p^\star$ is a mixture of densities from the dictionary. Crucially, we make no assumption on the base densities: their ratios may be unbounded and their supports may differ. For both problems, we identify the best possible high-probability guarantees in terms of the dictionary size, sample size, and confidence level. These optimal rates are higher than those achievable when density ratios are bounded by absolute constants; for mixture density estimation, they match existing lower bounds in the special case of discrete distributions. Our analysis of the mixture case hinges on two new covering results. First, we provide a sharp, distribution-free upper bound on the local Hellinger entropy of the class of mixtures of $M$ distributions. Second, we prove an optimal ratio covering theorem for convex sets: for every convex compact set $K \subset \mathbb{R}_+^d$, there exists a subset $A \subset K$ with at most $2^{O(d)}$ elements such that each element of $K$ is coordinate-wise dominated by an element of $A$ up to a universal constant factor. This geometric result is of independent interest; notably, it yields new cardinality estimates for $\varepsilon$-approximate Pareto sets in multi-objective optimization with convex feasible set.

Complexity in engineered systems presents one of the most persistent challenges in modern development since it is driving cost overruns, schedule delays, and outright project failures. Yet while architectural complexity has been studied, the structural complexity embedded within requirements specifications remains poorly understood and inadequately quantified. This gap is consequential: requirements fundamentally drive system design, and complexity introduced at this stage propagates through architecture, implementation, and integration. To address this gap, we build on Natural Language Processing methods that extract structural networks from textual requirements. Using these extracted structures, we conduct a controlled experiment employing molecular integration tasks as structurally isomorphic proxies for requirements integration -- leveraging the topological equivalence between molecular graphs and requirement networks while eliminating confounding factors such as domain expertise and semantic ambiguity. Our results demonstrate that spectral measures predict integration effort with correlations exceeding 0.95, while structural metrics achieve correlations above 0.89. Notably, density-based metrics show no significant predictive validity. These findings indicate that eigenvalue-derived measures capture cognitive and effort dimensions that simpler connectivity metrics cannot. As a result, this research bridges a critical methodological gap between architectural complexity analysis and requirements engineering practice, providing a validated foundation for applying these metrics to requirements engineering, where similar structural complexity patterns may predict integration effort.

This paper aims to provide a clear and rigorous understanding of commonly recognized safety constraints in physical human-robot interaction, particularly regarding ISO/TS 15066. We investigate the derivation of these constraints, critically examine the underlying assumptions, and evaluate their practical implications for system-level safety and performance in industrially relevant scenarios. Key design parameters within safety-critical control architectures are identified, and numerical examples are provided to quantify performance degradation arising from typical approximations and design decisions in manufacturing environments. Within this analysis, the fundamental role of energy in safety assessment is emphasized, providing focused insights into energy-based safety methodologies for collaborative industrial robot systems.

Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always practical or desirable to estimate a causal model at the granularity of given features in a particular dataset. There is a growing body of research on causal abstraction to address such problems. We contribute to this line of research by (i) providing novel graphical identifiability results for practically-relevant interventional settings, (ii) proposing an efficient, provably consistent algorithm for directly learning abstract causal graphs from interventional data with unknown intervention targets, and (iii) uncovering theoretical insights about the lattice structure of the underlying search space, with connections to the field of causal discovery more generally. As proof of concept, we apply our algorithm on synthetic and real datasets with known ground truths, including measurements from a controlled physical system with interacting light intensity and polarization.

Neural Network Field Theories (NN-FTs) typically describe Generalized Free Fields that lack a local stress-energy tensor in two dimensions, obstructing the realization of Virasoro symmetry. We present the ``Log-Kernel'' (LK) architecture, which enforces local conformal symmetry via a specific rotation-invariant spectral prior $p(k) \propto |k|^{-2}$. We analytically derive the emergence of the Virasoro algebra from the statistics of the neural ensemble. We validate this construction through numerical simulation, computing the central charge $c_{exp} = 0.9958 \pm 0.0196$ (theoretical $c=1$) and confirming the scaling dimensions of vertex operators. Furthermore, we demonstrate that finite-width corrections generate interactions scaling as $1/N$. Finally, we extend the framework to include fermions and boundary conditions, realizing the super-Virasoro algebra. We verify the $\mathcal{N}=1$ super-Virasoro algebra by measuring the supercurrent correlator to $96\%$ accuracy. We further demonstrate conformal boundary conditions on the upper half-plane, achieving 99\% agreement for boundary fermion and boson propagators.

The rapid proliferation of Artificial Intelligence Generated Content has precipitated a crisis of trust and urgent regulatory demands. However, existing identification tools suffer from fragmentation and a lack of support for visible compliance marking. To address these gaps, we introduce the \textbf{UniMark}, an open-source, unified framework for multimodal content governance. Our system features a modular unified engine that abstracts complexities across text, image, audio, and video modalities. Crucially, we propose a novel dual-operation strategy, natively supporting both \emph{Hidden Watermarking} for copyright protection and \emph{Visible Marking} for regulatory compliance. Furthermore, we establish a standardized evaluation framework with three specialized benchmarks (Image/Video/Audio-Bench) to ensure rigorous performance assessment. This toolkit bridges the gap between advanced algorithms and engineering implementation, fostering a more transparent and secure digital ecosystem.

In this paper, we introduce, MultiGA, an optimization framework which applies genetic algorithm principles to address complex natural language tasks and reasoning problems by sampling from a diverse population of LLMs to initialize the population of candidate solutions. MultiGA generates a range of outputs from various parent LLMs and uses a neutral fitness function to evaluate them. Through an iterative recombination process, we mix and refine these generations until an optimal solution is achieved. Our results show that MultiGA produces high accuracy across multiple benchmarks, and these insights lay the foundation for future research looking closer at integrating multiple LLMs for unexplored tasks in which selecting only one pre-trained model is unclear or suboptimal.

Context: Large Language Models (LLMs) rely on static, pre-deployment safety mechanisms that cannot adapt to adversarial threats discovered after release. Objective: To design a software architecture enabling LLM-based systems to autonomously detect safety failures and synthesize defense policies at runtime, without retraining or manual intervention. Method: We propose the Self-Improving Safety Framework (SISF), grounded in the MAPE-K reference model. The framework couples a target LLM with a feedback loop: an Adjudicator detects breaches, a Policy Synthesis Module generates dual-mechanism defense policies (heuristic and semantic), and a Warden enforces them. We conducted seven experiments (10,061 evaluations) across four model families. Results: Across five reproducibility trials, SISF achieved a mean Attack Success Rate (ASR) of 0.27% (+/-0.15%), autonomously generating 240 policies per trial. Cross-model evaluation confirmed deployment portability. A held-out test showed a 68.5% proactive interception rate on unseen attacks. Stacked behind Llama Guard 4, the combined defense reduced residual ASR from 7.88% to 0.00%. Ablation confirmed both heuristic and semantic policy types are architecturally required. Conclusion: Self-adaptive architecture is a viable approach to LLM safety. SISF achieves sub-1% ASR through synchronous output monitoring, progressively shifting enforcement to fast, local Warden policies via the MAPE-K loop, offering a new pattern for building resilient AI systems.

Automated program repair (APR) has recently shifted toward large language models and agent-based systems, yet most systems rely on local snapshot context, overlooking repository history. Prior work shows that repository history helps repair single-line bugs, since the last commit touching the buggy line is often the bug-introducing one. In this paper, we investigate whether repository history can also improve agentic APR systems at scale, especially for complex multi-hunk bugs. We present HAFixAgent, a History-Aware Bug-Fixing Agent that injects blame-derived repository heuristics into its repair loop. A preliminary study on 854 Defects4J (Java) and 501 BugsInPy (Python) bugs motivates our design, showing that bug-relevant history is widely available across both benchmarks. Using the same LLM (DeepSeek-V3.2-Exp) for all experiments, including replicated baselines, we show: (1) Effectiveness: HAFixAgent outperforms RepairAgent (+56.6\%) and BIRCH-feedback (+47.1\%) on Defects4J. Historical context further improves repair by +4.4\% on Defects4J and +38.6\% on BugsInPy, especially on single-file multi-hunk (SFMH) bugs. (2) Robustness: under noisy fault localization (+1/+3/+5 line shifts), history provides increasing resilience, maintaining 40 to 56\% success on SFMH bugs where the non-history baseline collapses to 0\%. (3) Efficiency: history does not significantly increase agent steps or token costs on either benchmark.

Malicious agents pose significant threats to the reliability and decision-making capabilities of Multi-Agent Systems (MAS) powered by Large Language Models (LLMs). Existing defenses often fall short due to reactive designs or centralized architectures which may introduce single points of failure. To address these challenges, we propose SentinelNet, the first decentralized framework for proactively detecting and mitigating malicious behaviors in multi-agent collaboration. SentinelNet equips each agent with a credit-based detector trained via contrastive learning on augmented adversarial debate trajectories, enabling autonomous evaluation of message credibility and dynamic neighbor ranking via bottom-k elimination to suppress malicious communications. To overcome the scarcity of attack data, it generates adversarial trajectories simulating diverse threats, ensuring robust training. Experiments on MAS benchmarks show SentinelNet achieves near-perfect detection of malicious agents, close to 100% within two debate rounds, and recovers 95% of system accuracy from compromised baselines. By exhibiting strong generalizability across domains and attack patterns, SentinelNet establishes a novel paradigm for safeguarding collaborative MAS.

The rise of large-scale pretrained models has made it feasible to generate predictive or synthetic features at low cost, raising the question of how to incorporate such surrogate predictions into downstream decision-making. We study this problem in the setting of online linear contextual bandits, where contexts may be complex, nonstationary, and only partially observed. In addition to bandit data, we assume access to an auxiliary dataset containing fully observed contexts--common in practice since such data are collected without adaptive interventions. We propose PULSE-UCB, an algorithm that leverages pretrained models trained on the auxiliary data to impute missing features during online decision-making. We establish regret guarantees that decompose into a standard bandit term plus an additional component reflecting pretrained model quality. In the i.i.d. context case with Hölder-smooth missing features, PULSE-UCB achieves near-optimal performance, supported by matching lower bounds. Our results quantify how uncertainty in predicted contexts affects decision quality and how much historical data is needed to improve downstream learning.

Android is the largest mobile platform, yet automatically building applications remains a practical challenge. While Large Language Models (LLMs) show promise for code repair, their use for fixing Android build errors remains underexplored. To address this gap, we first introduce AndroidBuildBench, a benchmark of 1,019 build failures curated from the commit histories of 43 open-source Android projects. Each problem is paired with a verified solution from a subsequent commit, ensuring that fixes are feasible. Second, we propose GradleFixer, an LLM agent with domain-specific tools for inspecting and manipulating the Gradle build environment. GradleFixer achieves a resolve rate of 81.4% (pass@1), significantly outperforming a state-of-the-art coding agent that relies on a general-purpose shell. GradleFixer's success suggests that while LLMs possess the high-level knowledge to solve these failures, they struggle to translate this knowledge into effective low-level actions using a general-purpose shell. We demonstrate the effectiveness of a strategy we term Tool Bridging, which replaces general-purpose shell commands with domain-aware abstractions. We hypothesize this approach works through two mechanisms: 1) it provides tools in an API-like format that LLMs use more reliably, and 2) it constrains the action space to relevant operations. This approach bridges the gap between the model's high-level reasoning and effective low-level execution.

Traditional conformal prediction methods construct prediction sets such that the true label falls within the set with a user-specified coverage level. However, poorly chosen coverage levels can result in uninformative predictions, either producing overly conservative sets when the coverage level is too high, or empty sets when it is too low. Moreover, the fixed coverage level cannot adapt to the specific characteristics of each individual example, limiting the flexibility and efficiency of these methods. In this work, we leverage recent advances in e-values and post-hoc conformal inference, which allow the use of data-dependent coverage levels while maintaining valid statistical guarantees. We propose to optimize an adaptive coverage policy by training a neural network using a leave-one-out procedure on the calibration set, allowing the coverage level and the resulting prediction set size to vary with the difficulty of each individual example. We support our approach with theoretical coverage guarantees and demonstrate its practical benefits through a series of experiments.

This paper studies the adversarial robustness of conformal novelty detection. In particular, we focus on two powerful learning-based frameworks that come with finite-sample false discovery rate (FDR) control: one is AdaDetect (by Marandon et al., 2024) that is based on the positive-unlabeled classifier, and the other is a one-class classifier-based approach (by Bates et al., 2023). While they provide rigorous statistical guarantees under benign conditions, their behavior under adversarial perturbations remains underexplored. We first formulate an oracle attack setup, under the AdaDetect formulation, that quantifies the worst-case degradation of FDR, deriving an upper bound that characterizes the statistical cost of attacks. This idealized formulation directly motivates a practical and effective attack scheme that only requires query access to the output labels of both frameworks. Coupling these formulations with two popular and complementary black-box adversarial algorithms, we systematically evaluate the vulnerability of both frameworks on synthetic and real-world datasets. Our results show that adversarial perturbations can significantly increase the FDR while maintaining high detection power, exposing fundamental limitations of current error-controlled novelty detection methods and motivating the development of more robust alternatives.

Program verification relies on loop invariants, yet automatically discovering strong invariants remains a long-standing challenge. We investigate whether large language models (LLMs) can accelerate program verification by generating useful loop invariants. We introduce Quokka, an evaluation-oriented framework for LLM-based invariant synthesis that provides sound evaluation and achieves state-of-the-art performance. Unlike prior work that treats LLM outputs as noisy symbolic material requiring substantial post-processing, Quokka adopts a simpler and evaluation-centric design that directly validates whether each LLM-generated invariant helps prove the target assertion. We construct a benchmark of 866 instances derived from SV-COMP and evaluate 9 state-of-the-art LLMs across multiple model families. We demonstrate that supervised fine-tuning and Best-of-N sampling yield measurable improvements, and we show that Quokka consistently outperforms prior LLM-based verifiers. Our code and data are publicly available at https://github.com/Anjiang-Wei/Quokka

In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate. In this paper, we propose a novel diffusion model -- the Pressure Threshold model (PT) -- for dynamically simulating the spread of influence through a social network. This model extends the popular Linear Threshold (LT) model by adjusting a node's outgoing influence in proportion to the influence it receives from its activated neighbors. We examine the Influence Maximization (IM) problem under this framework, which involves selecting seed nodes that yield maximal graph coverage after a diffusion process, and describe how the problem manifests under the PT model. Experiments on real-world networks, supported by enhancements to the open-source network-diffusion library CyNetDiff, reveal that greedy IM under PT can yield seed sets distinct from those under LT. Furthermore, the analyses show that densely connected networks amplify pressure effects far more strongly than sparse networks.

Safeguarding vision-language models (VLMs) is a critical challenge, as existing methods often suffer from over-defense, which harms utility, or rely on shallow alignment, failing to detect complex threats that require deep reasoning. To this end, we introduc PRISM (Principled Reasoning for Integrated Safety in Multimodality), a System 2-like framework that aligns VLMs through a structured four-stage reasoning process explicitly designed to handle three distinct categories of multimodal safety violations. Our framework consists of two key components: a structured reasoning pipeline that analyzes each violation category in dedicated stages, and PRISM-DPO, generated via Monte Carlo Tree Search (MCTS) to refine reasoning quality through Direct Preference Optimization. Comprehensive evaluations show that PRISM substantially reduces attack success rates on JailbreakV-28K and VLBreak, improves robustness against adaptive attacks, and generalizes to out-of-distribution multi-image threats, while better preserving model utility on benign multimodal benchmarks. Our code, data, and model weights available at https://github.com/SaFoLab-WISC/PRISM.

Metric aggregation divergence is a hidden confound in agent-based model policy search: when optimization, tournament evaluation, and statistical validation independently implement outcome metric extraction, champion selection reflects aggregation artifact rather than policy quality. We propose Hierarchical Evolutionary Agent Simulation (HEAS), a composable framework that eliminates this confound through a runtime-enforceable metric contract - a uniform metrics_episode() callable shared identically by all pipeline stages. Removing the confound yields robust champion selection: in a controlled experiment (n=30), HEAS reduces rank reversals by 50% relative to ad-hoc aggregation; the HEAS champion wins all 32 held-out ecological scenarios - a null-safety result that would be uninterpretable under aggregation divergence. The contract additionally reduces coupling code by 97% (160 to 5 lines) relative to Mesa 3.3.1. Three case studies validate composability across ecological, enterprise, and mean-field ordinary differential equation dynamics.

Retrieval-augmented generation has achieved strong performance on knowledge-intensive tasks where query-document relevance can be identified through direct lexical or semantic matches. However, many real-world queries involve abstract reasoning, analogical thinking, or multi-step inference, which existing retrievers often struggle to capture. To address this challenge, we present DIVER, a retrieval pipeline designed for reasoning-intensive information retrieval. It consists of four components. The document preprocessing stage enhances readability and preserves content by cleaning noisy texts and segmenting long documents. The query expansion stage leverages large language models to iteratively refine user queries with explicit reasoning and evidence from retrieved documents. The retrieval stage employs a model fine-tuned on synthetic data spanning medical and mathematical domains, along with hard negatives, enabling effective handling of reasoning-intensive queries. Finally, the reranking stage combines pointwise and listwise strategies to produce both fine-grained and globally consistent rankings. On the BRIGHT benchmark, DIVER achieves state-of-the-art nDCG@10 scores of 46.8 overall and 31.9 on original queries, consistently outperforming competitive reasoning-aware models. These results demonstrate the effectiveness of reasoning-aware retrieval strategies in complex real-world tasks.

Model predictive control (MPC) is widely used in process control due to its interpretability and ability to handle constraints. As a parametric policy in reinforcement learning (RL), MPC offers strong initial performance and low data requirements compared to black-box policies like neural networks. However, most RL methods rely on first-order updates, which scale well to large parameter spaces but converge at most linearly, making them inefficient when each policy update requires solving an optimal control problem, as is the case with MPC. While MPC policies are typically low parameterized and thus amenable to second-order approaches, existing second-order methods demand second-order policy derivatives, which can be computationally intractable. This work introduces a Gauss-Newton approximation of the deterministic policy Hessian that eliminates the need for second-order policy derivatives, enabling superlinear convergence with minimal computational overhead. To further improve robustness, we propose a momentum-based Hessian averaging scheme for stable training under noisy estimates coupled with an adaptive trustregion. We demonstrate the effectiveness of the approach on a nonlinear continuously stirred tank reactor (CSTR), showing faster convergence and improved data efficiency over state-of-the-art firstorder methods and deep RL approaches.

The The use of Large language models (LLMs) to summarise parliamentary proceedings presents a promising means of increasing the accessibility of democratic participation. However, as these systems increasingly mediate access to political information -- filtering and framing content before it reaches users -- there are important fairness considerations to address. In this work, we evaluate 5 LLMs (both proprietary and open-weight) in the summarisation of plenary debates from the European Parliament to investigate the representational biases that emerge in this context. We develop an attribution-aware evaluation framework to measure speaker-level inclusion and mis-representation in debate summaries. Across all models and experiments, we find that speakers are less accurately represented in the final summary on the basis of (i) their speaking-order (speeches in the middle of the debate were systematically excluded), (ii) language spoken (non-English speakers were less faithfully represented), and (iii) political affiliations (better outcomes for left-of-centre parties). We further show how biases in these contexts can be decomposed to distinguish inclusion bias (systematic omission) from hallucination bias (systematic misrepresentation), and explore the effect of different mitigation strategies. Prompting strategies do not affect these biases. Instead, we propose a hierarchical summarisation method that decomposes the task into simpler extraction and aggregation steps, which we show significantly improves the positional/speaking-order bias across all models. These findings underscore the need for domain-sensitive evaluation metrics and ethical oversight in the deployment of LLMs for multilingual democratic applications.

This paper presents a novel framework for pattern prediction and system prognostics centered on Spatiotemporal Permutation Entropy analysis integrated with Boosted Enhanced Quantile Regression Neural Networks (BEQRNNs). We address the challenge of understanding complex dynamical patterns in multidimensional systems through an approach that combines entropy-based complexity measures with advanced neural architectures. The system leverages dual computational stages: first implementing spatiotemporal entropy extraction optimized for multiscale temporal and spatial data streams, followed by an integrated BEQRNN layer that enables probabilistic pattern prediction with uncertainty quantification. This architecture achieves 81.17% accuracy in spatiotemporal pattern classification with prediction horizons up to 200 time steps and maintains robust performance across diverse regimes. Field testing across chaotic attractors, reaction-diffusion systems, and industrial datasets shows a 79% increase in critical transition detection accuracy and 81.22% improvement in long-term prediction reliability. The framework's effectiveness in processing complex, multimodal entropy features demonstrates significant potential for real-time prognostic applications.

Roll stabilization is a critical aspect of ship motion control, particularly for vessels operating in low-speed or zero-speed conditions, where traditional hydrodynamic fins lose their effectiveness. In this paper, we consider a roll damping system, developed by Navis JSC, based on two actively controlled zero-speed fins. Unlike conventional fin stabilizers, zero-speed fins employ a drag-based mechanism and active oscillations to generate stabilizing forces even when the vessel is stationary. We propose a simple linear control architecture that, however, accounts for nonlinear drag forces and actuator limitations. Simulation results on a high-fidelity vessel model used for HIL testing demonstrate the effectiveness of the proposed approach.

Binaural reproduction aims to deliver immersive spatial audio with high perceptual realism over headphones. Loss functions play a central role in optimizing and evaluating algorithms that generate binaural signals. However, traditional signal-related difference measures often fail to capture the perceptual properties that are essential to spatial audio quality. This review paper surveys recent loss functions that incorporate spatial perception cues relevant to binaural reproduction. It focuses on losses applied to binaural signals, which are often derived from microphone recordings or Ambisonics signals, while excluding those based on room impulse responses. Guided by the Spatial Audio Quality Inventory (SAQI), the review emphasizes perceptual dimensions related to source localization and room response, while excluding general spectral-temporal attributes. The literature survey reveals a strong focus on localization cues, such as interaural time and level differences (ITDs, ILDs), while reverberation and other room acoustic attributes remain less explored in loss function design. Recent works that estimate room acoustic parameters and develop embeddings that capture room characteristics indicate their potential for future integration into neural network training. The paper concludes by highlighting future research directions toward more perceptually grounded loss functions that better capture the listener's spatial experience.

In an era of AI-generated misinformation flooding the web, existing tools struggle to empower users with nuanced, transparent assessments of content credibility. They often default to binary (true/false) classifications without contextual justifications, leaving users vulnerable to disinformation. We address this gap by introducing TRACE: Transparent Reliability Assessment with Contextual Explanations, a unified framework that performs two key tasks: (1) it assigns a fine-grained, continuous reliability score (from 0.1 to 1.0) to web content, and (2) it generates a contextual explanation for its assessment. The core of TRACE is the TrueGL-1B model, fine-tuned on a novel, large-scale dataset of over 140,000 articles. This dataset's primary contribution is its annotation with 35 distinct continuous reliability scores, created using a Human-LLM co-creation and data poisoning paradigm. This method overcomes the limitations of binary-labeled datasets by populating the mid-ranges of reliability. In our evaluation, TrueGL-1B consistently outperforms other small-scale LLM baselines and rule-based approaches on key regression metrics, including MAE, RMSE, and R2. The model's high accuracy and interpretable justifications make trustworthy information more accessible. To foster future research, our code and model are made publicly available here: github.com/zade90/TrueGL.

Solving (Stampacchia) variational inequalities (SVIs) is a foundational problem at the heart of optimization. However, this expressivity comes at the cost of computational hardness. As a result, most research has focused on carving out specific subclasses that elude those intractability barriers. A classical property that goes back to the 1960s is the Minty condition, which postulates that the Minty VI (MVI) problem admits a solution. In this paper, we establish the first polynomial-time algorithm -- with complexity growing polynomially in the dimension $d$ and $\log(1/ε)$ -- for solving $ε$-SVIs for Lipschitz continuous mappings under the Minty condition. Prior approaches either incurred an exponentially worse dependence on $1/ε$ (and other natural parameters of the problem) or made more restrictive assumptions, such as monotonicity. To do so, we introduce a new variant of the ellipsoid algorithm whereby separating hyperplanes are obtained after taking a descent step from the center of the ellipsoid. It succeeds even though the set of SVIs can be nonconvex and not fully dimensional. Moreover, when our algorithm is applied to an instance with no MVI solution and fails to identify an SVI solution, it produces a succinct certificate of MVI infeasibility. We also show that deciding whether the Minty condition holds is $\mathsf{coNP}$-complete, thereby establishing that the disjunction of those two problems is polynomial-time solvable even though each problem is individually intractable. We provide several extensions and new applications of our main results. Most notably, we obtain the first polynomial-time algorithms for computing Nash equilibria in multi-player harmonic games. Finally, in two-player general-sum concave games, we give the first polynomial-time algorithm that outputs either a Nash equilibrium or a strict coarse correlated equilibrium.

We conduct an incentivized laboratory experiment to study people's perception of generative artificial intelligence (GenAI) alignment in the context of economic decision-making. Using a panel of economic problems spanning the domains of risk, time preference, social preference, and strategic interactions, we ask human subjects to make choices for themselves and to predict the choices made by GenAI on behalf of a human user. We find that people overestimate the degree of alignment between GenAI and human choices. In every problem, human subjects' average prediction about GenAI's choice is substantially closer to the average human-subject choice than it is to the GenAI choice. At the individual level, different subjects' predictions about GenAI's choice in a given problem are highly correlated with their own choices in the same problem. We explore the implications of people overestimating GenAI alignment in a simple theoretical model.

Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures that best approximates the target distribution. While much existing work relies on the Wasserstein distance to quantify approximation errors, maximum mean discrepancy (MMD) has received comparatively less attention, especially when allowing for variable particle weights. We argue that a Wasserstein-Fisher-Rao gradient flow is well-suited for designing quantizations optimal under MMD. We show that a system of interacting particles satisfying a set of ODEs discretizes this flow. We further derive a new fixed-point algorithm called mean shift interacting particles (MSIP). We show that MSIP extends the classical mean shift algorithm, widely used for identifying modes in kernel density estimators. Moreover, we show that MSIP can be interpreted as preconditioned gradient descent and that it acts as a relaxation of Lloyd's algorithm for clustering. Our unification of gradient flows, mean shift, and MMD-optimal quantization yields algorithms that are more robust than state-of-the-art methods, as demonstrated via high-dimensional and multi-modal numerical experiments.

We introduce a new method for estimating the Ideal Time-Frequency Representation (ITFR) of complex nonstationary signals. The Reconstructive Ideal Fractional Transform (RIFT) computes a constellation of Continuous Fractional Wavelet Transforms (CFWTs) aligned to different local time-frequency curvatures. This constellation is combined into a single optimised time-frequency energy representation via a localised entropy-based sparsity measure, designed to resolve auto-terms and attenuate cross-terms. Finally, a positivity-constrained Lucy-Richardson deconvolution with total-variation regularisation is applied to estimate the ITFR, achieving auto-term resolution comparable to that of the Wigner-Ville Distribution (WVD), yielding the high-resolution RIFT representation. The required Cohen's class convolutional kernels are fully derived in the paper for the chosen CFWT constellations. Additionally, the optimisation yields an Instantaneous Phase Direction (IPD) field, which allows the localised curvature in speech or music extracts to be visualised and utilised within a Kalman tracking scheme, enabling the extraction of signal component trajectories and the construction of the Spline-RIFT variant. Evaluation on synthetic and real-world signals demonstrates the algorithm's ability to effectively suppress cross-terms and achieve superior time-frequency precision relative to competing methods. This advance holds significant potential for a wide range of applications requiring high-resolution cross-term-free time-frequency analysis.

Deep learning-based image denoising techniques often struggle with poor generalization performance to out-of-distribution real-world noise. To tackle this challenge, we propose a novel noise translation framework that performs denoising on an image with translated noise rather than directly denoising an original noisy image. Specifically, our approach translates complex, unknown real-world noise into Gaussian noise, which is spatially uncorrelated and independent of image content, through a noise translation network. The translated noisy images are then processed by an image denoising network pretrained to effectively remove Gaussian noise, enabling robust and consistent denoising performance. We also design well-motivated loss functions and architectures for the noise translation network by leveraging the mathematical properties of Gaussian noise. Experimental results demonstrate that the proposed method substantially improves robustness and generalizability, outperforming state-of-the-art methods across diverse benchmarks. Visualized denoising results and the source code are available on our project page.