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arXiv:2310.12882v2 Announce Type: replace-cross Abstract: Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

arXiv:2509.06120v1 Announce Type: cross Abstract: Beginning with text and images, generative AI has expanded to audio, video, computer code, and molecules. Yet, if generative AI is the answer, what is the question? We explore the foundations of generation as a distinct machine learning task with connections to prediction, compression, and decision-making. We survey five major generative model families: autoregressive models, variational autoencoders, normalizing flows, generative adversarial networks, and diffusion models. We then introduce a probabilistic framework that emphasizes the distinction between density estimation and generation. We review a game-theoretic framework with a two-player adversary-learner setup to study generation. We discuss post-training modifications that prepare generative models for deployment. We end by highlighting some important topics in socially responsible generation such as privacy, detection of AI-generated content, and copyright and IP. We adopt a task-first framing of generation, focusing on what generation is as a machine learning problem, rather than only on how models implement it.

arXiv:2509.06154v1 Announce Type: cross Abstract: Neural operators (NOs) approximate mappings between infinite-dimensional function spaces but require large datasets and struggle with scarce training data. Many NO formulations don't explicitly encode causal, local-in-time structure of physical evolution. While autoregressive models preserve causality by predicting next time-steps, they suffer from rapid error accumulation. We employ Graph Neural Simulators (GNS) - a message-passing graph neural network framework - with explicit numerical time-stepping schemes to construct accurate forward models that learn PDE solutions by modeling instantaneous time derivatives. We evaluate our framework on three canonical PDE systems: (1) 2D Burgers' scalar equation, (2) 2D coupled Burgers' vector equation, and (3) 2D Allen-Cahn equation. Rigorous evaluations demonstrate GNS significantly improves data efficiency, achieving higher generalization accuracy with substantially fewer training trajectories compared to neural operator baselines like DeepONet and FNO. GNS consistently achieves under 1% relative L2 errors with only 30 training samples out of 1000 (3% of available data) across all three PDE systems. It substantially reduces error accumulation over extended temporal horizons: averaged across all cases, GNS reduces autoregressive error by 82.48% relative to FNO AR and 99.86% relative to DON AR. We introduce a PCA+KMeans trajectory selection strategy enhancing low-data performance. Results indicate combining graph-based local inductive biases with conventional time integrators yields accurate, physically consistent, and scalable surrogate models for time-dependent PDEs.

arXiv:2405.18081v2 Announce Type: replace-cross Abstract: We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm. We exploit our result on the dynamics of these algorithms to derive the optimal choices for the matrix and iterate denoisers. We show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.

arXiv:2509.05757v1 Announce Type: new Abstract: Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

arXiv:2509.06690v1 Announce Type: cross Abstract: Bioprinting is a rapidly advancing field that offers a transformative approach to fabricating tissue and organ models through the precise deposition of cell-laden bioinks. Ensuring the fidelity and consistency of printed structures in real-time remains a core challenge, particularly under constraints imposed by limited imaging data and resource-constrained embedded hardware. Semantic segmentation of the extrusion process, differentiating between nozzle, extruded bioink, and surrounding background, enables in situ monitoring critical to maintaining print quality and biological viability. In this work, we introduce a lightweight semantic segmentation framework tailored for real-time bioprinting applications. We present a novel, manually annotated dataset comprising 787 RGB images captured during the bioprinting process, labeled across three classes: nozzle, bioink, and background. To achieve fast and efficient inference suitable for integration with bioprinting systems, we propose a BioLite U-Net architecture that leverages depthwise separable convolutions to drastically reduce computational load without compromising accuracy. Our model is benchmarked against MobileNetV2 and MobileNetV3-based segmentation baselines using mean Intersection over Union (mIoU), Dice score, and pixel accuracy. All models were evaluated on a Raspberry Pi 4B to assess real-world feasibility. The proposed BioLite U-Net achieves an mIoU of 92.85% and a Dice score of 96.17%, while being over 1300x smaller than MobileNetV2-DeepLabV3+. On-device inference takes 335 ms per frame, demonstrating near real-time capability. Compared to MobileNet baselines, BioLite U-Net offers a superior tradeoff between segmentation accuracy, efficiency, and deployability, making it highly suitable for intelligent, closed-loop bioprinting systems.

arXiv:2509.05764v1 Announce Type: new Abstract: With the evolution of generative AI, multi - agent systems leveraging large - language models(LLMs) have emerged as a powerful tool for complex tasks. However, these systems face challenges in quantifying agent performance and lack mechanisms to assess agent credibility. To address these issues, we introduce DRF, a dynamic reputation filtering framework. DRF constructs an interactive rating network to quantify agent performance, designs a reputation scoring mechanism to measure agent honesty and capability, and integrates an Upper Confidence Bound - based strategy to enhance agent selection efficiency. Experiments show that DRF significantly improves task completion quality and collaboration efficiency in logical reasoning and code - generation tasks, offering a new approach for multi - agent systems to handle large - scale tasks.

arXiv:2509.06918v1 Announce Type: cross Abstract: Robust out-of-distribution (OOD) detection is an indispensable component of modern artificial intelligence (AI) systems, especially in safety-critical applications where models must identify inputs from unfamiliar classes not seen during training. While OOD detection has been extensively studied in the machine learning literature--with both post hoc and training-based approaches--its effectiveness under noisy training labels remains underexplored. Recent studies suggest that label noise can significantly degrade OOD performance, yet principled solutions to this issue are lacking. In this work, we demonstrate that directly combining existing label noise-robust methods with OOD detection strategies is insufficient to address this critical challenge. To overcome this, we propose a robust OOD detection framework that integrates loss correction techniques from the noisy label learning literature with low-rank and sparse decomposition methods from signal processing. Extensive experiments on both synthetic and real-world datasets demonstrate that our method significantly outperforms the state-of-the-art OOD detection techniques, particularly under severe noisy label settings.

arXiv:2509.05772v1 Announce Type: new Abstract: Decision-making under uncertainty in energy management is complicated by unknown parameters hindering optimal strategies, particularly in Battery Energy Storage System (BESS) operations. Predict-Then-Optimise (PTO) approaches treat forecasting and optimisation as separate processes, allowing prediction errors to cascade into suboptimal decisions as models minimise forecasting errors rather than optimising downstream tasks. The emerging Decision-Focused Learning (DFL) methods overcome this limitation by integrating prediction and optimisation; however, they are relatively new and have been tested primarily on synthetic datasets or small-scale problems, with limited evidence of their practical viability. Real-world BESS applications present additional challenges, including greater variability and data scarcity due to collection constraints and operational limitations. Because of these challenges, this work leverages Automated Feature Engineering (AFE) to extract richer representations and improve the nascent approach of DFL. We propose an AFE-DFL framework suitable for small datasets that forecasts electricity prices and demand while optimising BESS operations to minimise costs. We validate its effectiveness on a novel real-world UK property dataset. The evaluation compares DFL methods against PTO, with and without AFE. The results show that, on average, DFL yields lower operating costs than PTO and adding AFE further improves the performance of DFL methods by 22.9-56.5% compared to the same models without AFE. These findings provide empirical evidence for DFL's practical viability in real-world settings, indicating that domain-specific AFE enhances DFL and reduces reliance on domain expertise for BESS optimisation, yielding economic benefits with broader implications for energy management systems facing similar challenges.

arXiv:2504.13146v4 Announce Type: replace Abstract: Frontier models that generate extended reasoning traces inadvertently produce rich token sequences that can facilitate model distillation. Recognizing this vulnerability, model owners may seek sampling strategies that limit the effectiveness of distillation without compromising model performance. Antidistillation sampling provides exactly this capability. By strategically modifying a model's next-token probability distribution, antidistillation sampling poisons reasoning traces, rendering them significantly less effective for distillation while preserving the model's practical utility. For further details, see https://antidistillation.com.