We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

--In this work, we describe a multi-object grasping benchmark to evaluate the grasping and manipulation capabilities of robotic systems in both pile and surface scenarios. The benchmark introduces three robot multi-object grasping benchmarking protocols designed to challenge different aspects of robotic manipulation. These protocols are: 1) the Only-Pick-Once protocol, which assesses the robot's ability to efficiently pick multiple objects in a single attempt; 2) the Accurate pick-trnsferring protocol, which evaluates the robot's capacity to selectively grasp and transport a specific number of objects from a cluttered environment; and 3) the Pick-transferring-all protocol, which challenges the robot to clear an entire scene by sequentially grasping and transferring all available objects. These protocols are intended to be adopted by the broader robotics research community, providing a standardized method to assess and compare robotic systems' performance in multi-object grasping tasks. We establish baselines for these protocols using standard planning and perception algorithms on a Barrett hand, Robotiq parallel jar gripper, and the Pisa/IIT Softhand-2, which is a soft underactuated robotic hand. We discuss the results in relation to human performance in similar tasks we well. The authors are from the Robot Perception and Action Lab (RP AL) of Computer Science and Engineering Department, University of South Florida, Tampa, FL 33620, USA. The authors are with the Research Center "E. The author is with is with Rutgers University, New Brunswick, NJ 08901, USA. Related work was finished when Zihe Y e was a Master's student in the RP AL lab at USF. The author is with the Department of Excellence in Robotics & AI, Mechanical Intelligence Institute, Scuola Superiore Sant'Anna, Pisa, Italy.

Deepfake detection remains a critical challenge in the era of advanced generative models, particularly as synthetic media becomes more sophisticated. In this study, we explore the potential of state of the art multi-modal (reasoning) large language models (LLMs) for deepfake image detection such as (OpenAI O1/4o, Gemini thinking Flash 2, Deepseek Janus, Grok 3, llama 3.2, Qwen 2/2.5 VL, Mistral Pixtral, Claude 3.5/3.7 sonnet) . We benchmark 12 latest multi-modal LLMs against traditional deepfake detection methods across multiple datasets, including recently published real-world deepfake imagery. To enhance performance, we employ prompt tuning and conduct an in-depth analysis of the models' reasoning pathways to identify key contributing factors in their decision-making process. Our findings indicate that best multi-modal LLMs achieve competitive performance with promising generalization ability with zero shot, even surpass traditional deepfake detection pipelines in out-of-distribution datasets while the rest of the LLM families performs extremely disappointing with some worse than random guess. Furthermore, we found newer model version and reasoning capabilities does not contribute to performance in such niche tasks of deepfake detection while model size do help in some cases. This study highlights the potential of integrating multi-modal reasoning in future deepfake detection frameworks and provides insights into model interpretability for robustness in real-world scenarios.

--This paper presents a comprehensive comparative analysis of prominent clustering algorithms--K-means, DB-SCAN, and Spectral Clustering--on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering performance across multiple dimensionality reduction techniques (PCA, t-SNE, and UMAP) using diverse quantitative metrics. Experiments conducted on MNIST, Fashion-MNIST, and UCI HAR datasets reveal that preprocessing with UMAP consistently improves clustering quality across all algorithms, with Spectral Clustering demonstrating superior performance on complex manifold structures. Our findings show that algorithm selection should be guided by data characteristics, with K-means excelling in computational efficiency, DBSCAN in handling irregular clusters, and Spectral Clustering in capturing complex relationships. This research contributes a systematic approach for evaluating and selecting clustering techniques for high-dimensional data applications.

SHAP is one of the most popular local feature-attribution methods. Given a function f and an input x, it quantifies each feature's contribution to f(x). Recently, SHAP has been increasingly used for global insights: practitioners average the absolute SHAP values over many data points to compute global feature importance scores, which are then used to discard unimportant features. In this work, we investigate the soundness of this practice by asking whether small aggregate SHAP values necessarily imply that the corresponding feature does not affect the function. Unfortunately, the answer is no: even if the i-th SHAP value is 0 on the entire data support, there exist functions that clearly depend on Feature i. The issue is that computing SHAP values involves evaluating f on points outside of the data support, where f can be strategically designed to mask its dependence on Feature i. To address this, we propose to aggregate SHAP values over the extended support, which is the product of the marginals of the underlying distribution. With this modification, we show that a small aggregate SHAP value implies that we can safely discard the corresponding feature. We then extend our results to KernelSHAP, the most popular method to approximate SHAP values in practice. We show that if KernelSHAP is computed over the extended distribution, a small aggregate value justifies feature removal. This result holds independently of whether KernelSHAP accurately approximates true SHAP values, making it one of the first theoretical results to characterize the KernelSHAP algorithm itself. Our findings have both theoretical and practical implications. We introduce the Shapley Lie algebra, which offers algebraic insights that may enable a deeper investigation of SHAP and we show that randomly permuting each column of the data matrix enables safely discarding features based on aggregate SHAP and KernelSHAP values.

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of `asymptotic dependence' and `asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.

Link prediction also has significant implications from a fundamental point of view, as it allows for the identification of the elementary mechanisms behind the creation and decay of links in time-evolving networks (Leskovec et al., 2008). For example, triadic closure, at the core of standard methods of link prediction is considered as one of the driving forces for the creation of links in social networks (Kossinets and Watts, 2006). In general, link prediction consists in inferring the existence of a set of links from the observed structure of a network. The edges predicted may correspond to links that are bound to appear in the future, as in the seminal formulation by Liben-Nowell and Kleinberg (2007). They may also be existing links that have not been detected during the data collection process, in which case it is sometimes referred to as the missing link problem. In both cases, it can be described as a binary classification issue, where it is decided if a pair of nodes is connected or not. The features used are often based on the structural properties of the network of known interactions, either at a local scale (e.g. the number of common neighbors) or at a global scale (e.g.

Current approaches to sales conversation analysis and conversion prediction typically rely on Large Language Models (LLMs) combined with basic retrieval augmented generation (RAG). These systems, while capable of answering questions, fail to accurately predict conversion probability or provide strategic guidance in real time. In this paper, we present SalesRLAgent, a novel framework leveraging specialized reinforcement learning to predict conversion probability throughout sales conversations. Unlike systems from Kapa.ai, Mendable, Inkeep, and others that primarily use off-the-shelf LLMs for content generation, our approach treats conversion prediction as a sequential decision problem, training on synthetic data generated using GPT-4O to develop a specialized probability estimation model. Our system incorporates Azure OpenAI embeddings (3072 dimensions), turn-by-turn state tracking, and meta-learning capabilities to understand its own knowledge boundaries. Evaluations demonstrate that SalesRLAgent achieves 96.7% accuracy in conversion prediction, outperforming LLM-only approaches by 34.7% while offering significantly faster inference (85ms vs 3450ms for GPT-4). Furthermore, integration with existing sales platforms shows a 43.2% increase in conversion rates when representatives utilize our system's real-time guidance. SalesRLAgent represents a fundamental shift from content generation to strategic sales intelligence, providing moment-by-moment conversion probability estimation with actionable insights for sales professionals.

As large language models (LLMs) tackle increasingly complex tasks and longer documents, their computational and memory costs during inference become a major bottleneck. To address this, we propose PromptDistill, a novel, training-free method that improves inference efficiency while preserving generation quality. PromptDistill identifies and retains the most informative tokens by leveraging attention interactions in early layers, preserving their hidden states while reducing the computational burden in later layers. This allows the model to focus on essential contextual information without fully processing all tokens. Unlike previous methods such as H2O and SnapKV, which perform compression only after processing the entire input, or GemFilter, which selects a fixed portion of the initial prompt without considering contextual dependencies, PromptDistill dynamically allocates computational resources to the most relevant tokens while maintaining a global awareness of the input. Experiments using our method and baseline approaches with base models such as LLaMA 3.1 8B Instruct, Phi 3.5 Mini Instruct, and Qwen2 7B Instruct on benchmarks including LongBench, InfBench, and Needle in a Haystack demonstrate that PromptDistill significantly improves efficiency while having minimal impact on output quality compared to the original models. With a single-stage selection strategy, PromptDistill effectively balances performance and efficiency, outperforming prior methods like GemFilter, H2O, and SnapKV due to its superior ability to retain essential information. Specifically, compared to GemFilter, PromptDistill achieves an overall $1\%$ to $5\%$ performance improvement while also offering better time efficiency. Additionally, we explore multi-stage selection, which further improves efficiency while maintaining strong generation performance.

--In this paper, we study the underwater acoustic localization in the presence of environmental mismatch. Especially, we exploit a pre-trained neural network for the acoustic wave propagation in a gradient-based optimization framework to estimate the source location. T o alleviate the effect of mismatch between the training data and the test data, we simultaneously optimize over the network weights at the inference time, and provide conditions under which this method is effective. Moreover, we introduce a physics-inspired modularity in the forward model that enables us to learn the path lengths of the multipath structure in an end-to-end training manner without access to the specific path labels. We investigate the validity of the assumptions in a simple yet illustrative environment model.