We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, covariances collapse, and the learned representation becomes almost non-discriminative. Conversely, cross-entropy training yields excellent accuracy but decouples the head from the underlying generative model, leading to highly inconsistent parameter estimates. To reconcile generative structure with discriminative performance, we introduce the \emph{Discriminative Negative Log-Likelihood} (DNLL) loss, which augments the LDA log-likelihood with a simple penalty on the mixture density. DNLL can be interpreted as standard LDA NLL plus a term that explicitly discourages regions where several classes are simultaneously likely. Deep LDA trained with DNLL produces clean, well-separated latent spaces, matches the test accuracy of softmax classifiers on synthetic data and standard image benchmarks, and yields substantially better calibrated predictive probabilities, restoring a coherent probabilistic interpretation to deep discriminant models.

Earth's gravity has fundamentally shaped human development by guiding the brain's integration of vestibular, visual, and proprioceptive inputs into an internal model of gravity: a dynamic neural representation enabling prediction and interpretation of gravitational forces. This work presents a dual computational framework to quantitatively model these adaptations. The first component is a lightweight Multi-Layer Perceptron (MLP) that predicts g-load-dependent changes in key electroencephalographic (EEG) frequency bands, representing the brain's cortical state. The second component utilizes a suite of independent Gaussian Processes (GPs) to model the body's broader physiological state, including Heart Rate Variability (HRV), Electrodermal Activity (EDA), and motor behavior. Both models were trained on data derived from a comprehensive review of parabolic flight literature, using published findings as anchor points to construct robust, continuous functions. To complement this quantitative analysis, we simulated subjective human experience under different gravitational loads, ranging from microgravity (0g) and partial gravity (Moon 0.17g, Mars 0.38g) to hypergravity associated with spacecraft launch and re-entry (1.8g), using a large language model (Claude 3.5 Sonnet). The model was prompted with physiological parameters to generate introspective narratives of alertness and self-awareness, which closely aligned with the quantitative findings from both the EEG and physiological models. This combined framework integrates quantitative physiological modeling with generative cognitive simulation, offering a novel approach to understanding and predicting human performance in altered gravity

This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a two-component Gaussian mixture model within each class to fit data generated from a single Gaussian, analyzing both the algorithmic convergence of the Expectation-Maximization (EM) algorithm and the statistical classification error. We demonstrate that, with suitable initialization, the EM algorithm converges exponentially fast to the Bayes risk at the population level. Further, we extend our results to finite samples, showing that the classification error converges to Bayes risk with a rate $n^{-1/2}$ under mild conditions on the initial parameter estimates and sample size. This work provides a rigorous theoretical framework for understanding the performance of overspecified MDA, which is often used empirically in complex data settings, such as image and text classification. To validate our theory, we conduct experiments on remote sensing datasets.

Urban embodied AI agents, ranging from delivery robots to quadrupeds, are increasingly populating our cities, navigating chaotic streets to provide last-mile connectivity. Training such agents requires diverse, high-fidelity urban environments to scale, yet existing human-crafted or procedurally generated simulation scenes either lack scalability or fail to capture real-world complexity. We introduce UrbanVerse, a data-driven real-to-sim system that converts crowd-sourced city-tour videos into physics-aware, interactive simulation scenes. UrbanVerse consists of: (i) UrbanVerse-100K, a repository of 100k+ annotated urban 3D assets with semantic and physical attributes, and (ii) UrbanVerse-Gen, an automatic pipeline that extracts scene layouts from video and instantiates metric-scale 3D simulations using retrieved assets. Running in IsaacSim, UrbanVerse offers 160 high-quality constructed scenes from 24 countries, along with a curated benchmark of 10 artist-designed test scenes. Experiments show that UrbanVerse scenes preserve real-world semantics and layouts, achieving human-evaluated realism comparable to manually crafted scenes. In urban navigation, policies trained in UrbanVerse exhibit scaling power laws and strong generalization, improving success by +6.3% in simulation and +30.1% in zero-shot sim-to-real transfer comparing to prior methods, accomplishing a 300 m real-world mission with only two interventions.

Despite growing research on bias in large language models (LLMs), most work has focused on gender and race, with little attention to religious identity. This paper explores how religion is internally represented in LLMs and how it intersects with concepts of violence and geography. Using mechanistic interpretability and Sparse Autoencoders (SAEs) via the Neuronpedia API, we analyze latent feature activations across five models. We measure overlap between religion- and violence-related prompts and probe semantic patterns in activation contexts. While all five religions show comparable internal cohesion, Islam is more frequently linked to features associated with violent language. In contrast, geographic associations largely reflect real-world religious demographics, revealing how models embed both factual distributions and cultural stereotypes. These findings highlight the value of structural analysis in auditing not just outputs but also internal representations that shape model behavior.

In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme is proposed where the solution is iteratively updated following the updating of the physics-driven neural network (PDNN), the hyperparameters of which are optimized by minimizing the loss function which incorporates the constraints from the collected scattered fields and the prior information about scatterers. Unlike data-driven neural network solvers, PDNN is trained only requiring the input of collected scattered fields and the computation of scattered fields corresponding to predicted solutions, thus avoids the generalization problem. Moreover, to accelerate the imaging efficiency, the subregion enclosing the scatterers is identified. Numerical and experimental results demonstrate that the proposed scheme has high reconstruction accuracy and strong stability, even when dealing with composite lossy scatterers.

Colors are omnipresent in today's world and play a vital role in how humans perceive and interact with their surroundings. However, it is challenging for computers to imitate human color perception. This paper introduces the Human Perception-Based Fuzzy Color Model, COLIBRI (Color Linguistic-Based Representation and Interpretation), designed to bridge the gap between computational color representations and human visual perception. The proposed model uses fuzzy sets and logic to create a framework for color categorization. Using a three-phase experimental approach, the study first identifies distinguishable color stimuli for hue, saturation, and intensity through preliminary experiments, followed by a large-scale human categorization survey involving more than 1000 human subjects. The resulting data are used to extract fuzzy partitions and generate membership functions that reflect real-world perceptual uncertainty. The model incorporates a mechanism for adaptation that allows refinement based on feedback and contextual changes. Comparative evaluations demonstrate the model's alignment with human perception compared to traditional color models, such as RGB, HSV, and LAB. To the best of our knowledge, no previous research has documented the construction of a model for color attribute specification based on a sample of this size or a comparable sample of the human population (n = 2496). Our findings are significant for fields such as design, artificial intelligence, marketing, and human-computer interaction, where perceptually relevant color representation is critical.

We propose a computationally efficient method for real-time three-dimensional football trajectory reconstruction from a single broadcast camera. In contrast to previous work, our approach introduces a multi-mode state model with $W$ discrete modes to significantly accelerate optimization while preserving centimeter-level accuracy -- even in cases of severe occlusion, motion blur, and complex backgrounds. The system operates on standard CPUs and achieves low latency suitable for live broadcast settings. Extensive evaluation on a proprietary dataset of 6K-resolution Russian Premier League matches demonstrates performance comparable to multi-camera systems, without the need for specialized or costly infrastructure. This work provides a practical method for accessible and accurate 3D ball tracking in professional football environments.

Large language models (LLMs) often struggle to perform multi-target reasoning in long-context scenarios where relevant information is scattered across extensive documents. To address this challenge, we introduce NeuroSymbolic Augmented Reasoning (NSAR), which combines the benefits of neural and symbolic reasoning during inference. NSAR explicitly extracts symbolic facts from text and generates executable Python code to handle complex reasoning steps. Through extensive experiments across seven languages and diverse context lengths, we demonstrate that NSAR significantly outperforms both a vanilla RAG baseline and advanced prompting strategies in accurately identifying and synthesizing multiple pieces of information. Our results highlight the effectiveness of combining explicit symbolic operations with neural inference for robust, interpretable, and scalable reasoning in multilingual settings.

Table reasoning, encompassing tasks such as table question answering, fact verification, and text-to-SQL, requires precise understanding of structured tabular data, coupled with numerical computation and code manipulation for effective inference. Supervised fine-tuning (SFT) approaches have achieved notable success but often struggle with generalization and robustness due to biases inherent in imitative learning. We introduce Reasoning-Table, the first application of reinforcement learning (RL) to table reasoning, achieving state-of-the-art performance. Through rigorous data preprocessing, reward design, and tailored training strategies, our method leverages simple rule-based outcome rewards to outperform SFT across multiple benchmarks. Unified training across diverse tasks enables Reasoning-Table to emerge as a robust table reasoning large language model, surpassing larger proprietary models like Claude-3.7-Sonnet by 4.0% on table reasoning benchmarks. The approach also achieves excellent performance on text-to-SQL tasks, reaching 68.3% performance on the BIRD dev dataset with a 7B model. Further experiments demonstrate that Reasoning-Table enhances the model's generalization capabilities and robustness.