We focus on the task of learning a single index model \sigma(w \star \cdot x) with respect to the isotropic Gaussian distribution in d dimensions. Prior work has shown that the sample complexity of learning w \star is governed by the information exponent k \star of the link function \sigma, which is defined as the index of the first nonzero Hermite coefficient of \sigma . Ben Arous et al. (2021) showed that n \gtrsim d {k \star-1} samples suffice for learning w \star and that this is tight for online SGD. However, the CSQ lower bound for gradient based methods only shows that n \gtrsim d {k \star/2} samples are necessary. In this work, we close the gap between the upper and lower bounds by showing that online SGD on a smoothed loss learns w \star with n \gtrsim d {k \star/2} samples.

Large language models (LLMs) have shown emerging potential in spatiotemporal reasoning, making them promising candidates for building urban agents that support diverse urban downstream applications. Despite these benefits, existing studies primarily focus on evaluating urban LLM agent on outcome-level metrics (e.g., prediction accuracy, traffic efficiency), offering limited insight into their underlying reasoning processes. As a result, the strengths and limitations of urban LLM agents in spatiotemporal reasoning remain poorly understood. To this end, we introduce USTBench, the first benchmark to evaluate LLMs' spatiotemporal reasoning abilities as urban agents across four decomposed dimensions: spatiotemporal understanding, forecasting, planning, and reflection with feedback. Specifically, USTBench supports five diverse urban decision-making and four spatiotemporal prediction tasks, all running within our constructed interactive city environment UAgentEnv. The benchmark includes 62,466 structured QA pairs for process-level evaluation and standardized end-to-end task assessments, enabling fine-grained diagnostics and broad task-level comparison across diverse urban scenarios. Through extensive evaluation of thirteen leading LLMs, we reveal that although LLMs show promising potential across various urban downstream tasks, they still struggle in long-horizon planning and reflective adaptation in dynamic urban contexts. Notably, recent advanced reasoning models (e.g., DeepSeek-R1) trained on general logic or mathematical problems do not consistently outperform non-reasoning LLMs. This discrepancy highlights the need for domain-specialized adaptation methods to enhance urban spatiotemporal reasoning. Overall, USTBench provides a foundation to build more adaptive and effective LLM-based urban agents and broad smart city applications.

Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we propose Discrete Neural Flow Samplers (DNFS), a trainable and efficient framework for discrete sampling. DNFS learns the rate matrix of a continuous-time Markov chain such that the resulting dynamics satisfy the Kolmogorov equation. As this objective involves the intractable partition function, we then employ control variates to reduce the variance of its Monte Carlo estimation, leading to a coordinate descent learning algorithm. To further facilitate computational efficiency, we propose locally equivaraint Transformer, a novel parameterisation of the rate matrix that significantly improves training efficiency while preserving powerful network expressiveness. Empirically, we demonstrate the efficacy of DNFS in a wide range of applications, including sampling from unnormalised distributions, training discrete energy-based models, and solving combinatorial optimisation problems.

The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well understood in cases that essentially reduce to singular value decomposition of the data. Here, we consider the limit of a large dimension of the input space and a constant number of hidden units. In this limit, we simplify the standard RBM training objective into a form that is equivalent to the multi-index model with non-separable regularization. This opens a path to analyze training of the RBM using methods that are established for multi-index models, such as Approximate Message Passing (AMP) and its state evolution, and the analysis of Gradient Descent (GD) via the dynamical mean-field theory. We then give rigorous asymptotics of the training dynamics of RBM on data generated by the spiked covariance model as a prototype of a structure suitable for unsupervised learning. We show in particular that RBM reaches the optimal computational weak recovery threshold, aligning with the BBP transition, in the spiked covariance model.

We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test errors by mapping the $\ell_2$-regularized learning problem to a convex matrix sensing task with nuclear norm penalization. This reveals that capacity control in such networks emerges from a low-rank structure in the learned feature maps. Our results characterize the global minima of the loss and yield precise generalization thresholds, showing how the width of the target function governs learnability. This analysis bridges and extends ideas from spin-glass methods, matrix factorization, and convex optimization and emphasizes the deep link between low-rank matrix sensing and learning in quadratic neural networks.

Temporal Knowledge Graphs (TKGs) represent dynamic facts as timestamped relations between entities. TKG completion involves forecasting missing or future links, requiring models to reason over time-evolving structure. While LLMs show promise for this task, existing approaches often overemphasize supervised fine-tuning and struggle particularly when historical evidence is limited or missing. We introduce RECIPE-TKG, a lightweight and data-efficient framework designed to improve accuracy and generalization in settings with sparse historical context. It combines (1) rule-based multi-hop retrieval for structurally diverse history, (2) contrastive fine-tuning of lightweight adapters to encode relational semantics, and (3) test-time semantic filtering to iteratively refine generations based on embedding similarity. Experiments on four TKG benchmarks show that RECIPE-TKG outperforms previous LLM-based approaches, achieving up to 30.6\% relative improvement in Hits@10. Moreover, our proposed framework produces more semantically coherent predictions, even for the samples with limited historical context.

Evaluating the performance of a lecturer has been essential for enhancing teaching quality, improving student learning outcomes, and strengthening the institution's reputation. The absence of such a system brings about lecturer performance evaluation which was neither comprehensive nor holistic. This system was designed using a web-based platform, created a secure database, and by using a custom dataset, captured some performance metrics which included student evaluation scores, Research Publications, Years of Experience, and Administrative Duties. Multilayer Perceptron (MLP) algorithm was utilized due to its ability to process complex data patterns and generates accurate predictions in a lecturer's performance based on historical data. This research focused on designing multiple performance metrics beyond the standard ones, incorporating student participation, and integrating analytical tools to deliver a comprehensive and holistic evaluation of lecturers' performance and was developed using Object-Oriented Analysis and Design (OOAD) methodology. Lecturers' performance is evaluated by the model, and the evaluation accuracy is about 91% compared with actual performance. Finally, by evaluating the performance of the MLP model, it is concluded that MLP enhanced lecturer performance evaluation by providing accurate predictions, reducing bias, and supporting data-driven decisions, ultimately improving the fairness and efficiency of the evaluation process. The MLP model's performance was evaluated using Mean Squared Error (MSE) and Mean Absolute Error (MAE), achieved a test loss (MSE) of 256.99 and a MAE of 13.76, and reflected a high level of prediction accuracy. The model also demonstrated an estimated accuracy rate of approximately 96%, validated its effectiveness in predicting lecturer performance.

Open-source large language models (LLMs) still marginalise Moroccan Arabic (Darija), forcing practitioners either to bolt on heavyweight Arabic adapters or to sacrifice the very reasoning skills that make LLMs useful. We show that a rigorously quality-over-quantity alignment strategy can surface fluent Darija while safeguarding the backbone s cross-lingual reasoning at a sliver of the usual compute. We translate three compact instruction suites LIMA 1 K, DEITA 6 K and TULU 50 K into Darija, preserve 20 of the English originals, and add mathematics, coding and scientific prompts. A LoRA-tuned Gemma 3-4B trained on 5 K mixed instructions lifts DarijaMMLU from 32.8 to 42.7 ; adding the reasoning-dense TULU portion pushes it to 47.5 with no English regression. Scaling the identical recipe to Gemma 3-27B produces GemMaroc-27B, which matches Atlas-Chat on DarijaMMLU (61.6 ) and leaps ahead on Darija commonsense, scoring 60.5 on HellaSwag versus Atlas-Chat s 48.4 . Crucially, GemMaroc retains Gemma-27B s strong maths and general-reasoning ability, showing only minimal movement on GSM8K and English benchmarks. The entire model is trained in just 48 GPU.h, underscoring a Green AI pathway to inclusive, sustainable language technology. We release code, data and checkpoints to spur Darija-centric applications in education, public services and everyday digital interaction.

Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by grounding responses with retrieved information. As an emerging paradigm, Agentic RAG further enhances this process by introducing autonomous LLM agents into the information seeking process. However, existing benchmarks fall short in evaluating such systems, as they are confined to a static retrieval environment with a fixed, limited corpus} and simple queries that fail to elicit agentic behavior. Moreover, their evaluation protocols assess information seeking effectiveness by pre-defined gold sets of documents, making them unsuitable for the open-ended and dynamic nature of real-world web environments. To bridge this gap, we present InfoDeepSeek, a new benchmark with challenging questions designed for assessing agentic information seeking in real-world, dynamic web environments. We propose a systematic methodology for constructing challenging queries satisfying the criteria of determinacy, difficulty, and diversity. Based on this, we develop the first evaluation framework tailored to dynamic agentic information seeking, including fine-grained metrics about the accuracy, utility, and compactness of information seeking outcomes. Through extensive experiments across LLMs, search engines, and question types, InfoDeepSeek reveals nuanced agent behaviors and offers actionable insights for future research.

Live tracking of wildlife via high-resolution video processing directly onboard drones is widely unexplored and most existing solutions rely on streaming video to ground stations to support navigation. Yet, both autonomous animal-reactive flight control beyond visual line of sight and/or mission-specific individual and behaviour recognition tasks rely to some degree on this capability. In response, we introduce WildLive - a near real-time animal detection and tracking framework for high-resolution imagery running directly onboard uncrewed aerial vehicles (UAVs). The system performs multi-animal detection and tracking at 17.81fps for HD and 7.53fps on 4K video streams suitable for operation during higher altitude flights to minimise animal disturbance. Our system is optimised for Jetson Orin AGX onboard hardware. It integrates the efficiency of sparse optical flow tracking and mission-specific sampling with device-optimised and proven YOLO-driven object detection and segmentation techniques. Essentially, computational resource is focused onto spatio-temporal regions of high uncertainty to significantly improve UAV processing speeds. Alongside, we introduce our WildLive dataset, which comprises 200K+ annotated animal instances across 19K+ frames from 4K UAV videos collected at the Ol Pejeta Conservancy in Kenya. All frames contain ground truth bounding boxes, segmentation masks, as well as individual tracklets and tracking point trajectories. We compare our system against current object tracking approaches including OC-SORT, ByteTrack, and SORT. Our multi-animal tracking experiments with onboard hardware confirm that near real-time high-resolution wildlife tracking is possible on UAVs whilst maintaining high accuracy levels as needed for future navigational and mission-specific animal-centric operational autonomy. Our materials are available at: https://dat-nguyenvn.github.io/WildLive/