Large language models like ChatGPT are increasingly used in classrooms, but they often provide outdated or fabricated information that can mislead students. Retrieval Augmented Generation (RAG) improves reliability of LLMs by grounding responses in external resources. We investigate two accessible RAG paradigms, vector-based retrieval and graph-based retrieval to identify best practices for classroom question answering (QA). Existing comparative studies fail to account for pedagogical factors such as educational disciplines, question types, and practical deployment costs. Using a novel dataset, EduScopeQA, of 3,176 questions across academic subjects, we measure performance on various educational query types, from specific facts to broad thematic discussions. We also evaluate system alignment with a dataset of systematically altered textbooks that contradict the LLM's latent knowledge. We find that OpenAI Vector Search RAG (representing vector-based RAG) performs well as a low-cost generalist, especially for quick fact retrieval. On the other hand, GraphRAG Global excels at providing pedagogically rich answers to thematic queries, and GraphRAG Local achieves the highest accuracy with the dense, altered textbooks when corpus integrity is critical. Accounting for the 10-20x higher resource usage of GraphRAG (representing graph-based RAG), we show that a dynamic branching framework that routes queries to the optimal retrieval method boosts fidelity and efficiency. These insights provide actionable guidelines for educators and system designers to integrate RAG-augmented LLMs into learning environments effectively.

In modern online learning, understanding and predicting student behavior is crucial for enhancing engagement and optimizing educational outcomes. This systematic review explores the integration of biosensors and Multimodal Learning Analytics (MmLA) to analyze and predict student behavior during computer-based learning sessions. We examine key challenges, including emotion and attention detection, behavioral analysis, experimental design, and demographic considerations in data collection. Our study highlights the growing role of physiological signals, such as heart rate, brain activity, and eye-tracking, combined with traditional interaction data and self-reports to gain deeper insights into cognitive states and engagement levels. We synthesize findings from 54 key studies, analyzing commonly used methodologies such as advanced machine learning algorithms and multimodal data pre-processing techniques. The review identifies current research trends, limitations, and emerging directions in the field, emphasizing the transformative potential of biosensor-driven adaptive learning systems. Our findings suggest that integrating multimodal data can facilitate personalized learning experiences, real-time feedback, and intelligent educational interventions, ultimately advancing toward a more customized and adaptive online learning experience.

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Figure 1: We introduce OmniMap, a general online mapping framework integrating optics, geometry, and semantics. OmniMap incrementally maintains an open-vocabulary instance-level voxel representation and a 3DGS (3D Gaussian Splatting) representation, from which color and geometric meshes are derived. OmniMap supports multi-modal rendering (RGB / depth / normal / instance), and achieves state-of-the-art performance in rendering fidelity, mesh quality, and semantic understanding. This holistic framework enables versatile support for a wide range of downstream applications. Abstract--Robotic systems demand accurate and comprehensive 3D environment perception, requiring simultaneous capture of photo-realistic appearance (optical), precise layout shape (geometric), and open-vocabulary scene understanding (semantic). Existing methods typically achieve only partial fulfillment of these requirements while exhibiting optical blurring, geometric irregularities, and semantic ambiguities. T o address these challenges, we propose OmniMap. Overall, OmniMap represents the first online mapping framework that simultaneously captures optical, geometric, and semantic scene attributes while maintaining real-time performance and model compactness. This work is supported by the National Natural Science Foundation of China under Grant 92370203, 62473050, 62233002, Beijing Natural Science Foundation Undergraduate Research Program QY24180. Mengyin Fu is with the School of Automation, Beijing Institute of Technology, Beijing 100081, China, and the School of Automation, Nanjing University of Science and Technology, Nanjing 210018, China (e-mail: fumy@bit.edu.cn). The project page of OmniMap is available at https://omni-map.github.io/. At the implementation level, OmniMap identifies key challenges across different modalities and introduces several innovations: adaptive camera modeling for motion blur and exposure compensation, hybrid incremental representation with normal constraints, and probabilistic fusion for robust instance-level understanding. Extensive experiments show OmniMap's superior performance in rendering fidelity, geometric accuracy, and zero-shot semantic segmentation compared to state-of-the-art methods across diverse scenes. The framework's versatility is further evidenced through a variety of downstream applications, including multi-domain scene Q&A, interactive editing, perception-guided manipulation, and map-assisted navigation. The quality of a robot's 3D environmental representation, measured by its accuracy and dimensionality, fundamentally impacts the robot's task operational performance and execution capabilities.

We introduce a new convolutional AutoEncoder architecture for user modelling and recommendation tasks with several improvements over the state of the art. Firstly, our model has the flexibility to learn a set of associations and combinations between different interaction types in a way that carries over to each user and item. Secondly, our model is able to learn jointly from both the explicit ratings and the implicit information in the sampling pattern (which we refer to as `implicit feedback'). It can also make separate predictions for the probability of consuming content and the likelihood of granting it a high rating if observed. This not only allows the model to make predictions for both the implicit and explicit feedback, but also increases the informativeness of the predictions: in particular, our model can identify items which users would not have been likely to consume naturally, but would be likely to enjoy if exposed to them. Finally, we provide several generalization bounds for our model, which to the best of our knowledge, are among the first generalization bounds for auto-encoders in a Recommender Systems setting; we also show that optimizing our loss function guarantees the recovery of the exact sampling distribution over interactions up to a small error in total variation. In experiments on several real-life datasets, we achieve state-of-the-art performance on both the implicit and explicit feedback prediction tasks despite relying on a single model for both, and benefiting from additional interpretability in the form of individual predictions for the probabilities of each possible rating.

Existing evaluation studies on linguistic competence of large language models (LLM agents) have focused primarily on vocabulary learning, morphological rule induction, syntactic generalization, pragmatic inference, and cross-linguistic transfer. However, none assess whether LLM agents can acquire a language through pattern recognition and interactive feedback, a central feature of human language acquisition. We propose a novel experimental framework in which an LLM agent is evaluated on its ability to acquire and use a newly constructed language (Tinkatongue) in conversation with a bot that understands only Tinkatongue. Our findings show that LLM agents fail to establish a conversation within 100 responses, yet they adopt distinct strategies that mirror human approaches to language learning. The results suggest a new direction for evaluation benchmarks and open pathways to model designs that learn more effectively from interactive feedback.

Recommender systems are widely used across a broad range of applications, with recommendation algorithms serving as their core. Among the myriad of algorithmic paradigms, recommendation models based on deep neural networks (commonly referred to as Neural Collaborative Filtering, or NCF [1]) have garnered significant traction within the industry due to their implementation simplicity and high efficiency in delivering effective results [1-8]. Traditionally, these recommendation algorithms follow the conventional deep learning paradigm, where models are trained on fixed datasets and then applied to unseen data under the assumption of a static data distribution. However, in many real-world applications, such as music streaming [9], news recommendation [10], Point-Of-Interest (POI) recommendation [11], movie recommendation [12], and e-commerce platforms [13], recommender systems operate in dynamic environments where user interaction data stream is continuously generated [14-16], reflecting the evolving nature of users' preferences. This implies that incoming streaming data, which has not been observed during training, may differ significantly from the original training data in terms of distribution. As a result, models previously trained in static environments, when deployed under dynamic conditions for extended periods, often experience a decline in predictive performance [17].

Recent advances in large language models (LLMs) have been driven by pretraining, supervised fine tuning (SFT), and alignment tuning. Among these, SFT plays a crucial role in transforming a model 's general knowledge into structured responses tailored to specific tasks. However, there is no clearly established methodology for effective training data selection. Simply increasing the volume of data does not guarantee performance improvements, while preprocessing, sampling, and validation require substantial time and cost. To address this issue, a variety of data selection methods have been proposed. Among them, knowledge based selection approaches identify suitable training data by analyzing the model 's responses. Nevertheless, these methods typically rely on prompt engineering, making them sensitive to variations and incurring additional costs for prompt design. In this study, we propose Knowledge Analysis via Model Internal Representations (KAMIR), a novel approach that overcomes these limitations by analyzing data based on the model 's internal representations. KAMIR computes similarities between the hidden states of each layer (block) and the final hidden states for a given input to assess the data. Unlike prior methods that were largely limited to multiple choice tasks, KAMIR can be applied to a wide range of tasks such as machine reading comprehension and summarization. Moreover, it selects data useful for training based on the model 's familiarity with the input, even with a small dataset and a simple classifier architecture. Experiments across diverse task datasets demonstrate that training with less familiar data leads to better generalization performance.

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and port-Hamiltonian systems might share the same initial total energy of a closed system, it is challenging for a single Hamiltonian network model to capture the distinctive and varying motion dynamics and physics of a phase space, from sampled observational phase space trajectories. To address this complicated Hamiltonian manifold learning challenge, we extend sparse symplectic, random Fourier Gaussian processes learning with predictive successive numerical estimations of the Hamiltonian landscape, using a generalized form of state and conjugate momentum Hamiltonian dynamics, appropriate to different classes of conservative, dissipative and port-Hamiltonian physical systems. In addition to the kernelized evidence lower bound (ELBO) loss for data fidelity, we incorporate stability and conservation constraints as additional hyper-parameter balanced loss terms to regularize the model's multi-gradients, enforcing physics correctness for improved prediction accuracy with bounded uncertainty.

Solving inverse problems with Physics-Informed Neural Networks (PINNs) is computationally expensive for multi-query scenarios, as each new set of observed data requires a new, expensive training procedure. We present Inverse-Parameter Basis PINNs (IP-Basis PINNs), a meta-learning framework that extends the foundational work of Desai et al. (2022) to enable rapid and efficient inference for inverse problems. Our method employs an offline-online decomposition: a deep network is first trained offline to produce a rich set of basis functions that span the solution space of a parametric differential equation. For each new inverse problem online, this network is frozen, and solutions and parameters are inferred by training only a lightweight linear output layer against observed data. Key innovations that make our approach effective for inverse problems include: (1) a novel online loss formulation for simultaneous solution reconstruction and parameter identification, (2) a significant reduction in computational overhead via forward-mode automatic differentiation for PDE loss evaluation, and (3) a non-trivial validation and early-stopping mechanism for robust offline training. We demonstrate the efficacy of IP-Basis PINNs on three diverse benchmarks, including an extension to universal PINNs for unknown functional terms-showing consistent performance across constant and functional parameter estimation, a significant speedup per query over standard PINNs, and robust operation with scarce and noisy data.