This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics

Transformer models often exhibit brittle extrapolation, failing on inputs that are longer or structurally more complex than those seen during training. We introduce Counter-Example-Driven Curricula (CEDC), an automated framework that improves model robustness by iteratively focusing on its own failures. At each step, CEDC uses the current model to generate a diverse set of candidate problems, employs a fast, executable verifier to identify incorrect predictions (counter-examples), and then fine-tunes the model on a dataset enriched with these discovered failures. We evaluate CEDC on a suite of algorithmic and natural language tasks, including integer addition, sorting, Dyck-2 language recognition, and three text classification benchmarks. Compared to static training and standard curriculum learning baselines, CEDC achieves up to 30x greater length extrapolation, is 3.75x more computationally efficient than uniform data augmentation, and requires no manual difficulty heuristics. We provide a detailed analysis of the counter-examples, showing how the curriculum naturally adapts to target progressively more complex error modes. Our findings establish verifier-guided, failure-driven learning as a simple, powerful, and efficient paradigm for enhancing the generalization capabilities of Transformer models.

College students often face academic and life stressors affecting productivity, especially students with Attention Deficit Hyperactivity Disorder (ADHD) who experience executive functioning challenges. Conventional productivity tools typically demand sustained self-discipline and consistent use, which many students struggle with, leading to disruptive app-switching behaviors. Socially Assistive Robots (SARs), known for their intuitive and interactive nature, offer promising potential to support productivity in academic environments, having been successfully utilized in domains like education, cognitive development, and mental health. To leverage SARs effectively in addressing student productivity, this study employed a Participatory Design (PD) approach, directly involving college students and a Student Success and Well-Being Coach in the design process. Through interviews and a collaborative workshop, we gathered detailed insights on productivity challenges and identified desirable features for a productivity-focused SAR. Importantly, ethical considerations were integrated from the onset, facilitating responsible and user-aligned design choices. Our contributions include comprehensive insights into student productivity challenges, SAR design preferences, and actionable recommendations for effective robot characteristics. Additionally, we present stakeholder-derived ethical guidelines to inform responsible future implementations of productivity-focused SARs in higher education.

We study timestamped question answering over educational lecture videos under a single-GPU latency/memory budget. Given a natural-language query, the system retrieves relevant timestamped segments and synthesizes a grounded answer. We present CourseTimeQA (52.3 h, 902 queries across six courses) and a lightweight, latency-constrained cross-modal retriever (CrossFusion-RAG) that combines frozen encoders, a learned 512->768 vision projection, shallow query-agnostic cross-attention over ASR and frames with a temporal-consistency regularizer, and a small cross-attentive reranker. On CourseTimeQA, CrossFusion-RAG improves nDCG@10 by 0.10 and MRR by 0.08 over a strong BLIP-2 retriever while achieving approximately 1.55 s median end-to-end latency on a single A100. Closest comparators (zero-shot CLIP multi-frame pooling; CLIP + cross-encoder reranker + MMR; learned late-fusion gating; text-only hybrid with cross-encoder reranking and its MMR variant; caption-augmented text retrieval; non-learned temporal smoothing) are evaluated under matched hardware and indexing. We report robustness across ASR noise (WER quartiles), diagnostics for temporal localization, and full training/tuning details to support reproducible comparison.

Large language models (LLMs) are increasingly deployed as conversational tutors in STEM education, yet most systems still rely on a single LLM with a static retrieval-augmented generation (RAG) pipeline over course materials. This design struggles in complex domains such as digital signal processing (DSP), where tutors must maintain coherent long-term student models, manage heterogeneous knowledge bases, and adapt teaching strategies over extended interactions. We argue that retrieval, memory, and control should be treated as a coupled cognitive evolution process. We instantiate this view in CogEvo-Edu, a hierarchical educational multi-agent system comprising a Cognitive Perception Layer (CPL), a Knowledge Evolution Layer (KEL), and a Meta-Control Layer (MCL). CPL maintains dual memories and performs confidence-weighted consolidation to build structured, self-correcting student profiles under limited context. KEL assigns each knowledge chunk a spatiotemporal value that drives activation, semantic compression, and forgetting. MCL formulates tutoring as hierarchical sequential decision making, orchestrating specialized agents and jointly adapting CPL/KEL hyperparameters via a dual inner--outer loop. To evaluate CogEvo-Edu, we construct DSP-EduBench, a vertical benchmark for DSP tutoring with heterogeneous resources, simulated student profiles, and long-horizon interaction scripts. Using a three-model LLM-as-a-Judge ensemble, CogEvo-Edu raises the overall score from 5.32 to 9.23 and improves all six indicators over static RAG, simple memory, and a single-agent variant, demonstrating the value of jointly evolving student profiles, knowledge bases, and teaching policies.

Large language models (LLMs) demonstrate significant potential for educational applications. However, their unscrutinized deployment poses risks to educational standards, underscoring the need for rigorous evaluation. We introduce EduEval, a comprehensive hierarchical benchmark for evaluating LLMs in Chinese K-12 education. This benchmark makes three key contributions: (1) Cognitive Framework: We propose the EduAbility Taxonomy, which unifies Bloom's Taxonomy and Webb's Depth of Knowledge to organize tasks across six cognitive dimensions including Memorization, Understanding, Application, Reasoning, Creativity, and Ethics. (2) Authenticity: Our benchmark integrates real exam questions, classroom conversation, student essays, and expert-designed prompts to reflect genuine educational challenges; (3) Scale: EduEval comprises 24 distinct task types with over 11,000 questions spanning primary to high school levels. We evaluate 14 leading LLMs under both zero-shot and few-shot settings, revealing that while models perform well on factual tasks, they struggle with classroom dialogue classification and exhibit inconsistent results in creative content generation. Interestingly, several open source models outperform proprietary systems on complex educational reasoning. Few-shot prompting shows varying effectiveness across cognitive dimensions, suggesting that different educational objectives require tailored approaches. These findings provide targeted benchmarking metrics for developing LLMs specifically optimized for diverse Chinese educational tasks.

W e contend that embodied learning is fundamentally a life-cycle problem rather than a single-stage optimization. Systems that optimize only one link (data collection, simulation, learning, or deployment) rarely sustain improvement or generalize beyond narrow settings. W e introduce Arcadia, a closed-loop framework that operational-izes embodied lifelong learning by tightly coupling four stages: (1) Self-evolving exploration and grounding for autonomous data acquisition in physical environments, (2) Generative scene reconstruction and augmentation for realistic and extensible scene creation, (3) a Shared embodied representation architecture that unifies navigation and manipulation within a single multimodal backbone, and (4) Sim-from-real evaluation and evolution that closes the feedback loop through simulation-based adaptation. This coupling is non-decomposable: removing any stage breaks the improvement loop and reverts to one-shot training. Arcadia delivers consistent gains on navigation and manipulation benchmarks and transfers robustly to physical robots, indicating that a tightly coupled lifecycle: continuous real-world data acquisition, generative simulation update, and shared-representation learning, supports lifelong improvement and end-to-end generalization. W e release standardized interfaces enabling reproducible evaluation and cross-model comparison in reusable environments, positioning Arcadia as a scalable foundation for general-purpose embodied agents.

World models are emerging as a foundational paradigm for scalable, data-efficient embodied AI. In this work, we present GigaWorld-0, a unified world model framework designed explicitly as a data engine for Vision-Language-Action (VLA) learning. GigaWorld-0 integrates two synergistic components: GigaWorld-0-Video, which leverages large-scale video generation to produce diverse, texture-rich, and temporally coherent embodied sequences under fine-grained control of appearance, camera viewpoint, and action semantics; and GigaWorld-0-3D, which combines 3D generative modeling, 3D Gaussian Splatting reconstruction, physically differentiable system identification, and executable motion planning to ensure geometric consistency and physical realism. Their joint optimization enables the scalable synthesis of embodied interaction data that is visually compelling, spatially coherent, physically plausible, and instruction-aligned. Training at scale is made feasible through our efficient GigaTrain framework, which exploits FP8-precision and sparse attention to drastically reduce memory and compute requirements. We conduct comprehensive evaluations showing that GigaWorld-0 generates high-quality, diverse, and controllable data across multiple dimensions. Critically, VLA model (e.g., GigaBrain-0) trained on GigaWorld-0-generated data achieve strong real-world performance, significantly improving generalization and task success on physical robots without any real-world interaction during training.

This paper investigates the problem of Graph Spectral Clustering with negative similarities, resulting from document embeddings different from the traditional Term Vector Space (like doc2vec, GloVe, etc.). Solutions for combinatorial Laplacians and normalized Laplacians are discussed. An experimental investigation shows the advantages and disadvantages of 6 different solutions proposed in the literature and in this research. The research demonstrates that GloVe embeddings frequently cause failures of normalized Laplacian based GSC due to negative similarities. Furthermore, application of methods curing similarity negativity leads to accuracy improvement for both combinatorial and normalized Laplacian based GSC. It also leads to applicability for GloVe embeddings of explanation methods developed originally bythe authors for Term Vector Space embeddings.

An accidental leak revealed that Flock, which has cameras in thousands of US communities, is using workers in the Philippines to review and classify footage. Flock, the automatic license plate reader and AI-powered camera company, uses overseas workers from Upwork to train its machine learning algorithms, with training material telling workers how to review and categorize footage including images people and vehicles in the United States, according to material reviewed by 404 Media that was accidentally exposed by the company. The findings bring up questions about who exactly has access to footage collected by Flock surveillance cameras and where people reviewing the footage may be based. Flock has become a pervasive technology in the US, with its cameras present in thousands of communities that cops use every day to investigate things like carjackings. Local police have also performed numerous lookups for ICE in the system.