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Mathematical Foundations of Geometric Deep Learning

arXiv.org Artificial Intelligence

Since the dawn of civilization, humans have tried to understand the nature of intelligence. With the advent of computers, there have been attempts to emulate human intelligence using computer algorithms - a field that was dubbed'Artificial Intelligence' or'AI' by the computer scientist John McCarthy in 1956 and has recently enjoyed an explosion of popularity. Many efforts in AI research have focused on the study and replication of what is considered the hallmark of human cognition, such as playing intelligent games, the faculty of language, visual perception, and creativity. While at the time of writing we have multiple successful takes at the above - computers nowadays play chess and Go better than any human, can translate English into Chinese without a dictionary, automatically drive a car in a crowded city, and generate poetry and art that wins artistic competitions - it is fair to say that we still do not have a full understanding of what human-like or'general' intelligence entails and how to replicate it.


FedCD: A Fairness-aware Federated Cognitive Diagnosis Framework

arXiv.org Artificial Intelligence

Online intelligent education platforms have generated a vast amount of distributed student learning data. This influx of data presents opportunities for cognitive diagnosis (CD) to assess students' mastery of knowledge concepts while also raising significant data privacy and security challenges. To cope with this issue, federated learning (FL) becomes a promising solution by jointly training models across multiple local clients without sharing their original data. However, the data quality problem, caused by the ability differences and educational context differences between different groups/schools of students, further poses a challenge to the fairness of models. To address this challenge, this paper proposes a fairness-aware federated cognitive diagnosis framework (FedCD) to jointly train CD models built upon a novel parameter decoupling-based personalization strategy, preserving privacy of data and achieving precise and fair diagnosis of students on each client. As an FL paradigm, FedCD trains a local CD model for the students in each client based on its local student learning data, and each client uploads its partial model parameters to the central server for parameter aggregation according to the devised innovative personalization strategy. The main idea of this strategy is to decouple model parameters into two parts: the first is used as locally personalized parameters, containing diagnostic function-related model parameters, to diagnose each client's students fairly; the second is the globally shared parameters across clients and the server, containing exercise embedding parameters, which are updated via fairness-aware aggregation, to alleviate inter-school unfairness. Experiments on three real-world datasets demonstrate the effectiveness of the proposed FedCD framework and the personalization strategy compared to five FL approaches under three CD models.


Greening AI-enabled Systems with Software Engineering: A Research Agenda for Environmentally Sustainable AI Practices

arXiv.org Artificial Intelligence

The environmental impact of Artificial Intelligence (AI)-enabled systems is increasing rapidly, and software engineering plays a critical role in developing sustainable solutions. The "Greening AI with Software Engineering" CECAM-Lorentz workshop (no. 1358, 2025) funded by the Centre Européen de Calcul Atomique et Moléculaire and the Lorentz Center, provided an interdisciplinary forum for 29 participants, from practitioners to academics, to share knowledge, ideas, practices, and current results dedicated to advancing green software and AI research. The workshop was held February 3-7, 2025, in Lausanne, Switzerland. Through keynotes, flash talks, and collaborative discussions, participants identified and prioritized key challenges for the field. These included energy assessment and standardization, benchmarking practices, sustainability-aware architectures, runtime adaptation, empirical methodologies, and education. This report presents a research agenda emerging from the workshop, outlining open research directions and practical recommendations to guide the development of environmentally sustainable AI-enabled systems rooted in software engineering principles.


Assessing the Reliability and Validity of Large Language Models for Automated Assessment of Student Essays in Higher Education

arXiv.org Artificial Intelligence

This study investigates the reliability and validity of five advanced Large Language Models (LLMs)--Claude 3.5, DeepSeek v2, Gemini 2.5, GPT 4, and Mistral 24B--for automated essay scoring in a real-world higher education context. A total of 67 Italian-language student essays, written as part of a university psychology course, were evaluated using a four-criterion rubric (Pertinence, Coherence, Originality, Feasibility). Each model scored all essays across three prompt replications to assess intra-model stability. Human-LLM agreement was consistently low and non-significant (Quadratic Weighted Kappa), and within-model reliability across replications was similarly weak (median Kendall's W < .30). Systematic scoring divergences emerged, including a tendency to inflate Coherence and inconsistent handling of context-dependent dimensions. Inter-model agreement analysis revealed moderate convergence for Coherence and Originality, but negligible concordance for Pertinence and Feasibility. Although limited in scope, these findings suggest that current LLMs may struggle to replicate human judgment in tasks requiring disciplinary insight and contextual sensitivity. Human oversight remains critical when evaluating open-ended academic work, particularly in interpretive domains.


TRACEALIGN -- Tracing the Drift: Attributing Alignment Failures to Training-Time Belief Sources in LLMs

arXiv.org Artificial Intelligence

Large Language Models (LLMs) fine-tuned to align with human values often exhibit alignment drift, producing unsafe or policy-violating completions when exposed to adversarial prompts, decoding perturbations, or paraphrased jailbreaks. While prior work has behaviorally characterized alignment failure, little is known about the training-time belief sources underlying these failures. We introduce TraceAlign, a unified framework for tracing unsafe completions back to their root causes in the model's training corpus. Central to our approach is the Belief Conflict Index (BCI), which quantifies semantic inconsistency between generated spans and aligned policies, based on retrieved training documents using suffix-array matching. We propose three complementary interventions: (i) TraceShield, an inference-time safety filter that refuses completions with high-BCI spans, (ii) Contrastive Belief Deconfliction Loss, a contrastive fine-tuning objective penalizing high-BCI continuations during DPO, and (iii) Prov-Decode, a provenance-aware decoding strategy that vetoes beam expansions predicted to yield high-BCI spans. Together, these defenses reduce alignment drift by up to 85% on our curated Alignment Drift Benchmark (ADB) while preserving utility on standard tasks, with delta less than 0.2 and improved refusal quality. We further derive a theoretical upper bound on drift likelihood via suffix-array span statistics, linking memorization frequency and length to adversarial reactivation risk. TraceAlign thus provides the first scalable, traceable, and grounded toolkit for understanding and mitigating alignment failures at source. To encourage further exploration and development, we open-source our implementation at: https://anonymous.4open.science/r/tracealign-2DA7


Towards Actionable Pedagogical Feedback: A Multi-Perspective Analysis of Mathematics Teaching and Tutoring Dialogue

arXiv.org Artificial Intelligence

Effective feedback is essential for refining instructional practices in mathematics education, and researchers often turn to advanced natural language processing (NLP) models to analyze classroom dialogues from multiple perspectives. However, utterance-level discourse analysis encounters two primary challenges: (1) multifunctionality, where a single utterance may serve multiple purposes that a single tag cannot capture, and (2) the exclusion of many utterances from domain-specific discourse move classifications, leading to their omission in feedback. To address these challenges, we proposed a multi-perspective discourse analysis that integrates domain-specific talk moves with dialogue act (using the flattened multi-functional SWBD-MASL schema with 43 tags) and discourse relation (applying Segmented Discourse Representation Theory with 16 relations). Our top-down analysis framework enables a comprehensive understanding of utterances that contain talk moves, as well as utterances that do not contain talk moves. This is applied to two mathematics education datasets: TalkMoves (teaching) and SAGA22 (tutoring). Through distributional unigram analysis, sequential talk move analysis, and multi-view deep dive, we discovered meaningful discourse patterns, and revealed the vital role of utterances without talk moves, demonstrating that these utterances, far from being mere fillers, serve crucial functions in guiding, acknowledging, and structuring classroom discourse. These insights underscore the importance of incorporating discourse relations and dialogue acts into AI-assisted education systems to enhance feedback and create more responsive learning environments. Our framework may prove helpful for providing human educator feedback, but also aiding in the development of AI agents that can effectively emulate the roles of both educators and students.


Globally Optimal Data-Association-Free Landmark-Based Localization Using Semidefinite Relaxations

arXiv.org Artificial Intelligence

--This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally optimal fashion. Relative position measurements to a fixed set of known landmarks are used, but the data association is unknown in that the robot does not know which landmark each measurement is generated from. The relaxation is shown to be tight in a majority of cases for moderate noise levels. The proposed algorithm is compared to local Gauss-Newton baselines initialized at the dead-reckoned trajectory, and is shown to significantly improve convergence to the problem's global optimum in simulation and experiment. STIMA TING the state of a robot from noisy and incomplete sensor data is a central task associated with autonomy. In the landmark-based localization task, the robot infers its position and orientation from measurements from landmarks with known positions. State estimation methods for localization can be split into filtering methods and batch optimization methods [1].


Transparent Adaptive Learning via Data-Centric Multimodal Explainable AI

arXiv.org Artificial Intelligence

Artificial intelligence - driven adaptive learning systems are reshaping education through data - driven adaptation of learning experiences. Yet many of these systems lack transparency, offering limited insight into how decisions are made. Most explainable AI (XAI) techniques focus on technical outputs but neglect user roles and comprehension. This paper proposes a hybrid framework that integrates traditional XAI techniques with generative AI models and u ser personalisation to generate multimodal, personalised explanations tailored to user needs. We redefine explainability as a dynamic communication process tailored to user roles and learning goals. We outline the framework ' s design, key XAI limitations in education, and research directions on accuracy, fairness, and personalisation. Our aim is to move towards explainable AI that enhances transparency while supporting user - centred experiences.


Learning to Optimize Feedback for One Million Students: Insights from Multi-Armed and Contextual Bandits in Large-Scale Online Tutoring

arXiv.org Artificial Intelligence

We present an online tutoring system that learns to provide effective feedback to students after they answer questions incorrectly. Using data from one million students, the system learns which assistance action (e.g., one of multiple hints) to provide for each question to optimize student learning. Employing the multi-armed bandit (MAB) framework and offline policy evaluation, we assess 43,000 assistance actions, and identify trade-offs between assistance policies optimized for different student outcomes (e.g., response correctness, session completion). We design an algorithm that for each question decides on a suitable policy training objective to enhance students' immediate second attempt success and overall practice session performance. We evaluate the resulting MAB policies in 166,000 practice sessions, verifying significant improvements in student outcomes. While MAB policies optimize feedback for the overall student population, we further investigate whether contextual bandit (CB) policies can enhance outcomes by personalizing feedback based on individual student features (e.g., ability estimates, response times). Using causal inference, we examine (i) how effects of assistance actions vary across students and (ii) whether CB policies, which leverage such effect heterogeneity, outperform MAB policies. While our analysis reveals that some actions for some questions exhibit effect heterogeneity, effect sizes may often be too small for CB policies to provide significant improvements beyond what well-optimized MAB policies that deliver the same action to all students already achieve. We discuss insights gained from deploying data-driven systems at scale and implications for future refinements. Today, the teaching policies optimized by our system support thousands of students daily.


Multi-modal Relational Item Representation Learning for Inferring Substitutable and Complementary Items

arXiv.org Artificial Intelligence

We introduce a novel self-supervised multi-modal relational item representation learning framework designed to infer substitutable and complementary items. Existing approaches primarily focus on modeling item-item associations deduced from user behaviors using graph neural networks (GNNs) or leveraging item content information. However, these methods often overlook critical challenges, such as noisy user behavior data and data sparsity due to the long-tailed distribution of these behaviors. In this paper, we propose MMSC, a self-supervised multi-modal relational item representation learning framework to address these challenges. Specifically, MMSC consists of three main components: (1) a multi-modal item representation learning module that leverages a multi-modal foundational model and learns from item metadata, (2) a self-supervised behavior-based representation learning module that denoises and learns from user behavior data, and (3) a hierarchical representation aggregation mechanism that integrates item representations at both the semantic and task levels. Additionally, we leverage LLMs to generate augmented training data, further enhancing the denoising process during training. We conduct extensive experiments on five real-world datasets, showing that MMSC outperforms existing baselines by 26.1% for substitutable recommendation and 39.2% for complementary recommendation. In addition, we empirically show that MMSC is effective in modeling cold-start items.