Curriculum learning for training LLMs requires a difficulty signal that aligns with reasoning while remaining scalable and interpretable. We propose a simple premise: tasks that demand deeper depth of thought for humans should also be harder for models. Accordingly, we define difficulty as depth of thought (DoT) and operationalize it by counting the discrete steps in a teacher model's reasoning trace (e.g., Chain-of-Thought). We then train with a shallow to deep curriculum ordered by this DoT and outline how to derive, validate, and schedule it at scale. Our position yields three testable hypotheses: (i) DoT correlates with conventional difficulty on reasoning benchmarks, (ii) DoT-ordered curricula outperform length- or judge-scored curricula under matched budgets, and (iii) the difficulty is robust across teacher models given light formatting controls. We propose an evaluation framework and discuss threats to validity (teacher style, length confounds) alongside practical mitigations. Taken together, we aim to move toward cognitively grounded, interpretable curricula for reasoning-centric training.

This study provides a comprehensive analysis of the development, functioning, and application of generative artificial intelligence (GenAI) and large language models (LLMs), with an emphasis on their implications for research and education. It traces the conceptual evolution from artificial intelligence (AI) through machine learning (ML) and deep learning (DL) to transformer architectures, which constitute the foundation of contemporary generative systems. Technical aspects, including prompting strategies, word embeddings, and probabilistic sampling methods (temperature, top-k, and top-p), are examined alongside the emergence of autonomous agents. These elements are considered in relation to both the opportunities they create and the limitations and risks they entail. The work critically evaluates the integration of GenAI across the research process, from ideation and literature review to research design, data collection, analysis, interpretation, and dissemination. While particular attention is given to geographical research, the discussion extends to wider academic contexts. A parallel strand addresses the pedagogical applications of GenAI, encompassing course and lesson design, teaching delivery, assessment, and feedback, with geography education serving as a case example. Central to the analysis are the ethical, social, and environmental challenges posed by GenAI. Issues of bias, intellectual property, governance, and accountability are assessed, alongside the ecological footprint of LLMs and emerging technological strategies for mitigation. The concluding section considers near- and long-term futures of GenAI, including scenarios of sustained adoption, regulation, and potential decline. By situating GenAI within both scholarly practice and educational contexts, the study contributes to critical debates on its transformative potential and societal responsibilities.

Currently available grammatical error correction (GEC) datasets are compiled using well-formed written text, limiting the applicability of these datasets to other domains such as informal writing and dialog. In this paper, we present a novel parallel GEC dataset drawn from open-domain chatbot conversations; this dataset is, to our knowledge, the first GEC dataset targeted to a conversational setting. To demonstrate the utility of the dataset, we use our annotated data to fine-tune a state-of-the-art GEC model, resulting in a 16 point increase in model precision. This is of particular importance in a GEC model, as model precision is considered more important than recall in GEC tasks since false positives could lead to serious confusion in language learners. We also present a detailed annotation scheme which ranks errors by perceived impact on comprehensibility, making our dataset both reproducible and extensible. Experimental results show the effectiveness of our data in improving GEC model performance in conversational scenario.

Training models with synthetic data presents both a danger and a boon to artificial intelligence (AI). While some groups have aggressively pursued the use of model-generated data to train successors for greater accuracy and generalization, others have warned about the risks posed by AI ingesting its own output. The two views are not at odds. The question is when and where things go wrong. On the negative side, a flurry of papers published since 2021 have argued that, as the datasets used to pretrain foundation models incorporate more and more auto-generated data mined from the Internet, performance degrades and the models start to "unlearn" skills.

We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven applications. Our framework covers a wide class of stochastic variance-reduced schemes, including mini-batching, and control variate unbiased and biased estimators. We establish that our method achieves $\mathcal{O}(1/k^2)$ convergence rates in expectation on the squared norm of residual under the Lipschitz continuity and a ``co-hypomonotonicity-type'' assumptions, improving upon non-accelerated counterparts by a factor of $1/k$. We also prove faster $o(1/k^2)$ convergence rates, both in expectation and almost surely. In addition, we show that the sequence of iterates of our method almost surely converges to a solution of the underlying problem. We demonstrate the applicability of our method using general error bound criteria, covering mini-batch stochastic estimators as well as three well-known control variate estimators: loopless SVRG, SAGA, and loopless SARAH, for which the last three variants attain significantly better oracle complexity compared to existing methods. We validate our framework and theoretical results through two numerical examples. The preliminary results illustrate promising performance of our accelerated method over its non-accelerated counterparts.

Large Language Models (LLMs) have reshaped our world with significant advancements in science, engineering, and society through applications ranging from scientific discoveries and medical diagnostics to Chatbots. Despite their ubiquity and utility, the underlying mechanisms of LLM remain concealed within billions of parameters and complex structures, making their inner architecture and cognitive processes challenging to comprehend. We address this gap by adopting approaches to understanding emerging cognition in biology and developing a network-based framework that links cognitive skills, LLM architectures, and datasets, ushering in a paradigm shift in foundation model analysis. The skill distribution in the module communities demonstrates that while LLMs do not strictly parallel the focalized specialization observed in specific biological systems, they exhibit unique communities of modules whose emergent skill patterns partially mirror the distributed yet interconnected cognitive organization seen in avian and small mammalian brains. Our numerical results highlight a key divergence from biological systems to LLMs, where skill acquisition benefits substantially from dynamic, cross-regional interactions and neural plasticity. By integrating cognitive science principles with machine learning, our framework provides new insights into LLM interpretability and suggests that effective fine-tuning strategies should leverage distributed learning dynamics rather than rigid modular interventions.

Imagine decision-makers uploading data and, within minutes, receiving clear, actionable insights delivered straight to their fingertips. That is the promise of the AI Data Scientist, an autonomous Agent powered by large language models (LLMs) that closes the gap between evidence and action. Rather than simply writing code or responding to prompts, it reasons through questions, tests ideas, and delivers end-to-end insights at a pace far beyond traditional workflows. Guided by the scientific tenet of the hypothesis, this Agent uncovers explanatory patterns in data, evaluates their statistical significance, and uses them to inform predictive modeling. It then translates these results into recommendations that are both rigorous and accessible. At the core of the AI Data Scientist is a team of specialized LLM Subagents, each responsible for a distinct task such as data cleaning, statistical testing, validation, and plain-language communication. These Subagents write their own code, reason about causality, and identify when additional data is needed to support sound conclusions. Together, they achieve in minutes what might otherwise take days or weeks, enabling a new kind of interaction that makes deep data science both accessible and actionable.

Intersectionality has profoundly influenced research and political action by revealing how interconnected systems of privilege and oppression influence lived experiences, yet its integration into algorithmic fairness research remains limited. Existing approaches often rely on single - axis or formal subgroup frameworks that risk oversimplifying social realities and neglecting structural inequalities. We propose Substantive Intersectional Algorithmic Fairness, extending Green's (2022) notion of substantive algorithmic fairness with insights from intersectional feminist theory. Buil ding on this foundation, we introduce ten desiderata within the ROOF methodology to guide the design, assessment, and deployment of algorithmic systems in ways that address systemic inequities while mitigating harms to intersectionally marginalized communi ties . Rather than prescribing fixed operationalizations, these desiderata encourage reflection on assumptions of neutrality, the use of protect ed attributes, the inclusion of multiply marginalized groups, and enhancing algorithmic systems' potential. Our a pproach emphasizes that fairness cannot be separated from social context, and that in some cases, principled non - deployment may be necessary. By bridging computational and social science perspectives, we provide actionable guidance for more equitable, incl usive, and context - sensitive intersectional algorithmic practices.

This study investigates the layerwise importance of feed-forward networks (FFNs) in Transformer-based language models during pretraining. We introduce an experimental approach that, while maintaining the total parameter count, increases the FFN dimensions in some layers and completely removes the FFNs from other layers. Furthermore, since our focus is on the importance of FFNs during pretraining, we train models from scratch to examine whether the importance of FFNs varies depending on their layer positions, rather than using publicly available pretrained models as is frequently done. Through comprehensive evaluations of models with varying sizes (285M, 570M, and 1.2B parameters) and layer counts (12, 24, and 40 layers), we demonstrate that concentrating FFNs in 70% of the consecutive middle layers consistently outperforms standard configurations for multiple downstream tasks.

Recent advances in the intrinsic reasoning capabilities of large language models (LLMs) have given rise to LLM-based agent systems that exhibit near-human performance on a variety of automated tasks. However, although these systems share similarities in terms of their use of LLMs, different reasoning frameworks of the agent system steer and organize the reasoning process in different ways. In this survey, we propose a systematic taxonomy that decomposes agentic reasoning frameworks and analyze how these frameworks dominate framework-level reasoning by comparing their applications across different scenarios. Specifically, we propose an unified formal language to further classify agentic reasoning systems into single-agent methods, tool-based methods, and multi-agent methods. After that, we provide a comprehensive review of their key application scenarios in scientific discovery, healthcare, software engineering, social simulation, and economics. We also analyze the characteristic features of each framework and summarize different evaluation strategies. Our survey aims to provide the research community with a panoramic view to facilitate understanding of the strengths, suitable scenarios, and evaluation practices of different agentic reasoning frameworks.