Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest due to novel theoretical results pertaining to their information storage capabilities, and their relationship with SOTA AI architectures, such as Transformers and Diffusion Models. These connections open up possibilities for interpreting the computation of traditional AI networks through the theoretical lens of Associative Memories. Additionally, novel Lagrangian formulations of these networks make it possible to design powerful distributed models that learn useful representations and inform the design of novel architectures. This tutorial provides an approachable introduction to Associative Memories, emphasizing the modern language and methods used in this area of research, with practical hands-on mathematical derivations and coding notebooks.

In this paper, we study the use of robust model independent bounded extremum seeking (ES) feedback control to improve the robustness of deep reinforcement learning (DRL) controllers for a class of nonlinear time-varying systems. DRL has the potential to learn from large datasets to quickly control or optimize the outputs of many-parameter systems, but its performance degrades catastrophically when the system model changes rapidly over time. Bounded ES can handle time-varying systems with unknown control directions, but its convergence speed slows down as the number of tuned parameters increases and, like all local adaptive methods, it can get stuck in local minima. We demonstrate that together, DRL and bounded ES result in a hybrid controller whose performance exceeds the sum of its parts with DRL taking advantage of historical data to learn how to quickly control a many-parameter system to a desired setpoint while bounded ES ensures its robustness to time variations. We present a numerical study of a general time-varying system and a combined ES-DRL controller for automatic tuning of the Low Energy Beam Transport section at the Los Alamos Neutron Science Center linear particle accelerator.

The adoption of generative AI and large language models (LLMs) in education is still emerging. In this study, we explore the development and evaluation of AI teaching assistants that provide curriculum-based guidance using a retrieval-augmented generation (RAG) pipeline applied to selected open-source small language models (SLMs). We benchmarked eight SLMs, including LLaMA 3.1, IBM Granite 3.3, and Gemma 3 (7-17B parameters), against GPT-4o. Our findings show that with proper prompting and targeted retrieval, SLMs can match LLMs in delivering accurate, pedagogically aligned responses. Importantly, SLMs offer significant sustainability benefits due to their lower computational and energy requirements, enabling real-time use on consumer-grade hardware without depending on cloud infrastructure. This makes them not only cost-effective and privacy-preserving but also environmentally responsible, positioning them as viable AI teaching assistants for educational institutions aiming to scale personalized learning in a sustainable and energy-efficient manner.

We thank the reviewers for their careful consideration of our work. R2 suggested that an analysis on non-toy models would be interesting to see. R3 believed that the synthetic experiment was not suited to the model class. We expect our analysis on smaller models to extrapolate to larger ones (R2). We regret that we were not clearer about how our aim differs from these studies [McMurray et al. (2012), ME would aid downstream learning as we propose or as is observed in humans in lifelong learning settings.

A good teacher can adjust a curriculum based on students' learning history.

Can a simple yet effective algorithm be developed for estimating general exponential family distributions? There has been extensive prior work addressing this question.

To solve a new task from minimal experience, it is essential to effectively reuse knowledge from previous tasks, a problem known as meta-learning. Compositional solutions, where common elements of computation are flexibly recombined into new configurations, are particularly well-suited for meta-learning. Here, we propose a compositional meta-learning model that explicitly represents tasks as structured combinations of reusable computations. We achieve this by learning a generative model that captures the underlying components and their statistics shared across a family of tasks. This approach transforms learning a new task into a probabilistic inference problem, which allows for finding solutions without parameter updates through highly constrained hypothesis testing. Our model successfully recovers ground truth components and statistics in rule learning and motor learning tasks. We then demonstrate its ability to quickly infer new solutions from just single examples. Together, our framework joins the expressivity of neural networks with the data-efficiency of probabilistic inference to achieve rapid compositional meta-learning.

Training data plays a crucial role in Large Language Models (LLM) scaling, yet high quality data is of limited supply. Synthetic data techniques offer a potential path toward sidestepping these limitations. We conduct a large-scale empirical investigation (>1000 LLMs with >100k GPU hours) using a unified protocol and scaling laws, comparing natural web data, diverse synthetic types (rephrased text, generated textbooks), and mixtures of natural and synthetic data. Specifically, we found pre-training on rephrased synthetic data \textit{alone} is not faster than pre-training on natural web texts; while pre-training on 1/3 rephrased synthetic data mixed with 2/3 natural web texts can speed up 5-10x (to reach the same validation loss) at larger data budgets. Pre-training on textbook-style synthetic data \textit{alone} results in notably higher loss on many downstream domains especially at small data budgets. "Good" ratios of synthetic data in training data mixtures depend on the model size and data budget, empirically converging to ~30% for rephrased synthetic data. Larger generator models do not necessarily yield better pre-training data than ~8B-param models. These results contribute mixed evidence on "model collapse" during large-scale single-round (n=1) model training on synthetic data--training on rephrased synthetic data shows no degradation in performance in foreseeable scales whereas training on mixtures of textbook-style pure-generated synthetic data shows patterns predicted by "model collapse". Our work demystifies synthetic data in pre-training, validates its conditional benefits, and offers practical guidance.

Recent thinking models are capable of solving complex reasoning tasks by scaling test-time compute across various domains, but this scaling must be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient, generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under-and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention over a long reasoning trajectory to identify important steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate reasoning budget commensurate with example difficulty. Our approach improves accuracy, reduces reasoning steps, and enables adaptive thinking compared to base models and other RL baselines. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC also shows strong generalization: although our models are trained on math datasets, they show accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis further verifies that TRAAC provides fine-grained adjustments to thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks. Recent advancements in thinking models have enabled language models to solve complex reasoning tasks (DeepSeek-AI et al., 2025; OpenAI et al., 2024; Team, 2025). These models extend the chain-of-thought (CoT; Wei et al., 2023) paradigm with online reinforcement learning (RL; Shao et al., 2024), allowing them to refine intermediate solutions as well as sequentially scaling the number of tokens (i.e., compute) to arrive at the final answer. While such approaches show strong promise for harder problems in domains like mathematics, programming, and logical puzzles (Xie et al., 2025; Chen et al., 2025), their accuracy and utility remain capped by a failure to regulate their reasoning length.

The role that highly curated knowledge, provided by domain experts, could play in creating effective tutoring systems is often overlooked within the AI for education community. In this paper, we highlight this topic by discussing two ways such highly curated expert knowledge could help in creating novel educational systems. First, we will look at how one could use explainable AI (XAI) techniques to automatically create lessons. Most existing XAI methods are primarily aimed at debugging AI systems. However, we will discuss how one could use expert specified rules about solving specific problems along with novel XAI techniques to automatically generate lessons that could be provided to learners. Secondly, we will see how an expert specified curriculum for learning a target concept can help develop adaptive tutoring systems, that can not only provide a better learning experience, but could also allow us to use more efficient algorithms to create these systems. Finally, we will highlight the importance of such methods using a case study of creating a tutoring system for pollinator identification, where such knowledge could easily be elicited from experts.