Claim verification with large language models (LLMs) has recently attracted growing attention, due to their strong reasoning capabilities and transparent verification processes compared to traditional answer-only judgments. However, existing approaches to online claim verification, which requires iterative evidence retrieval and reasoning, still mainly rely on prompt engineering or pre-designed reasoning workflows, without unified training to improve necessary skills. Therefore, we introduce Veri-R1, an online reinforcement learning (RL) framework that enables an LLM to interact with a search engine and to receive reward signals that explicitly shape its planning, retrieval, and reasoning behaviors. This dynamic interaction of LLM with retrieval systems more accurately reflects real-world verification scenarios and fosters comprehensive verification skills. Empirical results show that Veri-R1 improves joint accuracy by up to 30% and doubles the evidence score, often surpassing its larger-scale model counterparts. Ablation studies further reveal the impact of reward components, and the link between output logits and label accuracy. Our results highlight the effectiveness of online RL for precise and faithful claim verification, providing an important foundation for future research. We release our code to support community progress in LLM empowered claim verification.

Model checking is a key technique for verifying safety-critical systems against formal specifications, where recent applications of deep learning have shown promise. However, while ubiquitous for vision and language domains, representation learning remains underexplored in formal verification. We introduce Contrastive Neural Model Checking (CNML), a novel method that leverages the model checking task as a guiding signal for learning aligned representations. CNML jointly embeds logical specifications and systems into a shared latent space through a self-supervised contrastive objective. On industry-inspired retrieval tasks, CNML considerably outperforms both algorithmic and neural baselines in cross-modal and intra-modal settings. We further show that the learned representations effectively transfer to downstream tasks and generalize to more complex formulas. These findings demonstrate that model checking can serve as an objective for learning representations for formal languages.

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.