Assessing and enhancing human learning through question-answering is vital, yet automating this process remains challenging. While large language models (LLMs) excel at summarization and query responses, their ability to generate meaningful questions for learners is underexplored. We propose Savaal, a scalable question-generation system with three objectives: (i) scalability, enabling question generation from hundreds of pages of text (ii) depth of understanding, producing questions beyond factual recall to test conceptual reasoning, and (iii) domain-independence, automatically generating questions across diverse knowledge areas. Instead of providing an LLM with large documents as context, Savaal improves results with a three-stage processing pipeline. Our evaluation with 76 human experts on 71 papers and PhD dissertations shows that Savaal generates questions that better test depth of understanding by 6.5X for dissertations and 1.5X for papers compared to a direct-prompting LLM baseline. Notably, as document length increases, Savaal's advantages in higher question quality and lower cost become more pronounced.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Motivated by alternating learning dynamics in two-player games, a recent work by Cevher et al.(2024) shows that $o(\sqrt{T})$ alternating regret is possible for any $T$-round adversarial Online Linear Optimization (OLO) problem, and left as an open question whether the same is true for general Online Convex Optimization (OCO). We answer this question in the affirmative by showing that the continuous Hedge algorithm achieves $\tilde{\mathcal{O}}(d^{\frac{2}{3}}T^{\frac{1}{3}})$ alternating regret for any adversarial $d$-dimensional OCO problems. We show that this implies an alternating learning dynamic that finds a Nash equilibrium for any convex-concave zero-sum games or a coarse correlated equilibrium for any convex two-player general-sum games at a rate of $\tilde{\mathcal{O}}(d^{\frac{2}{3}}/T^{\frac{2}{3}})$. To further improve the time complexity and/or the dimension dependence, we propose another simple algorithm, Follow-the-Regularized-Leader with a regularizer whose convex conjugate is 3rd-order smooth, for OCO with smooth and self-concordant loss functions (such as linear or quadratic losses). We instantiate our algorithm with different regularizers and show that, for example, when the decision set is the $\ell_2$ ball, our algorithm achieves $\tilde{\mathcal{O}}(T^{\frac{2}{5}})$ alternating regret with no dimension dependence (and a better $\tilde{\mathcal{O}}(T^{\frac{1}{3}})$ bound for quadratic losses). We complement our results by showing some algorithm-specific alternating regret lower bounds, including a somewhat surprising $\Omega(\sqrt{T})$ lower bound for a Regret Matching variant that is widely used in alternating learning dynamics.

We study an online forecasting setting in which, over $T$ rounds, $N$ strategic experts each report a forecast to a mechanism, the mechanism selects one forecast, and then the outcome is revealed. In any given round, each expert has a belief about the outcome, but the expert wishes to select its report so as to maximize the total number of times it is selected. The goal of the mechanism is to obtain low belief regret: the difference between its cumulative loss (based on its selected forecasts) and the cumulative loss of the best expert in hindsight (as measured by the experts' beliefs). We consider exactly truthful mechanisms for non-myopic experts, meaning that truthfully reporting its belief strictly maximizes the expert's subjective probability of being selected in any future round. Even in the full-information setting, it is an open problem to obtain the first no-regret exactly truthful mechanism in this setting. We develop the first no-regret mechanism for this setting via an online extension of the Independent-Event Lotteries Forecasting Competition Mechanism (I-ELF). By viewing this online I-ELF as a novel instance of Follow the Perturbed Leader (FPL) with noise based on random walks with loss-dependent perturbations, we obtain $\tilde{O}(\sqrt{T N})$ regret. Our results are fueled by new tail bounds for Poisson binomial random variables that we develop. We extend our results to the bandit setting, where we give an exactly truthful mechanism obtaining $\tilde{O}(T^{2/3} N^{1/3})$ regret; this is the first no-regret result even among approximately truthful mechanisms.

The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space. Here we consider a generalization of the kernel ridge regression problem, by introducing an extra matrix parameter $U$, which aims to detect the scale parameters and the feature variables in the data, and thereby improve the efficiency of kernel ridge regression. This naturally leads to a nonlinear variational problem to optimize the choice of $U$. We study various foundational mathematical aspects of this variational problem, and in particular how this behaves in the presence of multiscale structures in the data.

Continual learning is a rapidly growing subfield of deep learning devoted to enabling neural networks to incrementally learn new tasks, domains or classes while not forgetting previously learned ones. Such continual learning is crucial for addressing real-world problems where data are constantly changing, such as in healthcare, autonomous driving or robotics. Unfortunately, continual learning is challenging for deep neural networks, mainly due to their tendency to forget previously acquired skills when learning something new. Elastic Weight Consolidation (EWC) [1], developed by Kirkpatrick and colleagues from DeepMind, is one of the most popular methods for continual learning with deep neural networks. To this day, this method is featured as a baseline in a large proportion of continual learning studies. However, in the original paper the exact implementation of EWC was not well described, and no official code was provided. A previous blog post by Huszár [2] already addressed an issue relating to how EWC should behave when there are more than two tasks.

The foundation model enables general-purpose problem-solving and enjoys desirable rapid adaptation due to its adopted cross-task generalization paradigms, e.g., pretraining, meta-training, and finetuning. Recent advances in these paradigms show the crucial role of challenging tasks' prioritized sampling in enhancing adaptation robustness. However, ranking task difficulties exhausts massive task queries to evaluate, thus computation and annotation intensive, which is typically unaffordable in practice. This work underscores the criticality of both adaptation robustness and learning efficiency, especially in scenarios where tasks are risky or costly to evaluate, e.g., policy evaluations in Markov decision processes (MDPs) or inference with large models. To this end, we present Model Predictive Task Sampling (MPTS) to establish connections between the task space and adaptation risk landscape to form a theoretical guideline in robust active task sampling. MPTS characterizes the task episodic information with a generative model and directly predicts task-specific adaptation risk values from posterior inference. The developed risk learner can amortize expensive evaluation and provably approximately rank task difficulties in the pursuit of task robust adaptation. MPTS can be seamlessly integrated into zero-shot, few-shot, and many-shot learning paradigms. Extensive experimental results are conducted to exhibit the superiority of the proposed framework, remarkably increasing task adaptation robustness and retaining learning efficiency in contrast to existing state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

Despite exceptional capabilities in knowledge-intensive tasks, Large Language Models (LLMs) face a critical gap in understanding how they internalize new knowledge, particularly how to structurally embed acquired knowledge in their neural computations. We address this issue through the lens of knowledge circuit evolution, identifying computational subgraphs that facilitate knowledge storage and processing. Our systematic analysis of circuit evolution throughout continual pre-training reveals several key findings: (1) the acquisition of new knowledge is influenced by its relevance to pre-existing knowledge; (2) the evolution of knowledge circuits exhibits a distinct phase shift from formation to optimization; (3) the evolution of knowledge circuits follows a deep-to-shallow pattern. These insights not only advance our theoretical understanding of the mechanisms of new knowledge acquisition in LLMs, but also provide potential implications for improving continual pre-training strategies to enhance model performance. Code and data will be available at https://github.com/zjunlp/DynamicKnowledgeCircuits.

LLMs have immense potential for generating plans, transforming an initial world state into a desired goal state. A large body of research has explored the use of LLMs for various planning tasks, from web navigation to travel planning and database querying. However, many of these systems are tailored to specific problems, making it challenging to compare them or determine the best approach for new tasks. There is also a lack of clear and consistent evaluation criteria. Our survey aims to offer a comprehensive overview of current LLM planners to fill this gap. It builds on foundational work by Kartam and Wilkins (1990) and examines six key performance criteria: completeness, executability, optimality, representation, generalization, and efficiency. For each, we provide a thorough analysis of representative works and highlight their strengths and weaknesses. Our paper also identifies crucial future directions, making it a valuable resource for both practitioners and newcomers interested in leveraging LLM planning to support agentic workflows.

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof. Proof assistants like Lean offer a great remedy. They are designed for verifying each step of a proof in a formal language, and in recent years researchers have created AI models to generate proofs in their languages. However, the scarcity of large-scale datasets of Lean proofs restrict the performance of such Automated Theorem Proving (ATP) models. We developed LeanNavigator, a novel method for generating a large-scale dataset of Lean theorems and proofs by finding new ways to prove existing Lean theorems. By leveraging an interactive Lean client and an efficient method for proof step generation, LeanNavigator efficiently produces new theorems with corresponding proofs. Applying this approach to Mathlib4, we generated 4.7 million theorems totaling 1 billion tokens, surpassing previous datasets by more than an order of magnitude. Using this extensive dataset, we trained an AI model that outperforms the state-of-the-art ReProver model in theorem-proving tasks. These results confirm our hypothesis and demonstrate the critical role of large datasets in improving the performance of automated theorem provers.