Daily Papers

Artificial neural networks (ANN) are inspired by human learning. However, unlike human education, classical ANN does not use a curriculum. Curriculum Learning (CL) refers to the process of ANN training in which examples are used in a meaningful order. When using CL, training begins with a subset of the dataset and new samples are added throughout the training, or training begins with the entire dataset and the number of samples used is reduced. With these changes in training dataset size, better results can be obtained with curriculum, anti-curriculum, or random-curriculum methods than the vanilla method. However, a generally efficient CL method for various architectures and data sets is not found. In this paper, we propose cyclical curriculum learning (CCL), in which the data size used during training changes cyclically rather than simply increasing or decreasing. Instead of using only the vanilla method or only the curriculum method, using both methods cyclically like in CCL provides more successful results. We tested the method on 18 different data sets and 15 architectures in image and text classification tasks and obtained more successful results than no-CL and existing CL methods. We also have shown theoretically that it is less erroneous to apply CL and vanilla cyclically instead of using only CL or only vanilla method. The code of Cyclical Curriculum is available at https://github.com/CyclicalCurriculum/Cyclical-Curriculum.

An oft-cited open problem of federated learning is the existence of data heterogeneity at the clients. One pathway to understanding the drastic accuracy drop in federated learning is by scrutinizing the behavior of the clients' deep models on data with different levels of "difficulty", which has been left unaddressed. In this paper, we investigate a different and rarely studied dimension of FL: ordered learning. Specifically, we aim to investigate how ordered learning principles can contribute to alleviating the heterogeneity effects in FL. We present theoretical analysis and conduct extensive empirical studies on the efficacy of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random curriculum. We find that curriculum learning largely alleviates non-IIDness. Interestingly, the more disparate the data distributions across clients the more they benefit from ordered learning. We provide analysis explaining this phenomenon, specifically indicating how curriculum training appears to make the objective landscape progressively less convex, suggesting fast converging iterations at the beginning of the training procedure. We derive quantitative results of convergence for both convex and nonconvex objectives by modeling the curriculum training on federated devices as local SGD with locally biased stochastic gradients. Also, inspired by ordered learning, we propose a novel client selection technique that benefits from the real-world disparity in the clients. Our proposed approach to client selection has a synergic effect when applied together with ordered learning in FL.

Curriculum learning has shown promise in improving training efficiency and generalization in various machine learning domains, yet its potential in pretraining language models remains underexplored, prompting our work as the first systematic investigation in this area. We experimented with different settings, including vanilla curriculum learning, pacing-based sampling, and interleaved curricula-guided by six difficulty metrics spanning linguistic and information-theoretic perspectives. We train models under these settings and evaluate their performance on eight diverse benchmarks. Our experiments reveal that curriculum learning consistently improves convergence in early and mid-training phases, and can yield lasting gains when used as a warmup strategy with up to 3.5% improvement. Notably, we identify compression ratio, lexical diversity, and readability as effective difficulty signals across settings. Our findings highlight the importance of data ordering in large-scale pretraining and provide actionable insights for scalable, data-efficient model development under realistic training scenarios.

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.

Due to the scarcity of high-quality data, large language models (LLMs) are often trained on mixtures of data with varying quality levels, even after sophisticated data curation. A natural approach to better leverage high-quality data is curriculum-based pretraining, where the model is trained on data sorted in ascending order of quality as determined by a quality metric. However, prior studies have reported limited improvements from such curriculum-based pretraining strategies. This work identifies a critical factor constraining these methods: the incompatibility between the ascending data quality order and the decaying learning rate (LR) schedule. We find that while curriculum-based training substantially outperforms random shuffling when using a constant LR, its advantage diminishes under standard LR decay schedules. Our experiments show this incompatibility can be mitigated by two simple strategies: (1) employing a more moderate LR decay schedule, where the final LR is only moderately smaller than the peak LR, and (2) replacing LR decay with model averaging, i.e., computing a weighted average of the final few checkpoints. By combining these strategies, we improve the average score on a suite of standard benchmarks by 1.64% over random shuffling, without additional data refinement. Validated on 1.5B-parameter models trained over 30B tokens with various data-quality metrics, our findings call for a re-evaluation of curriculum-based LLM pretraining and underscore the potential of co-designing data curricula with optimization methods.

The dominant paradigm for instruction tuning is the random-shuffled training of maximally diverse instruction-response pairs. This paper explores the potential benefits of applying a structured cognitive learning approach to instruction tuning in contemporary large language models like ChatGPT and GPT-4. Unlike the previous conventional randomized instruction dataset, we propose a highly structured synthetic dataset that mimics the progressive and organized nature of human education. We curate our dataset by aligning it with educational frameworks, incorporating meta information including its topic and cognitive rigor level for each sample. Our dataset covers comprehensive fine-grained topics spanning diverse educational stages (from middle school to graduate school) with various questions for each topic to enhance conceptual depth using Bloom's taxonomy-a classification framework distinguishing various levels of human cognition for each concept. The results demonstrate that this cognitive rigorous training approach yields significant performance enhancements - +3.06 on the MMLU benchmark and an additional +1.28 on AI2 Reasoning Challenge (hard set) - compared to conventional randomized training, all while avoiding additional computational costs. This research highlights the potential of leveraging human learning principles to enhance the capabilities of language models in comprehending and responding to complex instructions and tasks.

Curriculum learning, a training technique where data is presented to the model in order of example difficulty (e.g., from simpler to more complex documents), has shown limited success for pre-training language models. In this work, we investigate whether curriculum learning becomes competitive if we replace conventional human-centered difficulty metrics with one that more closely corresponds to example difficulty as observed during model training. Specifically, we experiment with sorting training examples by their training data influence, a score which estimates the effect of individual training examples on the model's output. Models trained on our curricula are able to outperform ones trained in random order by over 10 percentage points in benchmarks, confirming that curriculum learning is beneficial for language model pre-training, as long as a more model-centric notion of difficulty is adopted.

Directly learning from examples of random difficulty levels is often challenging for both humans and machine learning models. A more effective strategy involves exposing learners to examples in a progressive order, from easy to difficult. Curriculum Learning (CL) has been proposed to implement this strategy in machine learning model training. However, two key challenges persist in CL framework design: defining the difficulty of training data and determining the appropriate amount of data to input at each training step. This paper presents a Psychology-based Unified Dynamic Framework for Curriculum Learning (PUDF), drawing inspiration from psychometrics. We quantify the difficulty of training data by applying Item Response Theory (IRT) to responses from Artificial Crowds (AC). This theory-driven IRT-AC approach leads to global (i.e., model-independent) and interpretable difficulty values. Leveraging IRT, we propose a Dynamic Data Selection via Model Ability Estimation (DDS-MAE) strategy to schedule the appropriate amount of data during model training. Since our difficulty labeling and model ability estimation are based on a consistent theory, namely IRT, their values are comparable within the same scope, potentially leading to a faster convergence compared to the other CL methods. Experimental results demonstrate that fine-tuning pre-trained language models with PUDF enhances their performance on the GLUE benchmark. Moreover, PUDF surpasses other state-of-the-art (SOTA) CL methods on the GLUE benchmark. We further explore the components of PUDF, namely the difficulty measurer (IRT-AC) and the training scheduler (DDS-MAE) qualitatively and quantitatively. Lastly, we conduct an ablation study to clarify which components of PUDF contribute to faster convergence and higher accuracy.

Curriculum Learning is the presentation of samples to the machine learning model in a meaningful order instead of a random order. The main challenge of Curriculum Learning is determining how to rank these samples. The ranking of the samples is expressed by the scoring function. In this study, scoring functions were compared using data set features, using the model to be trained, and using another model and their ensemble versions. Experiments were performed for 4 images and 4 text datasets. No significant differences were found between scoring functions for text datasets, but significant improvements were obtained in scoring functions created using transfer learning compared to classical model training and other scoring functions for image datasets. It shows that different new scoring functions are waiting to be found for text classification tasks.

Recent self-supervised learning approaches focus on using a few thousand data points to learn policies for high-level, low-dimensional action spaces. However, scaling this framework for high-dimensional control require either scaling up the data collection efforts or using a clever sampling strategy for training. We present a novel approach - Curriculum Accelerated Self-Supervised Learning (CASSL) - to train policies that map visual information to high-level, higher- dimensional action spaces. CASSL orders the sampling of training data based on control dimensions: the learning and sampling are focused on few control parameters before other parameters. The right curriculum for learning is suggested by variance-based global sensitivity analysis of the control space. We apply our CASSL framework to learning how to grasp using an adaptive, underactuated multi-fingered gripper, a challenging system to control. Our experimental results indicate that CASSL provides significant improvement and generalization compared to baseline methods such as staged curriculum learning (8% increase) and complete end-to-end learning with random exploration (14% improvement) tested on a set of novel objects.

Quantum computing offers a powerful new perspective on probabilistic and collective behaviors traditionally taught in statistical physics. This paper presents two classroom-ready modules that integrate quantum computing into the undergraduate curriculum using Qiskit: the quantum random walk and the Ising model. Both modules allow students to simulate and contrast classical and quantum systems, deepening their understanding of concepts such as superposition, interference, and statistical distributions. We outline the quantum circuits involved, provide sample code and student activities, and discuss how each example can be used to enhance student engagement with statistical physics. These modules are suitable for integration into courses in statistical mechanics, modern physics, or as part of an introductory unit on quantum computing.

Existing dialog state tracking (DST) models are trained with dialog data in a random order, neglecting rich structural information in a dataset. In this paper, we propose to use curriculum learning (CL) to better leverage both the curriculum structure and schema structure for task-oriented dialogs. Specifically, we propose a model-agnostic framework called Schema-aware Curriculum Learning for Dialog State Tracking (SaCLog), which consists of a preview module that pre-trains a DST model with schema information, a curriculum module that optimizes the model with CL, and a review module that augments mispredicted data to reinforce the CL training. We show that our proposed approach improves DST performance over both a transformer-based and RNN-based DST model (TripPy and TRADE) and achieves new state-of-the-art results on WOZ2.0 and MultiWOZ2.1.

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

This paper presents that the masked-modeling principle driving the success of large foundational vision models can be effectively applied to audio by making predictions in a latent space. We introduce Audio-based Joint-Embedding Predictive Architecture (A-JEPA), a simple extension method for self-supervised learning from the audio spectrum. Following the design of I-JEPA, our A-JEPA encodes visible audio spectrogram patches with a curriculum masking strategy via context encoder, and predicts the representations of regions sampled at well-designed locations. The target representations of those regions are extracted by the exponential moving average of context encoder, i.e., target encoder, on the whole spectrogram. We find it beneficial to transfer random block masking into time-frequency aware masking in a curriculum manner, considering the complexity of highly correlated in local time and frequency in audio spectrograms. To enhance contextual semantic understanding and robustness, we fine-tune the encoder with a regularized masking on target datasets, instead of input dropping or zero. Empirically, when built with Vision Transformers structure, we find A-JEPA to be highly scalable and sets new state-of-the-art performance on multiple audio and speech classification tasks, outperforming other recent models that use externally supervised pre-training.

The order of training samples plays a crucial role in large language models (LLMs), significantly impacting both their external performance and internal learning dynamics. Traditional methods for investigating this effect generally require retraining the model with various sample orders, which is computationally infeasible for LLMs. In this work, we improve traditional methods by designing a retraining-free framework. By approximating Adam optimizer updates with first- and second-order Taylor expansions and utilizing random projection methods to store intermediate checkpoints, our framework can efficiently estimate model parameters for arbitrary training sample orders. Next, we apply our framework to two downstream research problems: (1) Training curriculum design for LLMs -- we base our retraining-free framework to propose a novel curriculum learning strategy that augments curriculum proposals with estimated model performances, enabling more informed sample scheduling. (2) LLMs' memorization and generalization effect analysis -- we use our retraining-free framework to estimate how the positions of training samples influence LLMs' capacity for memorization and generalization. We conduct extensive experiments to validate the effectiveness of our retraining-free framework in reproducing the true model performances, and further demonstrate its potential in optimizing LLM training curricula and analyzing the memorization and generalization effects of LLMs.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

Curriculum design is a fundamental component of education. For example, when we learn mathematics at school, we build upon our knowledge of addition to learn multiplication. These and other concepts must be mastered before our first algebra lesson, which also reinforces our addition and multiplication skills. Designing a curriculum for teaching either a human or a machine shares the underlying goal of maximizing knowledge transfer from earlier to later tasks, while also minimizing forgetting of learned tasks. Prior research on curriculum design for image classification focuses on the ordering of training examples during a single offline task. Here, we investigate the effect of the order in which multiple distinct tasks are learned in a sequence. We focus on the online class-incremental continual learning setting, where algorithms or humans must learn image classes one at a time during a single pass through a dataset. We find that curriculum consistently influences learning outcomes for humans and for multiple continual machine learning algorithms across several benchmark datasets. We introduce a novel-object recognition dataset for human curriculum learning experiments and observe that curricula that are effective for humans are highly correlated with those that are effective for machines. As an initial step towards automated curriculum design for online class-incremental learning, we propose a novel algorithm, dubbed Curriculum Designer (CD), that designs and ranks curricula based on inter-class feature similarities. We find significant overlap between curricula that are empirically highly effective and those that are highly ranked by our CD. Our study establishes a framework for further research on teaching humans and machines to learn continuously using optimized curricula.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

Curriculum Learning has been a popular strategy to improve the cognitive plausibility of Small-Scale Language Models (SSLMs) in the BabyLM Challenge. However, it has not led to considerable improvements over non-curriculum models. We assess whether theoretical linguistic acquisition theories can be used to specify more fine-grained curriculum learning strategies, creating age-ordered corpora of Child-Directed Speech for four typologically distant language families to implement SSLMs and acquisition-inspired curricula cross-lingually. Comparing the success of three objective curricula (Growing, Inwards and MMM) that precisely replicate the predictions of acquisition theories on a standard SSLM architecture, we find fine-grained acquisition-inspired curricula can outperform non-curriculum baselines and performance benefits of curricula strategies in SSLMs can be derived by specifying fine-grained language-specific curricula that precisely replicate language acquisition theories.

Curriculum learning (CL) posits that machine learning models -- similar to humans -- may learn more efficiently from data that match their current learning progress. However, CL methods are still poorly understood and, in particular for natural language processing (NLP), have achieved only limited success. In this paper, we explore why. Starting from an attempt to replicate and extend a number of recent curriculum methods, we find that their results are surprisingly brittle when applied to NLP. A deep dive into the (in)effectiveness of the curricula in some scenarios shows us why: when curricula are employed in combination with the popular Adam optimisation algorithm, they oftentimes learn to adapt to suboptimally chosen optimisation parameters for this algorithm. We present a number of different case studies with different common hand-crafted and automated CL approaches to illustrate this phenomenon, and we find that none of them outperforms optimisation with only Adam with well-chosen hyperparameters. As such, our results contribute to understanding why CL methods work, but at the same time urge caution when claiming positive results.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.

Automatic Curriculum Learning (ACL) has become a cornerstone of recent successes in Deep Reinforcement Learning (DRL).These methods shape the learning trajectories of agents by challenging them with tasks adapted to their capacities. In recent years, they have been used to improve sample efficiency and asymptotic performance, to organize exploration, to encourage generalization or to solve sparse reward problems, among others. The ambition of this work is dual: 1) to present a compact and accessible introduction to the Automatic Curriculum Learning literature and 2) to draw a bigger picture of the current state of the art in ACL to encourage the cross-breeding of existing concepts and the emergence of new ideas.

Reinforcement Learning (RL) algorithms are often known for sample inefficiency and difficult generalization. Recently, Unsupervised Environment Design (UED) emerged as a new paradigm for zero-shot generalization by simultaneously learning a task distribution and agent policies on the generated tasks. This is a non-stationary process where the task distribution evolves along with agent policies; creating an instability over time. While past works demonstrated the potential of such approaches, sampling effectively from the task space remains an open challenge, bottlenecking these approaches. To this end, we introduce CLUTR: a novel unsupervised curriculum learning algorithm that decouples task representation and curriculum learning into a two-stage optimization. It first trains a recurrent variational autoencoder on randomly generated tasks to learn a latent task manifold. Next, a teacher agent creates a curriculum by maximizing a minimax REGRET-based objective on a set of latent tasks sampled from this manifold. Using the fixed-pretrained task manifold, we show that CLUTR successfully overcomes the non-stationarity problem and improves stability. Our experimental results show CLUTR outperforms PAIRED, a principled and popular UED method, in the challenging CarRacing and navigation environments: achieving 10.6X and 45\% improvement in zero-shot generalization, respectively. CLUTR also performs comparably to the non-UED state-of-the-art for CarRacing, while requiring 500X fewer environment interactions.

We describe our team's contribution to the STRICT-SMALL track of the BabyLM Challenge. The challenge requires training a language model from scratch using only a relatively small training dataset of ten million words. We experiment with three variants of cognitively-motivated curriculum learning and analyze their effect on the performance of the model on linguistic evaluation tasks. In the vocabulary curriculum, we analyze methods for constraining the vocabulary in the early stages of training to simulate cognitively more plausible learning curves. In the data curriculum experiments, we vary the order of the training instances based on i) infant-inspired expectations and ii) the learning behavior of the model. In the objective curriculum, we explore different variations of combining the conventional masked language modeling task with a more coarse-grained word class prediction task to reinforce linguistic generalization capabilities. Our results did not yield consistent improvements over our own non-curriculum learning baseline across a range of linguistic benchmarks; however, we do find marginal gains on select tasks. Our analysis highlights key takeaways for specific combinations of tasks and settings which benefit from our proposed curricula. We moreover determine that careful selection of model architecture, and training hyper-parameters yield substantial improvements over the default baselines provided by the BabyLM challenge.

Recent automatic curriculum learning algorithms, and in particular Teacher-Student algorithms, rely on the notion of learning progress, making the assumption that the good next tasks are the ones on which the learner is making the fastest progress or digress. In this work, we first propose a simpler and improved version of these algorithms. We then argue that the notion of learning progress itself has several shortcomings that lead to a low sample efficiency for the learner. We finally propose a new algorithm, based on the notion of mastering rate, that significantly outperforms learning progress-based algorithms.

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

Curriculum learning plays a crucial role in enhancing the training efficiency of large language models (LLMs) on reasoning tasks. However, existing methods often fail to adequately account for variations in prompt difficulty or rely on simplistic filtering mechanisms to select prompt datasets within a narrow criterion range, resulting in significant computational waste. In this work, we approach the problem from the perspective of reinforcement learning gradient optimization, offering a systematic and theoretical investigation into how to improve the training efficiency of LLMs. We identify two key factors influencing training efficiency: the selection of training prompts and the allocation of rollout quantities across different prompts. Our theoretical analysis reveals that the sampling distribution of prompts dictates the convergence rate of gradient descent, while the allocation of the rollout quantity influences the consistency and stability of overall gradient updates. Based on these insights, we propose CurES, an efficient training method that accelerates convergence and employs Bayesian posterior estimation to minimize computational overhead. Experiments demonstrate that our CurES outperforms Group Relative Policy Optimization (GRPO) by +3.30 points and +4.82 points with 1.5B and 7B models, respectively. Additionally, CurES exhibits faster convergence compared to baselines, including GRPO.

We teach goal-driven agents to interactively act and speak in situated environments by training on generated curriculums. Our agents operate in LIGHT (Urbanek et al. 2019) -- a large-scale crowd-sourced fantasy text adventure game wherein an agent perceives and interacts with the world through textual natural language. Goals in this environment take the form of character-based quests, consisting of personas and motivations. We augment LIGHT by learning to procedurally generate additional novel textual worlds and quests to create a curriculum of steadily increasing difficulty for training agents to achieve such goals. In particular, we measure curriculum difficulty in terms of the rarity of the quest in the original training distribution -- an easier environment is one that is more likely to have been found in the unaugmented dataset. An ablation study shows that this method of learning from the tail of a distribution results in significantly higher generalization abilities as measured by zero-shot performance on never-before-seen quests.

We introduce Prompt Curriculum Learning (PCL), a lightweight reinforcement learning (RL) algorithm that selects intermediate-difficulty prompts using a learned value model to post-train language models. Since post-training LLMs via RL remains sensitive to batching and prompt selection strategies, we first conduct a series of systematic experiments where we (1) determine the optimal training batch size that balances generation efficiency and gradient quality and (2) establish the importance of focusing on prompts of intermediate difficulty for the policy. We build upon these results to design PCL, which identifies prompts of intermediate difficulty for the current policy in an on-policy manner by using a value model that is concurrently updated based on the current policy. By focusing on informative prompts that yield high effective ratios, PCL achieves either the highest performance or requires significantly less time to reach comparable performance to its counterparts. Compared to rollout-based filtering methods, PCL avoids costly rollouts and achieves 12.1times and 16.9times faster speed on identifying intermediate-difficulty prompts when training on MATH and DeepScaleR, respectively. We further demonstrate that our value model accurately predicts prompt difficulty and allows PCL to focus on progressively more challenging prompts during RL. Our results present a new methodology that delivers improved tradeoff between upper-bound performance and efficiency for reasoning-focused RL.

Modern language models rely on static vocabularies, fixed before pretraining, in contrast to the adaptive vocabulary acquisition observed in human language learning. To bridge this gap, we introduce vocabulary curriculum learning, an approach that improves pretraining efficiency with log-linear scaling gains relative to vocabulary size. Our method alternates between entropy-guided vocabulary expansion and model optimization, enabling models to learn transferable representations across diverse tokenization granularities. This approach naturally gives rise to an optimal computation allocation pattern: longer tokens capture predictable content, while shorter tokens focus on more complex, harder-to-predict contexts. Experiments on small-scale GPT models demonstrate improved scaling efficiency, reinforcing the effectiveness of dynamic tokenization. We release our code to support further research and plan to extend our experiments to larger models and diverse domains.

Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation.

Retrieval-Augmented Language Models (RALMs) represent a classic paradigm where models enhance generative capabilities using external knowledge retrieved via a specialized module. Recent advancements in Agent techniques enable Large Language Models (LLMs) to autonomously utilize tools for retrieval, planning, and reasoning. While existing training-based methods show promise, their agentic abilities are limited by inherent characteristics of the task-specific data used during training. To further enhance the universal search capability of agents, we propose a novel pre-training framework, MaskSearch. In the pre-training stage, we introduce the Retrieval Augmented Mask Prediction (RAMP) task, where the model learns to leverage search tools to fill masked spans on a large number of pre-training data, thus acquiring universal retrieval and reasoning capabilities for LLMs. After that, the model is trained on downstream tasks to achieve further improvement. We apply both Supervised Fine-tuning (SFT) and Reinforcement Learning (RL) for training. For SFT, we combine agent-based and distillation-based methods to generate training data, starting with a multi-agent system consisting of a planner, rewriter, observer, and followed by a self-evolving teacher model. While for RL, we employ DAPO as the training framework and adopt a hybrid reward system consisting of answer rewards and format rewards. Additionally, we introduce a curriculum learning approach that allows the model to learn progressively from easier to more challenging instances based on the number of masked spans. We evaluate the effectiveness of our framework in the scenario of open-domain multi-hop question answering. Through extensive experiments, we demonstrate that MaskSearch significantly enhances the performance of LLM-based search agents on both in-domain and out-of-domain downstream tasks.

The superior performance of modern deep networks usually comes with a costly training procedure. This paper presents a new curriculum learning approach for the efficient training of visual backbones (e.g., vision Transformers). Our work is inspired by the inherent learning dynamics of deep networks: we experimentally show that at an earlier training stage, the model mainly learns to recognize some 'easier-to-learn' discriminative patterns within each example, e.g., the lower-frequency components of images and the original information before data augmentation. Driven by this phenomenon, we propose a curriculum where the model always leverages all the training data at each epoch, while the curriculum starts with only exposing the 'easier-to-learn' patterns of each example, and introduces gradually more difficult patterns. To implement this idea, we 1) introduce a cropping operation in the Fourier spectrum of the inputs, which enables the model to learn from only the lower-frequency components efficiently, 2) demonstrate that exposing the features of original images amounts to adopting weaker data augmentation, and 3) integrate 1) and 2) and design a curriculum learning schedule with a greedy-search algorithm. The resulting approach, EfficientTrain, is simple, general, yet surprisingly effective. As an off-the-shelf method, it reduces the wall-time training cost of a wide variety of popular models (e.g., ResNet, ConvNeXt, DeiT, PVT, Swin, and CSWin) by >1.5x on ImageNet-1K/22K without sacrificing accuracy. It is also effective for self-supervised learning (e.g., MAE). Code is available at https://github.com/LeapLabTHU/EfficientTrain.

Audio question answering (AQA) requires models to understand acoustic content and perform complex reasoning. Current models struggle with dataset imbalances and unstable training dynamics. This work combines curriculum learning with statistical data balancing to address these challenges. The method labels question difficulty using language models, then trains progressively from easy to hard examples. Statistical filtering removes overrepresented audio categories, and guided decoding constrains outputs to valid multiple-choice formats. Experiments on the DCASE 2025 training set and five additional public datasets show that data curation improves accuracy by 11.7% over baseline models, achieving 64.2% on the DCASE 2025 benchmark.

A major challenge in the Deep RL (DRL) community is to train agents able to generalize their control policy over situations never seen in training. Training on diverse tasks has been identified as a key ingredient for good generalization, which pushed researchers towards using rich procedural task generation systems controlled through complex continuous parameter spaces. In such complex task spaces, it is essential to rely on some form of Automatic Curriculum Learning (ACL) to adapt the task sampling distribution to a given learning agent, instead of randomly sampling tasks, as many could end up being either trivial or unfeasible. Since it is hard to get prior knowledge on such task spaces, many ACL algorithms explore the task space to detect progress niches over time, a costly tabula-rasa process that needs to be performed for each new learning agents, although they might have similarities in their capabilities profiles. To address this limitation, we introduce the concept of Meta-ACL, and formalize it in the context of black-box RL learners, i.e. algorithms seeking to generalize curriculum generation to an (unknown) distribution of learners. In this work, we present AGAIN, a first instantiation of Meta-ACL, and showcase its benefits for curriculum generation over classical ACL in multiple simulated environments including procedurally generated parkour environments with learners of varying morphologies. Videos and code are available at https://sites.google.com/view/meta-acl .

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Imitation learning uses data for training policies to solve complex tasks. However, when the training data is collected from human demonstrators, it often leads to multimodal distributions because of the variability in human actions. Most imitation learning methods rely on a maximum likelihood (ML) objective to learn a parameterized policy, but this can result in suboptimal or unsafe behavior due to the mode-averaging property of the ML objective. In this work, we propose Information Maximizing Curriculum, a curriculum-based approach that assigns a weight to each data point and encourages the model to specialize in the data it can represent, effectively mitigating the mode-averaging problem by allowing the model to ignore data from modes it cannot represent. To cover all modes and thus, enable diverse behavior, we extend our approach to a mixture of experts (MoE) policy, where each mixture component selects its own subset of the training data for learning. A novel, maximum entropy-based objective is proposed to achieve full coverage of the dataset, thereby enabling the policy to encompass all modes within the data distribution. We demonstrate the effectiveness of our approach on complex simulated control tasks using diverse human demonstrations, achieving superior performance compared to state-of-the-art methods.

Recent developments in Language Models (LMs) have shown their effectiveness in NLP tasks, particularly in knowledge-intensive tasks. However, the mechanisms underlying knowledge storage and memory access within their parameters remain elusive. In this paper, we investigate whether a generative LM (e.g., GPT-2) is able to access its memory sequentially or randomly. Through carefully-designed synthetic tasks, covering the scenarios of full recitation, selective recitation and grounded question answering, we reveal that LMs manage to sequentially access their memory while encountering challenges in randomly accessing memorized content. We find that techniques including recitation and permutation improve the random memory access capability of LMs. Furthermore, by applying this intervention to realistic scenarios of open-domain question answering, we validate that enhancing random access by recitation leads to notable improvements in question answering. The code to reproduce our experiments can be found at https://github.com/sail-sg/lm-random-memory-access.

In precision-oriented tasks like answer ranking, it is more important to rank many relevant answers highly than to retrieve all relevant answers. It follows that a good ranking strategy would be to learn how to identify the easiest correct answers first (i.e., assign a high ranking score to answers that have characteristics that usually indicate relevance, and a low ranking score to those with characteristics that do not), before incorporating more complex logic to handle difficult cases (e.g., semantic matching or reasoning). In this work, we apply this idea to the training of neural answer rankers using curriculum learning. We propose several heuristics to estimate the difficulty of a given training sample. We show that the proposed heuristics can be used to build a training curriculum that down-weights difficult samples early in the training process. As the training process progresses, our approach gradually shifts to weighting all samples equally, regardless of difficulty. We present a comprehensive evaluation of our proposed idea on three answer ranking datasets. Results show that our approach leads to superior performance of two leading neural ranking architectures, namely BERT and ConvKNRM, using both pointwise and pairwise losses. When applied to a BERT-based ranker, our method yields up to a 4% improvement in MRR and a 9% improvement in P@1 (compared to the model trained without a curriculum). This results in models that can achieve comparable performance to more expensive state-of-the-art techniques.

In this paper, we provide a finite random iterated function system satisfying the open set condition, for which the random version of Bowen's formula fails to hold. This counterexample shows that analogous results established for random recursive constructions are not always obtained for random iterated function systems.

Recent research highlights the challenges retrieval models face in retrieving useful contexts and the limitations of generation models in effectively utilizing those contexts in retrieval-augmented generation (RAG) settings. To address these challenges, we introduce RAG-RL, the first reasoning language model (RLM) specifically trained for RAG. RAG-RL demonstrates that stronger answer generation models can identify relevant contexts within larger sets of retrieved information -- thereby alleviating the burden on retrievers -- while also being able to utilize those contexts more effectively. Moreover, we show that curriculum design in the reinforcement learning (RL) post-training process is a powerful approach to enhancing model performance. We benchmark our method on two open-domain question-answering datasets and achieve state-of-the-art results, surpassing previous SOTA generative reader models. In addition, we offers empirical insights into various curriculum learning strategies, providing a deeper understanding of their impact on model performance.

Training Large Language Models (LLMs) incurs substantial data-related costs, motivating the development of data-efficient training methods through optimised data ordering and selection. Human-inspired learning strategies, such as curriculum learning, offer possibilities for efficient training by organising data according to common human learning practices. Despite evidence that fine-tuning with curriculum learning improves the performance of LLMs for natural language understanding tasks, its effectiveness is typically assessed using a single model. In this work, we extend previous research by evaluating both curriculum-based and non-curriculum-based learning strategies across multiple LLMs, using human-defined and automated data labels for medical question answering. Our results indicate a moderate impact of using human-inspired learning strategies for fine-tuning LLMs, with maximum accuracy gains of 1.77% per model and 1.81% per dataset. Crucially, we demonstrate that the effectiveness of these strategies varies significantly across different model-dataset combinations, emphasising that the benefits of a specific human-inspired strategy for fine-tuning LLMs do not generalise. Additionally, we find evidence that curriculum learning using LLM-defined question difficulty outperforms human-defined difficulty, highlighting the potential of using model-generated measures for optimal curriculum design.

Multi-token prediction (MTP) is a recently proposed pre-training objective for language models. Rather than predicting only the next token (NTP), MTP predicts the next k tokens at each prediction step, using multiple prediction heads. MTP has shown promise in improving downstream performance, inference speed, and training efficiency, particularly for large models. However, prior work has shown that smaller language models (SLMs) struggle with the MTP objective. To address this, we propose a curriculum learning strategy for MTP training, exploring two variants: a forward curriculum, which gradually increases the complexity of the pre-training objective from NTP to MTP, and a reverse curriculum, which does the opposite. Our experiments show that the forward curriculum enables SLMs to better leverage the MTP objective during pre-training, improving downstream NTP performance and generative output quality, while retaining the benefits of self-speculative decoding. The reverse curriculum achieves stronger NTP performance and output quality, but fails to provide any self-speculative decoding benefits.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Recent advances in pre-trained language models have improved the performance for text classification tasks. However, little attention is paid to the priority scheduling strategy on the samples during training. Humans acquire knowledge gradually from easy to complex concepts, and the difficulty of the same material can also vary significantly in different learning stages. Inspired by this insights, we proposed a novel self-paced dynamic curriculum learning (SPDCL) method for imbalanced text classification, which evaluates the sample difficulty by both linguistic character and model capacity. Meanwhile, rather than using static curriculum learning as in the existing research, our SPDCL can reorder and resample training data by difficulty criterion with an adaptive from easy to hard pace. The extensive experiments on several classification tasks show the effectiveness of SPDCL strategy, especially for the imbalanced dataset.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

The development of state-of-the-art large language models is commonly understood as a two-stage process involving pre-training and post-training. We point out the need for an additional intermediate stage called reinforcement mid-training with potential for strong performance gains. In this paper, we formally define the problem and identify three key challenges: (1) inefficient training due to excessive reasoning steps, (2) disregard of the imbalanced token entropy distribution, and (3) underutilization of token information. To address these challenges, we propose RMT, a framework for efficient, adaptive, and unified reinforcement mid-training with various innovative components. In particular, we first introduce a dynamic token budget mechanism that constrains unnecessary reasoning steps and mitigates model overthinking. Next, we design a curriculum-based adaptive sampling method that fosters a progressive learning trajectory from easy to hard tokens. Finally, we present a dual training strategy that combines reinforcement learning with next-token prediction, ensuring targeted learning on key tokens and full exploitation of all token information. Extensive experiments demonstrate the superiority of RMT over state-of-the-art methods, achieving up to +64.91% performance improvement with only 21% of the reasoning length in language modeling. We also show that checkpoints obtained after reinforcement mid-training can benefit the subsequent post-training, yielding up to +18.76% improvement in the mathematical domain.

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves both the efficiency and final accuracy of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets-including AMC, AIME, and IMO-style problems-demonstrate that AdaRFT significantly improves both training efficiency and reasoning performance. We evaluate AdaRFT across multiple data distributions and model sizes, showing that it reduces the number of training steps by up to 2x and improves accuracy by a considerable margin, offering a more scalable and effective RFT framework.

We discover that DALLE-2 seems to have a hidden vocabulary that can be used to generate images with absurd prompts. For example, it seems that Apoploe vesrreaitais means birds and Contarra ccetnxniams luryca tanniounons (sometimes) means bugs or pests. We find that these prompts are often consistent in isolation but also sometimes in combinations. We present our black-box method to discover words that seem random but have some correspondence to visual concepts. This creates important security and interpretability challenges.

We introduce a high-quality dataset that contains 3,397 samples comprising (i) multiple choice questions, (ii) answers (including distractors), and (iii) their source documents, from the educational domain. Each question is phrased in two forms, normal and close. Correct answers are linked to source documents with sentence-level annotations. Thus, our versatile dataset can be used for both question and distractor generation, as well as to explore new challenges such as question format conversion. Furthermore, 903 questions are accompanied by their cognitive complexity level as per Bloom's taxonomy. All questions have been generated by educational experts rather than crowd workers to ensure they are maintaining educational and learning standards. Our analysis and experiments suggest distinguishable differences between our dataset and commonly used ones for question generation for educational purposes. We believe this new dataset can serve as a valuable resource for research and evaluation in the educational domain. The dataset and baselines will be released to support further research in question generation.

Recent breakthroughs in large language models (LLMs) on reasoning tasks rely heavily on massive, high-quality datasets-typically human-annotated and thus difficult to scale. While data synthesis or distillation offers a promising alternative, existing methods struggle with inconsistent data quality and an inability to dynamically adapt to the evolving capabilities of the model, leading to suboptimal training signals. To address these limitations, we introduce Socratic-Zero, a fully autonomous framework that generates high-quality training data from minimal seed examples through the co-evolution of three agents: the Teacher, the Solver, and the Generator. The Solver continuously refines its reasoning by learning from preference feedback on both successful and failed trajectories; the Teacher adaptively crafts increasingly challenging questions based on the Solver's weaknesses; and the Generator distills the Teacher's question-design strategy to enable scalable, high-fidelity curriculum generation. This closed-loop system produces a self-improving curriculum-requiring no pre-existing tasks or labels. Remarkably, starting from only 100 seed questions, our Socratic-Solver-8B achieves an average gain of +20.2 percentage points over prior data synthesis methods across seven mathematical reasoning benchmarks (AMC23, AIME24-25, Olympiad, MATH-500, Minerva, and GSM8K), with consistent gains on both Qwen3 and GLM4 series models. Even more surprisingly, synthetic data from Socratic-Generator-32B enables student LLMs to achieve superior performance compared to other state-of-the-art (SOTA) commercial LLMs on these benchmarks, including Qwen3-235B-A22B, DeepSeek-V3.1-671B, GPT-5, Gemini-2.5-Pro, Grok-4, and Claude-4.1-Opus.

Multimodal large language models (MLLMs) still perform poorly on scientific tasks, particularly those requiring multi-step and interpretable reasoning. Their limitations include insufficient scientific reasoning patterns, lack of global coherence in multi-step inference, and the absence of reflective self-correction, making them unreliable in structured scientific contexts. We introduce EduFlow, the first end-to-end framework that covers the full pipeline of educational scientific reasoning, including data selection, MCTS-based trajectory construction, model training, and output optimization. At its core is EduPRM, a process-aware reward model that critiques reasoning steps with tags and justifications. EduPRM is trained via curriculum learning on three complementary supervision sources: MCTS-guided trajectories, error-injected critiques, and teacher-student dialogues, enabling dynamic adaptation to multi-stage problem solving and iterative refinement during inference. We further propose EduMCTS, a domain-adapted search framework that introduces bootstrapping actions specifically designed for educational reasoning, such as a self-reflection mechanism that promotes reflective error correction. It further leverages EduPRM's fine-grained feedback to guide the search toward higher-quality reasoning trajectories. By applying self-consistency and rejection sampling, we constructed EduMCTS-160K, a large-scale dataset of educational reasoning trajectories. Extensive experiments demonstrate that EduFlow enhances reasoning consistency and coherence. Code, data, and models will be released.

Policy-based reinforcement learning currently plays an important role in improving LLMs on mathematical reasoning tasks. However, existing rollout-based reinforcement learning methods (GRPO, DAPO, GSPO, etc.) fail to explicitly consider LLMs' learning ability for samples of different difficulty levels, which is contrary to the human cognitive process of mathematical reasoning tasks from easy to difficult. Intuitively, we find that the variance of the rollout group's reward in RLVR partly reflects the difficulty of the current sample for LLMs. Samples that are too easy or too difficult have a lower variance, while samples with moderate difficulty have a higher variance. Based on this, we propose VCRL, a curriculum reinforcement learning framework that dynamically controls the difficulty of training samples based on the variance of group rewards. Experiments on five mathematical benchmarks and two models reveal the advantages of VCRL over the current LLM RL baselines.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

Mathematical questioning is crucial for assessing students problem-solving skills. Since manually creating such questions requires substantial effort, automatic methods have been explored. Existing state-of-the-art models rely on fine-tuning strategies and struggle to generate questions that heavily involve multiple steps of logical and arithmetic reasoning. Meanwhile, large language models(LLMs) such as ChatGPT have excelled in many NLP tasks involving logical and arithmetic reasoning. Nonetheless, their applications in generating educational questions are underutilized, especially in the field of mathematics. To bridge this gap, we take the first step to conduct an in-depth analysis of ChatGPT in generating pre-university math questions. Our analysis is categorized into two main settings: context-aware and context-unaware. In the context-aware setting, we evaluate ChatGPT on existing math question-answering benchmarks covering elementary, secondary, and ternary classes. In the context-unaware setting, we evaluate ChatGPT in generating math questions for each lesson from pre-university math curriculums that we crawl. Our crawling results in TopicMath, a comprehensive and novel collection of pre-university math curriculums collected from 121 math topics and 428 lessons from elementary, secondary, and tertiary classes. Through this analysis, we aim to provide insight into the potential of ChatGPT as a math questioner.

Efficient exploration is essential for intelligent systems interacting with their environment, but existing language models often fall short in scenarios that require strategic information gathering. In this paper, we present PAPRIKA, a fine-tuning approach that enables language models to develop general decision-making capabilities that are not confined to particular environments. By training on synthetic interaction data from different tasks that require diverse strategies, PAPRIKA teaches models to explore and adapt their behavior on a new task based on environment feedback in-context without more gradient updates. Experimental results show that models fine-tuned with PAPRIKA can effectively transfer their learned decision-making capabilities to entirely unseen tasks without additional training. Unlike traditional training, our approach's primary bottleneck lies in sampling useful interaction data instead of model updates. To improve sample efficiency, we propose a curriculum learning strategy that prioritizes sampling trajectories from tasks with high learning potential. These results suggest a promising path towards AI systems that can autonomously solve novel sequential decision-making problems that require interactions with the external world.

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, the indiscriminate mixing of the two signals in existing methods, especially from the early stages, may lead to ambiguous guidance and limited gains. To address this issue, we propose **CAPO** (**C**urriculum **A**dvantage **P**olicy **O**ptimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization framework.

Despite impressive progress in areas like mathematical reasoning, large language models still face significant challenges in consistently solving complex problems. Drawing inspiration from key human learning strategies, we propose two novel strategies to enhance the capability of large language models to solve these complex problems. First, Adaptive Difficulty Curriculum Learning (ADCL) is a novel curriculum learning strategy that tackles the Difficulty Shift phenomenon (i.e., a model's perception of problem difficulty dynamically changes during training) by periodically re-estimating difficulty within upcoming data batches to maintain alignment with the model's evolving capabilities. Second, Expert-Guided Self-Reformulation (EGSR) is a novel reinforcement learning strategy that bridges the gap between imitation learning and pure exploration by guiding models to reformulate expert solutions within their own conceptual framework, rather than relying on direct imitation, fostering deeper understanding and knowledge assimilation. Extensive experiments on challenging mathematical reasoning benchmarks, using Qwen2.5-7B as the base model, demonstrate that these human-inspired strategies synergistically and significantly enhance performance. Notably, their combined application improves performance over the standard Zero-RL baseline by 10% on the AIME24 benchmark and 16.6% on AIME25.

Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

Large Language Models (LLMs) have shown strong in-context learning (ICL) abilities with a few demonstrations. However, one critical challenge is how to select demonstrations to elicit the full potential of LLMs. In this paper, we propose Curriculum Demonstration Selection (CDS), a novel demonstration selection method for ICL. Instead of merely using similarity, CDS additionally partitions samples by their complexity measurements. Following curriculum learning, CDS then selects demonstrations from easy to difficult. Thus the selected demonstrations cover a wide range of difficulty levels, enabling LLMs to learn from varied complexities within the training set. Experiments demonstrate that our CDS consistently outperforms baseline methods, achieving notable improvements across nine LLMs on three benchmarks. Moreover, CDS proves especially effective in enhancing LLM performance in solving challenging problems.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

Large Language Models (LLMs) have significantly advanced smart education in the Artificial General Intelligence (AGI) era. A promising application lies in the automatic generalization of instructional design for curriculum and learning activities, focusing on two key aspects: (1) Customized Generation: generating niche-targeted teaching content based on students' varying learning abilities and states, and (2) Intelligent Optimization: iteratively optimizing content based on feedback from learning effectiveness or test scores. Currently, a single large LLM cannot effectively manage the entire process, posing a challenge for designing intelligent teaching plans. To address these issues, we developed EduPlanner, an LLM-based multi-agent system comprising an evaluator agent, an optimizer agent, and a question analyst, working in adversarial collaboration to generate customized and intelligent instructional design for curriculum and learning activities. Taking mathematics lessons as our example, EduPlanner employs a novel Skill-Tree structure to accurately model the background mathematics knowledge of student groups, personalizing instructional design for curriculum and learning activities according to students' knowledge levels and learning abilities. Additionally, we introduce the CIDDP, an LLM-based five-dimensional evaluation module encompassing clarity, Integrity, Depth, Practicality, and Pertinence, to comprehensively assess mathematics lesson plan quality and bootstrap intelligent optimization. Experiments conducted on the GSM8K and Algebra datasets demonstrate that EduPlanner excels in evaluating and optimizing instructional design for curriculum and learning activities. Ablation studies further validate the significance and effectiveness of each component within the framework. Our code is publicly available at https://github.com/Zc0812/Edu_Planner

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

Data augmentation is one of the regularization strategies for the training of deep learning models, which enhances generalizability and prevents overfitting, leading to performance improvement. Although researchers have proposed various data augmentation techniques, they often lack consideration for the difficulty of augmented data. Recently, another line of research suggests incorporating the concept of curriculum learning with data augmentation in the field of natural language processing. In this study, we adopt curriculum data augmentation for image data augmentation and propose colorful cutout, which gradually increases the noise and difficulty introduced in the augmented image. Our experimental results highlight the possibility of curriculum data augmentation for image data. We publicly released our source code to improve the reproducibility of our study.

Large language models (LLM) have recently shown the extraordinary ability to perform unseen tasks based on few-shot examples provided as text, also known as in-context learning (ICL). While recent works have attempted to understand the mechanisms driving ICL, few have explored training strategies that incentivize these models to generalize to multiple tasks. Multi-task learning (MTL) for generalist models is a promising direction that offers transfer learning potential, enabling large parameterized models to be trained from simpler, related tasks. In this work, we investigate the combination of MTL with ICL to build models that efficiently learn tasks while being robust to out-of-distribution examples. We propose several effective curriculum learning strategies that allow ICL models to achieve higher data efficiency and more stable convergence. Our experiments reveal that ICL models can effectively learn difficult tasks by training on progressively harder tasks while mixing in prior tasks, denoted as mixed curriculum in this work. Our code and models are available at https://github.com/harmonbhasin/curriculum_learning_icl .

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH^2 - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH^2 than on MATH (b) Higher performance on MATH when using MATH^2 questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH^2 is the square on MATH, suggesting that successfully solving the question in MATH^2 requires a nontrivial combination of two distinct math skills.

Code language models have emerged as useful tools for various programming tasks, yet they often struggle when it comes to complex ones. In this paper, we explore the potential of curriculum learning in enhancing the performance of these models. While prior research has suggested that curriculum learning does not necessarily help in improving the performance of language models, our results surprisingly show that this may not be the case for code language models. We demonstrate that a well-designed curriculum learning approach significantly improves the accuracy of small decoder-only code language models on the task of code execution, while its effect on code completion is less significant. To explore the potential of curriculum learning, we train multiple GPT models with 1 million parameters each to predict the next token and evaluate them on code completion and execution tasks. Our contributions include proposing a novel code difficulty assessment metric by combining software code measures, investigating the effectiveness of Curriculum Learning for code language models, and introducing a Novel Curriculum Learning schedule that enhances the performance of small decoder-only language models in code execution tasks. The results of this paper open the door for more research on the use of curriculum learning for code language models.

We propose prioritized unit propagation with periodic resetting, which is a simple but surprisingly effective algorithm for solving random SAT instances that are meant to be hard. In particular, an evaluation on the Random Track of the 2017 and 2018 SAT competitions shows that a basic prototype of this simple idea already ranks at second place in both years. We share this observation in the hope that it helps the SAT community better understand the hardness of random instances used in competitions and inspire other interesting ideas on SAT solving.

This paper presents a case study on the design, administration, post-processing, and evaluation of surveys on large language models (LLMs). It comprises two components: (1) A statistical method for eliciting beliefs encoded in LLMs. We introduce statistical measures and evaluation metrics that quantify the probability of an LLM "making a choice", the associated uncertainty, and the consistency of that choice. (2) We apply this method to study what moral beliefs are encoded in different LLMs, especially in ambiguous cases where the right choice is not obvious. We design a large-scale survey comprising 680 high-ambiguity moral scenarios (e.g., "Should I tell a white lie?") and 687 low-ambiguity moral scenarios (e.g., "Should I stop for a pedestrian on the road?"). Each scenario includes a description, two possible actions, and auxiliary labels indicating violated rules (e.g., "do not kill"). We administer the survey to 28 open- and closed-source LLMs. We find that (a) in unambiguous scenarios, most models "choose" actions that align with commonsense. In ambiguous cases, most models express uncertainty. (b) Some models are uncertain about choosing the commonsense action because their responses are sensitive to the question-wording. (c) Some models reflect clear preferences in ambiguous scenarios. Specifically, closed-source models tend to agree with each other.

Crossword puzzles are popular linguistic games often used as tools to engage students in learning. Educational crosswords are characterized by less cryptic and more factual clues that distinguish them from traditional crossword puzzles. Despite there exist several publicly available clue-answer pair databases for traditional crosswords, educational clue-answer pairs datasets are missing. In this article, we propose a methodology to build educational clue generation datasets that can be used to instruct Large Language Models (LLMs). By gathering from Wikipedia pages informative content associated with relevant keywords, we use Large Language Models to automatically generate pedagogical clues related to the given input keyword and its context. With such an approach, we created clue-instruct, a dataset containing 44,075 unique examples with text-keyword pairs associated with three distinct crossword clues. We used clue-instruct to instruct different LLMs to generate educational clues from a given input content and keyword. Both human and automatic evaluations confirmed the quality of the generated clues, thus validating the effectiveness of our approach.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to random variables are discussed, including the approach based on completions in a Polish space. We apply the theory to the study of stochastic dynamical systems in discrete-time, and give a brief exposition of the Wiener process as a foundation for stochastic differential equations. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

We introduce Instruct-SkillMix, an automated approach for creating diverse, high quality SFT data. The Instruct-SkillMix pipeline involves two stages, each leveraging an existing powerful LLM: (1) Skill extraction: uses the LLM to extract core "skills" for instruction-following, either from existing datasets, or by directly prompting the model; (2) Data generation: uses the powerful LLM to generate (instruction, response) data that exhibit a randomly chosen pair of these skills. Here, the use of random skill combinations promotes diversity and difficulty. Vanilla SFT (i.e., no PPO, DPO, or RL methods) on data generated from Instruct-SkillMix leads to strong gains on instruction following benchmarks such as AlpacaEval 2.0, MT-Bench, and WildBench. With just 4K examples, LLaMA-3-8B-Base achieves 42.76% length-controlled win rate on AlpacaEval 2.0. To our knowledge, this achieves state-of-the-art performance among all models that have only undergone SFT (no RL methods) and competes with proprietary models such as Claude 3 Opus and LLaMA-3.1-405B-Instruct. Ablation studies also suggest plausible reasons for why creating open instruction-tuning datasets via naive crowd-sourcing has proved difficult. Introducing low quality answers ("shirkers") in 20% of Instruct-SkillMix examples causes performance to plummet, sometimes catastrophically. The Instruct-SkillMix pipeline is flexible and is adaptable to other settings.

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this limitation by enabling large language models (LLMs) to generate soft, abstract tokens, thus facilitating reasoning within a continuous concept space. This paper explores the `Soft Thinking' capabilities of various LLMs by examining the models' internal behavior using a suite of probing techniques. Contrary to the common belief that Soft Thinking enables the simultaneous exploration of diverse reasoning paths, our findings reveal that LLMs predominantly rely on the most influential component of the soft inputs during subsequent decoding steps. This reliance hinders the exploration of different reasoning paths and reduces vanilla Soft Thinking to a form of greedy decoding, obscuring the advantage of transmitting more information through Soft Tokens. To tackle this issue, we explore sampling strategies to introduce randomness, employing methods such as Dirichlet resampling and the Gumbel-Softmax trick. Our experiments demonstrate that incorporating randomness can alleviate the limitations of vanilla approaches and unleash the potential of Soft Thinking. Notably, the Gumbel-Softmax trick provides adequate randomness with controlled smoothness, resulting in superior performance across eight reasoning benchmarks.

Experience replay is a key component in reinforcement learning for stabilizing learning and improving sample efficiency. Its typical implementation samples transitions with replacement from a replay buffer. In contrast, in supervised learning with a fixed dataset, it is a common practice to shuffle the dataset every epoch and consume data sequentially, which is called random reshuffling (RR). RR enjoys theoretically better convergence properties and has been shown to outperform with-replacement sampling empirically. To leverage the benefits of RR in reinforcement learning, we propose sampling methods that extend RR to experience replay, both in uniform and prioritized settings. We evaluate our sampling methods on Atari benchmarks, demonstrating their effectiveness in deep reinforcement learning.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with ascending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.

Humans are good at learning on the job: We learn how to solve the tasks we face as we go along. Can a model do the same? We propose an agent that assembles a task-specific curriculum, called test-time curriculum (TTC-RL), and applies reinforcement learning to continue training the model for its target task. The test-time curriculum avoids time-consuming human curation of datasets by automatically selecting the most task-relevant data from a large pool of available training data. Our experiments demonstrate that reinforcement learning on a test-time curriculum consistently improves the model on its target tasks, across a variety of evaluations and models. Notably, on challenging math and coding benchmarks, TTC-RL improves the pass@1 of Qwen3-8B by approximately 1.8x on AIME25 and 2.1x on CodeElo. Moreover, we find that TTC-RL significantly raises the performance ceiling compared to the initial model, increasing pass@8 on AIME25 from 40% to 62% and on CodeElo from 28% to 43%. Our findings show the potential of test-time curricula in extending the test-time scaling paradigm to continual training on thousands of task-relevant experiences during test-time.

Recently, parallel text generation has received widespread attention due to its success in generation efficiency. Although many advanced techniques are proposed to improve its generation quality, they still need the help of an autoregressive model for training to overcome the one-to-many multi-modal phenomenon in the dataset, limiting their applications. In this paper, we propose latent-GLAT, which employs the discrete latent variables to capture word categorical information and invoke an advanced curriculum learning technique, alleviating the multi-modality problem. Experiment results show that our method outperforms strong baselines without the help of an autoregressive model, which further broadens the application scenarios of the parallel decoding paradigm.

AI creation, such as poem or lyrics generation, has attracted increasing attention from both industry and academic communities, with many promising models proposed in the past few years. Existing methods usually estimate the outputs based on single and independent visual or textual information. However, in reality, humans usually make creations according to their experiences, which may involve different modalities and be sequentially correlated. To model such human capabilities, in this paper, we define and solve a novel AI creation problem based on human experiences. More specifically, we study how to generate texts based on sequential multi-modal information. Compared with the previous works, this task is much more difficult because the designed model has to well understand and adapt the semantics among different modalities and effectively convert them into the output in a sequential manner. To alleviate these difficulties, we firstly design a multi-channel sequence-to-sequence architecture equipped with a multi-modal attention network. For more effective optimization, we then propose a curriculum negative sampling strategy tailored for the sequential inputs. To benchmark this problem and demonstrate the effectiveness of our model, we manually labeled a new multi-modal experience dataset. With this dataset, we conduct extensive experiments by comparing our model with a series of representative baselines, where we can demonstrate significant improvements in our model based on both automatic and human-centered metrics. The code and data are available at: https://github.com/Aman-4-Real/MMTG.

This paper presents teaching materials, particularly assignments and ideas for classroom activities, from a new course on large language models (LLMs) taught at Charles University. The assignments include experiments with LLM inference for weather report generation and machine translation. The classroom activities include class quizzes, focused research on downstream tasks and datasets, and an interactive "best paper" session aimed at reading and comprehension of research papers.

Large language models excel at short-horizon reasoning tasks, but performance drops as reasoning horizon lengths increase. Existing approaches to combat this rely on inference-time scaffolding or costly step-level supervision, neither of which scales easily. In this work, we introduce a scalable method to bootstrap long-horizon reasoning capabilities using only existing, abundant short-horizon data. Our approach synthetically composes simple problems into complex, multi-step dependency chains of arbitrary length. We train models on this data using outcome-only rewards under a curriculum that automatically increases in complexity, allowing RL training to be scaled much further without saturating. Empirically, our method generalizes remarkably well: curriculum training on composed 6th-grade level math problems (GSM8K) boosts accuracy on longer, competition-level benchmarks (GSM-Symbolic, MATH-500, AIME) by up to 2.06x. It also transfers significantly to diverse out-of-distribution ReasoningGym domains and long-context benchmarks, indicating broader generalization. Importantly, our long-horizon improvements are significantly higher than baselines even at high pass@k, showing that models can learn new reasoning paths under RL. Theoretically, we show that curriculum RL with outcome rewards achieves an exponential improvement in sample complexity over full-horizon training, providing training signal comparable to dense supervision. h1 therefore introduces an efficient path towards scaling RL for long-horizon problems using only existing data.

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle this challenge is to reformulate it as a multi-task RL problem, where the task space contains not only the challenging task of interest but also easier tasks that implicitly function as a curriculum. Such a reformulation opens up the possibility of running existing multi-task RL methods as a more efficient alternative to solving a single challenging task from scratch. In this work, we provide a theoretical framework that reformulates a single-task RL problem as a multi-task RL problem defined by a curriculum. Under mild regularity conditions on the curriculum, we show that sequentially solving each task in the multi-task RL problem is more computationally efficient than solving the original single-task problem, without any explicit exploration bonuses or other exploration strategies. We also show that our theoretical insights can be translated into an effective practical learning algorithm that can accelerate curriculum learning on simulated robotic tasks.

Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when generating random numbers, considering diverse configurations such as different model architectures, numerical ranges, temperature, and prompt languages. Our results reveal that, despite their stochastic transformers-based architecture, these models often exhibit deterministic responses when prompted for random numerical outputs. In particular, we find significant differences when changing the model, as well as the prompt language, attributing this phenomenon to biases deeply embedded within the training data. Models such as DeepSeek-R1 can shed some light on the internal reasoning process of LLMs, despite arriving to similar results. These biases induce predictable patterns that undermine genuine randomness, as LLMs are nothing but reproducing our own human cognitive biases.

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.

Large Language Models (LLMs) perform complex reasoning by generating explanations for their predictions. However, a complementary goal of explanations is to also communicate useful knowledge that improves weaker agents. Hence, we investigate whether LLMs also make good teachers for weaker agents. In particular, we consider a student-teacher framework between two LLM agents and study if, when, and how the teacher should intervene with natural language explanations to improve the student's performance. Since communication is expensive, we define a budget such that the teacher only communicates explanations for a fraction of the data, after which the student should perform well on its own. We decompose the teaching problem along four axes: (1) if teacher's test time intervention improve student predictions, (2) when it is worth explaining a data point, (3) how the teacher should personalize explanations to better teach the student, and (4) if teacher explanations also improve student performance on future unexplained data. We first show that teacher LLMs can indeed intervene on student reasoning to improve their performance. Next, we propose a Theory of Mind approach, in which the teacher builds two few-shot mental models of the student. The first model defines an Intervention Function that simulates the utility of an intervention, allowing the teacher to intervene when this utility is the highest and improving student performance at lower budgets. The second model enables the teacher to personalize explanations for a particular student and outperform unpersonalized teachers. We also demonstrate that in multi-turn interactions, teacher explanations generalize and learning from explained data improves student performance on future unexplained data. Finally, we also verify that misaligned teachers can lower student performance to random chance by intentionally misleading them.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

The recent advancement of large language models (LLMs) has been achieved through a combo of instruction tuning and human alignment. However, building manually crafted instruction datasets and performing human alignment become the bottleneck for scaling the development of LLMs. In this paper, we exploit the idea of leveraging AI models in lieu of humans as the teacher to train student LLMs. Our method is inspired by how human students refine their writing skills by following the rubrics and learning from the revisions offered by their tutors. Specifically, we employ a teacher LLM to create a curriculum for instruction tuning of the student LLM, namely Curriculum Instruction TunING (CITING). It encompasses two main steps: (1) the teacher LLM crafts the rubrics for evaluating the answers corresponding to various types of questions, and (2) the student LLM learns to follow the rubrics and perform self-correction from the revision made by the teacher. We further iteratively carry out it to embody the procedure of CITING. We compare CITING to a series of state-of-the-art baselines on four datasets. Our method demonstrates strong improvement in terms of articulate, in-depth, and comprehensive by GPT-4 evaluation. Specifically, it achieves an average winning rate of 79.4% over SFT, 73.4% over RLHF, 78.1% over RRHF, and 76.3% over RAFT, respectively.

Large language models (LLMs) have significant potential for generating educational questions and problems, enabling educators to create large-scale learning materials. However, LLMs are fundamentally limited by the ``Artificial Hivemind'' effect, where they generate similar responses within the same model and produce homogeneous outputs across different models. As a consequence, students may be exposed to overly similar and repetitive LLM-generated problems, which harms diversity of thought. Drawing inspiration from Wallas's theory of creativity and Guilford's framework of divergent-convergent thinking, we propose CreativeDC, a two-phase prompting method that explicitly scaffolds the LLM's reasoning into distinct phases. By decoupling creative exploration from constraint satisfaction, our method enables LLMs to explore a broader space of ideas before committing to a final problem. We evaluate CreativeDC for creative problem generation using a comprehensive set of metrics that capture diversity, novelty, and utility. The results show that CreativeDC achieves significantly higher diversity and novelty compared to baselines while maintaining high utility. Moreover, scaling analysis shows that CreativeDC generates a larger effective number of distinct problems as more are sampled, increasing at a faster rate than baseline methods.

In this paper, I introduce the retrieval problem, a simple reasoning task that can be solved only by transformers with a minimum number of layers. The task has an adjustable difficulty that can further increase the required number of layers to any arbitrary value. I demonstrate that large language models can solve the task under different prompting formulations without any fine-tuning. To understand how transformers solve the retrieval problem, I train several transformers on a minimal formulation. I find that successful learning occurs only under the presence of an implicit curriculum. I uncover the learned mechanisms by studying the attention maps in the trained transformers. I also study the training process, uncovering that attention heads always emerge in a specific sequence.

A common way of assessing language learners' mastery of vocabulary is via multiple-choice cloze (i.e., fill-in-the-blank) questions. But the creation of test items can be laborious for individual teachers or in large-scale language programs. In this paper, we evaluate a new method for automatically generating these types of questions using large language models (LLM). The VocaTT (vocabulary teaching and training) engine is written in Python and comprises three basic steps: pre-processing target word lists, generating sentences and candidate word options using GPT, and finally selecting suitable word options. To test the efficiency of this system, 60 questions were generated targeting academic words. The generated items were reviewed by expert reviewers who judged the well-formedness of the sentences and word options, adding comments to items judged not well-formed. Results showed a 75% rate of well-formedness for sentences and 66.85% rate for suitable word options. This is a marked improvement over the generator used earlier in our research which did not take advantage of GPT's capabilities. Post-hoc qualitative analysis reveals several points for improvement in future work including cross-referencing part-of-speech tagging, better sentence validation, and improving GPT prompts.

Multiple choice question answering (MCQA) is popular for LLM evaluation due to its simplicity and human-like testing, but we argue for its reform. We first reveal flaws in MCQA's format, as it struggles to: 1) test generation/subjectivity; 2) match LLM use cases; and 3) fully test knowledge. We instead advocate for generative formats based on human testing-where LLMs construct and explain answers-better capturing user needs and knowledge while remaining easy to score. We then show even when MCQA is a useful format, its datasets suffer from: leakage; unanswerability; shortcuts; and saturation. In each issue, we give fixes from education, like rubrics to guide MCQ writing; scoring methods to bridle guessing; and Item Response Theory to build harder MCQs. Lastly, we discuss LLM errors in MCQA-robustness, biases, and unfaithful explanations-showing how our prior solutions better measure or address these issues. While we do not need to desert MCQA, we encourage more efforts in refining the task based on educational testing, advancing evaluations.

The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

Recently, online Reinforcement Learning with Verifiable Rewards (RLVR) has become a key paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs). However, existing methods typically treat all training samples uniformly, overlooking the vast differences in problem difficulty relative to the model's current capabilities. This uniform training strategy leads to inefficient exploration of problems the model has already mastered, while concurrently lacking effective guidance on problems that are challenging its abilities the most, limiting both learning efficiency and upper-bound performance. To address this, we propose CLPO (Curriculum-guided Learning for Policy Optimization), a novel algorithm that creates a dynamic pedagogical feedback loop within the policy optimization process. The core of CLPO leverages the model's own rollout performance to conduct real-time difficulty assessment, thereby constructing an Online Curriculum. This curriculum then guides an Adaptive Problem Restructuring mechanism, where the model acts as its own teacher: it diversifies medium-difficulty problems to promote generalization and simplifies challenging problems to make them more attainable. Our approach transforms the static training procedure into a dynamic process that co-evolves with the model's capabilities. Experiments show that CLPO achieves state-of-the-art performance across eight challenging mathematical and general reasoning benchmarks, with an average pass@1 improvement of 6.96% over other methods, demonstrating its potential for more efficiently training more capable reasoning models.

Multiple choice question answering tasks evaluate the reasoning, comprehension, and mathematical abilities of Large Language Models (LLMs). While existing benchmarks employ automatic translation for multilingual evaluation, this approach is error-prone and potentially introduces culturally biased questions, especially in social sciences. We introduce the first multitask, multiple-choice Turkish QA benchmark, TurkishMMLU, to evaluate LLMs' understanding of the Turkish language. TurkishMMLU includes over 10,000 questions, covering 9 different subjects from Turkish high-school education curricula. These questions are written by curriculum experts, suitable for the high-school curricula in Turkey, covering subjects ranging from natural sciences and math questions to more culturally representative topics such as Turkish Literature and the history of the Turkish Republic. We evaluate over 20 LLMs, including multilingual open-source (e.g., Gemma, Llama, MT5), closed-source (GPT 4o, Claude, Gemini), and Turkish-adapted (e.g., Trendyol) models. We provide an extensive evaluation, including zero-shot and few-shot evaluation of LLMs, chain-of-thought reasoning, and question difficulty analysis along with model performance. We provide an in-depth analysis of the Turkish capabilities and limitations of current LLMs to provide insights for future LLMs for the Turkish language. We publicly release our code for the dataset and evaluation: https://github.com/ArdaYueksel/TurkishMMLU.

Designing high-quality educational questions is a challenging and time-consuming task. In this work, we propose a novel approach that utilizes prompt-based techniques to generate descriptive and reasoning-based questions. However, current question-answering (QA) datasets are inadequate for conducting our experiments on prompt-based question generation (QG) in an educational setting. Therefore, we curate a new QG dataset called EduProbe for school-level subjects, by leveraging the rich content of NCERT textbooks. We carefully annotate this dataset as quadruples of 1) Context: a segment upon which the question is formed; 2) Long Prompt: a long textual cue for the question (i.e., a longer sequence of words or phrases, covering the main theme of the context); 3) Short Prompt: a short textual cue for the question (i.e., a condensed representation of the key information or focus of the context); 4) Question: a deep question that aligns with the context and is coherent with the prompts. We investigate several prompt-based QG methods by fine-tuning pre-trained transformer-based large language models (LLMs), namely PEGASUS, T5, MBART, and BART. Moreover, we explore the performance of two general-purpose pre-trained LLMs such as Text-Davinci-003 and GPT-3.5-Turbo without any further training. By performing automatic evaluation, we show that T5 (with long prompt) outperforms all other models, but still falls short of the human baseline. Under human evaluation criteria, TextDavinci-003 usually shows better results than other models under various prompt settings. Even in the case of human evaluation criteria, QG models mostly fall short of the human baseline. Our code and dataset are available at: https://github.com/my625/PromptQG

Sparse reward environments in reinforcement learning (RL) pose significant challenges for exploration, often leading to inefficient or incomplete learning processes. To tackle this issue, this work proposes a teacher-student RL framework that leverages Large Language Models (LLMs) as "teachers" to guide the agent's learning process by decomposing complex tasks into subgoals. Due to their inherent capability to understand RL environments based on a textual description of structure and purpose, LLMs can provide subgoals to accomplish the task defined for the environment in a similar fashion to how a human would do. In doing so, three types of subgoals are proposed: positional targets relative to the agent, object representations, and language-based instructions generated directly by the LLM. More importantly, we show that it is possible to query the LLM only during the training phase, enabling agents to operate within the environment without any LLM intervention. We assess the performance of this proposed framework by evaluating three state-of-the-art open-source LLMs (Llama, DeepSeek, Qwen) eliciting subgoals across various procedurally generated environment of the MiniGrid benchmark. Experimental results demonstrate that this curriculum-based approach accelerates learning and enhances exploration in complex tasks, achieving up to 30 to 200 times faster convergence in training steps compared to recent baselines designed for sparse reward environments.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

Despite being trained specifically to follow user instructions, today's instructiontuned language models perform poorly when instructed to produce random outputs. For example, when prompted to pick a number uniformly between one and ten Llama-2-13B-chat disproportionately favors the number five, and when tasked with picking a first name at random, Mistral-7B-Instruct chooses Avery 40 times more often than we would expect based on the U.S. population. When these language models are used for real-world tasks where diversity of outputs is crucial, such as language model assisted dataset construction, their inability to produce diffuse distributions over valid choices is a major hurdle. In this work, we propose a fine-tuning method that encourages language models to output distributions that are diffuse over valid outcomes. The methods we introduce generalize across a variety of tasks and distributions and make large language models practical for synthetic dataset generation with little human intervention.

Natural-language prompts have recently been used to coax pretrained language models into performing other AI tasks, using a fill-in-the-blank paradigm (Petroni et al., 2019) or a few-shot extrapolation paradigm (Brown et al., 2020). For example, language models retain factual knowledge from their training corpora that can be extracted by asking them to "fill in the blank" in a sentential prompt. However, where does this prompt come from? We explore the idea of learning prompts by gradient descent -- either fine-tuning prompts taken from previous work, or starting from random initialization. Our prompts consist of "soft words," i.e., continuous vectors that are not necessarily word type embeddings from the language model. Furthermore, for each task, we optimize a mixture of prompts, learning which prompts are most effective and how to ensemble them. Across multiple English LMs and tasks, our approach hugely outperforms previous methods, showing that the implicit factual knowledge in language models was previously underestimated. Moreover, this knowledge is cheap to elicit: random initialization is nearly as good as informed initialization.

We study the relationship between vocabulary size and text length in a corpus of 75 literary works in English, authored by six writers, distinguishing between the contributions of three grammatical classes (or ``tags,'' namely, {\it nouns}, {\it verbs}, and {\it others}), and analyze the progressive appearance of new words of each tag along each individual text. While the power-law relation prescribed by Heaps' law is satisfactorily fulfilled by total vocabulary sizes and text lengths, the appearance of new words in each text is on the whole well described by the average of random shufflings of the text, which does not obey a power law. Deviations from this average, however, are statistically significant and show a systematic trend across the corpus. Specifically, they reveal that the appearance of new words along each text is predominantly retarded with respect to the average of random shufflings. Moreover, different tags are shown to add systematically distinct contributions to this tendency, with {\it verbs} and {\it others} being respectively more and less retarded than the mean trend, and {\it nouns} following instead this overall mean. These statistical systematicities are likely to point to the existence of linguistically relevant information stored in the different variants of Heaps' law, a feature that is still in need of extensive assessment.

Question answering (QA) is a fundamental means to facilitate assessment and training of narrative comprehension skills for both machines and young children, yet there is scarcity of high-quality QA datasets carefully designed to serve this purpose. In particular, existing datasets rarely distinguish fine-grained reading skills, such as the understanding of varying narrative elements. Drawing on the reading education research, we introduce FairytaleQA, a dataset focusing on narrative comprehension of kindergarten to eighth-grade students. Generated by educational experts based on an evidence-based theoretical framework, FairytaleQA consists of 10,580 explicit and implicit questions derived from 278 children-friendly stories, covering seven types of narrative elements or relations. Our dataset is valuable in two folds: First, we ran existing QA models on our dataset and confirmed that this annotation helps assess models' fine-grained learning skills. Second, the dataset supports question generation (QG) task in the education domain. Through benchmarking with QG models, we show that the QG model trained on FairytaleQA is capable of asking high-quality and more diverse questions.

Generating diverse responses from large language models (LLMs) is crucial for applications such as planning/search and synthetic data generation, where diversity provides distinct answers across generations. Prior approaches rely on increasing temperature to increase diversity. However, contrary to popular belief, we show not only does this approach produce lower quality individual generations as temperature increases, but it depends on model's next-token probabilities being similar to the true distribution of answers. We propose , an alternative approach that uses the language model itself to partition the space into strata. At inference, a random stratum is selected and a sample drawn from within the strata. To measure diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers, and assess diversity by measuring KL Divergence between the output distribution and uniform distribution over valid ground truth answers. As computing probability per response/solution for proprietary models is infeasible, we measure recall on ground truth solutions. Our evaluation show using SimpleStrat achieves higher recall by 0.05 compared to GPT-4o and 0.36 average reduction in KL Divergence compared to Llama 3.

Developing questions that are pedagogically sound, relevant, and promote learning is a challenging and time-consuming task for educators. Modern-day large language models (LLMs) generate high-quality content across multiple domains, potentially helping educators to develop high-quality questions. Automated educational question generation (AEQG) is important in scaling online education catering to a diverse student population. Past attempts at AEQG have shown limited abilities to generate questions at higher cognitive levels. In this study, we examine the ability of five state-of-the-art LLMs of different sizes to generate diverse and high-quality questions of different cognitive levels, as defined by Bloom's taxonomy. We use advanced prompting techniques with varying complexity for AEQG. We conducted expert and LLM-based evaluations to assess the linguistic and pedagogical relevance and quality of the questions. Our findings suggest that LLms can generate relevant and high-quality educational questions of different cognitive levels when prompted with adequate information, although there is a significant variance in the performance of the five LLms considered. We also show that automated evaluation is not on par with human evaluation.

Large language models (LLMs) are increasingly considered as tutoring aids in science education. Yet their readiness for unsupervised use in undergraduate instruction remains uncertain, as reliable teaching requires more than fluent recall: it demands consistent, principle-grounded reasoning. Thermodynamics, with its compact laws and subtle distinctions between state and path functions, reversibility, and entropy, provides an ideal testbed for evaluating such capabilities. Here we present UTQA, a 50-item undergraduate thermodynamics question answering benchmark, covering ideal-gas processes, reversibility, and diagram interpretation. No leading 2025-era model exceeded our 95\% competence threshold: the best LLMs achieved 82\% accuracy, with text-only items performing better than image reasoning tasks, which often fell to chance levels. Prompt phrasing and syntactic complexity showed modest to little correlation with performance. The gap concentrates in finite-rate/irreversible scenarios and in binding visual features to thermodynamic meaning, indicating that current LLMs are not yet suitable for unsupervised tutoring in this domain.

Socratic questioning is an educational method that allows students to discover answers to complex problems by asking them a series of thoughtful questions. Generation of didactically sound questions is challenging, requiring understanding of the reasoning process involved in the problem. We hypothesize that such questioning strategy can not only enhance the human performance, but also assist the math word problem (MWP) solvers. In this work, we explore the ability of large language models (LMs) in generating sequential questions for guiding math word problem-solving. We propose various guided question generation schemes based on input conditioning and reinforcement learning. On both automatic and human quality evaluations, we find that LMs constrained with desirable question properties generate superior questions and improve the overall performance of a math word problem solver. We conduct a preliminary user study to examine the potential value of such question generation models in the education domain. Results suggest that the difficulty level of problems plays an important role in determining whether questioning improves or hinders human performance. We discuss the future of using such questioning strategies in education.

While knowledge evaluation in large language models has predominantly focused on academic subjects like math and physics, these assessments often fail to capture the practical demands of real-world professions. In this paper, we introduce IndoCareer, a dataset comprising 8,834 multiple-choice questions designed to evaluate performance in vocational and professional certification exams across various fields. With a focus on Indonesia, IndoCareer provides rich local contexts, spanning six key sectors: (1) healthcare, (2) insurance and finance, (3) creative and design, (4) tourism and hospitality, (5) education and training, and (6) law. Our comprehensive evaluation of 27 large language models shows that these models struggle particularly in fields with strong local contexts, such as insurance and finance. Additionally, while using the entire dataset, shuffling answer options generally maintains consistent evaluation results across models, but it introduces instability specifically in the insurance and finance sectors.

The game show Lucky 13 differs from other television game shows in that contestants are required to place a bet on their own knowledge of trivia by selecting a range that contains the number of questions that they answered correctly. We present a model for this game show using binomial random variables and generate tables outlining the optimal range the player should select based on maximization of two different utility functions. After analyzing the decisions made by some actual contestants on this show, we present a numerical simulation for how many questions an average player is expected to answer correctly based on question categories observed for two sample contestants.

We explore the automatic generation of interactive, scenario-based lessons designed to train novice human tutors who teach middle school mathematics online. Employing prompt engineering through a Retrieval-Augmented Generation approach with GPT-4o, we developed a system capable of creating structured tutor training lessons. Our study generated lessons in English for three key topics: Encouraging Students' Independence, Encouraging Help-Seeking Behavior, and Turning on Cameras, using a task decomposition prompting strategy that breaks lesson generation into sub-tasks. The generated lessons were evaluated by two human evaluators, who provided both quantitative and qualitative evaluations using a comprehensive rubric informed by lesson design research. Results demonstrate that the task decomposition strategy led to higher-rated lessons compared to single-step generation. Human evaluators identified several strengths in the LLM-generated lessons, including well-structured content and time-saving potential, while also noting limitations such as generic feedback and a lack of clarity in some instructional sections. These findings underscore the potential of hybrid human-AI approaches for generating effective lessons in tutor training.

Reasoning-Oriented Reinforcement Learning (RORL) enhances the reasoning ability of Large Language Models (LLMs). However, due to the sparsity of rewards in RORL, effective training is highly dependent on the selection of problems of appropriate difficulty. Although curriculum learning attempts to address this by adjusting difficulty, it often relies on static schedules, and even recent online filtering methods lack theoretical grounding and a systematic understanding of their effectiveness. In this work, we theoretically and empirically show that curating the batch with the problems that the training model achieves intermediate accuracy on the fly can maximize the effectiveness of RORL training, namely balanced online difficulty filtering. We first derive that the lower bound of the KL divergence between the initial and the optimal policy can be expressed with the variance of the sampled accuracy. Building on those insights, we show that balanced filtering can maximize the lower bound, leading to better performance. Experimental results across five challenging math reasoning benchmarks show that balanced online filtering yields an additional 10% in AIME and 4% improvements in average over plain GRPO. Moreover, further analysis shows the gains in sample efficiency and training time efficiency, exceeding the maximum reward of plain GRPO within 60% training time and the volume of the training set.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

While automatic dialogue tutors hold great potential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. Collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data quality. To address this, we propose a framework to generate such dialogues by pairing human teachers with a Large Language Model (LLM) prompted to represent common student errors. We describe how we use this framework to collect MathDial, a dataset of 3k one-to-one teacher-student tutoring dialogues grounded in multi-step math reasoning problems. While models like GPT-3 are good problem solvers, they fail at tutoring because they generate factually incorrect feedback or are prone to revealing solutions to students too early. To overcome this, we let teachers provide learning opportunities to students by guiding them using various scaffolding questions according to a taxonomy of teacher moves. We demonstrate MathDial and its extensive annotations can be used to finetune models to be more effective tutors (and not just solvers). We confirm this by automatic and human evaluation, notably in an interactive setting that measures the trade-off between student solving success and telling solutions. The dataset is released publicly.

Randomized controlled trials (RCTs) are the benchmark for causal inference, yet field implementation can deviate. We here present a remote audit - a design-based, preregistrable diagnostic that uses only pre-treatment satellite imagery to test whether assignment is independent of local conditions. The conditional randomization test of the remote audit evaluates whether treatment assignment is more predictable from pre-treatment satellite features than expected under the experiment's registered mechanism, providing a finite-sample valid, design-based diagnostic that requires no parametric assumptions. The procedure is finite-sample valid, honors blocks and clusters, and controls multiplicity across image models and resolutions via a max-statistic. We illustrate with two RCTs: Uganda's Youth Opportunities Program, where the audit corroborates randomization and flags selection and missing-data risks; and a school-based trial in Bangladesh, where assignment is highly predictable from pre-treatment features relative to the stated design, consistent with independent concerns about irregularities. Remote audits complement balance tests, lower early-stage costs, and enable rapid design checks when baseline surveys are expensive or infeasible.

Selecting a sample generation scheme from multiple prompt-based generative models, including large language models (LLMs) and prompt-guided image and video generation models, is typically addressed by choosing the model that maximizes an averaged evaluation score. However, this score-based selection overlooks the possibility that different models achieve the best generation performance for different types of text prompts. An online identification of the best generation model for various input prompts can reduce the costs associated with querying sub-optimal models. In this work, we explore the possibility of varying rankings of text-based generative models for different text prompts and propose an online learning framework to predict the best data generation model for a given input prompt. The proposed PAK-UCB algorithm addresses a contextual bandit (CB) setting with shared context variables across the arms, utilizing the generated data to update kernel-based functions that predict the score of each model available for unseen text prompts. Additionally, we leverage random Fourier features (RFF) to accelerate the online learning process of PAK-UCB. Our numerical experiments on real and simulated text-to-image and image-to-text generative models show that RFF-UCB performs successfully in identifying the best generation model across different sample types. The code is available at: github.com/yannxiaoyanhu/dgm-online-select.

Large language models (LLMs) are revolutionizing education, with LLM-based agents playing a key role in simulating student behavior. A major challenge in student simulation is modeling the diverse learning patterns of students at various cognitive levels. However, current LLMs, typically trained as ``helpful assistants'', target at generating perfect responses. As a result, they struggle to simulate students with diverse cognitive abilities, as they often produce overly advanced answers, missing the natural imperfections that characterize student learning and resulting in unrealistic simulations. To address this issue, we propose a training-free framework for student simulation. We begin by constructing a cognitive prototype for each student using a knowledge graph, which captures their understanding of concepts from past learning records. This prototype is then mapped to new tasks to predict student performance. Next, we simulate student solutions based on these predictions and iteratively refine them using a beam search method to better replicate realistic mistakes. To validate our approach, we construct the Student\_100 dataset, consisting of 100 students working on Python programming and 5,000 learning records. Experimental results show that our method consistently outperforms baseline models, achieving 100% improvement in simulation accuracy.

Recent work has highlighted the culturally-contingent nature of commonsense knowledge. We introduce AMAMMER{epsilon}, a test set of 525 multiple-choice questions designed to evaluate the commonsense knowledge of English LLMs, relative to the cultural contexts of Ghana and the United States. To create AMAMMER{epsilon}, we select a set of multiple-choice questions (MCQs) from existing commonsense datasets and rewrite them in a multi-stage process involving surveys of Ghanaian and U.S. participants. In three rounds of surveys, participants from both pools are solicited to (1) write correct and incorrect answer choices, (2) rate individual answer choices on a 5-point Likert scale, and (3) select the best answer choice from the newly-constructed MCQ items, in a final validation step. By engaging participants at multiple stages, our procedure ensures that participant perspectives are incorporated both in the creation and validation of test items, resulting in high levels of agreement within each pool. We evaluate several off-the-shelf English LLMs on AMAMMER{epsilon}. Uniformly, models prefer answers choices that align with the preferences of U.S. annotators over Ghanaian annotators. Additionally, when test items specify a cultural context (Ghana or the U.S.), models exhibit some ability to adapt, but performance is consistently better in U.S. contexts than Ghanaian. As large resources are devoted to the advancement of English LLMs, our findings underscore the need for culturally adaptable models and evaluations to meet the needs of diverse English-speaking populations around the world.

Current Reinforcement Fine-tuning (RFT) paradigms for Large Language Models (LLMs) suffer from sample inefficiency due to the redundant exposure of identical queries under uniform data sampling. While previous work has explored curriculum learning via heuristic difficulty metrics, these strategies exhibit limitations by neglecting the intrinsic learning signals generated by the model itself, thus leading to suboptimal training regimes. In this paper, we identify a model-inherent signal termed angle concentration that effectively reflects an LLM's capacity to learn from specific data. We theoretically and empirically demonstrate a correlation between the angular distribution of token hidden state vectors and the resulting gradient, revealing a learning preference for data exhibiting higher angle concentration. Inspired by this finding, we propose GAIN-RL, a Gradient-driven Angle-Informed Navigated RL framework. By leveraging the model's intrinsic angle concentration signal, GAIN-RL dynamically selects training data in each epoch, ensuring consistently impactful gradient updates and thus significantly enhancing overall training efficiency. Empirical evaluations show that GAIN-RL (GRPO) achieves over a 2.5x acceleration in training efficiency across diverse mathematical and coding tasks and varying model scales. Furthermore, GAIN-RL (GRPO)'s efficient sampling yields data-efficient training, achieving better performance with half the original data compared to vanilla GRPO with full training data. Code is realsed at https://github.com/wangqinsi1/GAINRL/tree/main.

Eliciting information to reduce uncertainty about a latent entity is a critical task in many application domains, e.g., assessing individual student learning outcomes, diagnosing underlying diseases, or learning user preferences. Though natural language is a powerful medium for this purpose, large language models (LLMs) and existing fine-tuning algorithms lack mechanisms for strategically gathering information to refine their own understanding of the latent entity. To harness the generalization power and world knowledge of LLMs in developing effective information-gathering strategies, we propose an adaptive elicitation framework that actively reduces uncertainty on the latent entity. Since probabilistic modeling of an abstract latent entity is difficult, our framework adopts a predictive view of uncertainty, using a meta-learned language model to simulate future observations and enable scalable uncertainty quantification over complex natural language. Through autoregressive forward simulation, our model quantifies how new questions reduce epistemic uncertainty, enabling the development of sophisticated information-gathering strategies to choose the most informative next queries. In experiments on the 20 questions game, dynamic opinion polling, and adaptive student assessment, our method consistently outperforms baselines in identifying critical unknowns and improving downstream predictions, illustrating the promise of strategic information gathering in natural language settings.