Critical Learning Periods comprehend an important phenomenon involving deep learning, where early epochs play a decisive role in the success of many training recipes, such as data augmentation. Existing works confirm the existence of this phenomenon and provide useful insights. However, the literature lacks efforts to precisely identify when critical periods occur. In this work, we fill this gap by introducing a systematic approach for identifying critical periods during the training of deep neural networks, focusing on eliminating computationally intensive regularization techniques and effectively applying mechanisms for reducing computational costs, such as data pruning. Our method leverages generalization prediction mechanisms to pinpoint critical phases where training recipes yield maximum benefits to the predictive ability of models. By halting resource-intensive recipes beyond these periods, we significantly accelerate the learning phase and achieve reductions in training time, energy consumption, and CO$_2$ emissions. Experiments on standard architectures and benchmarks confirm the effectiveness of our method. Specifically, we achieve significant milestones by reducing the training time of popular architectures by up to 59.67%, leading to a 59.47% decrease in CO$_2$ emissions and a 60% reduction in financial costs, without compromising performance. Our work enhances understanding of training dynamics and paves the way for more sustainable and efficient deep learning practices, particularly in resource-constrained environments. In the era of the race for foundation models, we believe our method emerges as a valuable framework. The repository is available at https://github.com/baunilhamarga/critical-periods

Language model developers typically filter out high-risk content -- such as toxic or copyrighted text -- from their pre-training data to prevent models from generating similar outputs. However, removing such data altogether limits models' ability to recognize and appropriately respond to harmful or sensitive content. In this paper, we introduce Selective Loss to Understand but Not Generate (SLUNG), a pre-training paradigm through which models learn to understand high-risk data without learning to generate it. Instead of uniformly applying the next-token prediction loss, SLUNG selectively avoids incentivizing the generation of high-risk tokens while ensuring they remain within the model's context window. As the model learns to predict low-risk tokens that follow high-risk ones, it is forced to understand the high-risk content. Through our experiments, we show that SLUNG consistently improves models' understanding of high-risk data (e.g., ability to recognize toxic content) without increasing its generation (e.g., toxicity of model responses). Overall, our SLUNG paradigm enables models to benefit from high-risk text that would otherwise be filtered out.

This study delves into the plasticity of neural networks, offering empirical support for the notion that critical learning periods and warm-starting performance loss can be avoided through simple adjustments to learning hyperparameters. The critical learning phenomenon emerges when training is initiated with deficit data. Subsequently, after numerous deficit epochs, the network's plasticity wanes, impeding its capacity to achieve parity in accuracy with models trained from scratch, even when extensive clean data training follows deficit epochs. Building upon seminal research introducing critical learning periods, we replicate key findings and broaden the experimental scope of the main experiment from the original work. In addition, we consider a warm-starting approach and show that it can be seen as a form of deficit pretraining. In particular, we demonstrate that these problems can be averted by employing a cyclic learning rate schedule. Our findings not only impact neural network training practices but also establish a vital link between critical learning periods and ongoing research on warm-starting neural network training.

Language models trained with reinforcement learning (RL) can engage in reward hacking--the exploitation of unintended strategies for high reward--without revealing this behavior in their chain-of-thought reasoning. This makes the detection of reward hacking difficult, posing risks for high-stakes applications. We propose verbalization fine-tuning (VFT), a pre-RL fine-tuning intervention that trains models to explicitly acknowledge when they are influenced by prompt cues--hints which point to incorrect answers (e.g., "a Stanford professor thinks the answer is A"). To evaluate VFT, we subsequently train models with RL on environments where held-out prompt cues signal which incorrect answers will receive high reward, incentivizing models to exploit these cues instead of reasoning correctly. We measure how often models exploit these cues without verbalizing it. After RL, only 6% of the VFT-trained model's responses consist of undetected reward hacks. In comparison, when we perform RL without VFT, the rate of undetected reward hacks goes up to 88%; with a debiasing baseline intervention, this increases further to 99%. VFT achieves this by substantially increasing how often models verbalize the influence of cues, from 8% to 43% after VFT, and up to 94% after RL. Baselines remain low even after RL (11% and 1%). Our results show that teaching models to explicitly verbalize reward hacking behavior before RL significantly improves their detection, offering a practical path toward more transparent and safe AI systems.

Automatically generating high-quality mathematical problems that align with educational objectives is a crucial task in NLP-based educational technology. Traditional generation methods focus primarily on textual quality, but they often overlook educational objectives. Moreover, these methods address only single-dimensional, simple question generation, failing to meet complex, multifaceted educational requirements. To address these challenges, we constructed and annotated EduMath, a dataset of 16k mathematical questions with multi-dimensional educational objectives. Based on this dataset, we developed EQGEVAL, which incorporates three evaluation dimensions and is designed to assess the ability of models to generate educational questions. Drawing inspiration from teachers' problem design processes, we propose the Educational Question Planning with self-Reflection (EQPR) method for educational mathematical question generation, following a "plan-evaluate-optimize" approach. Specifically, by combining planning algorithm based on Monte Carlo Tree Search with the generative capabilities of Large Language Models, we continuously optimize questions through iterative feedback. This self-optimization mechanism ensures that the generated questions both fit the educational context and strategically achieve specific basic educational objectives. Through extensive experiments based on EQGEVAL, we have demonstrated that EQPR achieves significant improvements in generating questions that meet multi-dimensional educational objectives.

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools during long-form reasoning, such as search engines and code interpreters, to solve tasks beyond the capabilities of internal reasoning. While reinforcement learning (RL) has shown promise in training such agents, most of existing approaches typically optimize only for final correctness without considering the efficiency or necessity of external tool use. This often leads to excessive tool calling, incurring high computational costs and hindering the development of internal reasoning capabilities - a phenomenon known as \textit{cognitive offloading}. To this end, we propose Optimal Tool Call-controlled Policy Optimization (OTC-PO), a simple yet effective RL-based framework that encourages models to produce accurate answers with minimal tool calls. Our method introduces a tool-integrated reward that jointly considers answer correctness and corresponding tool use behavior of model to reach that answer. To validate the effectiveness, we introduce the metric of \textit{tool productivity}, defined as the ratio between the number of correct answers and the total number of tool calls across all test cases. This metric reflects how efficiently tool usage contributes to successful task completion, with higher values indicating smarter and more autonomous reasoning. We instantiate this framework within both Proximal Policy Optimization (PPO) and Group Relative Preference Optimization (GRPO), resulting in OTC-PPO and OTC-GRPO. Experiments with Qwen-2.5 and Qwen-Math across multiple QA benchmarks show that our approach reduces tool calls by up to 68.3\% and improves tool productivity by up to 215.4\%, while maintaining comparable answer accuracy.

LLM chatbot interfaces allow students to get instant, interactive assistance with homework, but doing so carelessly may not advance educational objectives. In this study, an interactive homework help system based on DeepSeek R1 is developed and first implemented for students enrolled in a large computer science beginning programming course. In addition to an assist button in a well-known code editor, our assistant also has a feedback option in our command-line automatic evaluator. It wraps student work in a personalized prompt that advances our educational objectives without offering answers straight away. We have discovered that our assistant can recognize students' conceptual difficulties and provide ideas, plans, and template code in pedagogically appropriate ways. However, among other mistakes, it occasionally incorrectly labels the correct student code as incorrect or encourages students to use correct-but-lesson-inappropriate approaches, which can lead to long and frustrating journeys for the students. After discussing many development and deployment issues, we provide our conclusions and future actions.

Asking questions is a fundamental aspect of learning that facilitates deeper understanding. However, characterizing and crafting questions that effectively improve learning remains elusive. To address this gap, we propose QUEST (Question Utility Estimation with Simulated Tests). QUEST simulates a learning environment that enables the quantification of a question's utility based on its direct impact on improving learning outcomes. Furthermore, we can identify high-utility questions and use them to fine-tune question generation models with rejection sampling. We find that questions generated by models trained with rejection sampling based on question utility result in exam scores that are higher by at least 20% than those from specialized prompting grounded on educational objectives literature and models fine-tuned with indirect measures of question quality, such as saliency and expected information gain.

Large Language Models (LLMs) often struggle when prompted to generate content under specific constraints. However, in such cases it is often easy to check whether these constraints are satisfied or violated. Recent works have shown that LLMs can benefit from such "corrective feedback". Here we claim that this skill of LLMs can be significantly enhanced via training. We introduce an RL framework for teaching models to use such rewards, by simulating interaction sessions, and rewarding the model according to its ability to satisfy the constraints. We refer to our method as CORGI (Controlled Generation with RL for Guided Interaction), and evaluate it on a variety of controlled generation tasks using unlabeled training data. We find that CORGI consistently outperforms the baseline reinforcement learning method that does not incorporate conversational feedback. Furthermore, CORGI's interactive framework enables meta-learning, allowing the LLM to generalize better to guided interaction in new tasks. Our results clearly show that conversational optimization, when combined with reinforcement learning, significantly improves the effectiveness of LLMs in controlled generation contexts.

Large language models (LLMs) deployed as agents solve user-specified tasks over multiple steps while keeping the required manual engagement to a minimum. Crucially, such LLMs need to ground their generations in any feedback obtained to reliably achieve desired outcomes. We propose an end-to-end reinforcement learning method for teaching models to leverage execution feedback in the realm of code synthesis, where state-of-the-art LLMs struggle to improve code iteratively compared to independent sampling. We benchmark on competitive programming tasks, where we achieve new start-of-the art results with both small (8B parameters) and large (70B) models while reducing the amount of samples required by an order of magnitude. Our analysis of inference-time behavior demonstrates that our method produces LLMs that effectively leverage automatic feedback over multiple steps.