Daily Papers

Chain-of-thought prompting (e.g., "Let's think step-by-step") primes large language models to verbalize rationalization for their predictions. While chain-of-thought can lead to dramatic performance gains, benefits appear to emerge only for sufficiently large models (beyond 50B parameters). We show that orders-of-magnitude smaller models (125M -- 1.3B parameters) can still benefit from chain-of-thought prompting. To achieve this, we introduce Symbolic Chain-of-Thought Distillation (SCoTD), a method to train a smaller student model on rationalizations sampled from a significantly larger teacher model. Experiments across several commonsense benchmarks show that: 1) SCoTD enhances the performance of the student model in both supervised and few-shot settings, and especially for challenge sets; 2) sampling many reasoning chains per instance from the teacher is paramount; and 3) after distillation, student chain-of-thoughts are judged by humans as comparable to the teacher, despite orders of magnitude fewer parameters. We test several hypotheses regarding what properties of chain-of-thought samples are important, e.g., diversity vs. teacher likelihood vs. open-endedness. We release our corpus of chain-of-thought samples and code.

Despite the success of distillation in large language models (LLMs), most prior work applies identical loss functions to both teacher- and student-generated data. These strategies overlook the synergy between loss formulations and data types, leading to a suboptimal performance boost in student models. To address this, we propose DistiLLM-2, a contrastive approach that simultaneously increases the likelihood of teacher responses and decreases that of student responses by harnessing this synergy. Our extensive experiments show that DistiLLM-2 not only builds high-performing student models across a wide range of tasks, including instruction-following and code generation, but also supports diverse applications, such as preference alignment and vision-language extensions. These findings highlight the potential of a contrastive approach to enhance the efficacy of LLM distillation by effectively aligning teacher and student models across varied data types.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

Distillation has shown remarkable success in transferring knowledge from a Large Language Model (LLM) teacher to a student LLM. However, current distillation methods predominantly require the same tokenizer between the teacher and the student, restricting their applicability to only a small subset of teacher-student pairs. In this work, we develop a cross-tokenizer distillation method to solve this crucial deficiency. Our method is the first to enable cross-tokenizer distillation without a next-token prediction loss as the main objective, instead purely maximizing the student predictions' similarity to the teacher's predictions (known as pure distillation), while also being robust to large mismatches between the teacher and the student tokenizer function and vocabulary. Empirically, our method enables substantially improved performance as tested on two use cases. First, we show that viewing tokenizer transfer as self-distillation enables unprecedently effective transfer across tokenizers. We transfer (subword-level) Llama and Gemma models to byte-level tokenization more effectively than prior methods transfer to a similar subword tokenizer under a comparable training budget. Transferring different base models to the same tokenizer also enables ensembling them (e.g., via averaging their predicted probabilities) which boosts performance. Second, we use our cross-tokenizer distillation method to distil a large maths-specialized LLM into a smaller model, achieving competitive maths problem-solving performance. Overall, our results make substantial strides toward better adaptability and enhanced interaction between different LLMs.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

Large Language Models (LLMs) are increasingly deployed in mission-critical systems, facilitating tasks such as satellite operations, command-and-control, military decision support, and cyber defense. Many of these systems are accessed through application programming interfaces (APIs). When such APIs lack robust access controls, they can expose full or top-k logits, creating a significant and often overlooked attack surface. Prior art has mainly focused on reconstructing the output projection layer or distilling surface-level behaviors. However, regenerating a black-box model under tight query constraints remains underexplored. We address that gap by introducing a constrained replication pipeline that transforms partial logit leakage into a functional deployable substitute model clone. Our two-stage approach (i) reconstructs the output projection matrix by collecting top-k logits from under 10k black-box queries via singular value decomposition (SVD) over the logits, then (ii) distills the remaining architecture into compact student models with varying transformer depths, trained on an open source dataset. A 6-layer student recreates 97.6% of the 6-layer teacher model's hidden-state geometry, with only a 7.31% perplexity increase, and a 7.58 Negative Log-Likelihood (NLL). A 4-layer variant achieves 17.1% faster inference and 18.1% parameter reduction with comparable performance. The entire attack completes in under 24 graphics processing unit (GPU) hours and avoids triggering API rate-limit defenses. These results demonstrate how quickly a cost-limited adversary can clone an LLM, underscoring the urgent need for hardened inference APIs and secure on-premise defense deployments.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

Search-augmented large language models (LLMs) trained with reinforcement learning (RL) have achieved strong results on open-domain question answering (QA), but training still remains a significant challenge. The optimization is often unstable due to sparse rewards and difficult credit assignments across reasoning and tool calls. To address this, we introduce Turn-Level Information Potential Reward Shaping (TIPS), a simple framework that assigns dense, turn-level rewards to each reasoning + tool-call segment based on the increased likelihood of the correct answer under a teacher model. By leveraging the potential-based reward shaping, TIPS offers fine-grained and policy-invariant guidance that overcomes the limitations of outcome-only optimization. Evaluated on seven QA benchmarks, TIPS consistently outperforms GRPO/PPO baselines and substantially improves training stability. For instance, with a Qwen-2.5 7B Instruct model, TIPS improves the average Exact Match score by 11.8% and F1 by 13.6% relative to PPO. Our results demonstrate that turn-level information-potential reward shaping provides an effective and general solution to sparse-reward credit assignment for multi-turn LLM reasoning.

The teaching career shares common global characteristics, such as internal promotion, performance evaluation, recruitment of top candidates, continuous training, specialization, and peer learning. This study aims to describe the factors associated with the value placed on the teaching career in Peru. A total of 28217 public school teachers were analyzed using data from the 2020 National Teacher Survey. A variable measuring the "value of the teaching career" was constructed using eight indicators and categorized as low, medium, or high. Another variable, vision of the future, was classified as pessimistic, conformist, or optimistic. This observational, cross-sectional, and analytical study included variables related to in-service training, working conditions, professional recognition, and sociodemographic characteristics. Among the teachers surveyed, 45.8 % expressed an optimistic outlook on the future of the profession, 48 % held a conformist view, and only 6.2 % reported a pessimistic perspective. A generalized linear model revealed that the value placed on the teaching career was significantly associated with male gender (p = 0.002), a professional career (p < 0.001), an optimistic outlook (p = 0.033), and working at the primary level (p < 0.001). It was concluded that Peruvian teachers predominantly hold conformist or optimistic views of their profession. This highlights the need to reinforce merit-based advancement, competency-based training, intrinsic motivation, and ongoing professional development

Synthesizing supervised finetuning (SFT) data from language models (LMs) to teach smaller models multilingual tasks has become increasingly common. However, teacher model selection is often ad hoc, typically defaulting to the largest available option, even though such models may have significant capability gaps in non-English languages. This practice can result in poor-quality synthetic data and suboptimal student downstream performance. In this work, we systematically characterize what makes an effective multilingual teacher. We measure intrinsic measures of data quality with extrinsic student model performance in a metric we call Polyglot Score; evaluating 10 LMs across 6 typologically diverse languages, generating over 1.4M SFT examples and training 240 student models. Among the models tested, Gemma 3 27B and Aya Expanse 32B emerge as consistently effective teachers across different student base model families. Further analyses reveal that model scale alone does not significantly predict teacher effectiveness; instead, data qualities such as prompt diversity, length, and response fluency capture over 93.3% of variance in intrinsic data quality and predict student performance. Finally, we provide practical recommendations, including matching the model families of teacher-student pairs and translating from or responding to existing prompts, which can yield improvements for less-resourced languages. We hope that our work advances data-centric research in multilingual synthetic data and LM development.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

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.

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that closely align with the model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

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.

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

Test-time compute allocation in large reasoning models (LRMs) is widely used and has applications in mathematical problem solving, code synthesis, and planning. Recent work has addressed this problem by scaling self-consistency and parallel thinking, adding generic ``thinking tokens'' and prompting models to re-read the question before answering. Unfortunately, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain -- and often ignore -- the spontaneous repetition that many LRMs exhibit at the head of their internal chains. In contrast, we analyze and harness the model's tendency to restate the question, which we term the Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism. We formalize its probabilistic cost by casting echo removal as rejection-based conditioning and defining the Echo Likelihood Gap ΔL as a computable proxy. This provides the missing theoretical link that links early repetition to likelihood gains and downstream accuracy. However, it does not by itself specify how to exploit EOP. Consequently, we develop Echo-Distilled SFT (ED-SFT) to instill an ``echo-then-reason'' pattern through supervised finetuning, and Echoic Prompting (EP) to re-ground the model mid-trace without training. While promising, quantifying benefits beyond verbosity is non-trivial. Therefore, we conduct length and suffix-controlled likelihood analyses together with layer-wise attention studies, showing that EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines. Code is available at https://github.com/hhh2210/echoes-as-anchors.

Estimating the difficulty of multiple-choice questions would be great help for educators who must spend substantial time creating and piloting stimuli for their tests, and for learners who want to practice. Supervised approaches to difficulty estimation have yielded to date mixed results. In this contribution we leverage an aspect of generative large models which might be seen as a weakness when answering questions, namely their uncertainty, and exploit it towards exploring correlations between two different metrics of uncertainty, and the actual student response distribution. While we observe some present but weak correlations, we also discover that the models' behaviour is different in the case of correct vs wrong answers, and that correlations differ substantially according to the different question types which are included in our fine-grained, previously unused dataset of 451 questions from a Biopsychology course. In discussing our findings, we also suggest potential avenues to further leverage model uncertainty as an additional proxy for item difficulty.

Adapting instruction to the fine-grained needs of individual students is a powerful application of recent advances in large language models. These generative AI models can create tasks that correspond to students' interests and enact context personalization, enhancing students' interest in learning academic content. However, when there is a teacher in-the-loop creating or modifying tasks with generative AI, it is unclear how efficient this process might be, despite commercial generative AI tools' claims that they will save teachers time. In the present study, we teamed 7 middle school mathematics teachers with ChatGPT to create personalized versions of problems in their curriculum, to correspond to their students' interests. We look at the prompting moves teachers made, their efficiency when creating problems, and the reactions of their 521 7th grade students who received the personalized assignments. We find that having a teacher-in-the-loop results in generative AI-enhanced personalization being enacted at a relatively broad grain size, whereas students tend to prefer a smaller grain size where they receive specific popular culture references that interest them. Teachers spent a lot of effort adjusting popular culture references and addressing issues with the depth or realism of the problems generated, giving higher or lower levels of ownership to the generative AI. Teachers were able to improve in their ability to craft interesting problems in partnership with generative AI, but this process did not appear to become particularly time efficient as teachers learned and reflected on their students' data, iterating their approaches.

Language models often show little to no improvement (i.e., "saturation") when trained via vanilla supervised fine-tuning (SFT) on data similar to what they saw in their training set (e.g., MATH). We introduce a new fine-tuning strategy, STAT, to train such a student model by using the metacognition ability of a stronger large language model (LLM) as the teacher. The teacher uses the task dataset to create a list of skills needed for the task, and then labels each data point with its required skills (Didolkar et al., 2024). By monitoring the student's answers, the teacher creates a Missing-Skill-Profile for the student, tracking how often they failed to apply each skill in their responses. We use this idea to build a modified training set in one of two ways. In STAT-Sel, the teacher uses an existing set of training examples but adaptively reweights them according to the Missing-Skill-Profile. In STAT-Syn, the teacher synthesizes additional examples involving missing skills. Across extensive experiments on Llama and Qwen models, our methods yield improvements of up to 7.5% on MATH, whereas SFT provides only limited gains. Furthermore, STAT enhances performance on out-of-distribution benchmarks (e.g., AIME24/25, AMC23, etc.) by an average of 4.6%. Crucially, we find that STAT is complementary to RL via GRPO (Shao et al., 2024): after the model is improved using STAT to address skill gaps, GRPO continues to add further gains. We conclude that skill-targeted adaptive training should broadly improve current training pipelines. Our code is available at: https://github.com/princeton-pli/STAT.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Factual consistency evaluation is often conducted using Natural Language Inference (NLI) models, yet these models exhibit limited success in evaluating summaries. Previous work improved such models with synthetic training data. However, the data is typically based on perturbed human-written summaries, which often differ in their characteristics from real model-generated summaries and have limited coverage of possible factual errors. Alternatively, large language models (LLMs) have recently shown promising results in directly evaluating generative tasks, but are too computationally expensive for practical use. Motivated by these limitations, we introduce TrueTeacher, a method for generating synthetic data by annotating diverse model-generated summaries using a LLM. Unlike prior work, TrueTeacher does not rely on human-written summaries, and is multilingual by nature. Experiments on the TRUE benchmark show that a student model trained using our data, substantially outperforms both the state-of-the-art model with similar capacity, and the LLM teacher. In a systematic study, we compare TrueTeacher to existing synthetic data generation methods and demonstrate its superiority and robustness to domain-shift. Using the the mFACE dataset, we also show that our method generalizes to multilingual scenarios. Finally, we release a large-scale synthetic dataset with 1.4M examples generated using TrueTeacher.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Coaching, which involves classroom observation and expert feedback, is a widespread and fundamental part of teacher training. However, the majority of teachers do not have access to consistent, high quality coaching due to limited resources and access to expertise. We explore whether generative AI could become a cost-effective complement to expert feedback by serving as an automated teacher coach. In doing so, we propose three teacher coaching tasks for generative AI: (A) scoring transcript segments based on classroom observation instruments, (B) identifying highlights and missed opportunities for good instructional strategies, and (C) providing actionable suggestions for eliciting more student reasoning. We recruit expert math teachers to evaluate the zero-shot performance of ChatGPT on each of these tasks for elementary math classroom transcripts. Our results reveal that ChatGPT generates responses that are relevant to improving instruction, but they are often not novel or insightful. For example, 82% of the model's suggestions point to places in the transcript where the teacher is already implementing that suggestion. Our work highlights the challenges of producing insightful, novel and truthful feedback for teachers while paving the way for future research to address these obstacles and improve the capacity of generative AI to coach teachers.

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

Simulating Professions (SP) enables Large Language Models (LLMs) to emulate professional roles. However, comprehensive psychological and ethical evaluation in these contexts remains lacking. This paper introduces EMNLP, an Educator-role Moral and Normative LLMs Profiling framework for personality profiling, moral development stage measurement, and ethical risk under soft prompt injection. EMNLP extends existing scales and constructs 88 teacher-specific moral dilemmas, enabling profession-oriented comparison with human teachers. A targeted soft prompt injection set evaluates compliance and vulnerability in teacher SP. Experiments on 12 LLMs show teacher-role LLMs exhibit more idealized and polarized personalities than human teachers, excel in abstract moral reasoning, but struggle with emotionally complex situations. Models with stronger reasoning are more vulnerable to harmful prompt injection, revealing a paradox between capability and safety. The model temperature and other hyperparameters have limited influence except in some risk behaviors. This paper presents the first benchmark to assess ethical and psychological alignment of teacher-role LLMs for educational AI. Resources are available at https://e-m-n-l-p.github.io/.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

Evaluating the pedagogical capabilities of AI-based tutoring models is critical for making guided progress in the field. Yet, we lack a reliable, easy-to-use, and simple-to-run evaluation that reflects the pedagogical abilities of models. To fill this gap, we present MathTutorBench, an open-source benchmark for holistic tutoring model evaluation. MathTutorBench contains a collection of datasets and metrics that broadly cover tutor abilities as defined by learning sciences research in dialog-based teaching. To score the pedagogical quality of open-ended teacher responses, we train a reward model and show it can discriminate expert from novice teacher responses with high accuracy. We evaluate a wide set of closed- and open-weight models on MathTutorBench and find that subject expertise, indicated by solving ability, does not immediately translate to good teaching. Rather, pedagogy and subject expertise appear to form a trade-off that is navigated by the degree of tutoring specialization of the model. Furthermore, tutoring appears to become more challenging in longer dialogs, where simpler questioning strategies begin to fail. We release the benchmark, code, and leaderboard openly to enable rapid benchmarking of future models.

Training student models on synthetic data generated by strong teacher models is a promising way to distilling the capabilities of teachers. However, recent studies show that stronger models are not always optimal teachers, revealing a mismatch between teacher outputs and student learnability. To address this issue, we propose PerSyn (Personalized data Synthesis), a novel synthesis strategy that operates under a new ``Route then Generate'' paradigm to create data tailored to each student model, enabling it to learn more effectively. Specifically, PerSyn first assigns each prompt to its optimal teacher via a query-level router that jointly considers student learnability and teacher response quality. Each teacher then synthesizes data only for its assigned prompts, making the process more efficient than the conventional ``Generate then Select'' paradigm, where all teachers must generate parallel responses for the entire prompt set before constructing the final dataset. Extensive experiments across different model families and scales demonstrate that PerSyn consistently achieves superior or comparable performance to all baselines in instruct tuning and math reasoning settings. Further analysis verifies the effectiveness of PerSyn and offers extra insights to propel future research.

Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the likelihood of preferred responses often decreases during training. The current work sheds light on the causes and implications of this counter-intuitive phenomenon, which we term likelihood displacement. We demonstrate that likelihood displacement can be catastrophic, shifting probability mass from preferred responses to responses with an opposite meaning. As a simple example, training a model to prefer No over Never can sharply increase the probability of Yes. Moreover, when aligning the model to refuse unsafe prompts, we show that such displacement can unintentionally lead to unalignment, by shifting probability mass from preferred refusal responses to harmful responses (e.g., reducing the refusal rate of Llama-3-8B-Instruct from 74.4% to 33.4%). We theoretically characterize that likelihood displacement is driven by preferences that induce similar embeddings, as measured by a centered hidden embedding similarity (CHES) score. Empirically, the CHES score enables identifying which training samples contribute most to likelihood displacement in a given dataset. Filtering out these samples effectively mitigated unintentional unalignment in our experiments. More broadly, our results highlight the importance of curating data with sufficiently distinct preferences, for which we believe the CHES score may prove valuable.

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.

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying.

The effectiveness of feedback in enhancing learning outcomes is well documented within Educational Data Mining (EDM). Various prior research has explored methodologies to enhance the effectiveness of feedback. Recent developments in Large Language Models (LLMs) have extended their utility in enhancing automated feedback systems. This study aims to explore the potential of LLMs in facilitating automated feedback in math education. We examine the effectiveness of LLMs in evaluating student responses by comparing 3 different models: Llama, SBERT-Canberra, and GPT4 model. The evaluation requires the model to provide both a quantitative score and qualitative feedback on the student's responses to open-ended math problems. We employ Mistral, a version of Llama catered to math, and fine-tune this model for evaluating student responses by leveraging a dataset of student responses and teacher-written feedback for middle-school math problems. A similar approach was taken for training the SBERT model as well, while the GPT4 model used a zero-shot learning approach. We evaluate the model's performance in scoring accuracy and the quality of feedback by utilizing judgments from 2 teachers. The teachers utilized a shared rubric in assessing the accuracy and relevance of the generated feedback. We conduct both quantitative and qualitative analyses of the model performance. By offering a detailed comparison of these methods, this study aims to further the ongoing development of automated feedback systems and outlines potential future directions for leveraging generative LLMs to create more personalized learning experiences.

In this report, we introduce DASD-4B-Thinking, a lightweight yet highly capable, fully open-source reasoning model. It achieves SOTA performance among open-source models of comparable scale across challenging benchmarks in mathematics, scientific reasoning, and code generation -- even outperforming several larger models. We begin by critically reexamining a widely adopted distillation paradigm in the community: SFT on teacher-generated responses, also known as sequence-level distillation. Although a series of recent works following this scheme have demonstrated remarkable efficiency and strong empirical performance, they are primarily grounded in the SFT perspective. Consequently, these approaches focus predominantly on designing heuristic rules for SFT data filtering, while largely overlooking the core principle of distillation itself -- enabling the student model to learn the teacher's full output distribution so as to inherit its generalization capability. Specifically, we identify three critical limitations in current practice: i) Inadequate representation of the teacher's sequence-level distribution; ii) Misalignment between the teacher's output distribution and the student's learning capacity; and iii) Exposure bias arising from teacher-forced training versus autoregressive inference. In summary, these shortcomings reflect a systemic absence of explicit teacher-student interaction throughout the distillation process, leaving the essence of distillation underexploited. To address these issues, we propose several methodological innovations that collectively form an enhanced sequence-level distillation training pipeline. Remarkably, DASD-4B-Thinking obtains competitive results using only 448K training samples -- an order of magnitude fewer than those employed by most existing open-source efforts. To support community research, we publicly release our models and the training dataset.

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.

Large Language Models (LLMs) are widely used to evaluate natural language generation tasks as automated metrics. However, the likelihood, a measure of LLM's plausibility for a sentence, can vary due to superficial differences in sentences, such as word order and sentence structure. It is therefore possible that there might be a likelihood bias if LLMs are used for evaluation: they might overrate sentences with higher likelihoods while underrating those with lower likelihoods. In this paper, we investigate the presence and impact of likelihood bias in LLM-based evaluators. We also propose a method to mitigate the likelihood bias. Our method utilizes highly biased instances as few-shot examples for in-context learning. Our experiments in evaluating the data-to-text and grammatical error correction tasks reveal that several LLMs we test display a likelihood bias. Furthermore, our proposed method successfully mitigates this bias, also improving evaluation performance (in terms of correlation of models with human scores) significantly.

The teacher-student framework, prevalent in semi-supervised semantic segmentation, mainly employs the exponential moving average (EMA) to update a single teacher's weights based on the student's. However, EMA updates raise a problem in that the weights of the teacher and student are getting coupled, causing a potential performance bottleneck. Furthermore, this problem may become more severe when training with more complicated labels such as segmentation masks but with few annotated data. This paper introduces Dual Teacher, a simple yet effective approach that employs dual temporary teachers aiming to alleviate the coupling problem for the student. The temporary teachers work in shifts and are progressively improved, so consistently prevent the teacher and student from becoming excessively close. Specifically, the temporary teachers periodically take turns generating pseudo-labels to train a student model and maintain the distinct characteristics of the student model for each epoch. Consequently, Dual Teacher achieves competitive performance on the PASCAL VOC, Cityscapes, and ADE20K benchmarks with remarkably shorter training times than state-of-the-art methods. Moreover, we demonstrate that our approach is model-agnostic and compatible with both CNN- and Transformer-based models. Code is available at https://github.com/naver-ai/dual-teacher.

Transferring knowledge from a cross-encoder teacher via Knowledge Distillation (KD) has become a standard paradigm for training retrieval models. While existing studies have largely focused on mining hard negatives to improve discrimination, the systematic composition of training data and the resulting teacher score distribution have received relatively less attention. In this work, we highlight that focusing solely on hard negatives prevents the student from learning the comprehensive preference structure of the teacher, potentially hampering generalization. To effectively emulate the teacher score distribution, we propose a Stratified Sampling strategy that uniformly covers the entire score spectrum. Experiments on in-domain and out-of-domain benchmarks confirm that Stratified Sampling, which preserves the variance and entropy of teacher scores, serves as a robust baseline, significantly outperforming top-K and random sampling in diverse settings. These findings suggest that the essence of distillation lies in preserving the diverse range of relative scores perceived by the teacher.

Recent work has explored the use of large language models (LLMs) to generate tutoring responses in mathematics, yet it remains unclear how closely their instructional behavior aligns with expert human practice. We analyze a dataset of math remediation dialogues in which expert tutors, novice tutors, and seven LLMs of varying sizes, comprising both open-weight and commercial models, respond to the same student errors. We examine instructional strategies and linguistic characteristics of tutoring responses, including uptake (restating and revoicing), pressing for accuracy and reasoning, lexical diversity, readability, politeness, and agency. We find that expert tutors produce higher-quality responses than novices, and that larger LLMs generally receive higher pedagogical quality ratings than smaller models, approaching expert performance on average. However, LLMs exhibit systematic differences in their instructional profiles: they underuse discursive strategies characteristic of expert tutors while generating longer, more lexically diverse, and more polite responses. Regression analyses show that pressing for accuracy and reasoning, restating and revoicing, and lexical diversity, are positively associated with perceived pedagogical quality, whereas higher levels of agentic and polite language are negatively associated. These findings highlight the importance of analyzing instructional strategies and linguistic characteristics when evaluating tutoring responses across human tutors and intelligent tutoring systems.

Math word problems (MWPs) are critical K-12 educational tools, and customizing them to students' interests and ability levels can increase learning outcomes. However, teachers struggle to find time to customize MWPs for each student given large class sizes and increasing burnout. We propose that LLMs can support math education by generating MWPs customized to student interests and math education standards. To this end, we use a joint human expert-LLM judge approach to evaluate over 11,000 MWPs generated by open and closed LLMs and develop the first teacher-annotated dataset for standards-aligned educational MWP generation. We show the value of our data by using it to train a 12B open model that matches the performance of larger and more capable open models. We also use our teacher-annotated data to train a text classifier that enables a 30B open LLM to outperform existing closed baselines without any training. Next, we show our models' MWPs are more similar to human-written MWPs than those from existing models. We conclude by conducting the first study of customized LLM-generated MWPs with grade school students, finding they perform similarly on our models' MWPs relative to human-written MWPs but consistently prefer our customized MWPs.

Reasoning distillation has attracted increasing attention. It typically leverages a large teacher model to generate reasoning paths, which are then used to fine-tune a student model so that it mimics the teacher's behavior in training contexts. However, previous approaches have lacked a detailed analysis of the origins of the distilled model's capabilities. It remains unclear whether the student can maintain consistent behaviors with the teacher in novel test-time contexts, or whether it regresses to its original output patterns, raising concerns about the generalization of distillation models. To analyse this question, we introduce a cross-model Reasoning Distillation Provenance Tracing framework. For each action (e.g., a sentence) produced by the distilled model, we obtain the predictive probabilities assigned by the teacher, the original student, and the distilled model under the same context. By comparing these probabilities, we classify each action into different categories. By systematically disentangling the provenance of each action, we experimentally demonstrate that, in test-time contexts, the distilled model can indeed generate teacher-originated actions, which correlate with and plausibly explain observed performance on distilled model. Building on this analysis, we further propose a teacher-guided data selection method. Unlike prior approach that rely on heuristics, our method directly compares teacher-student divergences on the training data, providing a principled selection criterion. We validate the effectiveness of our approach across multiple representative teacher models and diverse student models. The results highlight the utility of our provenance-tracing framework and underscore its promise for reasoning distillation. We hope to share Reasoning Distillation Provenance Tracing and our insights into reasoning distillation with the community.

Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based "foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Rigorous evaluation of large language models (LLMs) relies on comparing models by the prevalence of desirable or undesirable behaviors, such as task pass rates or policy violations. These prevalence estimates are produced by a classifier, either an LLM-as-a-judge or human annotators, making the choice of classifier central to trustworthy evaluation. Common metrics used for this choice, such as Accuracy, Precision, and F1, are sensitive to class imbalance and to arbitrary choices of positive class, and can favor judges that distort prevalence estimates. We show that Youden's J statistic is theoretically aligned with choosing the best judge to compare models, and that Balanced Accuracy is an equivalent linear transformation of J. Through both analytical arguments and empirical examples and simulations, we demonstrate how selecting judges using Balanced Accuracy leads to better, more robust classifier selection.

Today's generative AI systems are tuned to present information by default rather than engage users in service of learning as a human tutor would. To address the wide range of potential education use cases for these systems, we reframe the challenge of injecting pedagogical behavior as one of pedagogical instruction following, where training and evaluation examples include system-level instructions describing the specific pedagogy attributes present or desired in subsequent model turns. This framing avoids committing our models to any particular definition of pedagogy, and instead allows teachers or developers to specify desired model behavior. It also clears a path to improving Gemini models for learning -- by enabling the addition of our pedagogical data to post-training mixtures -- alongside their rapidly expanding set of capabilities. Both represent important changes from our initial tech report. We show how training with pedagogical instruction following produces a LearnLM model (available on Google AI Studio) that is preferred substantially by expert raters across a diverse set of learning scenarios, with average preference strengths of 31\% over GPT-4o, 11\% over Claude 3.5, and 13\% over the Gemini 1.5 Pro model LearnLM was based on.

When large language models (LMs) are applied in zero- or few-shot settings to discriminative tasks such as multiple-choice questions, their attentiveness (i.e., probability mass) is spread across many vocabulary tokens that are not valid choices. Such a spread across multiple surface forms with identical meaning is thought to cause an underestimation of a model's true performance, referred to as the "surface form competition" (SFC) hypothesis. This has motivated the introduction of various probability normalization methods. However, many core questions remain unanswered. How do we measure SFC or attentiveness? Are there direct ways of increasing attentiveness on valid choices? Does increasing attentiveness always improve task accuracy? We propose a mathematical formalism for studying this phenomenon, provide a metric for quantifying attentiveness, and identify a simple method for increasing it -- namely, in-context learning with even just one example containing answer choices. The formalism allows us to quantify SFC and bound its impact. Our experiments on three diverse datasets and six LMs reveal several surprising findings. For example, encouraging models to generate a valid answer choice can, in fact, be detrimental to task performance for some LMs, and prior probability normalization methods are less effective (sometimes even detrimental) to instruction-tuned LMs. We conclude with practical insights for effectively using prompted LMs for multiple-choice tasks.

Our work presents a novel angle for evaluating language models' (LMs) mathematical abilities, by investigating whether they can discern skills and concepts enabled by math content. We contribute two datasets: one consisting of 385 fine-grained descriptions of K-12 math skills and concepts, or standards, from Achieve the Core (ATC), and another of 9.9K problems labeled with these standards (MathFish). Working with experienced teachers, we find that LMs struggle to tag and verify standards linked to problems, and instead predict labels that are close to ground truth, but differ in subtle ways. We also show that LMs often generate problems that do not fully align with standards described in prompts. Finally, we categorize problems in GSM8k using math standards, allowing us to better understand why some problems are more difficult to solve for models than others.

In an educational setting, an estimate of the difficulty of multiple-choice questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment is costly from multiple points of view, automatic approaches to MCQ item difficulty estimation are investigated, yielding however mixed success until now. Our approach to this problem takes a different angle from previous work: asking various Large Language Models to tackle the questions included in two different MCQ datasets, we leverage model uncertainty to estimate item difficulty. By using both model uncertainty features as well as textual features in a Random Forest regressor, we show that uncertainty features contribute substantially to difficulty prediction, where difficulty is inversely proportional to the number of students who can correctly answer a question. In addition to showing the value of our approach, we also observe that our model achieves state-of-the-art results on the BEA publicly available dataset.

Automated evaluation of free-form outputs from large language models (LLMs) is challenging because many distinct answers can be equally valid. A common practice is to use LLMs themselves as judges, but the theoretical properties of this approach are not yet well understood. We show that a geometric framework that represents both judges and candidates as points on a probability simplex can provide helpful insight on what is or is not identifiable using LLM judges. Our theoretical analysis uncovers a "phase transition" in ranking identifiability: for binary scoring systems, true rankings are identifiable even with weak judges under mild assumptions, while rankings become non-identifiable for three or more scoring levels even with infinite data, absent additional prior knowledge. This non-identifiability highlights how uncertainty in rankings stems from not only aleatoric uncertainty (i.e., inherent stochasticity in the data) but also epistemic uncertainty regarding which assumptions hold, an aspect that has received limited attention until now. To integrate both types of uncertainty, we use Bayesian inference to encode assumptions as priors and conduct sensitivity analysis of ranking estimates and credible intervals. Empirical evaluations across multiple benchmarks demonstrate that Bayesian inference yields more accurate rankings and substantially improves coverage rates. These results underscore the importance of taking a more holistic approach to uncertainty quantification when using LLMs as judges.

The prior drift is crucial in Continual Test-Time Adaptation (CTTA) methods that only use unlabeled test data, as it can cause significant error propagation. In this paper, we introduce VCoTTA, a variational Bayesian approach to measure uncertainties in CTTA. At the source stage, we transform a pre-trained deterministic model into a Bayesian Neural Network (BNN) via a variational warm-up strategy, injecting uncertainties into the model. During the testing time, we employ a mean-teacher update strategy using variational inference for the student model and exponential moving average for the teacher model. Our novel approach updates the student model by combining priors from both the source and teacher models. The evidence lower bound is formulated as the cross-entropy between the student and teacher models, along with the Kullback-Leibler (KL) divergence of the prior mixture. Experimental results on three datasets demonstrate the method's effectiveness in mitigating prior drift within the CTTA framework.

We revisit the likelihood ratio between a pretrained large language model (LLM) and its finetuned variant as a criterion for out-of-distribution (OOD) detection. The intuition behind such a criterion is that, the pretrained LLM has the prior knowledge about OOD data due to its large amount of training data, and once finetuned with the in-distribution data, the LLM has sufficient knowledge to distinguish their difference. Leveraging the power of LLMs, we show that, the likelihood ratio can serve as an effective OOD detection criterion. Moreover, we apply the proposed LLM-based likelihood ratio to detect OOD questions in question-answering (QA) systems, which can be used to improve the performance of specialized LLMs for general questions. Given that likelihood can be easily obtained by the loss functions within contemporary neural network frameworks, it is straightforward to implement this approach in practice. Since both the pretrained LLMs and its various finetuned models are widely available from online platforms such as Hugging Face, our proposed criterion can be effortlessly incorporated for OOD detection without the need for further training. We conduct comprehensive evaluation across on multiple settings, including far OOD, near OOD, spam detection, and QA scenarios, to demonstrate the effectiveness of the method. Code can be found at https://github.com/andiac/LLMOODratio

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

A critical component of a successful language generation pipeline is the decoding algorithm. However, the general principles that should guide the choice of decoding algorithm remain unclear. Previous works only compare decoding algorithms in narrow scenarios and their findings do not generalize across tasks. To better structure the discussion, we introduce a taxonomy that groups decoding strategies based on their implicit assumptions about how well the model's likelihood is aligned with the task-specific notion of utility. We argue that this taxonomy allows a broader view of the decoding problem and can lead to generalizable statements because it is grounded on the interplay between the decoding algorithms and the likelihood-utility misalignment. Specifically, by analyzing the correlation between the likelihood and the utility of predictions across a diverse set of tasks, we provide the first empirical evidence supporting the proposed taxonomy, and a set of principles to structure reasoning when choosing a decoding algorithm. Crucially, our analysis is the first one to relate likelihood-based decoding strategies with strategies that rely on external information such as value-guided methods and prompting, and covers the most diverse set of tasks up-to-date.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

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.

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.

Knowledge Distillation (KD) is a model-agnostic technique to improve model quality while having a fixed capacity budget. It is a commonly used technique for model compression, where a larger capacity teacher model with better quality is used to train a more compact student model with better inference efficiency. Through distillation, one hopes to benefit from student's compactness, without sacrificing too much on model quality. Despite the large success of knowledge distillation, better understanding of how it benefits student model's training dynamics remains under-explored. In this paper, we categorize teacher's knowledge into three hierarchical levels and study its effects on knowledge distillation: (1) knowledge of the `universe', where KD brings a regularization effect through label smoothing; (2) domain knowledge, where teacher injects class relationships prior to student's logit layer geometry; and (3) instance specific knowledge, where teacher rescales student model's per-instance gradients based on its measurement on the event difficulty. Using systematic analyses and extensive empirical studies on both synthetic and real-world datasets, we confirm that the aforementioned three factors play a major role in knowledge distillation. Furthermore, based on our findings, we diagnose some of the failure cases of applying KD from recent studies.

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.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

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.

This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding of algebra by taking into account their current level of algebra comprehension. The data set comprises 55 misconceptions about algebra, common errors, and 220 diagnostic examples identified in previous peer-reviewed studies. We provide an example application using a large language model, observing a range of precision and recall scores depending on the topic and experimental setup that reaches 83.9% when including educator feedback and restricting it by topic. We found that topics such as ratios and proportions prove as difficult for LLMs as they are for students. We included a human assessment of LLMs results and feedback from five middle school math educators on the clarity and occurrence of misconceptions in the dataset and the potential use of AI in conjunction with the dataset. Most educators (80% or more) indicated that they encounter these misconceptions among their students, suggesting the relevance of the data set to teaching middle school algebra. Despite varying familiarity with AI tools, four out of five educators expressed interest in using the data set with AI to diagnose student misconceptions or train teachers. The results emphasize the importance of topic-constrained testing, the need for multimodal approaches, and the relevance of human expertise to gain practical insights when using AI for human learning.

Recent advancements in the collection and analysis of sequential educational data have brought time series analysis to a pivotal position in educational research, highlighting its essential role in facilitating data-driven decision-making. However, there is a lack of comprehensive summaries that consolidate these advancements. To the best of our knowledge, this paper is the first to provide a comprehensive review of time series analysis techniques specifically within the educational context. We begin by exploring the landscape of educational data analytics, categorizing various data sources and types relevant to education. We then review four prominent time series methods-forecasting, classification, clustering, and anomaly detection-illustrating their specific application points in educational settings. Subsequently, we present a range of educational scenarios and applications, focusing on how these methods are employed to address diverse educational tasks, which highlights the practical integration of multiple time series methods to solve complex educational problems. Finally, we conclude with a discussion on future directions, including personalized learning analytics, multimodal data fusion, and the role of large language models (LLMs) in educational time series. The contributions of this paper include a detailed taxonomy of educational data, a synthesis of time series techniques with specific educational applications, and a forward-looking perspective on emerging trends and future research opportunities in educational analysis. The related papers and resources are available and regularly updated at the project page.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, fundamentally reshaping the landscape of natural language processing (NLP) research. However, recent evaluation frameworks often rely on the output probabilities of LLMs for predictions, primarily due to computational constraints, diverging from real-world LLM usage scenarios. While widely employed, the efficacy of these probability-based evaluation strategies remains an open research question. This study aims to scrutinize the validity of such probability-based evaluation methods within the context of using LLMs for Multiple Choice Questions (MCQs), highlighting their inherent limitations. Our empirical investigation reveals that the prevalent probability-based evaluation method inadequately aligns with generation-based prediction. Furthermore, current evaluation frameworks typically assess LLMs through predictive tasks based on output probabilities rather than directly generating responses, owing to computational limitations. We illustrate that these probability-based approaches do not effectively correspond with generative predictions. The outcomes of our study can enhance the understanding of LLM evaluation methodologies and provide insights for future research in this domain.

We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is trained on a sentence of the form "A is B", it will not automatically generalize to the reverse direction "B is A". This is the Reversal Curse. For instance, if a model is trained on "Olaf Scholz was the ninth Chancellor of Germany", it will not automatically be able to answer the question, "Who was the ninth Chancellor of Germany?". Moreover, the likelihood of the correct answer ("Olaf Scholz") will not be higher than for a random name. Thus, models exhibit a basic failure of logical deduction and do not generalize a prevalent pattern in their training set (i.e. if "A is B'' occurs, "B is A" is more likely to occur). We provide evidence for the Reversal Curse by finetuning GPT-3 and Llama-1 on fictitious statements such as "Uriah Hawthorne is the composer of 'Abyssal Melodies'" and showing that they fail to correctly answer "Who composed 'Abyssal Melodies?'". The Reversal Curse is robust across model sizes and model families and is not alleviated by data augmentation. We also evaluate ChatGPT (GPT-3.5 and GPT-4) on questions about real-world celebrities, such as "Who is Tom Cruise's mother? [A: Mary Lee Pfeiffer]" and the reverse "Who is Mary Lee Pfeiffer's son?". GPT-4 correctly answers questions like the former 79% of the time, compared to 33% for the latter. This shows a failure of logical deduction that we hypothesize is caused by the Reversal Curse. Code is available at https://github.com/lukasberglund/reversal_curse.

Recent language models have a mysterious tendency to generate false but plausible-sounding text. Such "hallucinations" are an obstacle to the usability of language-based AI systems and can harm people who rely upon their outputs. This work shows shows that there is an inherent statistical reason that pretrained language models hallucinate certain types of facts, having nothing to do with the transformer LM architecture or data quality. For "arbitrary" facts whose veracity cannot be determined from the training data, we show that hallucination is necessary for language models that satisfy a statistical calibration condition appropriate for generative language models. Specifically, if the maximum probability of any fact is bounded, we show that the probability of generating a hallucination is close to the fraction of facts that occur exactly once in the training data (a "Good-Turing" estimate), even assuming ideal training data without errors. One conclusion is that models pretrained to be sufficiently good predictors (i.e., calibrated) may require post-training to mitigate hallucinations on the type of arbitrary facts that tend to appear once in the training set. However, our analysis also suggests that there is no statistical reason that pretraining will lead to hallucination on facts that tend to appear more than once in the training data (like references to publications such as articles and books, whose hallucinations have been particularly notable and problematic) or on systematic facts (like arithmetic calculations). Therefore, different architectures and learning algorithms may mitigate these latter types of hallucinations.