Question Answering (QA) poses a challenging and critical problem, particularly in today's age of interactive dialogue systems such as ChatGPT, Perplexity, Microsoft Copilot, etc. where users demand both accuracy and transparency in the model's outputs. Since smaller language models (SLMs) are computationally more efficient but often under-perform compared to larger models, Knowledge Distillation (KD) methods allow for finetuning these smaller models to improve their final performance. Lately, the intermediate tokens or the so called `reasoning' traces produced by Chain-of-Thought (CoT) or by reasoning models such as DeepSeek R1 are used as a training signal for KD. However, these reasoning traces are often verbose and difficult to interpret or evaluate. In this work, we aim to address the challenge of evaluating the faithfulness of these reasoning traces and their correlation with the final performance. To this end, we employ a KD method leveraging rule-based problem decomposition. This approach allows us to break down complex queries into structured sub-problems, generating interpretable traces whose correctness can be readily evaluated, even at inference time. Specifically, we demonstrate this approach on Open Book QA, decomposing the problem into a Classification step and an Information Retrieval step, thereby simplifying trace evaluation. Our SFT experiments with correct and incorrect traces on the CoTemp QA, Microsoft Machine Reading Comprehension QA, and Facebook bAbI QA datasets reveal the striking finding that correct traces do not necessarily imply that the model outputs the correct final solution. Similarly, we find a low correlation between correct final solutions and intermediate trace correctness. These results challenge the implicit assumption behind utilizing reasoning traces for improving SLMs' final performance via KD.

Recently, large reasoning models have achieved impressive performance on various tasks by employing human-like deep thinking. However, the lengthy thinking process substantially increases inference overhead, making efficiency a critical bottleneck. In this work, we first demonstrate that NoThinking, which prompts the reasoning model to skip thinking and directly generate the final solution, is a better choice for relatively simple tasks in terms of both performance and efficiency. Motivated by this, we propose AdaptThink, a novel RL algorithm to teach reasoning models to choose the optimal thinking mode adaptively based on problem difficulty. Specifically, AdaptThink features two core components: (1) a constrained optimization objective that encourages the model to choose NoThinking while maintaining the overall performance; (2) an importance sampling strategy that balances Thinking and NoThinking samples during on-policy training, thereby enabling cold start and allowing the model to explore and exploit both thinking modes throughout the training process. Our experiments indicate that AdaptThink significantly reduces the inference costs while further enhancing performance. Notably, on three math datasets, AdaptThink reduces the average response length of DeepSeek-R1-Distill-Qwen-1.5B by 53% and improves its accuracy by 2.4%, highlighting the promise of adaptive thinking-mode selection for optimizing the balance between reasoning quality and efficiency. Our codes and models are available at https://github.com/THU-KEG/AdaptThink.

Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present HARDMath2, a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students' understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.

We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and pairwise steps, but still achieving linear convergence for strongly convex functions, along with good practical performance. Our approach retains all favorable properties of conditional gradient algorithms, notably avoidance of projections onto P and maintenance of iterates as sparse convex combinations of a limited number of extreme points of P. The algorithm is lazy, making use of inexpensive inexact solutions of the linear programming subproblem that characterizes the conditional gradient approach. It decreases measures of optimality (primal and dual gaps) rapidly, both in the number of iterations and in wall-clock time, outperforming even the lazy conditional gradient algorithms of [arXiv:1410.8816]. We also present a streamlined version of the algorithm for the probability simplex.

A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike existing approaches which implicitly estimate such a function, like Gaussian Mixture Models (GMMs), the proposed approach bypasses any explicit modelling assumptions and exploits the flexible estimation potential of nonparametric smoothing. An intuitive approach for selecting the tuning parameters governing estimation is provided, which allows the proposed method to automatically determine both an appropriate level of flexibility and also the number of clusters to extract from a given data set. Experiments on a large collection of publicly available data sets are used to document the strong performance of the proposed approach, in comparison with relevant benchmarks from the literature. R code to implement the proposed approach is available from https://github.com/DavidHofmeyr/ I. Introduction Cluster analysis refers to the task of partitioning a set of data into groups (or clusters) in such a way that points within the same cluster tend to be more similar than points in different clusters.

Automated Machine Learning (AutoML) gained popularity due to the increased demand for Machine Learning (ML) specialists, allowing them to apply ML techniques effortlessly and quickly. AutoML implementations use optimisation methods to identify the most effective ML solution for a given dataset, aiming to improve one or more predefined metrics. However, most implementations focus on model selection and hyperparameter tuning. Despite being an important factor in obtaining high-performance ML systems, data quality is usually an overlooked part of AutoML and continues to be a manual and time-consuming task. This work presents EDCA, an Evolutionary Data Centric AutoML framework. In addition to the traditional tasks such as selecting the best models and hyperparameters, EDCA enhances the given data by optimising data processing tasks such as data reduction and cleaning according to the problems' needs. All these steps create an ML pipeline that is optimised by an evolutionary algorithm. To assess its effectiveness, EDCA was compared to FLAML and TPOT, two frameworks at the top of the AutoML benchmarks. The frameworks were evaluated in the same conditions using datasets from AMLB classification benchmarks. EDCA achieved statistically similar results in performance to FLAML and TPOT but used significantly less data to train the final solutions. Moreover, EDCA experimental results reveal that a good performance can be achieved using less data and efficient ML algorithm aspects that align with Green AutoML guidelines

The paper addresses an important topic (implicit regularization in deep learning), is well-written, and although I did not verify proofs in the appendixes, I believe it is mathematically solid. Nonetheless, I have several concerns with regards to originality, significance and clarity (see below), which ultimately lead me to vote against its acceptance. This is true for the proof techniques as well. The only part I view as potentially novel is the perturbation analysis, but that is unfortunately not discussed at all in the body of the paper. I recommend to the authors to put much more focus on this aspect, as without it the paper is merely a straightforward extension of prior work.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by $9\%$ on the MATH dataset.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

Large language models (LLMs) showcase impressive reasoning capabilities when coupled with Chain-of-Thought (CoT) prompting. However, the robustness of this approach warrants further investigation. In this paper, we introduce a novel scenario termed preemptive answers, where the LLM obtains an answer before engaging in reasoning. This situation can arise inadvertently or induced by malicious users by prompt injection attacks. Experiments reveal that preemptive answers significantly impair the model's reasoning capability across various CoT methods and a broad spectrum of datasets. To bolster the robustness of reasoning, we propose two measures aimed at mitigating this issue to some extent.