Scholastic Aptitude Test (SAT) is crucial for college admissions but its effectiveness and relevance are increasingly questioned. This paper enhances Synthetic Control methods by introducing "Transformed Control", a novel method that employs Large Language Models (LLMs) powered by Artificial Intelligence to generate control groups. We utilize OpenAI's API to generate a control group where GPT-4, or ChatGPT, takes multiple SATs annually from 2008 to 2023. This control group helps analyze shifts in SAT math difficulty over time, starting from the baseline year of 2008. Using parallel trends, we calculate the Average Difference in Scores (ADS) to assess changes in high school students' math performance. Our results indicate a significant decrease in the difficulty of the SAT math section over time, alongside a decline in students' math performance. The analysis shows a 71-point drop in the rigor of SAT math from 2008 to 2023, with student performance decreasing by 36 points, resulting in a 107-point total divergence in average student math performance. We investigate possible mechanisms for this decline in math proficiency, such as changing university selection criteria, increased screen time, grade inflation, and worsening adolescent mental health. Disparities among demographic groups show a 104-point drop for White students, 84 points for Black students, and 53 points for Asian students. Male students saw a 117-point reduction, while female students had a 100-point decrease.
In this report, we introduce the Qwen2.5-Coder series, a significant upgrade from its predecessor, CodeQwen1.5. This series includes six models: Qwen2.5-Coder-(0.5B/1.5B/3B/7B/14B/32B). As a code-specific model, Qwen2.5-Coder is built upon the Qwen2.5 architecture and continues pretrained on a vast corpus of over 5.5 trillion tokens. Through meticulous data cleaning, scalable synthetic data generation, and balanced data mixing, Qwen2.5-Coder demonstrates impressive code generation capabilities while retaining general and math skills. These models have been evaluated on a wide range of code-related tasks, achieving state-of-the-art (SOTA) performance across more than 10 benchmarks, including code generation, completion, reasoning, and repair, consistently outperforming larger models of the same model size. We believe that the release of the Qwen2.5-Coder series will advance research in code intelligence and, with its permissive licensing, support wider adoption by developers in real-world applications.
Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.
Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a quantitative meta-analysis covering over 100 papers using CoT and ran our own evaluations of 20 datasets across 14 models. Our results show that CoT gives strong performance benefits primarily on tasks involving math or logic, with much smaller gains on other types of tasks. On MMLU, directly generating the answer without CoT leads to almost identical accuracy as CoT unless the question or model's response contains an equals sign, indicating symbolic operations and reasoning. Following this finding, we analyze the behavior of CoT on these problems by separating planning and execution and comparing against tool-augmented LLMs. Much of CoT's gain comes from improving symbolic execution, but it underperforms relative to using a symbolic solver. Our results indicate that CoT can be applied selectively, maintaining performance while saving inference costs. Furthermore, they suggest a need to move beyond prompt-based CoT to new paradigms that better leverage intermediate computation across the whole range of LLM applications.
Mixture-of-Experts (MoE) models scale more effectively than dense models due to sparse computation through expert routing, selectively activating only a small subset of expert modules. However, sparse computation challenges traditional training practices, as discrete expert routing hinders standard backpropagation and thus gradient-based optimization, which are the cornerstone of deep learning. To better pursue the scaling power of MoE, we introduce GRIN (GRadient-INformed MoE training), which incorporates sparse gradient estimation for expert routing and configures model parallelism to avoid token dropping. Applying GRIN to autoregressive language modeling, we develop a top-2 16$\times$3.8B MoE model. Our model, with only 6.6B activated parameters, outperforms a 7B dense model and matches the performance of a 14B dense model trained on the same data. Extensive evaluations across diverse tasks demonstrate the potential of GRIN to significantly enhance MoE efficacy, achieving 79.4 on MMLU, 83.7 on HellaSwag, 74.4 on HumanEval, and 58.9 on MATH.
In this report, we present a series of math-specific large language models: Qwen2.5-Math and Qwen2.5-Math-Instruct-1.5B/7B/72B. The core innovation of the Qwen2.5 series lies in integrating the philosophy of self-improvement throughout the entire pipeline, from pre-training and post-training to inference: (1) During the pre-training phase, Qwen2-Math-Instruct is utilized to generate large-scale, high-quality mathematical data. (2) In the post-training phase, we develop a reward model (RM) by conducting massive sampling from Qwen2-Math-Instruct. This RM is then applied to the iterative evolution of data in supervised fine-tuning (SFT). With a stronger SFT model, it's possible to iteratively train and update the RM, which in turn guides the next round of SFT data iteration. On the final SFT model, we employ the ultimate RM for reinforcement learning, resulting in the Qwen2.5-Math-Instruct. (3) Furthermore, during the inference stage, the RM is used to guide sampling, optimizing the model's performance. Qwen2.5-Math-Instruct supports both Chinese and English, and possess advanced mathematical reasoning capabilities, including Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR). We evaluate our models on 10 mathematics datasets in both English and Chinese, such as GSM8K, MATH, GaoKao, AMC23, and AIME24, covering a range of difficulties from grade school level to math competition problems.
Large language models (LLMs) have exhibited remarkable few-shot learning capabilities and unified the paradigm of NLP tasks through the in-context learning (ICL) technique. Despite the success of ICL, the quality of the exemplar demonstrations can significantly influence the LLM's performance. Existing exemplar selection methods mainly focus on the semantic similarity between queries and candidate exemplars. On the other hand, the logical connections between reasoning steps can be beneficial to depict the problem-solving process as well. In this paper, we proposes a novel method named Reasoning Graph-enhanced Exemplar Retrieval (RGER). RGER first quires LLM to generate an initial response, then expresses intermediate problem-solving steps to a graph structure. After that, it employs graph kernel to select exemplars with semantic and structural similarity. Extensive experiments demonstrate the structural relationship is helpful to the alignment of queries and candidate exemplars. The efficacy of RGER on math and logit reasoning tasks showcases its superiority over state-of-the-art retrieval-based approaches. Our code is released at https://github.com/Yukang-Lin/RGER.
We introduce NVLM 1.0, a family of frontier-class multimodal large language models (LLMs) that achieve state-of-the-art results on vision-language tasks, rivaling the leading proprietary models (e.g., GPT-4o) and open-access models (e.g., Llama 3-V 405B and InternVL 2). Remarkably, NVLM 1.0 shows improved text-only performance over its LLM backbone after multimodal training. In terms of model design, we perform a comprehensive comparison between decoder-only multimodal LLMs (e.g., LLaVA) and cross-attention-based models (e.g., Flamingo). Based on the strengths and weaknesses of both approaches, we propose a novel architecture that enhances both training efficiency and multimodal reasoning capabilities. Furthermore, we introduce a 1-D tile-tagging design for tile-based dynamic high-resolution images, which significantly boosts performance on multimodal reasoning and OCR-related tasks. Regarding training data, we meticulously curate and provide detailed information on our multimodal pretraining and supervised fine-tuning datasets. Our findings indicate that dataset quality and task diversity are more important than scale, even during the pretraining phase, across all architectures. Notably, we develop production-grade multimodality for the NVLM-1.0 models, enabling them to excel in vision-language tasks while maintaining and even improving text-only performance compared to their LLM backbones. To achieve this, we craft and integrate a high-quality text-only dataset into multimodal training, alongside a substantial amount of multimodal math and reasoning data, leading to enhanced math and coding capabilities across modalities. To advance research in the field, we release the model weights at https://huggingface.co/nvidia/NVLM-D-72B and will open-source the training code for the community soon.
Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.
While knowledge evaluation in large language models has predominantly focused on academic subjects like math and physics, these assessments often fail to capture the practical demands of real-world professions. In this paper, we introduce IndoCareer, a dataset comprising 8,834 multiple-choice questions designed to evaluate performance in vocational and professional certification exams across various fields. With a focus on Indonesia, IndoCareer provides rich local contexts, spanning six key sectors: (1) healthcare, (2) insurance and finance, (3) creative and design, (4) tourism and hospitality, (5) education and training, and (6) law. Our comprehensive evaluation of 27 large language models shows that these models struggle particularly in fields with strong local contexts, such as insurance and finance. Additionally, while using the entire dataset, shuffling answer options generally maintains consistent evaluation results across models, but it introduces instability specifically in the insurance and finance sectors.
Post-training, particularly reinforcement learning (RL) using self-play-generated data, has become a new learning paradigm for large language models (LLMs). However, scaling RL to develop a general reasoner remains a research challenge, as existing methods focus on task-specific reasoning without adequately addressing generalization across a broader range of tasks. Moreover, unlike traditional RL with limited action space, LLMs operate in an infinite space, making it crucial to search for valuable and diverse strategies to solve problems effectively. To address this, we propose searching within the action space on high-level abstract plans to enhance model generalization and introduce Critical Plan Step Learning (CPL), comprising: 1) searching on plan, using Monte Carlo Tree Search (MCTS) to explore diverse plan steps in multi-step reasoning tasks, and 2) learning critical plan steps through Step-level Advantage Preference Optimization (Step-APO), which integrates advantage estimates for step preference obtained via MCTS into Direct Preference Optimization (DPO). This combination helps the model effectively learn critical plan steps, enhancing both reasoning capabilities and generalization. Experimental results demonstrate that our method, trained exclusively on GSM8K and MATH, not only significantly improves performance on GSM8K (+10.5%) and MATH (+6.5%), but also enhances out-of-domain reasoning benchmarks, such as HumanEval (+12.2%), GPQA (+8.6%), ARC-C (+4.0%), MMLU-STEM (+2.2%), and BBH (+1.8%).
To make sense of massive data, we often fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster. However, these parameters are often high-dimensional and hard to interpret. To make model parameters directly interpretable, we introduce a family of statistical models -- including clustering, time series, and classification models -- parameterized by natural language predicates. For example, a cluster of text about COVID could be parameterized by the predicate "discusses COVID". To learn these statistical models effectively, we develop a model-agnostic algorithm that optimizes continuous relaxations of predicate parameters with gradient descent and discretizes them by prompting language models (LMs). Finally, we apply our framework to a wide range of problems: taxonomizing user chat dialogues, characterizing how they evolve across time, finding categories where one language model is better than the other, clustering math problems based on subareas, and explaining visual features in memorable images. Our framework is highly versatile, applicable to both textual and visual domains, can be easily steered to focus on specific properties (e.g. subareas), and explains sophisticated concepts that classical methods (e.g. n-gram analysis) struggle to produce.
Knowledge tagging for questions is vital in modern intelligent educational applications, including learning progress diagnosis, practice question recommendations, and course content organization. Traditionally, these annotations have been performed by pedagogical experts, as the task demands not only a deep semantic understanding of question stems and knowledge definitions but also a strong ability to link problem-solving logic with relevant knowledge concepts. With the advent of advanced natural language processing (NLP) algorithms, such as pre-trained language models and large language models (LLMs), pioneering studies have explored automating the knowledge tagging process using various machine learning models. In this paper, we investigate the use of a multi-agent system to address the limitations of previous algorithms, particularly in handling complex cases involving intricate knowledge definitions and strict numerical constraints. By demonstrating its superior performance on the publicly available math question knowledge tagging dataset, MathKnowCT, we highlight the significant potential of an LLM-based multi-agent system in overcoming the challenges that previous methods have encountered. Finally, through an in-depth discussion of the implications of automating knowledge tagging, we underscore the promising results of deploying LLM-based algorithms in educational contexts.
Variational Autoencoders are widespread in Machine Learning, but are typically explained with dense math notation or static code examples. This paper presents VAE Explainer, an interactive Variational Autoencoder running in the browser to supplement existing static documentation (e.g., Keras Code Examples). VAE Explainer adds interactions to the VAE summary with interactive model inputs, latent space, and output. VAE Explainer connects the high-level understanding with the implementation: annotated code and a live computational graph. The VAE Explainer interactive visualization is live at https://xnought.github.io/vae-explainer and the code is open source at https://github.com/xnought/vae-explainer.
We demonstrate that preference optimization methods can effectively enhance LLM safety. Applying various alignment techniques to the Falcon 11B model using safety datasets, we achieve a significant boost in global safety score (from $57.64\%$ to $99.90\%$) as measured by LlamaGuard 3 8B, competing with state-of-the-art models. On toxicity benchmarks, average scores in adversarial settings dropped from over $0.6$ to less than $0.07$. However, this safety improvement comes at the cost of reduced general capabilities, particularly in math, suggesting a trade-off. We identify noise contrastive alignment (Safe-NCA) as an optimal method for balancing safety and performance. Our study ultimately shows that alignment techniques can be sufficient for building safe and robust models.
Ongoing advancements in Generative AI (GenAI) have boosted the potential of applying long-standing learning-by-teaching practices in the form of a teachable agent (TA). Despite the recognized roles and opportunities of TAs, less is known about how GenAI could create synergy or introduce challenges in TAs and how students perceived the application of GenAI in TAs. This study explored middle school students perceived roles, benefits, and challenges of GenAI-powered TAs in an authentic mathematics classroom. Through classroom observation, focus-group interviews, and open-ended surveys of 108 sixth-grade students, we found that students expected the GenAI-powered TA to serve as a learning companion, facilitator, and collaborative problem-solver. Students also expressed the benefits and challenges of GenAI-powered TAs. This study provides implications for the design of educational AI and AI-assisted instruction.
Federated instruction tuning enables multiple clients to collaboratively fine-tune a shared large language model (LLM) that can follow humans' instructions without directly sharing raw data. However, existing literature impractically requires that all the clients readily hold instruction-tuning data (i.e., structured instruction-response pairs), which necessitates massive human annotations since clients' data is usually unstructured text instead. Addressing this, we propose a novel and flexible framework FedIT-U2S, which can automatically transform unstructured corpus into structured data for federated instruction tuning. FedIT-U2S consists two key steps: (1) few-shot instruction-tuning data generation, where each unstructured data piece together with several examples is combined to prompt an LLM in generating an instruction-response pair. To further enhance the flexibility, a retrieval-based example selection technique is proposed, where the examples are automatically selected based on the relatedness between the client's data piece and example pool, bypassing the need of determining examples in advance. (2) A typical federated instruction tuning process based on the generated data. Overall, FedIT-U2S can be applied to diverse scenarios as long as the client holds valuable text corpus, broadening the application scope of federated instruction tuning. We conduct a series of experiments on three domains (medicine, knowledge, and math), showing that our proposed FedIT-U2S can consistently and significantly brings improvement over the base LLM.
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However, existing efforts are largely limited to creating formalized versions of proofs from extensive online mathematical corpora, struggling to keep pace with the rapidly evolving nature of mathematics. To bridge the gap between traditional and computerized proof techniques, this paper explores the use of Large Language Models (LLMs) to generate formal proof steps and complete formalized proofs. By converting natural language (NL) mathematical proofs into formalized versions, this work introduces the basic structure and tactics of the Lean 4 language. The goal is to determine how AI can be leveraged to assist the mathematical formalization process and improve its performance. Several examples are provided that demonstrate solving problems using both traditional and Lean 4-based approaches. Ultimately, this paper presents an explanation of the foundations of Lean 4 and comparative analyses of the mathematical formalization process using traditional and AI-augmented techniques. The findings indicate that AI- powered tools have significant potential to accelerate and enhance the formalization of mathematical proofs, paving the way for more efficient and reliable theorem-proving for AI for Math in the future.
Large Language Models (LLM) often needs to be Continual Pre-Trained (CPT) to obtain the unfamiliar language skill or adapt into new domains. The huge training cost of CPT often asks for cautious choice of key hyper-parameters such as the mixture ratio of extra language or domain corpus. However, there is no systematic study which bridge the gap between the optimal mixture ratio and the actual model performance, and the gap between experimental scaling law and the actual deployment in the full model size. In this paper, we perform CPT on Llama-3 8B and 70B to enhance its Chinese ability. We study the optimal correlation between the Additional Language Mixture Ratio (ALMR) and the Learning Rate (LR) on the 8B size which directly indicate the optimal experimental set up. By thorough choice of hyper-parameter, and subsequent fine-tuning, the model capability is improved not only on the Chinese-related benchmark, but also some specific domains including math, coding and emotional intelligence. We deploy the final 70B version of LLM on an real-life chat system which obtain satisfying performance.
With the blossom of large language models (LLMs), inference efficiency becomes increasingly important. Various approximation methods are proposed to reduce the cost at inference time. Contextual Sparsity (CS) is appealing for its training-free nature and its ability to reach a higher compression ratio seemingly without quality degradation. However, after a comprehensive evaluation of contextual sparsity methods on various complex generation tasks, we find that although CS succeeds in prompt-understanding tasks, CS significantly degrades the model performance for reasoning, deduction, and knowledge-based tasks. Despite the gap in end-to-end accuracy, we observed that sparse models often share general problem-solving logic and require only a few token corrections to recover the original model performance. This paper introduces Sirius, an efficient correction mechanism, which significantly recovers CS models quality on reasoning tasks while maintaining its efficiency gain. Sirius is evaluated on 6 models with 8 difficult generation tasks in reasoning, math, and coding and shows consistent effectiveness and efficiency. Also, we carefully develop a system implementation for Sirius and show that Sirius achieves roughly 20% reduction in latency for 8B model on-chip and 35% reduction for 70B model offloading. We open-source our implementation of Sirius at https://github.com/Infini-AI-Lab/Sirius.git.