Large Language Models excel in reasoning yet often rely on Chain-of-Thought prompts, limiting performance on tasks demanding more nuanced topological structures. We present SOLAR (Scalable Optimization of Large-scale Architecture for Reasoning), a framework that dynamically optimizes Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT) topologies to boost accuracy and efficiency. Our Topological-Annotation-Generation (TAG) system automates dataset creation, annotation, and difficulty segmentation, leading to stronger post training and test-time performance. We also propose Topological-Scaling, a curriculum-learning-based approach that adaptively combines post training and inference scaling to each task. On MATH and GSM8K, SOLAR delivers notable gains: +5% accuracy with Topological Tuning, +9% with Topological Rewarding, and +10.02% with Hybrid Scaling, while reducing response length by over 5%, lowering inference latency. To further enhance efficiency, we introduce a multi-task Topological Reward Model (M-TRM) that selects both the optimal reasoning topology and final answer in a single pass, eliminating multiple single-task TRMs. Remarkably, M-TRM also surpasses all single-task TRMs, improving accuracy by +10% and rank correlation by +9%. Overall, SOLAR establishes a new benchmark for scalable, high-precision LLM reasoning and introduces a fully automated, dynamic topology competition mechanism.
The mathematical problem-solving capabilities of large language models have become a focal point of research, with growing interests in leveraging self-generated reasoning paths as a promising way to refine and enhance these models. These paths capture step-by-step logical processes while requiring only the correct answer for supervision. The self-training method has been shown to be effective in reasoning tasks while eliminating the need for external models and manual annotations. However, optimizing the use of self-generated data for model training remains an open challenge. In this work, we propose Entropy-Based Adaptive Weighting for Self-Training (EAST), an adaptive weighting strategy designed to prioritize uncertain data during self-training. Specifically, EAST employs a mapping function with a tunable parameter that controls the sharpness of the weighting, assigning higher weights to data where the model exhibits greater uncertainty. This approach guides the model to focus on more informative and challenging examples, thereby enhancing its reasoning ability. We evaluate our approach on GSM8K and MATH benchmarks. Empirical results show that, while the vanilla method yields virtually no improvement (0%) on MATH, EAST achieves around a 1% gain over backbone model. On GSM8K, EAST attains a further 1-2% performance boost compared to the vanilla method.
We introduce ToRL (Tool-Integrated Reinforcement Learning), a framework for training large language models (LLMs) to autonomously use computational tools via reinforcement learning. Unlike supervised fine-tuning, ToRL allows models to explore and discover optimal strategies for tool use. Experiments with Qwen2.5-Math models show significant improvements: ToRL-7B reaches 43.3\% accuracy on AIME~24, surpassing reinforcement learning without tool integration by 14\% and the best existing Tool-Integrated Reasoning (TIR) model by 17\%. Further analysis reveals emergent behaviors such as strategic tool invocation, self-regulation of ineffective code, and dynamic adaptation between computational and analytical reasoning, all arising purely through reward-driven learning.
Generating high-quality stories spanning thousands of tokens requires competency across a variety of skills, from tracking plot and character arcs to keeping a consistent and engaging style. Due to the difficulty of sourcing labeled datasets and precise quality measurements, most work using large language models (LLMs) for long-form story generation uses combinations of hand-designed prompting techniques to elicit author-like behavior. This is a manual process that is highly dependent on the specific story-generation task. Motivated by the recent success of applying RL with Verifiable Rewards to domains like math and coding, we propose a general story-generation task (Next-Chapter Prediction) and a reward formulation (Verified Rewards via Completion Likelihood Improvement) that allows us to use an unlabeled book dataset as a learning signal for reasoning. We learn to reason over a story's condensed information and generate a detailed plan for the next chapter. Our reasoning is evaluated via the chapters it helps a story-generator create, and compared against non-trained and supervised finetuning (SFT) baselines. Pairwise human judgments reveal the chapters our learned reasoning produces are preferred across almost all metrics, and the effect is more pronounced in Scifi and Fantasy genres.
Nonlinear matrix decomposition (NMD) with the ReLU function, denoted ReLU-NMD, is the following problem: given a sparse, nonnegative matrix $X$ and a factorization rank $r$, identify a rank-$r$ matrix $\Theta$ such that $X\approx \max(0,\Theta)$. This decomposition finds application in data compression, matrix completion with entries missing not at random, and manifold learning. The standard ReLU-NMD model minimizes the least squares error, that is, $\|X - \max(0,\Theta)\|_F^2$. The corresponding optimization problem is nondifferentiable and highly nonconvex. This motivated Saul to propose an alternative model, Latent-ReLU-NMD, where a latent variable $Z$ is introduced and satisfies $\max(0,Z)=X$ while minimizing $\|Z - \Theta\|_F^2$ (``A nonlinear matrix decomposition for mining the zeros of sparse data'', SIAM J. Math. Data Sci., 2022). Our first contribution is to show that the two formulations may yield different low-rank solutions $\Theta$; in particular, we show that Latent-ReLU-NMD can be ill-posed when ReLU-NMD is not, meaning that there are instances in which the infimum of Latent-ReLU-NMD is not attained while that of ReLU-NMD is. We also consider another alternative model, called 3B-ReLU-NMD, which parameterizes $\Theta=WH$, where $W$ has $r$ columns and $H$ has $r$ rows, allowing one to get rid of the rank constraint in Latent-ReLU-NMD. Our second contribution is to prove the convergence of a block coordinate descent (BCD) applied to 3B-ReLU-NMD and referred to as BCD-NMD. Our third contribution is a novel extrapolated variant of BCD-NMD, dubbed eBCD-NMD, which we prove is also convergent under mild assumptions. We illustrate the significant acceleration effect of eBCD-NMD compared to BCD-NMD, and also show that eBCD-NMD performs well against the state of the art on synthetic and real-world data sets.
Large language models (LLMs) have demonstrated strong potential and impressive performance in automating the generation and optimization of workflows. However, existing approaches are marked by limited reasoning capabilities, high computational demands, and significant resource requirements. To address these issues, we propose DebFlow, a framework that employs a debate mechanism to optimize workflows and integrates reflexion to improve based on previous experiences. We evaluated our method across six benchmark datasets, including HotpotQA, MATH, and ALFWorld. Our approach achieved a 3\% average performance improvement over the latest baselines, demonstrating its effectiveness in diverse problem domains. In particular, during training, our framework reduces resource consumption by 37\% compared to the state-of-the-art baselines. Additionally, we performed ablation studies. Removing the Debate component resulted in a 4\% performance drop across two benchmark datasets, significantly greater than the 2\% drop observed when the Reflection component was removed. These findings strongly demonstrate the critical role of Debate in enhancing framework performance, while also highlighting the auxiliary contribution of reflexion to overall optimization.
Recent studies have shown that Large Language Models (LLMs) augmented with chain-of-thought (CoT) reasoning demonstrate impressive problem-solving abilities. However, in this work, we identify a recurring issue where these models occasionally generate overly short reasoning, leading to degraded performance on even simple mathematical problems. Specifically, we investigate how reasoning length is embedded in the hidden representations of reasoning models and its impact on accuracy. Our analysis reveals that reasoning length is governed by a linear direction in the representation space, allowing us to induce overly short reasoning by steering the model along this direction. Building on this insight, we introduce ThinkEdit, a simple yet effective weight-editing approach to mitigate the issue of overly short reasoning. We first identify a small subset of attention heads (approximately 2%) that predominantly drive short reasoning behavior. We then edit the output projection weights of these heads to suppress the short reasoning direction. With changes to only 0.1% of the model's parameters, ThinkEdit effectively reduces overly short reasoning and yields notable accuracy gains for short reasoning outputs (+5.44%), along with an overall improvement across multiple math benchmarks (+2.43%). Our findings provide new mechanistic insights into how reasoning length is controlled within LLMs and highlight the potential of fine-grained model interventions to improve reasoning quality. Our code is available at https://github.com/Trustworthy-ML-Lab/ThinkEdit
Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, Gemini-2.5-Pro, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly: only Gemini-2.5-Pro achieves a non-trivial score of 25%, while all other models achieve less than 5%. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.
Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.
This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need for sampling multiple completions for each question. Our experiment and theoretical analysis reveals that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training -- their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experimental results demonstrate that CPPO achieves up to $8.32\times$ speedup on GSM8K and $3.51\times$ on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.
In recent years, the rapid development of large reasoning models has resulted in the saturation of existing benchmarks for evaluating mathematical reasoning, highlighting the urgent need for more challenging and rigorous evaluation frameworks. To address this gap, we introduce OlymMATH, a novel Olympiad-level mathematical benchmark, designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions. The problems are systematically organized into two distinct difficulty tiers: (1) AIME-level problems (easy) that establish a baseline for mathematical reasoning assessment, and (2) significantly more challenging problems (hard) designed to push the boundaries of current state-of-the-art models. In our benchmark, these problems span four core mathematical fields, each including a verifiable numerical solution to enable objective, rule-based evaluation. Empirical results underscore the significant challenge presented by OlymMATH, with state-of-the-art models including DeepSeek-R1, OpenAI's o3-mini and Gemini 2.5 Pro Exp demonstrating notably limited accuracy on the hard subset. Furthermore, the benchmark facilitates comprehensive bilingual assessment of mathematical reasoning abilities-a critical dimension that remains largely unaddressed in mainstream mathematical reasoning benchmarks. We release the benchmark, evaluation code, detailed results and a data visualization tool at https://github.com/RUCAIBox/OlymMATH.
Large language Models (LLMs) have demonstrated remarkable skills across various domains. Understanding the mechanisms behind their abilities and implementing controls over them is becoming increasingly important for developing better models. In this paper, we focus on skill unlearning in LLMs, specifically unlearning a particular skill while retaining their overall capabilities. We introduce two lightweight, training-free machine skill unlearning techniques for LLMs. First, we observe that the pre-activation distribution of neurons in each Feed-Forward Layer (FFL) differs when the model demonstrates different skills. Additionally, we find that queries triggering the same skill cluster within the FFL key space and can be separated from other queries using a hypercube. Based on these observations, we propose two lightweight, training-free skill unlearning methods via \textit{intervention} and \textit{abstention} respectively: \texttt{Neuron Adjust} and \texttt{Key Space Detection}. We evaluate our methods on unlearning math-solving, Python-coding, and comprehension skills across seven different languages. The results demonstrate their strong unlearning capabilities for the designated skills. Specifically, \texttt{Key Space Detection} achieves over 80\% relative performance drop on the forgetting skill and less than 10\% relative performance drop on other skills and the model's general knowledge (MMLU) for most unlearning tasks. Our code is available at https://github.com/Trustworthy-ML-Lab/effective_skill_unlearning
Using large teacher models to guide the training of smaller student models has become the prevailing paradigm for efficient and effective learning. However, vocabulary mismatches between teacher and student language models pose significant challenges in language modeling, resulting in divergent token sequences and output distributions. To overcome these limitations, we propose Vocabulary-agnostic Teacher Guided Language Modeling (VocAgnoLM), a novel approach that bridges the gap caused by vocabulary mismatch through two key methods: (1) Token-level Lexical Alignment, which aligns token sequences across mismatched vocabularies, and (2) Teacher Guided Loss, which leverages the loss of teacher model to guide effective student training. We demonstrate its effectiveness in language modeling with 1B student model using various 7B teacher models with different vocabularies. Notably, with Qwen2.5-Math-Instruct, a teacher model sharing only about 6% of its vocabulary with TinyLlama, VocAgnoLM achieves a 46% performance improvement compared to naive continual pretraining. Furthermore, we demonstrate that VocAgnoLM consistently benefits from stronger teacher models, providing a robust solution to vocabulary mismatches in language modeling.
As language model (LM) outputs get more and more natural, it is becoming more difficult than ever to evaluate their quality. Simultaneously, increasing LMs' "thinking" time through scaling test-time compute has proven an effective technique to solve challenging problems in domains such as math and code. This raises a natural question: can an LM's evaluation capability also be improved by spending more test-time compute? To answer this, we investigate employing reasoning models-LMs that natively generate long chain-of-thought reasoning-as evaluators. Specifically, we examine methods to leverage more test-time compute by (1) using reasoning models, and (2) prompting these models to evaluate not only the response as a whole (i.e., outcome evaluation) but also assess each step in the response separately (i.e., process evaluation). In experiments, we observe that the evaluator's performance improves monotonically when generating more reasoning tokens, similar to the trends observed in LM-based generation. Furthermore, we use these more accurate evaluators to rerank multiple generations, and demonstrate that spending more compute at evaluation time can be as effective as using more compute at generation time in improving an LM's problem-solving capability.
Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current models are constrained by limitations in handling long texts and reinforcement learning (RL) training efficiency. To address these issues, we propose a simple yet effective test-time scaling approach Multi-round Thinking. This method iteratively refines model reasoning by leveraging previous answers as prompts for subsequent rounds. Extensive experiments across multiple models, including QwQ-32B and DeepSeek-R1, consistently show performance improvements on various benchmarks such as AIME 2024, MATH-500, GPQA-diamond, and LiveCodeBench. For instance, the accuracy of QwQ-32B improved from 80.3% (Round 1) to 82.1% (Round 2) on the AIME 2024 dataset, while DeepSeek-R1 showed a similar increase from 79.7% to 82.0%. These results confirm that Multi-round Thinking is a broadly applicable, straightforward approach to achieving stable enhancements in model performance, underscoring its potential for future developments in test-time scaling techniques. The key prompt: {Original question prompt} The assistant's previous answer is: <answer> {last round answer} </answer>, and please re-answer.
The AM-DeepSeek-R1-Distilled is a large-scale dataset with thinking traces for general reasoning tasks, composed of high-quality and challenging reasoning problems. These problems are collected from a multitude of open-source datasets, subjected to semantic deduplication and meticulous cleaning to eliminate test set contamination. All responses within the dataset are distilled from reasoning models (predominantly DeepSeek-R1) and have undergone rigorous verification procedures. Mathematical problems are validated by checking against reference answers, code problems are verified using test cases, and other tasks are evaluated with the aid of a reward model. The AM-Distill-Qwen-32B model, which was trained through only simple Supervised Fine-Tuning (SFT) using this batch of data, outperformed the DeepSeek-R1-Distill-Qwen-32B model on four benchmarks: AIME2024, MATH-500, GPQA-Diamond, and LiveCodeBench. Additionally, the AM-Distill-Qwen-72B model surpassed the DeepSeek-R1-Distill-Llama-70B model on all benchmarks as well. We are releasing these 1.4 million problems and their corresponding responses to the research community with the objective of fostering the development of powerful reasoning-oriented Large Language Models (LLMs). The dataset was published in \href{https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M}{https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M}.
We introduce Gemma 3, a multimodal addition to the Gemma family of lightweight open models, ranging in scale from 1 to 27 billion parameters. This version introduces vision understanding abilities, a wider coverage of languages and longer context - at least 128K tokens. We also change the architecture of the model to reduce the KV-cache memory that tends to explode with long context. This is achieved by increasing the ratio of local to global attention layers, and keeping the span on local attention short. The Gemma 3 models are trained with distillation and achieve superior performance to Gemma 2 for both pre-trained and instruction finetuned versions. In particular, our novel post-training recipe significantly improves the math, chat, instruction-following and multilingual abilities, making Gemma3-4B-IT competitive with Gemma2-27B-IT and Gemma3-27B-IT comparable to Gemini-1.5-Pro across benchmarks. We release all our models to the community.
We introduce LogQuant, a groundbreaking 2-bit quantization technique for KV Cache in large language model (LLM) inference, delivering substantial memory savings while preserving superior performance. Previous methods either assume that later tokens are more important or attempt to predict important tokens based on earlier attention patterns. Both approaches, however, can result in performance bottlenecks or frequent mispredictions. LogQuant takes a different approach. By applying a log-based filtering mechanism, it selectively compresses the KV Cache across the entire context, achieving better performance with the same or even reduced memory footprint compared to existing methods. In benchmark tests, it enhances throughput by 25% and boosts batch size by 60% without increasing memory consumption. For challenging tasks such as Math and Code Completion, LogQuant improves accuracy by 40% to 200% at the same compression ratio, outperforming comparable techniques.LogQuant integrates effortlessly with popular inference frameworks like Python's transformers library. Implementation can be available in https://github.com/Concyclics/LogQuantKV.
With high-stakes machine learning applications increasingly moving to untrusted end-user or cloud environments, safeguarding pre-trained model parameters becomes essential for protecting intellectual property and user privacy. Recent advancements in hardware-isolated enclaves, notably Intel SGX, hold the promise to secure the internal state of machine learning applications even against compromised operating systems. However, we show that privileged software adversaries can exploit input-dependent memory access patterns in common neural network activation functions to extract secret weights and biases from an SGX enclave. Our attack leverages the SGX-Step framework to obtain a noise-free, instruction-granular page-access trace. In a case study of an 11-input regression network using the Tensorflow Microlite library, we demonstrate complete recovery of all first-layer weights and biases, as well as partial recovery of parameters from deeper layers under specific conditions. Our novel attack technique requires only 20 queries per input per weight to obtain all first-layer weights and biases with an average absolute error of less than 1%, improving over prior model stealing attacks. Additionally, a broader ecosystem analysis reveals the widespread use of activation functions with input-dependent memory access patterns in popular machine learning frameworks (either directly or via underlying math libraries). Our findings highlight the limitations of deploying confidential models in SGX enclaves and emphasise the need for stricter side-channel validation of machine learning implementations, akin to the vetting efforts applied to secure cryptographic libraries.
DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.