FISolver trains a compact LLM on backward-generated (differential equation, first integral) pairs and uses guided reinforcement learning to outperform larger models and Mathematica on first-integral benchmarks at lower cost.
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WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct
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abstract
Large language models (LLMs), such as GPT-4, have shown remarkable performance in natural language processing (NLP) tasks, including challenging mathematical reasoning. However, most existing open-source models are only pre-trained on large-scale internet data and without math-related optimization. In this paper, we present WizardMath, which enhances the mathematical CoT reasoning abilities of LLMs without using external python tools, by applying our proposed Reinforcement Learning from Evol-Instruct Feedback (RLEIF) method to the domain of math. Through extensive experiments on two mathematical reasoning benchmarks, namely GSM8k and MATH, we reveal the extraordinary capabilities of our model. Remarkably, WizardMath-Mistral 7B surpasses top-tier open-source LLMs by a substantial margin with higher data efficiency. Furthermore, WizardMath 70B even outperforms GPT-3.5-Turbo, Claude 2, Gemini Pro and GPT-4-early-version. Additionally, our preliminary exploration highlights the pivotal role of instruction evolution and process supervision in achieving exceptional math performance. For more details refer to https://github.com/nlpxucan/WizardLM
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representative citing papers
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MathVerse is a benchmark that tests multi-modal LLMs on visual math by providing each problem in six versions with progressively less diagram and text information to measure true visual understanding.
CodeMind evaluates ten LLMs on four benchmarks using three new code reasoning tasks, finding performance varies by model size and drops with complexity while showing no correlation with bug repair ability.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
DEL is a new loss for LLM numerical learning that applies supervised digit entropy optimization and extends to floating-point numbers, showing improved accuracy and distance metrics over prior methods on math benchmarks.
FireFly inverts task synthesis by exploring real MCP servers first via pairwise tool graphs and sub-DAG sampling, then generates 5,144 verified tasks backward from outcomes to train a 4B model that matches Claude Sonnet 4.6 on tool-calling benchmarks.
A distribution-correction framework for offline LLM reasoning distillation improves accuracy on math benchmarks by adaptively aligning teacher supervision with the student's inference-time distribution.
CROP uses compositional reasoning and expert preference alignment in VLMs to produce aesthetic crops that match human experts more closely than previous methods.
RL training compute for logical reasoning follows a power law with horizon depth whose exponent rises with logical expressiveness, yielding better downstream transfer when models train on richer logics.
SAPO introduces segment-level policy optimization using a step-wise MDP abstraction to better align RL updates with reasoning structure in multi-modal LLM tasks.
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Fin-PRM is a domain-specialized process reward model that supplies binary step-level and trajectory-level supervision signals for financial reasoning in LLMs and outperforms general PRMs on CFLUE and FinQA benchmarks.
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Step-DPO performs preference optimization on individual reasoning steps rather than complete answers, producing nearly 3% accuracy gains on MATH for 70B+ parameter models with 10K preference pairs.
DeepSeekMath 7B reaches 51.7% on MATH via continued pretraining on curated web math data and Group Relative Policy Optimization.
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Continued pretraining of Code Llama on Proof-Pile-2 yields Llemma, an open math-specialized LLM that beats known open base models on MATH and supports tool use plus formal proving out of the box.
citing papers explorer
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Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models
The paper surveys reinforced reasoning techniques for LLMs, covering automated data construction, learning-to-reason methods, and test-time scaling as steps toward Large Reasoning Models.