L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
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MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models
Baseline reference. 62% of citing Pith papers use this work as a benchmark or comparison.
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external citations · Pith
Baseline
62% of classified citations
abstract
Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.
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representative citing papers
HARP is a train-based data selector for LLM finetuning that uses hierarchical active region pruning and empirical Bayes posteriors to achieve up to 8.9 point gains with roughly 7 times fewer training examples.
DART adapts a scoring matrix at inference time via gradient updates on pseudo-labels from top/bottom documents to gain +2.1% mean NDCG@10 on six BEIR benchmarks with under 10ms added latency.
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.
An RL agent learns domain re-weighting policies from evaluation feedback to improve balanced performance in continual pre-training of LLMs across source and target domains.
DeepSeek-V2 delivers top-tier open-source LLM performance using only 21B active parameters by compressing the KV cache 93.3% and cutting training costs 42.5% via MLA and DeepSeekMoE.
EPnG reallocates LoRA capacity in MoE models by pruning experts with low router gate probabilities and expanding high-importance ones via rank growth, outperforming standard LoRA and nearing full fine-tuning performance with 0.55-0.72% parameters updated.
Active-GRPO reaches 0.1773 average SRxSim on TOMG-Bench MOLOPT by adaptively switching between imitation and self-reinforcement while upgrading references, outperforming GRPO and RePO.
CLExEval introduces a human-annotated evaluation framework on 40 rare cases that identifies verbosity bias, hidden knowledge paradox, and 68.6% reasoning-to-output mismatch in LLMs while showing LLM-as-a-Judge overestimates reliability.
RASFT is an adaptive SFT method that strengthens or relaxes expert imitation per problem based on on-policy rollout solvability and adds clipped reference-policy ratio to limit drift, reporting better results than standard SFT and RL on math and code benchmarks.
SafeSteer restricts reverse KL penalty to safety tokens selected via activation steering, achieving strong safety on seven benchmarks with minimal degradation on five capability benchmarks using only 100 harmful samples and no general data.
FedSmoothLoRA improves federated LoRA fine-tuning by constructing local initializations from a round-matching matrix for cross-round continuity and a gradient-aligned matrix for client-specific guidance, yielding faster convergence than prior methods in image and text tasks.
FuRA uses block tensor-train factorization with fixed pretrained SVD basis to achieve full-rank spectral preconditioning, outperforming Full FT by +1.37 on LLaMA-3-8B commonsense reasoning and surpassing QLoRA in quantized settings.
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
SeedRG generates novel, leakage-free RAG benchmark examples from seed data by mapping reasoning structures and swapping entities while applying consistency and leakage checks.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
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.
NeWTral is a non-linear weight translation framework using MoE routing that reduces average attack success rate from 70% to 13% on unsafe domain adapters across Llama, Mistral, Qwen, and Gemma models up to 72B while retaining 90% knowledge fidelity.
JACTUS unifies low-rank compression and task adaptation via a task-aware union of subspaces and global rank allocation by marginal gain, outperforming 100% PEFT methods like DoRA on ViT-Base (89.2% avg) and Llama2-7B (80.9% avg) at 80% retained parameters.
Sharpness-aware pretraining and related flat-minima interventions reduce catastrophic forgetting by up to 80% after post-training across 20M-150M models and by 31-40% at 1B scale.
TLoRA jointly optimizes LoRA initialization via task-data SVD and sensitivity-driven rank allocation, delivering stronger results than standard LoRA across NLU, reasoning, math, code, and chat tasks while using fewer trainable parameters.
A cooperative system with one SLM distilling stepwise hints from a large model to guide another SLM's math reasoning yields consistent accuracy gains on benchmarks.
In Llama 3.1 8B, task-sensitive layers cluster late while RoPE adaptation is strongest early, yet applying both adaptations only to sensitivity-identified layers outperforms other layer choices by 4-16 points on MMLU, GPQA, HumanEval+, MATH, MGSM and ARC.
A modified divergence decouples top-K teacher probabilities from the distribution tail during distillation, yielding competitive performance on decoder models with standard compute.
citing papers explorer
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Transformers Provably Learn to Internalize Chain-of-Thought
L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
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HARP: Efficient Data Selection for Finetuning Large Language Models
HARP is a train-based data selector for LLM finetuning that uses hierarchical active region pruning and empirical Bayes posteriors to achieve up to 8.9 point gains with roughly 7 times fewer training examples.
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Test-Time Training for Zero-Resource Dense Retrieval Reranking
DART adapts a scoring matrix at inference time via gradient updates on pseudo-labels from top/bottom documents to gain +2.1% mean NDCG@10 on six BEIR benchmarks with under 10ms added latency.
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Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning
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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Data Mixing Agent: Learning to Re-weight Domains for Continual Pre-training
An RL agent learns domain re-weighting policies from evaluation feedback to improve balanced performance in continual pre-training of LLMs across source and target domains.
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DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model
DeepSeek-V2 delivers top-tier open-source LLM performance using only 21B active parameters by compressing the KV cache 93.3% and cutting training costs 42.5% via MLA and DeepSeekMoE.
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EPnG: Adaptive Expert Prune-and-Grow for Parameter-Efficient MoE Fine-tuning
EPnG reallocates LoRA capacity in MoE models by pruning experts with low router gate probabilities and expanding high-importance ones via rank growth, outperforming standard LoRA and nearing full fine-tuning performance with 0.55-0.72% parameters updated.
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Active-GRPO: Adaptive Imitation and Self-Improving Reasoning for Molecular Optimization
Active-GRPO reaches 0.1773 average SRxSim on TOMG-Bench MOLOPT by adaptively switching between imitation and self-reinforcement while upgrading references, outperforming GRPO and RePO.
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CLExEval: A Human-in-the-Loop Framework for Qualitative Evaluation of LLM Clinical Reasoning
CLExEval introduces a human-annotated evaluation framework on 40 rare cases that identifies verbosity bias, hidden knowledge paradox, and 68.6% reasoning-to-output mismatch in LLMs while showing LLM-as-a-Judge overestimates reliability.
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RASFT: Rollout-Adaptive Supervised Fine-Tuning for Reasoning
RASFT is an adaptive SFT method that strengthens or relaxes expert imitation per problem based on on-policy rollout solvability and adds clipped reference-policy ratio to limit drift, reporting better results than standard SFT and RL on math and code benchmarks.
-
SafeSteer: Localized On-Policy Distillation for Efficient Safety Alignment
SafeSteer restricts reverse KL penalty to safety tokens selected via activation steering, achieving strong safety on seven benchmarks with minimal degradation on five capability benchmarks using only 100 harmful samples and no general data.
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FedSmoothLoRA: Toward Smoother and Faster Convergence in Federated Low-Rank Adaptation
FedSmoothLoRA improves federated LoRA fine-tuning by constructing local initializations from a round-matching matrix for cross-round continuity and a gradient-aligned matrix for client-specific guidance, yielding faster convergence than prior methods in image and text tasks.
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FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning
FuRA uses block tensor-train factorization with fixed pretrained SVD basis to achieve full-rank spectral preconditioning, outperforming Full FT by +1.37 on LLaMA-3-8B commonsense reasoning and surpassing QLoRA in quantized settings.
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Self-Supervised On-Policy Distillation for Reasoning Language Models
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
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Generating Leakage-Free Benchmarks for Robust RAG Evaluation
SeedRG generates novel, leakage-free RAG benchmark examples from seed data by mapping reasoning structures and swapping entities while applying consistency and leakage checks.
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Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
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Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key
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.
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You Snooze, You Lose: Automatic Safety Alignment Restoration through Neural Weight Translation
NeWTral is a non-linear weight translation framework using MoE routing that reduces average attack success rate from 70% to 13% on unsafe domain adapters across Llama, Mistral, Qwen, and Gemma models up to 72B while retaining 90% knowledge fidelity.
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Compress Then Adapt? No, Do It Together via Task-aware Union of Subspaces
JACTUS unifies low-rank compression and task adaptation via a task-aware union of subspaces and global rank allocation by marginal gain, outperforming 100% PEFT methods like DoRA on ViT-Base (89.2% avg) and Llama2-7B (80.9% avg) at 80% retained parameters.
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Sharpness-Aware Pretraining Mitigates Catastrophic Forgetting
Sharpness-aware pretraining and related flat-minima interventions reduce catastrophic forgetting by up to 80% after post-training across 20M-150M models and by 31-40% at 1B scale.
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TLoRA: Task-aware Low Rank Adaptation of Large Language Models
TLoRA jointly optimizes LoRA initialization via task-data SVD and sensitivity-driven rank allocation, delivering stronger results than standard LoRA across NLU, reasoning, math, code, and chat tasks while using fewer trainable parameters.
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HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models
A cooperative system with one SLM distilling stepwise hints from a large model to guide another SLM's math reasoning yields consistent accuracy gains on benchmarks.
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Sensitivity-Positional Co-Localization in GQA Transformers
In Llama 3.1 8B, task-sensitive layers cluster late while RoPE adaptation is strongest early, yet applying both adaptations only to sensitivity-identified layers outperforms other layer choices by 4-16 points on MMLU, GPQA, HumanEval+, MATH, MGSM and ARC.
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Don't Ignore the Tail: Decoupling top-K Probabilities for Efficient Language Model Distillation
A modified divergence decouples top-K teacher probabilities from the distribution tail during distillation, yielding competitive performance on decoder models with standard compute.
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Towards Efficient Large Language Reasoning Models via Extreme-Ratio Chain-of-Thought Compression
A pipeline combining a question-aware formula-preserving compressor, mixed-ratio SFT, and hierarchical RL compresses CoT on math benchmarks to ~27% of original tokens while preserving or slightly improving accuracy.
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Multi-Token Prediction via Self-Distillation
Self-distillation turns pretrained autoregressive LMs into multi-token predictors that decode over 3x faster with under 5% accuracy drop on GSM8K.
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Vision-aligned Latent Reasoning for Multi-modal Large Language Model
VaLR generates vision-aligned latent tokens before each reasoning step to preserve perceptual cues, improving VSI-Bench accuracy from 33.0% to 52.9%.
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Fin-PRM: A Domain-Specialized Process Reward Model for Financial Reasoning in Large Language Models
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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InternBootcamp Technical Report: Boosting LLM Reasoning with Verifiable Task Scaling
InternBootcamp supplies 1000+ verifiable, auto-generated task environments across domains that enable task scaling to improve LLM reasoning, producing a 32B model with state-of-the-art results on the new Bootcamp-EVAL benchmark.
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League of LLMs: A Benchmark-Free Paradigm for Mutual Evaluation of Large Language Models
League of LLMs organizes LLMs into a self-governed mutual evaluation league using dynamic, transparent, objective, and professional criteria to distinguish model capabilities with 70.7% top-k ranking stability.
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MLorc: Momentum Low-rank Compression for Memory Efficient Large Language Model Adaptation
MLorc compresses optimizer momentum with low-rank methods to enable memory-efficient full fine-tuning of LLMs, outperforming LoRA and GaLore while matching full-parameter performance at small ranks.
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FoNE: Precise Single-Token Number Embeddings via Fourier Features
FoNE encodes numbers as single tokens via Fourier features and outperforms subword and digit-wise embeddings on addition, subtraction, and multiplication with far less data.
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Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling
InternVL 2.5 is the first open-source MLLM to surpass 70% on the MMMU benchmark via model, data, and test-time scaling, with a 3.7-point gain from chain-of-thought reasoning.
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Scaling Synthetic Data Creation with 1,000,000,000 Personas
A curated set of one billion personas enables scalable, diverse synthetic data generation for LLM training across reasoning, instructions, knowledge, NPCs, and tools.
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Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs
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.
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Improve Mathematical Reasoning in Language Models by Automated Process Supervision
OmegaPRM automates collection of 1.5 million process supervision labels via binary-search MCTS, raising Gemini Pro math accuracy from 51% to 69.4% on MATH500 and Gemma2 27B from 42.3% to 58.2%.
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DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
DeepSeekMath 7B reaches 51.7% on MATH via continued pretraining on curated web math data and Group Relative Policy Optimization.
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Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Math-Shepherd is an automatically trained process reward model that scores solution steps to verify and reinforce LLMs, lifting Mistral-7B from 77.9% to 89.1% on GSM8K and 28.6% to 43.5% on MATH.
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Llemma: An Open Language Model For Mathematics
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.
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MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning
MAmmoTH models trained via hybrid CoT-PoT instruction tuning on MathInstruct outperform prior open-source LLMs by 16-32% average accuracy on nine math datasets, reaching 33% and 44% on MATH for 7B and 34B scales.
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DAG-MoE: From Simple Mixture to Structural Aggregation in Mixture-of-Experts
DAG-MoE uses a lightweight module to learn DAG-based structural aggregation of selected experts, expanding combination space and enabling intra-layer multi-step reasoning compared to standard weighted-sum MoE.
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Tailoring the Curriculum: Student-Centered Reasoning Distillation via Dynamic Data-Model Compatibility
The paper proposes the DMC metric for assessing dataset suitability in reasoning distillation and shows that DMC-guided and dynamic data selection improves performance across student models and tasks.
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LoCO: Low-rank Compositional Rotation Fine-tuning
LoCO is a PEFT technique that constructs orthogonal transformations via low-rank skew-symmetric matrices and compositional rotation chains with a parallelizable approximation, validated on transformer adaptations.
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Strategic Over-Parameterization for Generalizable Low-Rank Adaptation
LoRA-Over injects auxiliary parameters into low-rank adapters during training and decomposes them back into standard LoRA at inference, with static or dynamic scheduling to allocate extra capacity where needed, yielding better generalization than vanilla LoRA on GLUE, MT-Bench, GSM8K and HumanEval.
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Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
Pion is an optimizer that preserves the singular values of weight matrices in LLM training by applying orthogonal equivalence transformations.
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Near-Policy: Accelerating On-Policy Distillation via Asynchronous Generation and Selective Packing
NPD accelerates on-policy distillation 8.1 times faster than baselines by using asynchronous SFT with Δ-IFD filtering, outperforming standard SFT and enabling a 1B model to achieve 68.73% SOTA score.
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NoisyCoconut: Counterfactual Consensus via Latent Space Reasoning
Injecting noise into LLM latent trajectories creates diverse reasoning paths whose agreement acts as a confidence signal for selective abstention, cutting error rates from 40-70% to under 15% on math tasks.
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Rethinking Local Learning: A Cheaper and Faster Recipe for LLM Post-Training
LoPT splits LLM post-training at the midpoint with task loss on the second half and feature reconstruction on the first half to reduce cost and interference.
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Post-Optimization Adaptive Rank Allocation for LoRA
PARA uses post-optimization SVD with a global singular-value threshold to allocate non-uniform ranks to LoRA layers, cutting parameters 75-90% with no loss in benchmark performance.
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NVIDIA Nemotron 3: Efficient and Open Intelligence
NVIDIA releases the Nemotron 3 model family with hybrid Mamba-Transformer architecture, LatentMoE, NVFP4 training, MTP layers, and multi-environment RL post-training for reasoning and agentic tasks.