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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MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning
35 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 16% and 32%. Remarkably, our MAmmoTH-7B model reaches 33% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 23%, and the MAmmoTH-34B model achieves 44% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.
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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.
An interactive AI workbench for mathematicians achieves 48% on FrontierMath Tier 4 and helped solve open problems in early tests.
Supervised fine-tuning of LLMs often fails to fully internalize all training instances due to five recurring causes including missing prerequisites and data conflicts, as diagnosed via a new framework across multiple models.
EDUMATH introduces the first teacher-annotated dataset for standards-aligned math word problem generation and demonstrates that it enables smaller open LLMs to match larger models while producing problems students prefer over human-written ones.
Magpie synthesizes 300K high-quality alignment instructions from Llama-3-Instruct via auto-regressive prompting on partial templates, enabling fine-tuned models to match official instruct performance on AlpacaEval, ArenaHard, and WildBench.
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.
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.
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.
GLR formulates latent reasoning as geometric path approximation in pretrained embedding space and reports shorter LLM generations on math tasks without an explicit length penalty.
MAGS learns low-dimensional subspaces from correct versus incorrect reasoning traces and applies targeted projection corrections to attention heads when they deviate from the correctness manifold during inference.
VaLR generates vision-aligned latent tokens before each reasoning step to preserve perceptual cues, improving VSI-Bench accuracy from 33.0% to 52.9%.
SmolVLM-256M outperforms a 300-times larger model using under 1 GB GPU memory, while the 2.2B version matches state-of-the-art VLMs at half the memory cost.
MathFlow decouples perception and inference stages in MLLMs for visual math, with a dedicated perception model delivering gains on the FlowVerse benchmark when paired with existing reasoners.
Muon optimizer with weight decay and update scaling achieves ~2x efficiency over AdamW for large LLMs, shown via the Moonlight 3B/16B MoE model trained on 5.7T tokens.
PRIME enables online process reward model updates in LLM RL using implicit rewards from rollouts and outcome labels, yielding 15.1% average gains on reasoning benchmarks and surpassing a stronger instruct model with 10% of the data.
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.
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.
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.
ToRA trains language models on interactive tool-use trajectories with imitation learning and output shaping to integrate reasoning and external tools, yielding 13-19% gains on math datasets and new highs like 44.6% on MATH for a 7B model.
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.
Cosine similarity poorly predicts performance degradation from layer removal in LLMs, making direct accuracy-drop ablation a more reliable relevance metric.
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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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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