Mathematical Reasoning With Mixture Of Experts

via “multi-step mathematical reasoning benchmark evaluation”

8.5K grade school math problems — multi-step reasoning, verifiable solutions, reasoning benchmark.

Unique: Uses linguistically diverse, human-authored grade school problems (not synthetic) that require genuine multi-step reasoning with basic arithmetic, combined with a standardized answer extraction format (#### delimiter) that enables reproducible evaluation across heterogeneous model outputs

vs others: More challenging than simple arithmetic benchmarks (requires 2-8 reasoning steps) yet more accessible than advanced math benchmarks, making it ideal for measuring practical reasoning improvements in production models

via “mathematical-reasoning-with-instruction-tuning”

Mistral's mixture-of-experts model with 176B total parameters.

Unique: Achieves 90.8% on GSM8K through instruction-tuning that teaches explicit step-by-step mathematical reasoning, with majority voting over 8 samples. This approach trades inference cost (8x sampling) for accuracy, making it suitable for applications where reasoning transparency is valued over single-sample speed.

vs others: Strong grade-school math performance (90.8% GSM8K) comparable to GPT-3.5-turbo; weaker on competition-level math (44.6% MATH) than GPT-4 or specialized math models; open-source licensing enables fine-tuning for domain-specific math tasks.

via “mathematical reasoning with math benchmark 80+ and structured problem-solving”

Alibaba's 72B open model trained on 18T tokens.

Unique: Integrates three distinct reasoning paradigms (CoT for symbolic reasoning, PoT for code-based computation, TIR for external tool orchestration) within single 72B dense model, enabling flexible problem-solving strategies without model switching. 128K context window allows full problem histories and solution verification within single inference call.

vs others: Outperforms Llama 2 70B (significantly lower math performance) and matches Llama 3 70B on general benchmarks while offering specialized math reasoning patterns; Qwen2.5-Math 72B variant provides deeper specialization but general-purpose 72B enables seamless math-to-code-to-text transitions without model switching.

via “mathematical reasoning and problem-solving”

671B MoE model matching GPT-4o at fraction of training cost.

Unique: Achieves 90.2% on MATH benchmark through MoE architecture that routes mathematical reasoning tokens through specialized expert parameters, enabling efficient scaling of reasoning capability without proportional increase in active parameters per token

vs others: Matches GPT-4o mathematical reasoning performance (90.2% MATH) while using 37B active parameters vs GPT-4o's undisclosed parameter count, reducing inference latency and cost for math-heavy workloads

via “mathematical problem solving with symbolic reasoning”

Cost-efficient reasoning model with configurable effort levels.

Unique: Implements specialized mathematical reasoning patterns with step-by-step derivation generation, achieving competition-level math performance through domain-specific training rather than general reasoning

vs others: Matches o3 on mathematical benchmarks at lower cost; outperforms standard LLMs (GPT-4, Claude) on competition-level problems due to reasoning-grade capabilities

via “mathematical reasoning and logic problem evaluation with specialized scoring”

ReLE评测：中文AI大模型能力评测（持续更新）：目前已囊括374个大模型，覆盖chatgpt、gpt-5.4、谷歌gemini-3.1-pro、Claude-4.6、文心ERNIE-X1.1、ERNIE-5.0、qwen3.6-max、qwen3.6-plus、百川、讯飞星火、商汤senseChat等商用模型， 以及step3.5-flash、kimi-k2.6、ernie4.5、MiniMax-M2.7、deepseek-v4、Qwen3.6、llama4、智谱GLM-5.1、MiMo-V2、LongCat、gemma4、mistral等开源大模型。不仅提供排行榜，也提供规模超200万的大

Unique: Evaluates mathematical reasoning with 1-5 quality scale for reasoning steps rather than binary correctness, enabling partial credit for correct methodology with computational errors. Combines final answer accuracy with reasoning quality assessment to capture mathematical thinking capability. Includes multi-step reasoning problems and logical inference tasks beyond simple arithmetic.

vs others: More nuanced mathematical assessment than MMLU (binary correctness) and captures reasoning quality vs answer-only evaluation

via “mathematical-problem-solving-with-symbolic-reasoning”

Gemini 2.5 Pro is Google’s state-of-the-art AI model designed for advanced reasoning, coding, mathematics, and scientific tasks. It employs “thinking” capabilities, enabling it to reason through responses with enhanced accuracy...

Unique: Leverages extended internal reasoning to explore multiple mathematical approaches and verify symbolic manipulations before responding, providing higher confidence in mathematical correctness than models without reasoning capabilities.

vs others: Exceeds GPT-4 and Claude on complex mathematics by using internal reasoning to validate symbolic steps, reducing hallucinated solutions and improving explanation quality for educational use cases.

via “mathematical-reasoning-with-mixture-of-experts”

INTELLECT-3 is a 106B-parameter Mixture-of-Experts model (12B active) post-trained from GLM-4.5-Air-Base using supervised fine-tuning (SFT) followed by large-scale reinforcement learning (RL). It offers state-of-the-art performance for its size across math,...

Unique: Uses Mixture-of-Experts routing with only 12B active parameters from a 106B total model, enabling efficient mathematical reasoning without full model activation; post-trained with RL specifically optimized for mathematical correctness rather than general-purpose chat

vs others: Outperforms similarly-sized dense models (e.g., Llama 2 70B) on mathematical benchmarks while using 40% fewer active parameters, making it cost-effective for math-heavy workloads

via “mathematical reasoning evaluation”

UGI-Leaderboard — AI demo on HuggingFace

Unique: Isolates mathematical reasoning as a distinct evaluation dimension on the leaderboard, enabling models to be ranked separately on math vs general generation, revealing capability specialization.

vs others: Simpler than running MATH or GSM8K locally with custom evaluation scripts, but less transparent than open-source math benchmarks regarding problem selection and difficulty.

via “mathematical-reasoning-and-problem-solving”

Hermes 4 70B is a hybrid reasoning model from Nous Research, built on Meta-Llama-3.1-70B. It introduces the same hybrid mode as the larger 405B release, allowing the model to either...

Unique: Trained on mathematical problem datasets with explicit step-by-step annotations, enabling the model to generate intermediate steps that match human problem-solving patterns rather than jumping directly to answers

vs others: More transparent than Wolfram Alpha for showing reasoning steps, though less reliable for advanced mathematics; stronger than GPT-3.5 on symbolic manipulation due to larger parameter count

via “mathematical reasoning and symbolic computation”

This is Mistral AI's flagship model, Mistral Large 2 (version mistral-large-2407). It's a proprietary weights-available model and excels at reasoning, code, JSON, chat, and more. Read the launch announcement [here](https://mistral.ai/news/mistral-large-2407/)....

Unique: Trained on mathematical datasets with chain-of-thought reasoning to prioritize step-by-step problem solving, using attention mechanisms that track variable relationships and equation transformations

vs others: Comparable to GPT-4 on mathematical reasoning, while maintaining lower cost; outperforms Llama 2 on complex multi-step problems due to larger parameter count and specialized training

via “mathematical reasoning and symbolic computation”

GLM 4 32B is a cost-effective foundation language model. It can efficiently perform complex tasks and has significantly enhanced capabilities in tool use, online search, and code-related intelligent tasks. It...

Unique: GLM 4 32B includes specialized training on mathematical reasoning datasets, enabling it to show work and explain reasoning — not just generate answers — which is critical for educational and verification use cases

vs others: More cost-effective than Wolfram Alpha for symbolic reasoning while providing better explanations than calculators, though less precise than dedicated symbolic engines for complex expressions

via “mixture-of-experts conditional computation for specialized task routing”

Qwen3, the latest generation in the Qwen large language model series, features both dense and mixture-of-experts (MoE) architectures to excel in reasoning, multilingual support, and advanced agent tasks. Its unique...

Unique: Qwen3's MoE implementation combines top-k gating with auxiliary load-balancing losses and implicit task specialization, enabling efficient multi-task handling without explicit task routing logic — the model learns which experts to activate for different input patterns

vs others: More efficient than dense 70B models for diverse workloads while maintaining better task specialization than simple mixture-of-experts alternatives through learned routing patterns

via “mathematical reasoning and symbolic computation”

Mistral's official instruct fine-tuned version of [Mixtral 8x22B](/models/mistralai/mixtral-8x22b). It uses 39B active parameters out of 141B, offering unparalleled cost efficiency for its size. Its strengths include: - strong math, coding,...

Unique: Combines sparse MoE routing with instruction fine-tuning specifically optimized for mathematical reasoning, allowing different experts to specialize in algebra, calculus, statistics, and logic domains while maintaining unified instruction-following interface.

vs others: Outperforms GPT-3.5 on mathematical reasoning benchmarks while being significantly cheaper, though slightly behind GPT-4 on advanced symbolic manipulation tasks.

via “mathematical problem solving with step-by-step verification”

The o-series of models are trained with reinforcement learning to think before they answer and perform complex reasoning. The o3-pro model uses more compute to think harder and provide consistently...

Unique: Applies extended reasoning to mathematical problem-solving, enabling explicit step-by-step verification and error-checking within the reasoning phase. Unlike standard LLMs that may skip steps or make calculation errors, o3-pro's reasoning allows it to catch and correct mistakes before output.

vs others: Achieves 90%+ accuracy on AIME and MATH benchmarks compared to 50-70% for GPT-4, due to reasoning-enabled verification and multi-path exploration.

via “mathematical reasoning and symbolic problem-solving”

Qwen2.5 72B is the latest series of Qwen large language models. Qwen2.5 brings the following improvements upon Qwen2: - Significantly more knowledge and has greatly improved capabilities in coding and...

Unique: Qwen2.5 series explicitly improves mathematical reasoning capabilities over Qwen2 through enhanced training on mathematical datasets and reasoning patterns; achieves improved performance on MATH and similar benchmarks while maintaining general conversational ability

vs others: More reliable mathematical reasoning than Llama 2 70B; comparable to GPT-3.5 for standard problems but at lower cost; weaker than specialized math models like Minerva but more general-purpose

via “sparse-mixture-of-experts reasoning with selective parameter activation”

Qwen3-235B-A22B-Thinking-2507 is a high-performance, open-weight Mixture-of-Experts (MoE) language model optimized for complex reasoning tasks. It activates 22B of its 235B parameters per forward pass and natively supports up to 262,144...

Unique: Uses learned gating mechanisms to route tokens to 22B active experts from a 235B total pool, implementing true sparse MoE rather than dense-with-pruning approaches. The A22B designation indicates Alibaba's specific expert configuration and routing strategy, which differs from standard MoE implementations in how experts are specialized and load-balanced.

vs others: Achieves 235B-parameter reasoning quality at ~10% of dense inference cost compared to Llama 405B or GPT-4, while maintaining faster latency than dense models through selective expert activation

via “mathematical reasoning and problem solving”

Qwen2.5 7B is the latest series of Qwen large language models. Qwen2.5 brings the following improvements upon Qwen2: - Significantly more knowledge and has greatly improved capabilities in coding and...

Unique: Qwen2.5 7B incorporates enhanced mathematical reasoning capabilities over Qwen2 through specialized training on mathematical problem datasets and improved chain-of-thought patterns for multi-step calculations

vs others: Provides reasonable mathematical problem-solving at 7B scale where most competitors require 13B+ parameters, enabling cost-effective deployment for math-focused applications

via “mathematical-reasoning-and-problem-solving”

Trinity Large Thinking is a powerful open source reasoning model from the team at Arcee AI. It shows strong performance in PinchBench, agentic workloads, and reasoning tasks. Launch video: https://youtu.be/Gc82AXLa0Rg?si=4RLn6WBz33qT--B7

Unique: Applies extended reasoning specifically to mathematical problem-solving, allowing the model to explore multiple solution paths, validate intermediate steps, and provide confidence assessments. Unlike standard LLMs that may hallucinate mathematical steps, Trinity's reasoning budget enables verification and backtracking.

vs others: Provides more detailed reasoning than standard LLMs while remaining more accessible than specialized math engines; ideal for educational contexts where understanding the process matters as much as the answer.

via “mathematical problem solving with step-by-step proof generation”

Qwen3-30B-A3B-Thinking-2507 is a 30B parameter Mixture-of-Experts reasoning model optimized for complex tasks requiring extended multi-step thinking. The model is designed specifically for “thinking mode,” where internal reasoning traces are separated...

Unique: Allocates specialized mathematical reasoning experts through MoE routing, enabling step-by-step proof generation with explicit symbolic and logical reasoning rather than pattern-matching mathematical solutions

vs others: Provides verifiable step-by-step mathematical reasoning unlike standard LLMs, though with higher latency and no formal correctness guarantees