Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Math
On the map: LLM reasoning → Mathematical reasoning
Abstract (arXiv)
Chain-of-Thought (CoT) significantly enhances formal reasoning capabilities in Large Language Models (LLMs) by training them to explicitly generate intermediate reasoning steps. While LLMs readily benefit from such techniques, improving reasoning in Small Language Models (SLMs) remains challenging due to their limited model capacity. Recent work by Deepseek-R1 demonstrates that distillation from LLM-generated synthetic data can substantially improve the reasoning ability of SLM. However, the detailed modeling recipe is not disclosed. In this work, we present a systematic training recipe for SLMs that consists of four steps: (1) large-scale mid-training on diverse distilled long-CoT data, (2) supervised fine-tuning on high-quality long-CoT data, (3) Rollout DPO leveraging a carefully curated preference dataset, and (4) Reinforcement Learning (RL) with Verifiable Reward. We apply our method on Phi-4-Mini, a compact 3.8B-parameter model. The resulting Phi-4-Mini-Reasoning model exceeds, on math reasoning tasks, much larger reasoning models, e.g., outperforming DeepSeek-R1-Distill-Qwen-7B by 3.2 points and DeepSeek-R1-Distill-Llama-8B by 7.7 points on Math-500. Our results validate that a carefully designed training recipe, with large-scale high-quality CoT data, is effective to unlock strong reasoning capabilities even in resource-constrained small models.
Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 17 of its 33 references that are in the map. First posted on arXiv 30 Apr 2025.
Builds on
17 of 33 references.
Closest ancestors · 2
Same direction, newest first
- 2025LIMO: Less is More for Reasoning5 Feb
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models5 Feb
Other references · 15
- 2023GPT-4 Technical Reportcited by 18,396
- 2017Proximal Policy Optimization Algorithmscited by 15,215
- 2024The Llama 3 Herd of Modelscited by 14,715
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
- 2023Let's Verify Step by Stepcited by 3,789
- 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,986
- 2025s1: Simple test-time scalingcited by 1,341
- 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 735
- 2025Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAscited by 521
- 2023MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuningcited by 487
- 2024From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Modelscited by 137
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Citing papers per year: 2025: 27; 2026: 17.
44 papers.
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- 2025Leaky Thoughts: Large Reasoning Models Are Not Private Thinkerscited by 28
- 2025VeriThinker: Learning to Verify Makes Reasoning Model Efficientcited by 24
- 2025BLEUBERI: BLEU is a surprisingly effective reward for instruction followingcited by 17
- 2025Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoningcited by 17
- 2025Reinforcement Learning vs. Distillation: Understanding Accuracy and Capability in LLM Reasoningcited by 14
- 2025Energy Use of AI Inference, Efficiency Pathways, and Test-Time Scalingcited by 13
- 2025Self-Jailbreaking: Language Models Can Reason Themselves Out of Safety Alignment After Benign Reasoning Trainingcited by 12
- 2025Decoder-Hybrid-Decoder Architecture for Efficient Reasoning with Long Generationcited by 11
- 2026OPRD: On-Policy Representation Distillationcited by 11
- 2025G2RPO-A: Guided Group Relative Policy Optimization with Adaptive Guidancecited by 10
- 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibilitycited by 6
- 2025SHARP: Synthesizing High-quality Aligned Reasoning Problems for Large Reasoning Models Reinforcement Learningcited by 5
32 more
- 2025Path Drift in Large Reasoning Models:How First-Person Commitments Override Safetycited by 5
- 2025One Token Embedding Is Enough to Deadlock Your Large Reasoning Modelcited by 5
- 2025Reasoning Up the Instruction Ladder for Controllable Language Modelscited by 5
- 2025Warm Up Before You Train: Unlocking General Reasoning in Resource-Constrained Settingscited by 4
- 2025Recall-Extend Dynamics: Enhancing Small Language Models through Controlled Exploration and Refined Offline Integrationcited by 3
- 2025Poivre: Self-Refining Visual Pointing with Reinforcement Learningcited by 3
- 2025Learning to Reason as Action Abstractions with Scalable Mid-Training RLcited by 3
- 2025Concise Reasoning in the Lens of Lagrangian Optimizationcited by 3
- 2025When Reasoning Meets Its Lawscited by 3
- 2026DICE: Diffusion Large Language Models Excel at Generating CUDA Kernelscited by 3
- 2026Learning from Partial Chain-of-Thought via Truncated-Reasoning Self-Distillationcited by 3
- 2025In Their Own Words: Reasoning Traces Tailored for Small Models Make Them Better Reasonerscited by 2
- 2025LogiNumSynth: Synthesizing Joint Logical-Numerical Reasoning Problems for Language Modelscited by 2
- 2025Distractor Injection Attacks on Large Reasoning Models: Characterization and Defensecited by 2
- 2026UrduBench: An Urdu Reasoning Benchmark using Contextually Ensembled Translations with Human-in-the-Loopcited by 2
- 2026HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Modelscited by 2
- 2026Think Multilingual, Not Harder: A Data-Efficient Framework for Teaching Reasoning Models to Code-Switchcited by 2
- 2026Sliding-window beats linear attentioncited by 2
- 2025RAISE: Enhancing Scientific Reasoning in LLMs via Step-by-Step Retrievalcited by 1
- 2025CAC-CoT: Connector-Aware Compact Chain-of-Thought for Efficient Reasoning Data Synthesis Across Dual-System Cognitive Taskscited by 1
- 2026Benchmarking Small Language Models and Small Reasoning Language Models on System Log Severity Classificationcited by 1
- 2026CORE: Collaborative Reasoning via Cross Teachingcited by 1
- 2026Directional Reasoning Trajectory Change (DRTC): Identifying Critical Trace Segments in Reasoning Modelscited by 1
- 2026LexChronos: An Agentic Framework for Structured Event Timeline Extraction in Indian Jurisprudencecited by 1
- 2026DenseSteer: Steering Small Language Models towards Dense Math Reasoningcited by 1
- 2025Dissecting Clinical Reasoning in Language Models: A Comparative Study of Prompts and Model Adaptation Strategiescited by 0
- 2025Schema Lineage Extraction at Scale: Multilingual Pipelines, Composite Evaluation, and Language-Model Benchmarkscited by 0
- 2025WRAVAL -- WRiting Assist eVALuationcited by 0
- 2026Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answeringcited by 0
- 2026Efficient Reasoning on the Edgecited by 0
- 2026ExpRL: Exploratory RL for LLM Mid-Trainingcited by 0
- 2026RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfercited by 0
- 2026Sliding-window beats linear attention28 Aug 2026
- 2026RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer6 Aug 2026
- 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility4 Aug 2026
- 2026ExpRL: Exploratory RL for LLM Mid-Training15 Jun 2026
- 2026OPRD: On-Policy Representation Distillation4 Jun 2026
- 2026DenseSteer: Steering Small Language Models towards Dense Math Reasoning28 May 2026
- 2026Think Multilingual, Not Harder: A Data-Efficient Framework for Teaching Reasoning Models to Code-Switch16 Apr 2026
- 2026HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models14 Apr 2026
- 2026Efficient Reasoning on the Edge17 Mar 2026
- 2026LexChronos: An Agentic Framework for Structured Event Timeline Extraction in Indian Jurisprudence2 Mar 2026
- 2026Learning from Partial Chain-of-Thought via Truncated-Reasoning Self-Distillation27 Feb 2026
- 2026Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering26 Feb 2026
32 more
- 2026Directional Reasoning Trajectory Change (DRTC): Identifying Critical Trace Segments in Reasoning Models17 Feb 2026
- 2026DICE: Diffusion Large Language Models Excel at Generating CUDA Kernels12 Feb 2026
- 2026CORE: Collaborative Reasoning via Cross Teaching29 Jan 2026
- 2026UrduBench: An Urdu Reasoning Benchmark using Contextually Ensembled Translations with Human-in-the-Loop28 Jan 2026
- 2026Benchmarking Small Language Models and Small Reasoning Language Models on System Log Severity Classification12 Jan 2026
- 2025WRAVAL -- WRiting Assist eVALuation19 Dec 2025
- 2025When Reasoning Meets Its Laws19 Dec 2025
- 2025Reasoning Up the Instruction Ladder for Controllable Language Models30 Oct 2025
- 2025Self-Jailbreaking: Language Models Can Reason Themselves Out of Safety Alignment After Benign Reasoning Training23 Oct 2025
- 2025Distractor Injection Attacks on Large Reasoning Models: Characterization and Defense17 Oct 2025
- 2025LogiNumSynth: Synthesizing Joint Logical-Numerical Reasoning Problems for Language Models13 Oct 2025
- 2025One Token Embedding Is Enough to Deadlock Your Large Reasoning Model12 Oct 2025
- 2025Concise Reasoning in the Lens of Lagrangian Optimization11 Oct 2025
- 2025Path Drift in Large Reasoning Models:How First-Person Commitments Override Safety11 Oct 2025
- 2025Learning to Reason as Action Abstractions with Scalable Mid-Training RL30 Sep 2025
- 2025Poivre: Self-Refining Visual Pointing with Reinforcement Learning28 Sep 2025
- 2025In Their Own Words: Reasoning Traces Tailored for Small Models Make Them Better Reasoners26 Sep 2025
- 2025Energy Use of AI Inference, Efficiency Pathways, and Test-Time Scaling24 Sep 2025
- 2025CAC-CoT: Connector-Aware Compact Chain-of-Thought for Efficient Reasoning Data Synthesis Across Dual-System Cognitive Tasks26 Aug 2025
- 2025Recall-Extend Dynamics: Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration21 Aug 2025
- 2025G2RPO-A: Guided Group Relative Policy Optimization with Adaptive Guidance18 Aug 2025
- 2025Schema Lineage Extraction at Scale: Multilingual Pipelines, Composite Evaluation, and Language-Model Benchmarks10 Aug 2025
- 2025Decoder-Hybrid-Decoder Architecture for Efficient Reasoning with Long Generation9 Jul 2025
- 2025Dissecting Clinical Reasoning in Language Models: A Comparative Study of Prompts and Model Adaptation Strategies5 Jul 2025
- 2025Leaky Thoughts: Large Reasoning Models Are Not Private Thinkers18 Jun 2025
- 2025Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoning11 Jun 2025
- 2025RAISE: Enhancing Scientific Reasoning in LLMs via Step-by-Step Retrieval10 Jun 2025
- 2025VeriThinker: Learning to Verify Makes Reasoning Model Efficient23 May 2025
- 2025Reinforcement Learning vs. Distillation: Understanding Accuracy and Capability in LLM Reasoning20 May 2025
- 2025SHARP: Synthesizing High-quality Aligned Reasoning Problems for Large Reasoning Models Reinforcement Learning20 May 2025
- 2025Warm Up Before You Train: Unlocking General Reasoning in Resource-Constrained Settings19 May 2025
- 2025BLEUBERI: BLEU is a surprisingly effective reward for instruction following16 May 2025
- 2025Leaky Thoughts: Large Reasoning Models Are Not Private Thinkerscited by 28
- 2025VeriThinker: Learning to Verify Makes Reasoning Model Efficientcited by 24
- 2025Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoningcited by 17
- 2025Reinforcement Learning vs. Distillation: Understanding Accuracy and Capability in LLM Reasoningcited by 14
- 2025Self-Jailbreaking: Language Models Can Reason Themselves Out of Safety Alignment After Benign Reasoning Trainingcited by 12
- 2025Decoder-Hybrid-Decoder Architecture for Efficient Reasoning with Long Generationcited by 11
- 2025G2RPO-A: Guided Group Relative Policy Optimization with Adaptive Guidancecited by 10
- 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibilitycited by 6
- 2025SHARP: Synthesizing High-quality Aligned Reasoning Problems for Large Reasoning Models Reinforcement Learningcited by 5
- 2025Path Drift in Large Reasoning Models:How First-Person Commitments Override Safetycited by 5
- 2025One Token Embedding Is Enough to Deadlock Your Large Reasoning Modelcited by 5
- 2025Reasoning Up the Instruction Ladder for Controllable Language Modelscited by 5
12 most cited of 36 All 36 (JSON)
- 2026RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer6 Aug 2026
- 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility4 Aug 2026
- 2026ExpRL: Exploratory RL for LLM Mid-Training15 Jun 2026
- 2026DenseSteer: Steering Small Language Models towards Dense Math Reasoning28 May 2026
- 2026Think Multilingual, Not Harder: A Data-Efficient Framework for Teaching Reasoning Models to Code-Switch16 Apr 2026
- 2026HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models14 Apr 2026
- 2026Efficient Reasoning on the Edge17 Mar 2026
- 2026Learning from Partial Chain-of-Thought via Truncated-Reasoning Self-Distillation27 Feb 2026
- 2026Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering26 Feb 2026
- 2026Directional Reasoning Trajectory Change (DRTC): Identifying Critical Trace Segments in Reasoning Models17 Feb 2026
- 2026CORE: Collaborative Reasoning via Cross Teaching29 Jan 2026
- 2026UrduBench: An Urdu Reasoning Benchmark using Contextually Ensembled Translations with Human-in-the-Loop28 Jan 2026
12 newest of 36 All 36 (JSON)
- 2026OPRD: On-Policy Representation Distillationcited by 11
- 2026OPRD: On-Policy Representation Distillation4 Jun 2026
- 2026Sliding-window beats linear attentioncited by 2
- 2026Sliding-window beats linear attention28 Aug 2026
Similar, not cited
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- 2024Small Language Models are Equation Reasoners
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