Fathom R1 14B

🚀 Fathom-R1-14B: $499 Training Recipe for Unlocking Math Reasoning at o4-mini level using R1-distilled-14B model under 16K context

This project presents Fathom-R1-14B, a 14-billion-parameter reasoning language model. It achieves SOTA mathematical reasoning performance within a 16K context window at a low cost of $499, outperforming many baseline models on challenging exams.

🚀 Quick Start

This README provides detailed information about the Fathom-R1-14B model, including its overview, motivation, training dataset, post-training strategies, evaluation, and results. You can directly refer to the corresponding sections according to your needs.

✨ Features

• Cost-Effective: Post-trained at an affordable cost of only $499, achieving SOTA mathematical reasoning performance within a 16K context window.
• High Performance: Surpasses many baseline models on challenging olympiad level exams like AIME-25 and HMMT-25.
• Optimized Strategies: Uses specific training approaches such as supervised fine-tuning (SFT) and model merging to achieve excellent performance.

📦 Installation

No installation steps are provided in the original README.

💻 Usage Examples

No code examples are provided in the original README.

📚 Documentation

Overview

Reasoning models often require high post-training budgets and extremely long reasoning chains(think 32k/64k) for maximising performance. Can we improve these models even if both these parameters are capped?

To this end, we first introduce: Fathom-R1-14B, a 14-billion-parameter reasoning language model derived from Deepseek-R1-Distilled-Qwen-14B, post-trained at an affordable cost of only $499, and achieving SOTA mathematical reasoning performance within a 16K context window. On the latest olympiad level exams: AIME-25 and HMMT-25, our model not only surpasses o3-mini-low, o1-mini and LightR1-14B(16k) at pass@1 scores (averaged over 64 runs) but also delivers performance rivaling closed-source o4-mini (low) w.r.t cons@64 — all while staying within a 16K context window. It achieves 52.71% Pass@1 accuracy on AIME2025 and 35.26% Pass@1 accuracy on HMMT25 (+7.2% and +5.2% improvement over the base model respectively). When provided with additional test-time compute in the form of cons@64, it achieves an impressive 76.7% accuracy on AIME2025 and 56.7% accuracy on HMMT25 (+13.4% and +6.7% improvement over the base model respectively). We perform supervised fine-tuning (SFT) on carefully curated datasets using a specific training approach, followed by model merging, achieving this performance at a total cost of just $499!

We also introduce Fathom-R1-14B-RS, another model achieving performance comparable to our first, at a total post-training cost of just $967. It leverages post-training techniques—including reinforcement learning and supervised fine-tuning—in a multi-stage, cost-effective manner, followed by model merging.

We are open-sourcing our models, post-training recipes and datasets which we believe will help the community to progress further in the reasoning domain.

🧪 Motivation

Thinking longer during inference time has shown to unlock superior reasoning abilities and expert level performance on challenging queries and tasks. Since the open-source release of DeepSeek R1 series models, multiple open-source efforts [s1, LIMO, Light-R1] have focused on reproducing the results (easpecially at <=32B scale) either via distillation or RL based fine-tuning on top of non-reasoning models. Though in most cases, these efforts at best, could come close to the performance R1 series models but are unable to surpass them. In parallel, certain recent methods [DeepScaleR, DeepCoder, Light-R1] started with the existing reasoning models and have managed to extend the performance of these models. However, the training runs for these methods are often costly and they rely on longer sequence lengths for higher accuracy.

Given the latest findings [Proof or Bluff ?, Reasoning models don't always say what they think] that raises the question on the correctness of the intermediate steps of the long COT in reasoning models, its important from interpretability, reliability and safety pov to ensure the reasoning chains are not inefficiently long. Hence, in this study, we work towards unlocking performance improvement of the reasoning models without training at very high (24k/32k) sequence length and restricting it to 16k context. We believe, while extremely long reasoning chains are still necessary for really challenging tasks, its also important to maximize the performance at lower context first before we proceed towards extending reasoning chains.

Training Dataset

We begin by curating a high-quality mathematical corpus from the following open-source datasets:

• Open-R1 - default subset
• Numina – Olympiads & AOPS_forum (word problems, float type answers)
• After rigorous deduplication and decontamination, we consolidated approximately ~100K unique problems, forming the initial corpus for all subsequent trainings.

🏗️ Post-Training Strategies

Training Recipe for Fathom-R1-14B-v0.6

SFT on difficult questions and their reasoning chains has been shown to be effective for improving reasoning ability. For this checkpoint, we build on top of this. This training stage focuses on improving the model’s performance on mathematical problems covering a spectrum of hard diffuculty level through a iterative curriculum learning strategy at max 16k sequence length. Curriculum learning (CL) is a well-established technique for training LLMs, where the model is progressively exposed to more difficult tasks. The idea is to gradually scaffold more complex reasoning, thereby enhancing generalization and reducing overfitting. However, in our case we perform this in an iterative manner, which essentially means we do multiple iterations of CL.

For the dataset preparation, we begin by annotating each question’s difficulty using OpenAI's o3mini model. We retain only those questions rated above average (in relative sense) and further filter them to include only those having solve rates between certain range (0.2 < pass_rate < 0.7). This yields the Iterative Curriculum Learning dataset comprising of 5K examples.

Total H100 GPU Hours: 48
Cost: $136

Training Recipe for Fathom-R1-14B-v0.4-RS

The core strategy used behind creating this checkpoint is a two-stage pipeline: First, leverage GRPO to improve reasoning of Deepseek-R1-Distilled-Qwen-14B at a lower sequence length, 6k, on a carefully curated dataset to ensure rapid improvement with minimal training steps. Second, we perform SFT, at max 16k tokens sequence length, on a carefully curated dataset of questions ( hard to very hard difficulty spectrum) and the corresponding shortest possible reasoning solution for each question.

• First Stage (Leveraging RL for effecient test-time thinking): We start with curating a seed dataset which ensures the policy receives minumium reward while still having room for growth. The dataset comparises of questions having solve rates (at lower sequence length) between a certain range. This forms our RL Compression dataset comprising of 7.7K questions. Staring from DeepSeek-R1-Distill-Qwen-14B as the base model, we train the model using the GRPO algorithm, with a 6k token sequence length limit. We see a consistent increase in performance as the model learns to generate concise responses from the decreasing clip ratio, response length and increasing reward. The obtained model has learnt to generate responses below 6k tokens and outperforms the base model at lower token limits.

• Second Stage (Leveraging SFT to improve reasoning efficiently at higher sequence length): We build upon the RL checkpoint and perform SFT under a 16K context window to encourage more detailed reasoning that would be required for solving more complex problems. For this stage, we strategically curate a dataset consisting of hard problems — specifically, questions with lower solve rates (0 < pass_rate <=0.4). Then, we obtain the shortest possible reasoning chains for these questions forming the SFT Shortest Chains dataset comprising of 9.5K examples. Through supervised fine-tuning on this dataset, the model is able to stablize its reasoning at sequence length upto 16K. The resulting model is named Fathom-R1-14B-v0.4, optimized for concise yet accurate mathematical reasoning.

Total H100 GPU Hours: 293
Cost: $831

Training Recipe for Fathom-R1-14B-v0.4

Given the performance improvement we noticed during the second fine-tuning stage of developing Fathom-R1-14B-v0.4-RS and in attempt to further reduce the cost, we experiment by eliminating RL and directly performing second stage SFT on Deepseek-R1-Distilled-Qwen-14B base model.

Total H100 GPU Hours: 128
Cost: $363

Model Merging

Given v0.6 and v0.4 models have been developed by following different training methodologies, we perform linear merging to combine the strengths to obtain final 2 checkpoints.

• Fathom-R1-14B: Obtained via merging Fathom-R1-14B-V0.6 (Iterative Curriculum SFT) and Fathom-R1-14B-V0.4 (SFT-Shortest-Chains)
• Fathom-R1-14B-RS: Obtained via merging Fathom-R1-14B-V0.6 (Iterative Curriculum SFT) and Fathom-R1-14B-V0.4 (RL-compression + SFT-Shortest-Chains)

💰 Post-Training Cost

We developed Fathom-R1-14B models using a focused, resource-efficient strategy that balances performance with compute budget. Below is the GPU time utilized and the cost incurred

So, the final Fathom-R1-14B took just 499$ to be trained overall! This low training cost highlights the efficiency of our method — enabling high-level mathematical reasoning comparable to o4-mini in $499 , all within a 16k sequence length budget.

📊 Evaluation

We evaluate Fathom‑R1-14B using the same metrics and sampling configuration introduced in the DeepSeek‑R1 paper, namely pass@1 and cons@64. However, our evaluation is conducted under a reduced output budget of 16,384 tokens, compared to DeepSeek‑R1’s 32,768 tokens, to better reflect practical deployment constraints.

• pass@1: Pass@1 is computed as the average correctness over k sampled solution chains per problem (in our experiments we keep k=64).
• cons@64: Assesses consistency by sampling 64 reasoning chains per question and computing the majority vote accuracy.

Evaluation Configuration:

• Temperature: 0.6
• top_p: 0.95
• Number of sampled chains: 64
• Context: 16,384 tokens

This setup allows us to benchmark Fathom-R1-14B’s reasoning performance and stability under realistic memory and inference budgets, while maintaining compatibility with the DeepSeek‑R1 evaluation protocol.

We utilize the evaluation framework provided by the LIMO repository to run inference and compute metrics. For detailed instructions and implementation details, please refer to eval/README.md.

Results

We evaluate and compare Fathom‑R1-14B with several baseline models across 3 challenging benchmarks: AIME25, HMMT25, and GPQA. For each, we report pass@1 and cons@64, following the same evaluation configuration.

🔧 Technical Details

The README provides detailed information about the model's training strategies, dataset preparation, and evaluation methods, which can be considered as technical details. For example, the iterative curriculum learning strategy in the training recipe for Fathom-R1-14B-v0.6, and the two-stage pipeline for Fathom-R1-14B-v0.4-RS.

📄 License

The project uses the MIT license.