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SIFT: Grounding LLM Reasoning in Contexts via Stickers

Zihao Zeng, Xuyao Huang, Boxiu Li, Zhijie Deng

TL;DR

The paper addresses factual drift in LLM reasoning, where context is misinterpreted during multi-step inference. It introduces SIFT, a training-free framework that grounds reasoning in context by generating a Sticker from the query, producing two predictions (Sticker-only and Query+Sticker), and refining the Sticker via Forward Optimization and Inverse Generation until the predictions align. Across models from 3B to 100B+ and benchmarks such as GSM8K, MATH-500, GPQA-Diamond, and AIME2024, SIFT delivers consistent improvements, including a pass@1 gain on AIME2024 for DeepSeek-R1 from $78.33\%$ to $85.67\%$ and about a $1.03$ percentage-point boost on MATH-500 from a baseline of $97.3\%$, establishing a new open-source state-of-the-art. The approach also synergizes with Self-Consistency, demonstrates iterative optimization benefits, and relies on a clear Consensus Prediction strategy, all while avoiding additional training data. Code for SIFT is publicly available, enabling practitioners to adopt fact-grounded reasoning in diverse settings.

Abstract

This paper identifies the misinterpretation of the context can be a significant issue during the reasoning process of large language models, spanning from smaller models like Llama3.2-3B-Instruct to cutting-edge ones like DeepSeek-R1. For example, in the phrase "10 dollars per kilo," LLMs might not recognize that "per" means "for each," leading to calculation errors. We introduce a novel, post-training approach called **Stick to the Facts (SIFT)** to tackle this. SIFT leverages increasing inference-time compute to ground LLM reasoning in contexts. At the core of SIFT lies the *Sticker*, which is generated by the model itself to explicitly emphasize the key information within the context. Given the curated Sticker, SIFT generates two predictions -- one from the original query and one from the query augmented with the Sticker. If they differ, the Sticker is sequentially refined via *forward* optimization (to better align the extracted facts with the query) and *inverse* generation (to conform with the model's inherent tendencies) for more faithful reasoning outcomes. Studies across diverse models (from 3B to 100B+) and benchmarks (e.g., GSM8K, MATH-500) reveal consistent performance improvements. Notably, SIFT improves the pass@1 accuracy of DeepSeek-R1 on AIME2024 from 78.33% to **85.67**%, establishing a new state-of-the-art in the open-source community. The code is available at https://github.com/zhijie-group/SIFT.

SIFT: Grounding LLM Reasoning in Contexts via Stickers

TL;DR

The paper addresses factual drift in LLM reasoning, where context is misinterpreted during multi-step inference. It introduces SIFT, a training-free framework that grounds reasoning in context by generating a Sticker from the query, producing two predictions (Sticker-only and Query+Sticker), and refining the Sticker via Forward Optimization and Inverse Generation until the predictions align. Across models from 3B to 100B+ and benchmarks such as GSM8K, MATH-500, GPQA-Diamond, and AIME2024, SIFT delivers consistent improvements, including a pass@1 gain on AIME2024 for DeepSeek-R1 from to and about a percentage-point boost on MATH-500 from a baseline of , establishing a new open-source state-of-the-art. The approach also synergizes with Self-Consistency, demonstrates iterative optimization benefits, and relies on a clear Consensus Prediction strategy, all while avoiding additional training data. Code for SIFT is publicly available, enabling practitioners to adopt fact-grounded reasoning in diverse settings.

Abstract

This paper identifies the misinterpretation of the context can be a significant issue during the reasoning process of large language models, spanning from smaller models like Llama3.2-3B-Instruct to cutting-edge ones like DeepSeek-R1. For example, in the phrase "10 dollars per kilo," LLMs might not recognize that "per" means "for each," leading to calculation errors. We introduce a novel, post-training approach called **Stick to the Facts (SIFT)** to tackle this. SIFT leverages increasing inference-time compute to ground LLM reasoning in contexts. At the core of SIFT lies the *Sticker*, which is generated by the model itself to explicitly emphasize the key information within the context. Given the curated Sticker, SIFT generates two predictions -- one from the original query and one from the query augmented with the Sticker. If they differ, the Sticker is sequentially refined via *forward* optimization (to better align the extracted facts with the query) and *inverse* generation (to conform with the model's inherent tendencies) for more faithful reasoning outcomes. Studies across diverse models (from 3B to 100B+) and benchmarks (e.g., GSM8K, MATH-500) reveal consistent performance improvements. Notably, SIFT improves the pass@1 accuracy of DeepSeek-R1 on AIME2024 from 78.33% to **85.67**%, establishing a new state-of-the-art in the open-source community. The code is available at https://github.com/zhijie-group/SIFT.

Paper Structure

This paper contains 13 sections, 15 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Factual Drift in LLM Reasoning
  5. Stick to the Facts (SIFT)
  6. Experiments
  7. Enhancing LLM Reasoning with SIFT
  8. Iterative Optimization
  9. Sample Augmentation
  10. Ablation
  11. Conclusion
  12. More Results
  13. Prompting for SIFT

Figures (15)

  • Figure 1: Applying SIFT to DeepSeek-R1 demonstrates highly competitive reasoning performance on AIME2024, AIME2025, and MATH-500 (pass@1 accuracy). The results for o1-mini and o3-mini on AIME are referenced from ye2025aimepreview.
  • Figure 2: An example of a query and its Sticker.
  • Figure 3: Factual drift occurs during (i) Sticker generation and (ii) prediction generation from Sticker.
  • Figure 4: Self-verification occurs during DeepSeek-R1's reasoning, where the model revisiting the query, focusing on key information, and paraphrasing it.
  • Figure 5: Four core operations in SIFT: (i) Sticker Generation (SG), (ii) Consensus Prediction (CP), (iii) Forward Optimization (FO), (iv) Inverse Generation (IG).
  • ...and 10 more figures