# CoIn: Counting the Invisible Reasoning Tokens in Commercial Opaque LLM APIs

arXiv: https://arxiv.org/abs/2505.13778 · HTML: https://mlsanity.com/paper/2505.13778/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 19 May 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [The Impact of Reasoning Step Length on Large Language Models](https://mlsanity.com/paper/2401.04925/) (2024)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Auditing language models for hidden objectives](https://mlsanity.com/paper/2503.10965/) (2025)
- [LLM Pruning and Distillation in Practice: The Minitron Approach](https://mlsanity.com/paper/2408.11796/) (2024)
- [LLM Reasoners: New Evaluation, Library, and Analysis of Step-by-Step Reasoning with Large Language Models](https://mlsanity.com/paper/2404.05221/) (2024)
- [Pairwise Proximal Policy Optimization: Harnessing Relative Feedback for LLM Alignment](https://mlsanity.com/paper/2310.00212/) (2023)
- [Understanding Aha Moments: from External Observations to Internal Mechanisms](https://mlsanity.com/paper/2504.02956/) (2025)
- [Are You Getting What You Pay For? Auditing Model Substitution in LLM APIs](https://mlsanity.com/paper/2504.04715/) (2025)
- [CALM: Curiosity-Driven Auditing for Large Language Models](https://mlsanity.com/paper/2501.02997/) (2025)
- [Trust, but verify](https://mlsanity.com/paper/2504.13443/) (2025)

## Built on by (most cited first, 14 of 14)

- [Is Your LLM Overcharging You? Tokenization, Transparency, and Incentives](https://mlsanity.com/paper/2505.21627/) (2025)
- [Predictive Auditing of Hidden Tokens in LLM APIs via Reasoning Length Estimation](https://mlsanity.com/paper/2508.00912/) (2025)
- [Auditing Pay-Per-Token in Large Language Models](https://mlsanity.com/paper/2510.05181/) (2025)
- [Test-Time Compute Games](https://mlsanity.com/paper/2601.21839/) (2026)
- [IMMACULATE: A Practical LLM Auditing Framework via Verifiable Computation](https://mlsanity.com/paper/2602.22700/) (2026)
- [Your "Pro" LLM Subscription May Actually Be "Free": Exposing Fingerprint Spoofing Risks in LLM Inference Services](https://mlsanity.com/paper/2606.16100/) (2026)
- [Resource Consumption Threats in Large Language Models](https://mlsanity.com/paper/2603.16068/) (2026)
- [RRTL: Red Teaming Reasoning Large Language Models in Tool Learning](https://mlsanity.com/paper/2505.17106/) (2025)
- [TRUST: A Decentralized Framework for Auditing Large Language Model Reasoning](https://mlsanity.com/paper/2510.20188/) (2025)
- [Token Inflation: How Dishonest Providers Can Overcharge for Large Language Model Usage](https://mlsanity.com/paper/2605.30040/) (2026)
- [Tokenization Multiplicity Leads to Arbitrary Price Variation in LLM-as-a-service](https://mlsanity.com/paper/2506.06446/) (2025)
- [Computational Challenges in Token Economics: Bridging Economic Theory and AI System Design](https://mlsanity.com/paper/2605.17410/) (2026)
- [Strategic Self-Consistency](https://mlsanity.com/paper/2609.30352/) (2026)
- [Paying for Too Many Tokens? Valid and Cost-Efficient Multimodal LLM Annotation with Simple Heuristics](https://mlsanity.com/paper/2610.00809/) (2026)

## Abstract (arXiv)

As post-training techniques evolve, large language models (LLMs) are increasingly augmented with structured multi-step reasoning abilities, often optimized through reinforcement learning. These reasoning-enhanced models outperform standard LLMs on complex tasks and now underpin many commercial LLM APIs. However, to protect proprietary behavior and reduce verbosity, providers typically conceal the reasoning traces while returning only the final answer. This opacity introduces a critical transparency gap: users are billed for invisible reasoning tokens, which often account for the majority of the cost, yet have no means to verify their authenticity. This opens the door to token count inflation, where providers may overreport token usage or inject synthetic, low-effort tokens to inflate charges. To address this issue, we propose CoIn, a verification framework that audits both the quantity and semantic validity of hidden tokens. CoIn constructs a verifiable hash tree from token embedding fingerprints to check token counts, and uses embedding-based relevance matching to detect fabricated reasoning content. Experiments demonstrate that CoIn, when deployed as a trusted third-party auditor, can effectively detect token count inflation with a success rate reaching up to 94.7%, showing the strong ability to restore billing transparency in opaque LLM services. The dataset and code are available at https://github.com/CASE-Lab-UMD/LLM-Auditing-CoIn.