# The Quantization Trap: Breaking Linear Scaling Laws in Multi-Hop Reasoning

arXiv: https://arxiv.org/abs/2602.13595 · HTML: https://mlsanity.com/paper/2602.13595/

## Key facts

- Cited by 2 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 18 of its 36 references that are in the map.
- First posted on arXiv 14 Feb 2026.

## 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, 18 of 18)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [How Language Model Hallucinations Can Snowball](https://mlsanity.com/paper/2305.13534/) (2023)
- [Atom: Low-bit Quantization for Efficient and Accurate LLM Serving](https://mlsanity.com/paper/2310.19102/) (2023)
- [Towards the Systematic Reporting of the Energy and Carbon Footprints of Machine Learning](https://mlsanity.com/paper/2002.05651/) (2020)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [The De-democratization of AI: Deep Learning and the Compute Divide in Artificial Intelligence Research](https://mlsanity.com/paper/2010.15581/) (2020)
- [Quantization Meets Reasoning: Exploring LLM Low-Bit Quantization Degradation for Mathematical Reasoning](https://mlsanity.com/paper/2501.03035/) (2025)
- [Sustainable LLM Inference for Edge AI: Evaluating Quantized LLMs for Energy Efficiency, Output Accuracy, and Inference Latency](https://mlsanity.com/paper/2504.03360/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Institutional Scaling Law: Non-Monotonic Fitness, Capability-Trust Divergence, and Symbiogenetic Scaling in Generative AI](https://mlsanity.com/paper/2603.14126/) (2026)
- [Punctuated Equilibria in Artificial Intelligence: The Institutional Scaling Law and the Speciation of Sovereign AI](https://mlsanity.com/paper/2603.14664/) (2026)

## Abstract (arXiv)

Neural scaling laws provide a predictable recipe for AI advancement: reducing numerical precision should linearly improve computational efficiency and energy profile (E propto bits). In this paper, we demonstrate that this scaling law breaks in the context of multi-hop reasoning. We reveal a 'quantization trap' where reducing precision from 16-bit to 8/4-bit paradoxically increases net energy consumption while degrading reasoning accuracy. We provide a rigorous theoretical decomposition that attributes this failure to hardware casting overhead, the hidden latency cost of dequantization kernels, which becomes a dominant bottleneck in sequential reasoning chains, as well as to a sequential energy amortization failure. As a result, scaling law breaking is unavoidable in practice. We formalize a Critical Model Scale N^* that predicts when the trap dissolves or deepens as a function of model size, batch size, and hardware configuration, validated across a 120× range (0.6B--72B) on six GPU architectures. Our findings suggest that the industry's "smaller-is-better" heuristic is mathematically counterproductive for complex reasoning tasks.