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arXiv · 2602.13595

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

Henry Han·Xiyang Liu·Xiaodong Wang·Fei Han·Xiaodong Li
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Abstract

Neural scaling laws provide a predictable recipe for AI advancement: reducing numerical precision should linearly improve computational efficiency and energy profile ($E \propto \mathrm{bits}$). 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$\times$ 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.

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Henry Han, Xiyang Liu, Xiaodong Wang, Fei Han, Xiaodong Li. 2026-02-14. The Quantization Trap: Breaking Linear Scaling Laws in Multi-Hop Reasoning. https://arxiv.org/abs/2602.13595

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