无线基础模型大小受物理信道维度限制,过大无益。
How Big Should a Wireless Foundation Model Be?

- 以信道非线性流形维数为瓶颈,决定模型最大有效规模。
- 超过3000万参数后性能提升骤降,7000万以上进入随机渐近区。
- 小模型通过测试时训练可超越大模型,适合资源受限场景。
无线基础模型正成为智能通信系统的关键,但其规模应多大仍无定论。本文提出基于物理原理的解答:信道非线性流形维数(dNL)是根本瓶颈,决定了数据充足后的模型上限。该维度由麦克斯韦方程、有限散射体和天线孔径等物理因素决定,在真实室外测量与3GPP标准信道模型中范围为5-35,远低于语言模型约1000维的语义空间。以卫星信道为例(dNL ≈ 14),模型参数超过3000万后增益迅速下降,7000万以上进入随机渐近区,参数从9600万增至15000万仅提升0.52 dB。此时,通过导频辅助的测试时训练(TTT)实现轻量级推理适应更高效:1200万参数模型在20dB SNR下比静态9600万模型高9.9 dB(NMSE),10dB SNR下高7.6 dB(MCM)。dNL分布已在真实室内大规模MIMO测量中验证,相关缩放规律与TTT增益通过卫星链路仿真证实。研究重新定义无线AI设计范式:信道几何结构而非模型规模,才是物理层无线AI的主导因素。
原文摘要 · Abstract (English)
Wireless foundation models are rapidly emerging as a key enabler of AI-native communication systems, yet a fundamental question remains unanswered: how large should these models be? We present a principled, physics-grounded answer, showing that the intrinsic dimensionality (dNL, the nonlinear manifold dimension of the channel) acts as the fundamental bottleneck, defining the scaling ceiling once a data-sufficient regime is reached. This dimensionality is not a design choice but a physical constraint: Maxwell's equations, finite scatterers, and antenna aperture inherently constrain wireless propagation environments to a limited number of degrees of freedom -- spanning 5-35 across both real-world OTA measurements and 3GPP-standardized channel models we evaluate -- orders of magnitude below the ~1,000-dimensional semantic space of language. As a consequence, we propose a scaling framework for wireless AI: taking NTN satellite channels as a representative case (dNL ~= 14), scaling gains diminish rapidly beyond ~30 million parameters, entering a stochastic asymptote above 70M where a further 1.6x increase (96M->150M) yields only 0.52 dB. Beyond this ceiling, inference-time adaptation via pilot-aided test-time training (TTT) is far more effective: a compact 12M-parameter model surpasses a static 96M model by 9.9 dB (NMSE, SNR = 20 dB) / 7.6 dB (MCM, SNR = 10 dB) at one-eighth the parameters. With dNL distributions validated across real-world indoor massive MIMO measurements, our scaling laws and TTT gains are demonstrated through NTN satellite simulations, reframing wireless AI design: channel geometry -- not model size -- fundamentally governs the scaling laws of physical-layer wireless AI.
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