Audio anti-spoofing systems increasingly combine self-supervised learning, parameter-efficient fine-tuning, and graph-attention-based backends. However, performance gains in such systems are often entangled with concurrent changes in the backbone, fine-tuning strategy, and training protocol, making the independent contribution of graph attention design difficult to isolate. To address this issue, we conduct a systematic controlled study of the graph attention layer under a unified experimental setting. We decompose the layer into three independently testable design dimensions: scoring symmetry, temperature learnability, and routing granularity. These are instantiated as a concat-based scoring branch, a LearnT branch with learnable temperature, and a multi-temperature routing branch, respectively. Each dimension is implemented as an independently gated residual branch, enabling the evaluation of both individual variants and their combinations under the same experimental setting. Experiments on five evaluation sets with five random seeds show that the LearnT branch achieves the best average equal error rate (EER), yielding a 16.1% relative improvement over the baseline. In contrast, the multi-temperature routing branch does not improve average performance on its own, but substantially reduces cross-seed standard deviation when combined with the concat-based scoring branch. Moreover, two individually effective branches degrade performance when used together, resulting in a 25.6% relative deterioration compared with the baseline. This finding reveals strong non-additive interactions among graph attention design dimensions. Overall, the results suggest that, under parameter-constrained fine-tuning, improvements in graph attention layers depend more on capacity allocation and branch interaction than on simply adding more learnable parameters.

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