Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension
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arXiv
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| Format: | Preprint |
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2026
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| author | Guo, Dongxin Wu, Jikun Yiu, Siu Ming |
| author_facet | Guo, Dongxin Wu, Jikun Yiu, Siu Ming |
| contents | Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first comprehensive expressivity theory for spiking self-attention. We prove that spiking attention with Leaky Integrate-and-Fire neurons is a universal approximator of continuous permutation-equivariant functions, providing explicit spike circuit constructions including a novel lateral inhibition network for softmax normalization with proven $O(1/\sqrt{T})$ convergence. We derive tight spike-count lower bounds via rate-distortion theory: $\varepsilon$-approximation requires $Ω(L_f^2 nd/\varepsilon^2)$ spikes, with rigorous information-theoretic derivation. Our key insight is input-dependent bounds using measured effective dimensions ($d_{\text{eff}}=47$--$89$ for CIFAR/ImageNet), explaining why $T=4$ timesteps suffice despite worst-case $T \geq 10{,}000$ predictions. We provide concrete design rules with calibrated constants ($C=2.3$, 95\% CI: $[1.9, 2.7]$). Experiments on Spikformer, QKFormer, and SpikingResformer across vision and language benchmarks validate predictions with $R^2=0.97$ ($p<0.001$). Our framework provides the first principled foundation for neuromorphic transformer design. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_15769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension Guo, Dongxin Wu, Jikun Yiu, Siu Ming Machine Learning Artificial Intelligence 68T07, 92B20 I.2.6; I.5.1 Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first comprehensive expressivity theory for spiking self-attention. We prove that spiking attention with Leaky Integrate-and-Fire neurons is a universal approximator of continuous permutation-equivariant functions, providing explicit spike circuit constructions including a novel lateral inhibition network for softmax normalization with proven $O(1/\sqrt{T})$ convergence. We derive tight spike-count lower bounds via rate-distortion theory: $\varepsilon$-approximation requires $Ω(L_f^2 nd/\varepsilon^2)$ spikes, with rigorous information-theoretic derivation. Our key insight is input-dependent bounds using measured effective dimensions ($d_{\text{eff}}=47$--$89$ for CIFAR/ImageNet), explaining why $T=4$ timesteps suffice despite worst-case $T \geq 10{,}000$ predictions. We provide concrete design rules with calibrated constants ($C=2.3$, 95\% CI: $[1.9, 2.7]$). Experiments on Spikformer, QKFormer, and SpikingResformer across vision and language benchmarks validate predictions with $R^2=0.97$ ($p<0.001$). Our framework provides the first principled foundation for neuromorphic transformer design. |
| title | Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension |
| topic | Machine Learning Artificial Intelligence 68T07, 92B20 I.2.6; I.5.1 |
| url | https://arxiv.org/abs/2604.15769 |