Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension
Summary: arXiv:2604.15769v1 Announce Type: cross
Abstract: 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.
The research highlights that spiking attention utilizing Leaky Integrate-and-Fire neurons functions as a universal approximator for continuous permutation-equivariant functions. This discovery is accompanied by explicit spike circuit constructions, including an innovative lateral inhibition network designed for softmax normalization, which demonstrates a proven convergence rate of $O(1/\sqrt{T})$. Furthermore, the study introduces tight spike-count lower bounds derived from rate-distortion theory, indicating that an $\varepsilon$-approximation necessitates $\Omega(L_f^2 nd/\varepsilon^2)$ spikes, supported by rigorous information-theoretic derivations.
The key insight presented in the paper revolves around input-dependent bounds utilizing measured effective dimensions. For instance, the effective dimensions for CIFAR and ImageNet datasets are reported to be between $d_{\text{eff}}=47$ and $d_{\text{eff}}=89$. This finding elucidates why a mere $T=4$ timesteps are sufficient for predictions, contrasting with the worst-case scenario where $T$ could exceed $10{,}000$.
Key Contributions
- Expressivity Theory: The establishment of a comprehensive expressivity theory for spiking self-attention.
- Universal Approximation: Proving that spiking attention with Leaky Integrate-and-Fire neurons serves as a universal approximator.
- Lateral Inhibition Network: Introduction of a novel lateral inhibition network for softmax normalization.
- Spike-Count Lower Bounds: Deriving tight lower bounds for spike counts through rate-distortion theory.
- Effective Dimension Insights: Utilizing measured effective dimensions to provide input-dependent bounds.
- Design Rules: Offering concrete design rules with calibrated constants for spiking transformers.
Experimental Validation
The paper further substantiates its theoretical findings through extensive experiments conducted on various models, including Spikformer, QKFormer, and SpikingResformer. The experiments span multiple vision and language benchmarks, validating the predictions with a remarkable coefficient of determination of $R^2=0.97$. This high degree of accuracy in experimental results showcases the potential of spiking transformers in practical applications.
Conclusion
In summary, the research presents a significant advancement in the theoretical understanding of spiking transformers, addressing the existing gap between theory and practice. By establishing a solid framework and providing experimental evidence, this study paves the way for the optimized design and implementation of spiking transformers in real-world applications, potentially transforming the landscape of energy-efficient artificial intelligence systems.