Potential–Time Dual Representations for TTFS Transformer Conversion

Time-to-first-spike (TTFS) coding represents each value by a single spike time, reducing the number of spikes required to represent an activation. Converting a pretrained Transformer into a TTFS-based continuous-time spiking neural network (SNN), however, requires composing Transformer operations from analog-compatible operators and evaluating the converted model under timing noise. We propose a $\Phi /\Psi$ conversion framework based on the dual relationship between membrane-potential space $\mathcal{V}$ and spike-time space $\mathcal{T}$. The framework composes a small set of fixed primitive operators with known hardware realizations to implement affine transformations, attention, LayerNorm/RMSNorm, GELU, and SwiGLU. Across pretrained ViT, RoBERTa, GPT-2, and Llama 2 7B models, conversion reduces classification accuracy by at most $0.11$ pp (one fewer correct SST-2 prediction out of 872), while the absolute WikiText-2 perplexity change is below $0.00021$. We model spike-time noise and the resulting deadline misses, parameterizing the noise with BrainScaleS-2 measurements from the physical paths implementing the linear and logarithmic $\varphi$ operators. Code is available at https://anonymous.4open.science/r/52AD.