Abstract:Self-attention in Transformers is typically implemented as $\mathrm{softmax}(QK^\top/\sqrt{d})V$, where $Q=XW_Q$, $K=XW_K$, and $V=XW_V$ are learned linear projections of the input $X$. We ask whether these learned projections are necessary, or whether they can be replaced by a simpler similarity-based diffusion operator. We introduce \textbf{Gaussian Kernel Attention} (GKA), a drop-in replacement for dot-product attention that computes token affinities directly using a Gaussian radial basis function (RBF) kernel applied to per-head token features. Each head learns only a bandwidth parameter $\sigma_h$, while a single output projection $W_O$ preserves compatibility with the standard Transformer interface. GKA can be interpreted as normalized kernel regression over tokens, linking modern Transformer architectures to classical non-local filtering and kernel smoothing methods. We evaluate GKA in both vision and language modeling settings. For autoregressive language modeling within the \texttt{nanochat} framework, we implement causal masking and sliding-window constraints by masking and renormalizing the Gaussian kernel. At depth 20, a GKA model with $0.42\times$ the parameters and $0.49\times$ the total training FLOPs of a standard attention baseline trains stably, exhibits a near-zero train-validation gap, and demonstrates competitive behavior on standard benchmarks, albeit with higher bits-per-byte (BPB) at this compute scale. Overall, GKA provides a minimal, interpretable attention mechanism with an explicit locality scale, offering a dimension in the accuracy-efficiency trade-off for Transformer design.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.02144 [cs.LG] |
| (or arXiv:2605.02144v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.02144 arXiv-issued DOI via DataCite (pending registration) |
From: Debarshi Kundu [view email]
[v1]
Mon, 4 May 2026 01:57:59 UTC (26,479 KB)
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