Tabula RASA: Exposing and Breaking the Relational Bottleneck in Transformers

Transformers achieve remarkable performance across many domains, yet struggle with tasks requiring multi-hop relational reasoning over structured data. We analyze this limitation through circuit complexity: standard transformers are $\mathsf{TC}^0$-complete and require $Ω(k)$ layers for $k$-hop reasoning. We introduce RASA (Relation-Aware Sparse Attention), a minimal modification adding: (1) edge-type embeddings that inject relational structure into attention scores, and (2) sparse masking that restricts attention to graph-adjacent positions. While RASA has the same asymptotic depth requirements, sparse masking reduces the attention search space from $O(2^{n^2})$ to $O(2^m)$ patterns, and edge biases provide explicit relation routing. Empirically, on MetaQA (1/2/3-hop) and WebQuestionsSP, RASA outperforms standard transformers and matches GPT-4 at lower cost, with advantages growing with reasoning depth (+7.1 points on 3-hop). We do not claim formal learnability guarantees; the contribution is empirical validation that minimal structural modifications substantially improve multi-hop reasoning.