Universal Transformers for Circuit Computations: Perfect Length Generalization in Tiny Transformers
Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and length generalization benchmarks. We present a provably correct, transformer parameterization (with only 280 learnable parameters for Boolean algebra tasks) capable of learning and evaluating problems of any depth or length. We assume inputs are fully parenthesized, well-formed expressions. Our approach conceptualizes algorithmic tasks as circuit models embedded in transformers, enabling depth-1 circuit reduction in a single forward pass. To achieve depth generalization, we introduce a positional encoding that tracks each gate's depth within the...
| Authors | Takuya Ito, Ruchir Puri, Murray Campbell et al. |
|---|---|
| Primary category | cs.LG |
| Published | 31 August 2026 |
| Last updated at source | 31 August 2026 |
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