M$^2$RNN: Non-Linear RNNs with Matrix-Valued States for Scalable Language Modeling
Transformers are highly parallel but are limited to computations in the TC$^0$ complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revisit non-linear Recurrent Neural Networks (RNNs) for language modeling and introduce Matrix-to-Matrix RNN (M$^2$RNN): an architecture with matrix-valued hidden states and expressive non-linear state transitions. We demonstrate that the language modeling performance of non-linear RNNs is limited by their state size, and show how the state size expansion mechanism enables efficient use of tensor cores. Empirically, M$^2$RNN achieves perfect state tracking...
| Authors | Mayank Mishra, Shawn Tan, Ion Stoica et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 March 2026 |
| Last updated at source | 13 May 2026 |
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