Recurrent neural networks approximate continuous functions
Classical approximation theorems ask for a new neural network whenever the target accuracy is improved. This paper studies the opposite possibility: can the network be chosen once and for all, and can accuracy be bought only by letting it run longer? We prove that this is possible for every continuous function on [-1,1]. More precisely, each such function is uniformly approximated by the time evolution of a single ReLU recurrent neural network with fixed weights and fixed hidden dimension. The mechanism behind the construction is a new intermediate model, the Turing machine with neural units (TMNU). This model retains the algorithmic freedom needed to implement polynomial approximation sc...
| Authors | Valentin Abadie, Clemens Hutter, Helmut Bölcskei |
|---|---|
| Primary category | cs.LG |
| Published | 18 June 2026 |
| Last updated at source | 18 June 2026 |
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