Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity
We show that, in a precise sense, a broad class of feedforward neural networks learn (have finite sample complexity) in the PAC model: every fixed finite feedforward architecture whose layers are definable in an o-minimal structure has finite sample complexity in the agnostic PAC setting, even with unbounded parameters. This covers standard fixed-size MLPs, CNNs, GNNs, and transformers with fixed sequence length, together with the operations and layers typically used in such architectures, including linear projections, residual connections, attention mechanisms, pooling layers, normalization layers, and admissible positional encodings. Hence, distribution-free learnability for modern non-...
| Authors | Anastasis Kratsios, Gregory Cousins, Haitz Sáez de Ocáriz Borde et al. |
|---|---|
| Primary category | stat.ML |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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