Shallower ReLU Network Representations via Exact Linear Algebra
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arXiv:2607.21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$. The constructions are obtained by reducing the problem to exact rational linear algebra: after a symmetry reduction, the necessary cancellations are encoded in finite linear systems over $\mathbb{Q}$, which we solve and verify computationally. The representation of $\max_{10}$ has a structured first hidden layer…
1Key Takeaways
- arXiv:2607.21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$.
- The constructions are obtained by reducing the problem to exact rational linear algebra: after a symmetry reduction, the necessary cancellations are encoded in finite linear systems over $\mathbb{Q}$, which we solve and verify computationally.
- The representation of $\max_{10}$ has a structured first hidden layer….
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3Why it matters
Research breakthroughs often arrive in products months later—early signals matter for strategy. arXiv ML reports that arXiv:2607.21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$.
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