Coin Flipping Neural Networks
This work addresses the computational and accuracy limitations of neural networks for machine learning practitioners, though it appears incremental by building on existing randomness-based methods.
The paper tackles the problem of neural network efficiency by introducing Coin-Flipping Neural Networks (CFNNs) that use randomness to outperform deterministic networks, achieving an exponential reduction in neurons for approximating a d-dimensional ball and a 9.25% accuracy improvement on CIFAR benchmarks.
We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a $d$-dimensional ball to arbitrary accuracy with only 2 layers and $\mathcal{O}(1)$ neurons, where a 2-layer deterministic network was shown to require $Ω(e^d)$ neurons, an exponential improvement (arXiv:1610.09887). We prove a highly non-trivial result, that for almost any classification problem, there exists a trivially simple network that solves it given a sufficiently powerful generator for the network's weights. Combining these results we conjecture that for most classification problems, there is a CFNN which solves them with higher accuracy or fewer neurons than any deterministic network. Finally, we verify our proofs experimentally using novel CFNN architectures on CIFAR10 and CIFAR100, reaching an improvement of 9.25\% from the baseline.