We present BitFlow, a method for training neural networks with 1-bit weights using evolutionarysingle-bit mutations with incremental evaluation. The key insight, adapted from the NNUEarchitecture used in chess engines, is that flipping a single weight bit in a binary network affectsonly one neuron, enabling an evaluation scheme that is 112× faster than full-network evaluation— achieving over 10,000 effective training steps per second on a single CPU core. We compareagainst a baseline using the same evolutionary strategy without incremental evaluation: incrementalreaches 86.3% on MNIST in 10 minutes, while the baseline reaches only 42.1% in the same time,demonstrating that incremental evaluation is what makes the method viable. On binarized MNIST,a single BitFlow perceptron reaches 87.1% test accuracy (within 0.9 points of a float perceptron), andan ensemble of 24 models reaches 93.4%. On Fashion-MNIST, BitFlow reaches 73.5% in 10 minutes.We further demonstrate generality by training a binary autoencoder that achieves 93.4% pixel-levelreconstruction accuracy, though its learned features do not improve downstream classification —confirming that depth does not help in the 1-bit regime. All inference uses XNOR and populationcount instructions, achieving 4.45 microseconds per sample with a 60 KB model on a single core ofan Intel i9-13900HX.
Jesús Armando Mendoza Ramos (Sat,) studied this question.