# Threshold-Based Early Stopping of Accumulations in Neural Networks with Binary Activation

arXiv: https://arxiv.org/abs/2608.06177 · HTML: https://mlsanity.com/paper/2608.06177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [Dynamic Channel Pruning: Feature Boosting and Suppression](https://mlsanity.com/paper/1810.05331/) (2018)
- [Incomplete Dot Products for Dynamic Computation Scaling in Neural Network Inference](https://mlsanity.com/paper/1710.07830/) (2017)

## Abstract (arXiv)

Binary neural networks are very attractive for constrained deployment, enabling small footprint and low-power inference. For binary activations, the dot products become sign-controlled additions or subtractions, but the number of operations is unchanged. Indeed, every neuron or output channel still accumulates all of its input, even though only the sign will be retained, which is often wasteful. As the accumulation progresses, the running partial sum frequently drifts so far from zero that its final sign becomes highly predictable long before the last term is reached; every contribution evaluated after that point changes the value of the sum but not the final output activation. This paper turns this observation into a post-training early-stopping mechanism. We characterize the behavior of the running accumulations on the training dataset and use this information to predict the final sign as soon as possible. No model parameter is retrained. We count the number of operations under an idealized ordering of weights. On VGG11 applied to the CIFAR-10 dataset, the method removes 86.6% of the accumulation terms of the deepest convolution for a 0.37-point accuracy drop, and 25% of the full-network arithmetic when used on the three deepest convolutions simultaneously, for a 1.36-point drop.