# CosineGate: Semantic Dynamic Routing via Cosine Incompatibility in Residual Networks

arXiv: https://arxiv.org/abs/2512.22206 · HTML: https://mlsanity.com/paper/2512.22206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Convolutional Networks with Adaptive Inference Graphs](https://mlsanity.com/paper/1711.11503/) (2017)
- [Memory and information processing in neuromorphic systems](https://mlsanity.com/paper/1506.03264/) (2015)

## Abstract (arXiv)

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.