# Exponentially Increasing the Capacity-to-Computation Ratio for Conditional Computation in Deep Learning

arXiv: https://arxiv.org/abs/1406.7362 · HTML: https://mlsanity.com/paper/1406.7362/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2014.

## Built on by (most cited first, 24 of 24)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
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- [Scaling Diffusion Transformers to 16 Billion Parameters](https://mlsanity.com/paper/2407.11633/) (2024)
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- [ScrollNet: Dynamic Weight Importance for Continual Learning](https://mlsanity.com/paper/2308.16567/) (2023)
- [Deconstructing Pre-training: Knowledge Attribution Analysis in MoE and Dense Models](https://mlsanity.com/paper/2601.08383/) (2026)
- [Memorization Capacity of Neural Networks with Conditional Computation](https://mlsanity.com/paper/2303.11247/) (2023)
- [Dynamic Multi-Branch Layers for On-Device Neural Machine Translation](https://mlsanity.com/paper/2105.06679/) (2021)
- [Switchable Representation Learning Framework with Self-compatibility](https://mlsanity.com/paper/2206.08289/) (2022)
- [CNN with large memory layers](https://mlsanity.com/paper/2101.11685/) (2021)
- [MoIN: Mixture of Introvert Experts to Upcycle an LLM](https://mlsanity.com/paper/2410.09687/) (2024)
- [MoECodec: Image Compression for joint human and machine perception via Mixture-of-Experts](https://mlsanity.com/paper/2606.21033/) (2026)

## Abstract (arXiv)

Many state-of-the-art results obtained with deep networks are achieved with the largest models that could be trained, and if more computation power was available, we might be able to exploit much larger datasets in order to improve generalization ability. Whereas in learning algorithms such as decision trees the ratio of capacity (e.g., the number of parameters) to computation is very favorable (up to exponentially more parameters than computation), the ratio is essentially 1 for deep neural networks. Conditional computation has been proposed as a way to increase the capacity of a deep neural network without increasing the amount of computation required, by activating some parameters and computation "on-demand", on a per-example basis. In this note, we propose a novel parametrization of weight matrices in neural networks which has the potential to increase up to exponentially the ratio of the number of parameters to computation. The proposed approach is based on turning on some parameters (weight matrices) when specific bit patterns of hidden unit activations are obtained. In order to better control for the overfitting that might result, we propose a parametrization that is tree-structured, where each node of the tree corresponds to a prefix of a sequence of sign bits, or gating units, associated with hidden units.