# Implicit Deep Learning

## TL;DR

Implicit deep learning introduces a framework where neural network predictions are defined by fixed-point equations, simplifying notation and enabling new research directions in architecture, robustness, interpretability, and optimization.

## Contribution

The paper formalizes implicit deep learning prediction rules, expanding the theoretical foundation and opening avenues for novel architectures and analysis methods.

## Key findings

- Simplifies deep learning notation
- Enables new architectures and algorithms
- Facilitates robustness and interpretability analysis

## Abstract

Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only implicitly defined. The implicit framework greatly simplifies the notation of deep learning, and opens up many new possibilities, in terms of novel architectures and algorithms, robustness analysis and design, interpretability, sparsity, and network architecture optimization.