Study the paper

Deep Residual Learning for Image Recognition

Lessons, visuals, quizzes, flashcards, and resourcesβ€”organized in teaching order.

All activities

Introduction to Residual Learning

Introduction to Residual Learning

Introduction to Residual Learning

The Degradation Problem in Deep Networks

Sources

S1.p3.1

When deeper networks are able to start converging, a degradation problem has been exposed: with the network depth increasing, accuracy gets saturated (which might be unsurprising) and then degrades rapidly. Unexpectedly, such degradation is not caused by overfitting, and adding more layers to a suitably deep model leads to higher training error, as reported in [11, 42] and thoroughly verified by our experiments. Fig. 1 shows a typical example.

As network depth increases, accuracy saturates and then degrades rapidly. This phenomenon is known as the degradation problem. Crucially, this degradation is not caused by overfitting, because adding more layers to a sufficiently deep model leads to higher training error, not just higher test error.

Sources

S1.p3.1

When deeper networks are able to start converging, a degradation problem has been exposed: with the network depth increasing, accuracy gets saturated (which might be unsurprising) and then degrades rapidly. Unexpectedly, such degradation is not caused by overfitting, and adding more layers to a suitably deep model leads to higher training error, as reported in [11, 42] and thoroughly verified by our experiments. Fig. 1 shows a typical example.

The Residual Learning Formulation

Sources

S1.p5.3

In this paper, we address the degradation problem by introducing a deep residual learning framework. Instead of hoping each few stacked layers directly fit a desired underlying mapping, we explicitly let these layers fit a residual mapping. Formally, denoting the desired underlying mapping as ℋ​(𝐱)ℋ𝐱\mathcal{H}(\mathbf{x}), we let the stacked nonlinear layers fit another mapping of ℱ​(𝐱):=ℋ​(𝐱)βˆ’π±assignℱ𝐱ℋ𝐱𝐱\mathcal{F}(\mathbf{x}):=\mathcal{H}(\mathbf{x})-\mathbf{x}. The original mapping is recast into ℱ​(𝐱)+𝐱ℱ𝐱𝐱\mathcal{F}(\mathbf{x})+\mathbf{x}. We hypothesize that it is easier to optimize the residual mapping than to optimize the original, unreferenced mapping. To the extreme, if an identity mapping were optimal, it would be easier to push the residual to zero than to fit an identity mapping by a stack of nonlinear layers.

To address the degradation problem, we reformulate the mapping of stacked nonlinear layers. Instead of expecting these layers to directly fit a desired underlying mapping H(x)\mathcal{H}(\mathbf{x}), we let them fit a residual mapping F(x):=H(x)βˆ’x\mathcal{F}(\mathbf{x}) := \mathcal{H}(\mathbf{x}) - \mathbf{x}. The original mapping is thus recast into F(x)+x\mathcal{F}(\mathbf{x}) + \mathbf{x}. It is hypothesized that optimizing this residual mapping is easier than optimizing the original, unreferenced mapping.

Sources

S1.p5.3

In this paper, we address the degradation problem by introducing a deep residual learning framework. Instead of hoping each few stacked layers directly fit a desired underlying mapping, we explicitly let these layers fit a residual mapping. Formally, denoting the desired underlying mapping as ℋ​(𝐱)ℋ𝐱\mathcal{H}(\mathbf{x}), we let the stacked nonlinear layers fit another mapping of ℱ​(𝐱):=ℋ​(𝐱)βˆ’π±assignℱ𝐱ℋ𝐱𝐱\mathcal{F}(\mathbf{x}):=\mathcal{H}(\mathbf{x})-\mathbf{x}. The original mapping is recast into ℱ​(𝐱)+𝐱ℱ𝐱𝐱\mathcal{F}(\mathbf{x})+\mathbf{x}. We hypothesize that it is easier to optimize the residual mapping than to optimize the original, unreferenced mapping. To the extreme, if an identity mapping were optimal, it would be easier to push the residual to zero than to fit an identity mapping by a stack of nonlinear layers.