Which examples maximally activate a neuron? Example selection

$\bf{x}_0 = \operatorname{argmax}_{\bf{x} \in \text{Te}} \Phi^l_n\left(\bf{x}; \theta\right)$
Our top example - what does this tell us?
ZeilerNet top-9 examples for 9 different neurons in layer 1
ZeilerNet top-9 examples for 16 different neurons in layer 2
ZeilerNet top-9 examples for 12 different neurons in layer 3
ZeilerNet top-9 examples for 4 different neurons in layer 4
ZeilerNet top-9 examples for 4 different neurons in layer 5
ZeilerNet top-9 examples for 4 different neurons in layer 5
Figures from Zeiler & Fergus - 2013

Activation Maximisation

How about synthesizing images that maxmially activate a neuron using gradient ascent.

Let $I = \{0..255\}^{W \times H \times 3}$

$\bf{x}_0 = \underset{\bf{x} \in I}{\operatorname{argmax}} \Phi^l_n\left(\bf{x}; \theta\right)$

Implementing activation maximisation

1. Initialise $\bf{x}_0$ with random noise
2. Repeat $n$ times (e.g. $n = 2000$):
1. Compute the partial derivatives of the neuron activation with respect to each input pixel: $\nabla_{\bf{x}}\Phi^l_n(\bf{x}; \theta)$
2. Update image: $\bf{x}_{m + 1} = \bf{x}_m + \lambda \nabla_{\bf{x}_m}\Phi^l_n(\bf{x}_m; \theta)$

Recall that $\nabla_{\bf{x}}\Phi^l_n(\bf{x}; \theta)$ is made up of partial derivatives $\frac{\partial \Phi^l_n(\bf{x}; \theta)}{\partial x_{i,j}}$

Improving the quality of synthetic images

We know a lot about images, we can utilise this knowledge to guide the optimisation process

The synthetic images has high frequency noise, we can discourage that by penialising it:

• $L_n$ regularisation
• Blurring in between optimisation steps
• Total variation regularisation

Transformations preserving semantic contents:

• Blurring
• Shifting
• Rotating
• Scaling
• Changing brightness
Feature Visualisation (2017)

Encoding prior knowledge with a generative network

Synthetic examples computed via activation maximisation on CaffeNet trained on ImageNet.
Synthetic examples computed via activation maximisation on AlexNet trained on MIT Places.
Synthesizing the preferred inputs for neurons in neural networks via deep generator networks - Nguyen et al (2016)

Multifaceted Neurons

Dataset examples maximally activating a chosen neuron.
Synthetic examples for the same neuron
Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks- Nguyen et al (2016)