<p>As described in the <a href="https://arxiv.org/pdf/1704.04861.pdf" rel="noreferrer">paper</a>: </p>

<ol>
<li><p>The role of the <strong>width multiplier <em>α</em></strong> is to thin a network uniformly at each layer. for a given layer and width multiplier <em>α</em>, the number of input channels <em>M</em> becomes <em>αM</em> and the number of output channels <em>N</em> becomes <em>αN</em>.</p></li>
<li><p>The <strong>resolution multiplier <em>ρ</em></strong> is applied to the input image and the internal representation of every layer is subsequently reduced by the same multiplier. In practice we <strong>implicitly</strong> set <em>ρ</em> by setting the input resolution.</p></li>
</ol>

<p>In the <a href="https://github.com/tensorflow/models/blob/9f7a5fa353df0ee2010f8e7a5494ca6b188af8bc/research/slim/nets/mobilenet_v1.py#L216" rel="noreferrer">code</a>:
The <strong>depth_multiplier</strong> is used to reduce the number of channels at each layer. <strong>So the depth_multiplier corresponds the width multiplier <em>α</em>.</strong></p>
What is MobileNetv1 depth_multiplier?
<p>Refering to tensorflow mobilenetv1 model: <a href="https://github.com/tensorflow/models/blob/9f7a5fa353df0ee2010f8e7a5494ca6b188af8bc/research/slim/nets/mobilenet_v1.py#L171" rel="noreferrer">https://github.com/tensorflow/models/blob/9f7a5fa353df0ee2010f8e7a5494ca6b188af8bc/research/slim/nets/mobilenet_v1.py#L171</a></p>

<p>The param depth_multiplier is documented as:</p>

<blockquote>
  <p>depth_multiplier: Float multiplier for the depth (number of channels)
        for all convolution ops. The value must be greater than zero. Typical
        usage will be to set this value in (0, 1) to reduce the number of
        parameters or computation cost of the model</p>
</blockquote>

<p>But in the (<a href="https://arxiv.org/pdf/1704.04861.pdf" rel="noreferrer">paper</a>), they mention 2 types of multipliers: width multiplier and resolution multiplier, so which one correspond to depth multiplier?</p>

<p>On <a href="https://keras.rstudio.com/reference/application_mobilenet.html" rel="noreferrer">Keras</a>, they say that:</p>

<blockquote>
  <p>depth_multiplier:  depth multiplier for depthwise convolution (also
  called the resolution multiplier)</p>
</blockquote>

<p>I'm so confused!</p>