<p>I have found from paper <code>&lt;&lt;Very Deep Convolutional Networks for Large-Scale Image Recognition&gt;&gt;</code>.</p>

<blockquote>
  <p>Rather than using relatively large receptive fields in the first conv. layers (e.g. 11×11with stride 4 in (Krizhevsky et al., 2012), or 7×7 with stride 2 in (Zeiler &amp; Fergus, 2013; Sermanet et al., 2014)), we use very small 3 × 3 receptive fields throughout the whole net, which are convolved with the input at every pixel (with stride 1). It is easy to see that a stack of two 3×3 conv.layers (without spatial poolingin between) has an effective receptive field of 5×5; three such layers have a 7 × 7 effective receptive field. </p>
</blockquote>

<ol>
<li><p>two 3*3 convolution filter is equivalent to one 5*5 convolution filter.</p></li>
<li><p>two 3*3 convolution filter will have less parameters than one 5*5 convolution filter.</p></li>
<li><p>two 3*3 convolution filter will make network more deep and extract more complex features than one 5*5 convolution filter.</p></li>
</ol>

<p>paper:<a href="https://arxiv.org/pdf/1409.1556.pdf" rel="nofollow noreferrer">https://arxiv.org/pdf/1409.1556.pdf</a></p>
In deep learning what's difference between two 3*3 convolution filters and one 5*5 convolution filters?
<p>For example, as to the <code>famous AlexNet architecutre</code>  <a href="https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf" rel="nofollow noreferrer">(original paper)</a>, what's the difference of using <code>two 3*3  convolution filters</code> between using <code>one 5*5 convolution filter</code> ?</p>

<p>The <code>two 3*3  convolution filters</code> and <code>one 5*5 convolution filter</code> have been highlighted by <code>red rectangle</code> in the below image.</p>

<p><a href="https://i.stack.imgur.com/sY2pe.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/sY2pe.png" alt="https://medium.com/@smallfishbigsea/a-walk-through-of-alexnet-6cbd137a5637"></a></p>

<p><a href="https://i.stack.imgur.com/CWVZr.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/CWVZr.png" alt="enter image description here"></a></p>

<p>What about use another <code>5*5 convolution filter</code> to supersede the <code>two 3*3  convolution filters</code>, or  vice verse?</p>