<p>Using convolutions as FCs can be done (for example) with filters of spatial size (1,1) and with depth of the same size as the FC input size.</p>
<p>The resulting feature map would be of the same size as the input feature map, but each pixel would be the output of a &quot;FC&quot; layer whose weights are the weights of the shared 1x1 conv filter.</p>
<p>This kind of thing is used mainly for semantic segmentation, meaning classification per pixel. <a href="https://arxiv.org/abs/1505.04597" rel="nofollow noreferrer">U-net</a> is a good example if memory serves.</p>
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<p>Also see <a href="https://stats.stackexchange.com/questions/194142/what-does-1x1-convolution-mean-in-a-neural-network">this</a>.<br />
Also note that 1x1 convolutions have <a href="https://machinelearningmastery.com/introduction-to-1x1-convolutions-to-reduce-the-complexity-of-convolutional-neural-networks/" rel="nofollow noreferrer">other uses</a> as well.<br />
<a href="https://paperswithcode.com/task/semantic-segmentation" rel="nofollow noreferrer">paperswithcode</a> probably some of the nets there use this trick.</p>
Can I use a convolution filter instead of a dense layer for clasification?
<p>I was reading a decent paper <a href="https://paperswithcode.com/paper/from-open-set-to-closed-set-counting-objects" rel="nofollow noreferrer">S-DCNet</a> and I fell upon a section (page3,table1,classifier) where a convolution layer has been used on the feature map in order to produce a binary classification output as part of an internal process. Since I am a noob and when someone talks to me about classification I automatically make a synapse relating to FCs combined with softmax, I started wondering ... Is this a possible thing to do? Can indeed a convolutional layer be used to classify a binary outcome? The whole concept triggered my imagination so much that I insist on getting answers...</p>
<p><strong>Honestly, how does this actually work? What is the difference between using a convolution filter instead of a fully connected layer for classification purposes?</strong></p>
<p>Edit (Uncertain answer on how does it work): <em>I asked a colleague and he told me that using a filter of the same shape as the length-width shape of the feature map at the current stage, may lead to a learnable binary output (considering that you also reduce the #channels of the feature map to a single channel). But I still don't understand the motivations behind such a technique ..</em></p>