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See the NOTICE file + distributed with this work for additional information + regarding copyright ownership. The ASF licenses this file + to you under the Apache License, Version 2.0 (the + "License"); you may not use this file except in compliance + with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, + software distributed under the License is distributed on an + "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + KIND, either express or implied. See the License for the + specific language governing permissions and limitations + under the License. +--><div class="section" id="neural-net"> +<h1>Neural Net<a class="headerlink" href="#neural-net" title="Permalink to this headline">¶</a></h1> +<p><code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> in SINGA represents an instance of userâs neural net model. As the +neural net typically consists of a set of layers, <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> comprises +a set of unidirectionally connected <a class="reference external" href="layer.html">Layer</a>s. +This page describes how to convert an userâs neural net into +the configuration of <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code>.</p> +<img src="../_static/images/model-category.png" align="center" width="200px"/> +<span><strong>Figure 1 - Categorization of popular deep learning models.</strong></span><div class="section" id="net-structure-configuration"> +<h2>Net structure configuration<a class="headerlink" href="#net-structure-configuration" title="Permalink to this headline">¶</a></h2> +<p>Users configure the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> by listing all layers of the neural net and +specifying each layerâs source layer names. Popular deep learning models can be +categorized as Figure 1. The subsequent sections give details for each +category.</p> +<div class="section" id="feed-forward-models"> +<h3>Feed-forward models<a class="headerlink" href="#feed-forward-models" title="Permalink to this headline">¶</a></h3> +<div align = "left"> +<img src="../_static/images/mlp-net.png" align="center" width="200px"/> +<span><strong>Figure 2 - Net structure of a MLP model.</strong></span> +</div><p>Feed-forward models, e.g., CNN and MLP, can easily get configured as their layer +connections are undirected without circles. The +configuration for the MLP model shown in Figure 1 is as follows,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="p">{</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s1">'data"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kData</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s1">'image"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kImage</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s1">'data'</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s1">'label"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kLabel</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s1">'data'</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s1">'hidden"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kHidden</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s1">'image'</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s1">'softmax"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kSoftmaxLoss</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s1">'hidden'</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s1">'label'</span> + <span class="p">}</span> +<span class="p">}</span> +</pre></div> +</div> +</div> +<div class="section" id="energy-models"> +<h3>Energy models<a class="headerlink" href="#energy-models" title="Permalink to this headline">¶</a></h3> +<img src="../_static/images/rbm-rnn.png" align="center" width="500px"/> +<span><strong>Figure 3 - Convert connections in RBM and RNN.</strong></span><p>For energy models including RBM, DBM, +etc., their connections are undirected (i.e., Category B). To represent these models using +<code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code>, users can simply replace each connection with two directed +connections, as shown in Figure 3a. In other words, for each pair of connected layers, their source +layer field should include each otherâs name. +The full <a class="reference external" href="rbm.html">RBM example</a> has +detailed neural net configuration for a RBM model, which looks like</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="p">{</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s2">"vis"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kVisLayer</span> + <span class="n">param</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s2">"w1"</span> + <span class="p">}</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s2">"hid"</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s2">"hid"</span> + <span class="nb">type</span> <span class="p">:</span> <span class="n">kHidLayer</span> + <span class="n">param</span> <span class="p">{</span> + <span class="n">name</span> <span class="p">:</span> <span class="s2">"w2"</span> + <span class="n">share_from</span><span class="p">:</span> <span class="s2">"w1"</span> + <span class="p">}</span> + <span class="n">srclayer</span><span class="p">:</span> <span class="s2">"vis"</span> + <span class="p">}</span> +<span class="p">}</span> +</pre></div> +</div> +</div> +<div class="section" id="rnn-models"> +<h3>RNN models<a class="headerlink" href="#rnn-models" title="Permalink to this headline">¶</a></h3> +<p>For recurrent neural networks (RNN), users can remove the recurrent connections +by unrolling the recurrent layer. For example, in Figure 3b, the original +layer is unrolled into a new layer with 4 internal layers. In this way, the +model is like a normal feed-forward model, thus can be configured similarly. +The <a class="reference external" href="rnn.html">RNN example</a> has a full neural net +configuration for a RNN model.</p> +</div> +</div> +<div class="section" id="configuration-for-multiple-nets"> +<h2>Configuration for multiple nets<a class="headerlink" href="#configuration-for-multiple-nets" title="Permalink to this headline">¶</a></h2> +<p>Typically, a training job includes three neural nets for +training, validation and test phase respectively. The three neural nets share most +layers except the data layer, loss layer or output layer, etc.. To avoid +redundant configurations for the shared layers, users can uses the <code class="docutils literal notranslate"><span class="pre">exclude</span></code> +filed to filter a layer in the neural net, e.g., the following layer will be +filtered when creating the testing <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code>.</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">layer</span> <span class="p">{</span> + <span class="o">...</span> + <span class="n">exclude</span> <span class="p">:</span> <span class="n">kTest</span> <span class="c1"># filter this layer for creating test net</span> +<span class="p">}</span> +</pre></div> +</div> +</div> +<div class="section" id="neural-net-partitioning"> +<h2>Neural net partitioning<a class="headerlink" href="#neural-net-partitioning" title="Permalink to this headline">¶</a></h2> +<p>A neural net can be partitioned in different ways to distribute the training +over multiple workers.</p> +<div class="section" id="batch-and-feature-dimension"> +<h3>Batch and feature dimension<a class="headerlink" href="#batch-and-feature-dimension" title="Permalink to this headline">¶</a></h3> +<img src="../_static/images/partition_fc.png" align="center" width="400px"/> +<span><strong>Figure 4 - Partitioning of a fully connected layer.</strong></span><p>Every layerâs feature blob is considered a matrix whose rows are feature +vectors. Thus, one layer can be split on two dimensions. Partitioning on +dimension 0 (also called batch dimension) slices the feature matrix by rows. +For instance, if the mini-batch size is 256 and the layer is partitioned into 2 +sub-layers, each sub-layer would have 128 feature vectors in its feature blob. +Partitioning on this dimension has no effect on the parameters, as every +<a class="reference external" href="param.html">Param</a> object is replicated in the sub-layers. Partitioning on dimension +1 (also called feature dimension) slices the feature matrix by columns. For +example, suppose the original feature vector has 50 units, after partitioning +into 2 sub-layers, each sub-layer would have 25 units. This partitioning may +result in <a class="reference external" href="param.html">Param</a> object being split, as shown in +Figure 4. Both the bias vector and weight matrix are +partitioned into two sub-layers.</p> +</div> +<div class="section" id="partitioning-configuration"> +<h3>Partitioning configuration<a class="headerlink" href="#partitioning-configuration" title="Permalink to this headline">¶</a></h3> +<p>There are 4 partitioning schemes, whose configurations are give below,</p> +<ol> +<li><p class="first">Partitioning each singe layer into sub-layers on batch dimension (see +below). It is enabled by configuring the partition dimension of the layer to +0, e.g.,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="c1"># with other fields omitted</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">partition_dim</span><span class="p">:</span> <span class="mi">0</span> + <span class="p">}</span> +</pre></div> +</div> +</li> +<li><p class="first">Partitioning each singe layer into sub-layers on feature dimension (see +below). It is enabled by configuring the partition dimension of the layer to +1, e.g.,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="c1"># with other fields omitted</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">partition_dim</span><span class="p">:</span> <span class="mi">1</span> + <span class="p">}</span> +</pre></div> +</div> +</li> +<li><p class="first">Partitioning all layers into different subsets. It is enabled by +configuring the location ID of a layer, e.g.,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="c1"># with other fields omitted</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">1</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">0</span> + <span class="p">}</span> +</pre></div> +</div> +</li> +<li><p class="first">Hybrid partitioning of strategy 1, 2 and 3. The hybrid partitioning is +useful for large models. An example application is to implement the +<a class="reference external" href="http://arxiv.org/abs/1404.5997";>idea proposed by Alex</a>. +Hybrid partitioning is configured like,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="c1"># with other fields omitted</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">1</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">0</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">partition_dim</span><span class="p">:</span> <span class="mi">0</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">0</span> + <span class="p">}</span> + <span class="n">layer</span> <span class="p">{</span> + <span class="n">partition_dim</span><span class="p">:</span> <span class="mi">1</span> + <span class="n">location</span><span class="p">:</span> <span class="mi">0</span> + <span class="p">}</span> +</pre></div> +</div> +</li> +</ol> +<p>Currently SINGA supports strategy-2 well. Other partitioning strategies are +are under test and will be released in later version.</p> +</div> +</div> +<div class="section" id="parameter-sharing"> +<h2>Parameter sharing<a class="headerlink" href="#parameter-sharing" title="Permalink to this headline">¶</a></h2> +<p>Parameters can be shared in two cases,</p> +<ul class="simple"> +<li>sharing parameters among layers via user configuration. For example, the +visible layer and hidden layer of a RBM shares the weight matrix, which is configured through +the <code class="docutils literal notranslate"><span class="pre">share_from</span></code> field as shown in the above RBM configuration. The +configurations must be the same (except name) for shared parameters.</li> +<li>due to neural net partitioning, some <code class="docutils literal notranslate"><span class="pre">Param</span></code> objects are replicated into +different workers, e.g., partitioning one layer on batch dimension. These +workers share parameter values. SINGA controls this kind of parameter +sharing automatically, users do not need to do any configuration.</li> +<li>the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> for training and testing (and validation) share most layers +, thus share <code class="docutils literal notranslate"><span class="pre">Param</span></code> values.</li> +</ul> +<p>If the shared <code class="docutils literal notranslate"><span class="pre">Param</span></code> instances resident in the same process (may in different +threads), they use the same chunk of memory space for their values. But they +would have different memory spaces for their gradients. In fact, their +gradients will be averaged by the stub or server.</p> +</div> +<div class="section" id="advanced-user-guide"> +<h2>Advanced user guide<a class="headerlink" href="#advanced-user-guide" title="Permalink to this headline">¶</a></h2> +<div class="section" id="creation"> +<h3>Creation<a class="headerlink" href="#creation" title="Permalink to this headline">¶</a></h3> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">static</span> <span class="n">NeuralNet</span><span class="o">*</span> <span class="n">NeuralNet</span><span class="p">::</span><span class="n">Create</span><span class="p">(</span><span class="n">const</span> <span class="n">NetProto</span><span class="o">&</span> <span class="n">np</span><span class="p">,</span> <span class="n">Phase</span> <span class="n">phase</span><span class="p">,</span> <span class="nb">int</span> <span class="n">num</span><span class="p">);</span> +</pre></div> +</div> +<p>The above function creates a <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> for a given phase, and returns a +pointer to the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> instance. The phase is in {kTrain, +kValidation, kTest}. <code class="docutils literal notranslate"><span class="pre">num</span></code> is used for net partitioning which indicates the +number of partitions. Typically, a training job includes three neural nets for +training, validation and test phase respectively. The three neural nets share most +layers except the data layer, loss layer or output layer, etc.. The <code class="docutils literal notranslate"><span class="pre">Create</span></code> +function takes in the full net configuration including layers for training, +validation and test. It removes layers for phases other than the specified +phase based on the <code class="docutils literal notranslate"><span class="pre">exclude</span></code> field in +<a class="reference external" href="layer.html">layer configuration</a>:</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">layer</span> <span class="p">{</span> + <span class="o">...</span> + <span class="n">exclude</span> <span class="p">:</span> <span class="n">kTest</span> <span class="c1"># filter this layer for creating test net</span> +<span class="p">}</span> +</pre></div> +</div> +<p>The filtered net configuration is passed to the constructor of <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code>:</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">NeuralNet</span><span class="p">::</span><span class="n">NeuralNet</span><span class="p">(</span><span class="n">NetProto</span> <span class="n">netproto</span><span class="p">,</span> <span class="nb">int</span> <span class="n">npartitions</span><span class="p">);</span> +</pre></div> +</div> +<p>The constructor creates a graph representing the net structure firstly in</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Graph</span><span class="o">*</span> <span class="n">NeuralNet</span><span class="p">::</span><span class="n">CreateGraph</span><span class="p">(</span><span class="n">const</span> <span class="n">NetProto</span><span class="o">&</span> <span class="n">netproto</span><span class="p">,</span> <span class="nb">int</span> <span class="n">npartitions</span><span class="p">);</span> +</pre></div> +</div> +<p>Next, it creates a layer for each node and connects layers if their nodes are +connected.</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">void</span> <span class="n">NeuralNet</span><span class="p">::</span><span class="n">CreateNetFromGraph</span><span class="p">(</span><span class="n">Graph</span><span class="o">*</span> <span class="n">graph</span><span class="p">,</span> <span class="nb">int</span> <span class="n">npartitions</span><span class="p">);</span> +</pre></div> +</div> +<p>Since the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> instance may be shared among multiple workers, the +<code class="docutils literal notranslate"><span class="pre">Create</span></code> function returns a pointer to the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> instance .</p> +</div> +<div class="section" id="id1"> +<h3>Parameter sharing<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3> +<p><code class="docutils literal notranslate"><span class="pre">Param</span></code> sharing +is enabled by first sharing the Param configuration (in <code class="docutils literal notranslate"><span class="pre">NeuralNet::Create</span></code>) +to create two similar (e.g., the same shape) Param objects, and then calling +(in <code class="docutils literal notranslate"><span class="pre">NeuralNet::CreateNetFromGraph</span></code>),</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">void</span> <span class="n">Param</span><span class="p">::</span><span class="n">ShareFrom</span><span class="p">(</span><span class="n">const</span> <span class="n">Param</span><span class="o">&</span> <span class="n">from</span><span class="p">);</span> +</pre></div> +</div> +<p>It is also possible to share <code class="docutils literal notranslate"><span class="pre">Param</span></code>s of two nets, e.g., sharing parameters of +the training net and the test net,</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">void</span> <span class="n">NeuralNet</span><span class="p">:</span><span class="n">ShareParamsFrom</span><span class="p">(</span><span class="n">NeuralNet</span><span class="o">*</span> <span class="n">other</span><span class="p">);</span> +</pre></div> +</div> +<p>It will call <code class="docutils literal notranslate"><span class="pre">Param::ShareFrom</span></code> for each Param object.</p> +</div> +<div class="section" id="access-functions"> +<h3>Access functions<a class="headerlink" href="#access-functions" title="Permalink to this headline">¶</a></h3> +<p><code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> provides a couple of access function to get the layers and params +of the net:</p> +<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">const</span> <span class="n">std</span><span class="p">::</span><span class="n">vector</span><span class="o"><</span><span class="n">Layer</span><span class="o">*>&</span> <span class="n">layers</span><span class="p">()</span> <span class="n">const</span><span class="p">;</span> +<span class="n">const</span> <span class="n">std</span><span class="p">::</span><span class="n">vector</span><span class="o"><</span><span class="n">Param</span><span class="o">*>&</span> <span class="n">params</span><span class="p">()</span> <span class="n">const</span> <span class="p">;</span> +<span class="n">Layer</span><span class="o">*</span> <span class="n">name2layer</span><span class="p">(</span><span class="n">string</span> <span class="n">name</span><span class="p">)</span> <span class="n">const</span><span class="p">;</span> +<span class="n">Param</span><span class="o">*</span> <span class="n">paramid2param</span><span class="p">(</span><span class="nb">int</span> <span class="nb">id</span><span class="p">)</span> <span class="n">const</span><span class="p">;</span> +</pre></div> +</div> +</div> +<div class="section" id="partitioning"> +<h3>Partitioning<a class="headerlink" href="#partitioning" title="Permalink to this headline">¶</a></h3> +<div class="section" id="implementation"> +<h4>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline">¶</a></h4> +<p>SINGA partitions the neural net in <code class="docutils literal notranslate"><span class="pre">CreateGraph</span></code> function, which creates one +node for each (partitioned) layer. For example, if one layerâs partition +dimension is 0 or 1, then it creates <code class="docutils literal notranslate"><span class="pre">npartition</span></code> nodes for it; if the +partition dimension is -1, a single node is created, i.e., no partitioning. +Each node is assigned a partition (or location) ID. If the original layer is +configured with a location ID, then the ID is assigned to each newly created node. +These nodes are connected according to the connections of the original layers. +Some connection layers will be added automatically. +For instance, if two connected sub-layers are located at two +different workers, then a pair of bridge layers is inserted to transfer the +feature (and gradient) blob between them. When two layers are partitioned on +different dimensions, a concatenation layer which concatenates feature rows (or +columns) and a slice layer which slices feature rows (or columns) would be +inserted. These connection layers help making the network communication and +synchronization transparent to the users.</p> +</div> +<div class="section" id="dispatching-partitions-to-workers"> +<h4>Dispatching partitions to workers<a class="headerlink" href="#dispatching-partitions-to-workers" title="Permalink to this headline">¶</a></h4> +<p>Each (partitioned) layer is assigned a location ID, based on which it is dispatched to one +worker. Particularly, the pointer to the <code class="docutils literal notranslate"><span class="pre">NeuralNet</span></code> instance is passed +to every worker within the same group, but each worker only computes over the +layers that have the same partition (or location) ID as the workerâs ID. When +every worker computes the gradients of the entire model parameters +(strategy-2), we refer to this process as data parallelism. When different +workers compute the gradients of different parameters (strategy-3 or +strategy-1), we call this process model parallelism. The hybrid partitioning +leads to hybrid parallelism where some workers compute the gradients of the +same subset of model parameters while other workers compute on different model +parameters. For example, to implement the hybrid parallelism in for the +<a class="reference external" href="http://arxiv.org/abs/1404.5997";>DCNN model</a>, we set <code class="docutils literal notranslate"><span class="pre">partition_dim</span> <span class="pre">=</span> <span class="pre">0</span></code> for +lower layers and <code class="docutils literal notranslate"><span class="pre">partition_dim</span> <span class="pre">=</span> <span class="pre">1</span></code> for higher layers.</p> +</div> +</div> +</div> +</div> + + + </div> + + </div> + <footer> + + + <hr/> + + <div role="contentinfo"> + <p> + © Copyright 2019 The Apache Software Foundation. All rights reserved. Apache SINGA, Apache, the Apache feather logo, and the Apache SINGA project logos are trademarks of The Apache Software Foundation. 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See the License for the + specific language governing permissions and limitations + under the License. +--><p>These are some examples in IPython notebooks.</p> +<p>You can open them in <a class="reference external" href="http://nbviewer.jupyter.org/github/apache/incubator-singa/blob/master/doc/en/docs/notebook/index.ipynb";>notebook viewer</a>.</p> + + + </div> + + </div> + <footer> + + + <hr/> + + <div role="contentinfo"> + <p> + © Copyright 2019 The Apache Software Foundation. All rights reserved. Apache SINGA, Apache, the Apache feather logo, and the Apache SINGA project logos are trademarks of The Apache Software Foundation. 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href="http://singa.apache.org/v0.3.0/";>0.3</a></dd> + <dd><a href="http://singa.apache.org/v1.1.0/";>1.1</a></dd> + </dl> + + </div> + <a href="http://incubator.apache.org/";> <img src= "../_static/apache.png" style="background-color:white;"> </a> + + <a href="https://github.com/apache/incubator-singa"; class="fa fa-github" style="padding: 10px; font-size: 20px; width: 30px; text-align: center; text-decoration: none; margin: 5px 2px;"></a> + <a href="https://aws.amazon.com/marketplace/seller-profile?id=5bcac385-12c4-4802-aec7-351e09b77b4c"; class="fab fa-aws" style="padding: 10px; font-size: 20px; width: 30px; text-align: center; text-decoration: none; margin: 5px 2px;"></a> + <a href="https://hub.docker.com/r/apache/singa/"; class="fab fa-docker" style="padding: 10px; font-size: 20px; width: 30px; text-align: center; text-decoration: none; margin: 5px 2px;"></a> + <a href="https://www.linkedin.com/groups/13550034"; class="fa fa-linkedin" style="padding: 10px; font-size: 20px; width: 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