Radio Buttons inside a nested for each loop of html doesn't check

Question

I have multiple for loops and each are being bind with relevant list of items. Example: Layer. revision. exposure. and each of these are repeated n number of times and they are looped in following way

self.exposureArray = ko.observable("Combined");
    self.current_litho_layer_definition.subscribe(function(new_def) {
      if (!new_def) return;

      self.is_fetching(true);
      self.message_for_fetching("Fetching layer: " + new_def.layer_name + " ...");
      $.ajax('webapi/layer/arrays/'+new_def.layer_definition_sk, {
        dataType: 'json',
        data: {expose_array_names: self.exposureArray},
        success: function(arrs) {
          self.current_litho_exposure_arrays(arrs);
        },
        complete: function() {
          self.is_fetching(false);
          self.message_for_fetching("");
        }
      });
    });

<script src="https://cdnjs.cloudflare.com/ajax/libs/knockout/2.0.0/knockout-min.js"></script>
<div style="position:absolute;top:600px">
    <h4>Litho Layers</h4>
    <hr class="no-margin"/>
    <!-- ko foreach: litho_layer_name_selected_definitions -->
      <div class="well pull-left clearfix " style="height:200px;margin:5px;width:90px;padding:5px;" data-bind="click: $root.select_litho_layer_definition, css: {'background-highlight': $root.current_litho_layer_definition() === $data}">
        <p class="text-center tight-padding no-margin"><strong data-bind="text: layer_name"></strong></p>
        <div class="btn-group" style="width:90px">
          <button class="btn btn-mini dropdown-toggle" data-toggle="dropdown" style="width:90px">
            <span data-bind="text: 'Rev.' + revision"></span>
            <span class="caret"></span>
          </button>
          <ul class="dropdown-menu small-list" data-bind="foreach: $root.litho_layer_name_definitions()[_.indexOf($root.litho_layer_names(), layer_name)]" style="width:90px">
            <li><a data-bind="text: 'Rev.' + revision, click: $root.litho_layer_name_select_revision"></a></li>
          </ul>
        </div>
        <!-- ko foreach: exposure_array_names -->    
       <input type="radio" name="layer_name" value ="$root.exposureArray" id="$root.createId"
                data-bind="click: $root.select_litho_layer_definition,
                checkedValue:$data,
                uniqueName: true,
                checked:$root.exposureArray" />
                
                <span data-bind="text: $data"></span><br>
            
                
        <!-- /ko -->
      </div>