    // Copyright (C) 2015  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #undef DLIB_DNn_CORE_ABSTRACT_H_
    #ifdef DLIB_DNn_CORE_ABSTRACT_H_

    #include "../cuda/tensor_abstract.h"
    #include <memory>
    #include <type_traits>
    #include <tuple>
    #include <vector>
    #include "../rand.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        template <
            typename... T
            >
        auto tuple_tail(
            const std::tuple<T...>& item
        );
        /*!
            ensures
                - returns a tuple that contains everything in item except for tuple_head(item).
                  The items will be in the same order as they are in item, just without
                  tuple_head(item).
                - This function will correctly handle nested tuples.
        !*/

        template <typename... T>
        auto tuple_head (
            const std::tuple<T...>& item
        );
        /*!
            ensures
                - returns a copy of the first thing in the tuple that isn't a std::tuple.
                  Essentially, this function calls std::get<0>() recursively on item until
                  a non-std::tuple object is found.
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        double get_learning_rate_multiplier(
            const T& obj
        );
        /*!
            ensures
                - if (obj has a get_learning_rate_multiplier() member function) then
                    - returns obj.get_learning_rate_multiplier()
                - else
                    - returns 1
        !*/

        template <typename T>
        void set_learning_rate_multiplier(
            T& obj,
            double learning_rate_multiplier
        );
        /*!
            requires
                - learning_rate_multiplier >= 0
            ensures
                - if (obj has a set_learning_rate_multiplier() member function) then
                    - calls obj.set_learning_rate_multiplier(learning_rate_multiplier)
                - else
                    - does nothing
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        double get_bias_learning_rate_multiplier(
            const T& obj
        );
        /*!
            ensures
                - if (obj has a get_bias_learning_rate_multiplier() member function) then
                    - returns obj.get_bias_learning_rate_multiplier()
                - else
                    - returns 1
        !*/

        template <typename T>
        void set_bias_learning_rate_multiplier(
            T& obj,
            double bias_learning_rate_multiplier
        );
        /*!
            requires
                - bias_learning_rate_multiplier >= 0
            ensures
                - if (obj has a set_bias_learning_rate_multiplier() member function) then
                    - calls obj.set_bias_learning_rate_multiplier(bias_learning_rate_multiplier)
                - else
                    - does nothing
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        double get_weight_decay_multiplier(
            const T& obj
        );
        /*!
            ensures
                - if (obj has a get_weight_decay_multiplier() member function) then
                    - returns obj.get_weight_decay_multiplier()
                - else
                    - returns 1
        !*/

        template <typename T>
        void set_weight_decay_multiplier(
            T& obj,
            double weight_decay_multiplier
        );
        /*!
            requires
                - weight_decay_multiplier >= 0
            ensures
                - if (obj has a set_weight_decay_multiplier() member function) then
                    - calls obj.set_weight_decay_multiplier(weight_decay_multiplier)
                - else
                    - does nothing
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        double get_bias_weight_decay_multiplier(
            const T& obj
        );
        /*!
            ensures
                - if (obj has a get_bias_weight_decay_multiplier() member function) then
                    - returns obj.get_bias_weight_decay_multiplier()
                - else
                    - returns 1
        !*/

        template <typename T>
        void set_bias_weight_decay_multiplier(
            T& obj,
            double bias_weight_decay_multiplier
        );
        /*!
            requires:
                - bias_weight_decay_multiplier >= 0
            ensures
                - if (obj has a set_bias_weight_decay_multiplier() member function) then
                    - calls obj.set_bias_weight_decay_multiplier(bias_weight_decay_multiplier)
                - else
                    - does nothing
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        void disable_bias(
            T& obj
        );
        /*!
            ensures
                - if (obj has a disable_bias() member function) then
                    - calls obj.disable_bias()
                - else
                    - does nothing
        !*/

    // ----------------------------------------------------------------------------------------

        bool dnn_prefer_fastest_algorithms(
        );
        /*!
            ensures
                - If dlib should prefer to use fast algorithms rather than ones that use less
                  RAM then this function returns true and false otherwise.
                - On program startup this function will default to true.
        !*/

        void set_dnn_prefer_fastest_algorithms(
        );
        /*!
            ensures
                - #dnn_prefer_fastest_algorithms() == true
        !*/

        void set_dnn_prefer_smallest_algorithms(
        );
        /*!
            ensures
                - #dnn_prefer_fastest_algorithms() == false
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        class sstack
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a basic stack of T objects.  It contains no data itself but simply
                    points to a memory range of T object and allows you to access that block of
                    T objects as a stack.
            !*/

        public:
            typedef T value_type;

            sstack() = delete;

            sstack (
                T* data,
                size_t s
            );
            /*!
                ensures
                    - #size() == s
                    - #top() == *data
                    - #pop(i).top() == data[i]
            !*/

            const T& top(
            ) const;
            /*!
                requires
                    - size() != 0
                ensures
                    - returns the top element of the stack.
            !*/

            T& top(
            );
            /*!
                requires
                    - size() != 0
                ensures
                    - returns the top element of the stack.
            !*/

            size_t size(
            ) const;
            /*!
                ensures
                    - returns the number of elements in this stack.
            !*/

            sstack pop(
                size_t num = 1
            );
            /*!
                requires
                    - num <= size()
                ensures
                    - returns a reference to the sub-stack S such that:
                        - S.size() == size()-num.
                        - S.top() is num elements down the stack.
            !*/
        };

        template <
            typename T
            >
        sstack<T> make_sstack(
            std::vector<T>& item
        ) { return sstack<T>(item.data(), item.size()); }
        /*!
            ensures
                - returns a sstack that sits on top of the given std::vector.
        !*/

    // ----------------------------------------------------------------------------------------

        enum class zero_gradients : uint8_t
        {
            no,
            yes
        };

    // ----------------------------------------------------------------------------------------

        template <
            typename LAYER_DETAILS,
            typename SUBNET
            >
        class add_layer
        {
            /*!
                REQUIREMENTS ON LAYER_DETAILS
                    - Must be a type that implements the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                      defined in layers_abstract.h

                REQUIREMENTS ON SUBNET
                    - One of the following must be true:
                        - SUBNET implements the EXAMPLE_INPUT_LAYER interface defined in
                          input_abstract.h.
                        - SUBNET is an add_layer object.
                        - SUBNET is an add_tag_layer object.
                        - SUBNET is an add_skip_layer object.
                        - SUBNET is a repeat object.

                WHAT THIS OBJECT REPRESENTS
                    This object represents a deep neural network.  In particular, it is a tool
                    for adding another layer on top of the neural network of type SUBNET, which
                    is specified as a template argument.  The specific layer added is defined
                    by the LAYER_DETAILS details template argument.
            !*/

        public:
            typedef LAYER_DETAILS layer_details_type;
            typedef SUBNET subnet_type;
            typedef typename subnet_type::input_type input_type;
            typedef typename subnet_type::input_layer_type input_layer_type;
            // num_computational_layers will always give the number of layers in the network
            // that transform tensors (i.e. layers defined by something that implements the
            // EXAMPLE_COMPUTATIONAL_LAYER_ interface).  This is all the layers except for
            // loss, tag, and skip layers.
            const static size_t num_computational_layers = subnet_type::num_computational_layers + 1;
            // num_layers counts all the layers in the network regardless of their type.
            const static size_t num_layers = subnet_type::num_layers + 1;

            add_layer(
            );
            /*!
                ensures
                    - default constructs all the layers in this network.
                    - #sample_expansion_factor() == 0
            !*/

            add_layer(const add_layer&) = default;
            add_layer(add_layer&&) = default;
            add_layer& operator=(add_layer&&) = default;
            add_layer& operator=(const add_layer&) = default;
            /*!
                ensures
                    - this object is copyable and movable.
            !*/

            template <typename T, typename U>
            add_layer(
                const add_layer<T,U>& item
            );
            /*!
                ensures
                    - This constructor allows you to copy neural network objects from one to
                      another as long as their corresponding layers can be constructed from
                      each other.
                    - #layer_details() == layer_details_type(item.layer_details())
                    - #subnet()        == subnet_type(item.subnet())
                    - #sample_expansion_factor() == item.sample_expansion_factor()
            !*/

            template <typename ...T, typename LD, typename ...U>
            add_layer(
                const std::tuple<LD,U...>& layer_det,
                T&& ...args
            );
            /*!
                ensures
                    - #layer_details() == layer_details_type(tuple_head(layer_det))
                    - #subnet()        == subnet_type(tuple_tail(layer_det),args)
                    - #sample_expansion_factor() == 0
            !*/

            template <typename ...T>
            add_layer(
                const layer_details_type& layer_det,
                T&& ...args
            );
            /*!
                ensures
                    - #layer_details() == layer_details_type(layer_det)
                    - #subnet()        == subnet_type(args)
                    - #sample_expansion_factor() == 0
            !*/

            template <typename ...T>
            add_layer(
                T&& ...args
            );
            /*!
                ensures
                    - This version of the constructor is only called if layer_details_type
                      can't be constructed from the first thing in args.  In this case, the
                      args are simply passed on to the sub layers in their entirety.
                    - #layer_details() == layer_details_type()
                    - #subnet()        == subnet_type(args)
                    - #sample_expansion_factor() == 0
            !*/

            template <typename ...T>
            add_layer(
                layer_details_type&& layer_det,
                T&& ...args
            );
            /*!
                ensures
                    - #layer_details() == layer_det
                    - #subnet()        == subnet_type(args)
                    - #sample_expansion_factor() == 0
            !*/

            template <typename forward_iterator>
            void to_tensor (
                forward_iterator ibegin,
                forward_iterator iend,
                resizable_tensor& data
            ) const;
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                ensures
                    - Converts the iterator range into a tensor and stores it into #data.
                    - #data.num_samples()%distance(ibegin,iend) == 0.
                    - #sample_expansion_factor() == #data.num_samples()/distance(ibegin,iend).
                    - #sample_expansion_factor() > 0
                    - The data in the ith sample of #data corresponds to the input_type object
                      *(ibegin+i/#sample_expansion_factor()).
                    - Invokes data.async_copy_to_device() so that the data begins transferring
                      to the GPU device, if present.
                    - This function is implemented by calling the to_tensor() routine defined
                      at the input layer of this network.
            !*/

            unsigned int sample_expansion_factor (
            ) const;
            /*!
                ensures
                    - When to_tensor() is invoked on this network's input layer it converts N
                      input objects into M samples, all stored inside a resizable_tensor.  It
                      is always the case that M is some integer multiple of N.
                      sample_expansion_factor() returns the value of this multiplier.  To be
                      very specific, it is always true that M==I*N where I is some integer.
                      This integer I is what is returned by sample_expansion_factor().
            !*/

            const subnet_type& subnet(
            ) const;
            /*!
                ensures
                    - returns the immediate subnetwork of *this network.
            !*/

            subnet_type& subnet(
            );
            /*!
                ensures
                    - returns the immediate subnetwork of *this network.
            !*/

            const input_layer_type& input_layer(
            ) const;
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

            input_layer_type& input_layer(
            );
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

            const layer_details_type& layer_details(
            ) const;
            /*!
                ensures
                    - returns the layer_details_type instance that defines the behavior of the
                      layer at the top of this network.  I.e. returns the layer details that
                      defines the behavior of the layer nearest to the network output rather
                      than the input layer.
            !*/

            layer_details_type& layer_details(
            );
            /*!
                ensures
                    - returns the layer_details_type instance that defines the behavior of the
                      layer at the top of this network.  I.e. returns the layer details that
                      defines the behavior of the layer nearest to the network output rather
                      than the input layer.
            !*/

            template <typename forward_iterator>
            const tensor& operator() (
                forward_iterator ibegin,
                forward_iterator iend
            );
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                ensures
                    - runs [ibegin,iend) through the network and returns the results.
                      In particular, this function performs:
                        to_tensor(ibegin,iend,temp_tensor);
                        return forward(temp_tensor);
                    - The return value from this function is also available in #get_output().
                      i.e. this function returns #get_output().
                    - have_same_dimensions(#get_gradient_input(), #get_output()) == true.
                    - All elements of #get_gradient_input() are set to 0.
                      i.e. calling this function clears out #get_gradient_input() and ensures
                      it has the same dimensions as the most recent output.
            !*/

            const tensor& operator() (
                const input_type& x
            );
            /*!
                ensures
                    - runs a single x through the network and returns the output.
                      I.e. returns (*this)(&x, &x+1);
            !*/

            const tensor& forward(
                const tensor& x
            );
            /*!
                requires
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                ensures
                    - Runs x through the network and returns the results.  In particular, this
                      function performs the equivalent of:
                        subnet().forward(x);
                        if (this is the first time forward() has been called) then
                            layer_details().setup(subnet());
                        layer_details().forward(subnet(), get_output());
                    - The return value from this function is also available in #get_output().
                      i.e. this function returns #get_output().
                    - have_same_dimensions(#get_gradient_input(), #get_output()) == true
                    - All elements of #get_gradient_input() are set to 0.
                      i.e. calling this function clears out #get_gradient_input() and ensures
                      it has the same dimensions as the most recent output.
            !*/

            const tensor& get_output(
            ) const;
            /*!
                ensures
                    - returns the output for the last tensor that was run through the network.
                      If nothing has been run through the network yet then returns an empty
                      tensor.
            !*/

            tensor& get_gradient_input(
            );
            /*!
                ensures
                    - returns the error gradient for this network.  That is, this is the error
                      gradient that this network will use to compute parameter gradients when
                      back_propagate_error() is called.  Therefore, when performing back
                      propagation, layers that sit on top of this network layer write their
                      back-propagated error gradients into get_gradient_input().  Or to put it
                      another way, during back-propagation, layers take the contents of their
                      get_gradient_input() and back-propagate it through themselves and store
                      the result into their subnetwork's get_gradient_input().

                      This means you should consider get_gradient_input() as an input to the
                      back_propagate_error() method.
            !*/

            const tensor& get_final_data_gradient(
            ) const;
            /*!
                ensures
                    - if back_propagate_error() has been called to back-propagate a gradient
                      through this network then you can call get_final_data_gradient() to
                      obtain the last data gradient computed.  That is, this function returns
                      the gradient of the network with respect to its inputs.
                    - Note that there is only one "final data gradient" for an entire network,
                      not one per layer, since there is only one input to the entire network.
            !*/

            const tensor& get_parameter_gradient(
            ) const;
            /*!
                ensures
                    - if back_propagate_error() has been called then you can call
                      get_parameter_gradient() to find the gradient of this layer's parameters.
                      When we update the parameters by calling update_parameters(), it will use
                      the gradient in get_parameter_gradient() to perform the update.
                      Therefore, you should consider get_parameter_gradient() as an input to
                      update_parameters().
            !*/

            tensor& get_parameter_gradient (
            );
            /*!
                ensures
                    - returns a non-const reference to the tensor returned by the above
                      get_parameter_gradient() method.  You could use this method to modify the
                      parameter gradient in some way before invoking update_parameters().
            !*/

            void back_propagate_error(
                const tensor& x,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - forward(x) was called to forward propagate x though the network.
                      Moreover, this was the most recent call to forward() and x has not been
                      subsequently modified in any way.
                    - get_gradient_input() has been set equal to the gradient of this network's
                      output with respect to some loss function.
                ensures
                    - Back propagates the error gradient, get_gradient_input(), through this
                      network and computes parameter and data gradients, via backpropagation.
                      Specifically, this function populates get_final_data_gradient() and also,
                      for each layer, the tensor returned by get_parameter_gradient().
                    - All elements of #get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - have_same_dimensions(#get_final_data_gradient(), x) == true.
                    - have_same_dimensions(#get_parameter_gradient(), layer_details().get_layer_params()) == true.
                    - #get_final_data_gradient() contains the gradient of the network with
                      respect to x.
            !*/

            void back_propagate_error(
                const tensor& x,
                const tensor& gradient_input,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - forward(x) was called to forward propagate x though the network.
                      Moreover, this was the most recent call to forward() and x has not been
                      subsequently modified in any way.
                    - have_same_dimensions(gradient_input, get_output()) == true
                ensures
                    - This function is identical to the version of back_propagate_error()
                      defined immediately above except that it back-propagates gradient_input
                      through the network instead of get_gradient_input().  Therefore, this
                      version of back_propagate_error() is equivalent to performing:
                        get_gradient_input() = gradient_input;
                        back_propagate_error(x);
                      Except that calling back_propagate_error(x,gradient_input) avoids the
                      copy and is therefore slightly more efficient.
                    - All elements of #get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - have_same_dimensions(#get_final_data_gradient(), x) == true.
                    - have_same_dimensions(#get_parameter_gradient(), layer_details().get_layer_params()) == true.
                    - #get_final_data_gradient() contains the gradient of the network with
                      respect to x.
            !*/

            template <typename solver_type>
            void update_parameters(
                sstack<solver_type> solvers,
                double learning_rate
            );
            /*!
                requires
                    - solver_type is an implementation of the EXAMPLE_SOLVER interface defined
                      in solvers_abstract.h
                    - back_propagate_error() has been called.
                    - The given solvers have only ever been used with this network.  That is,
                      if you want to call update_parameters() on some other neural network
                      object then you must NOT reuse the same solvers object.
                    - solvers.size() >= num_computational_layers
                    - 0 < learning_rate <= 1
                ensures
                    - Updates all the parameters in the network.  In particular, we pass each
                      layer's parameter gradient (i.e. the tensor returned by the layer's
                      get_parameter_gradient() member) through that layer's corresponding
                      solver object.  This produces a parameter delta vector which we add to
                      the layer's parameters.
                    - The solvers use the given learning rate.
            !*/

            template <typename solver_type>
            void update_parameters(std::vector<solver_type>& solvers, double learning_rate)
            { update_parameters(make_sstack(solvers), learning_rate); }
            /*!
                Convenience method for calling update_parameters()
            !*/

            void set_gradient_inputs_to_zero(
            );
            /*!
                ensures
                    - Sets all elements in all gradient inputs in the network to 0.
                      That is, for each layer, we will have:
                        - get_gradient_input() == 0
                    - Note that You only need to call this method if you manually called either
                        - back_propagate_error
                        - compute_parameter_gradients
                      with the zero_grads parameter set to zero_gradients::no.
                    - invokes subnet().set_gradient_inputs_to_zero()
            !*/

            void clean(
            );
            /*!
                ensures
                    - Causes the network to forget about everything but its parameters.
                      That is, for each layer we will have:
                        - get_output().num_samples() == 0
                        - get_gradient_input().num_samples() == 0
                      However, running new input data though this network will still produce
                      the same output it would have produced regardless of any calls to
                      clean().  The purpose of clean() is to compact the network object prior
                      to saving it to disk so that it takes up less space and the IO is
                      quicker.
                    - This also calls the .clean() method on any layer details objects that
                      define a .clean() method.
            !*/

        };

        template <typename T, typename U>
        std::ostream& operator<<(std::ostream& out, const add_layer<T,U>& item);
        /*!
            prints the network architecture to the given output stream.
        !*/

        template <typename T, typename U>
        void serialize(const add_layer<T,U>& item, std::ostream& out);
        template <typename T, typename U>
        void deserialize(add_layer<T,U>& item, std::istream& in);
        /*!
            provides serialization support
        !*/

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        class no_label_type;

        template <
            typename LOSS_DETAILS,
            typename SUBNET
            >
        class add_loss_layer
        {
            /*!
                REQUIREMENTS ON LOSS_DETAILS
                    - Must be a type that implements the EXAMPLE_LOSS_LAYER_ interface defined
                      in loss_abstract.h

                REQUIREMENTS ON SUBNET
                    - One of the following must be true:
                        - SUBNET is an add_layer object.
                        - SUBNET is an add_tag_layer object.
                        - SUBNET is an add_skip_layer object.
                        - SUBNET is a repeat object.

                WHAT THIS OBJECT REPRESENTS
                    This object represents a deep neural network.  In particular, it is a tool
                    for adding a loss layer on top of the neural network of type SUBNET, which
                    is specified as a template argument.  The specific layer added is defined
                    by the LOSS_DETAILS details template argument.  Importantly, a loss layer
                    is the last layer in a deep neural network.  So once it is added you can't
                    add any other layers of any type.
            !*/

        public:
            typedef LOSS_DETAILS loss_details_type;
            typedef SUBNET subnet_type;
            typedef typename subnet_type::input_type input_type;
            typedef typename subnet_type::input_layer_type input_layer_type;
            const static size_t num_computational_layers = subnet_type::num_computational_layers;
            const static size_t num_layers = subnet_type::num_layers + 1;
            // If LOSS_DETAILS is an unsupervised loss then training_label_type==no_label_type.
            // Otherwise it is defined as follows:
            typedef typename LOSS_DETAILS::training_label_type training_label_type;
            // Similarly, if LOSS_DETAILS doesn't provide any output conversion then
            // output_label_type==no_label_type.
            typedef typename LOSS_DETAILS::output_label_type output_label_type;

            add_loss_layer() = default;
            /*!
                ensures
                    - default constructs all the layers in this network.
            !*/

            add_loss_layer(const add_loss_layer&) = default;
            add_loss_layer(add_loss_layer&&) = default;
            add_loss_layer& operator=(add_loss_layer&&) = default;
            add_loss_layer& operator=(const add_loss_layer&) = default;
            /*!
                ensures
                    - this object is copyable and movable.
            !*/

            template <typename T, typename U>
            add_loss_layer(
                const add_loss_layer<T,U>& item
            );
            /*!
                ensures
                    - This constructor allows you to copy neural network objects from one to
                      another as long as their corresponding layers can be constructed from
                      each other.
                    - #loss_details() == loss_details_type(item.loss_details())
                    - #subnet()       == subnet_type(item.subnet())
            !*/

            template <typename ...T>
            add_loss_layer(
                const LOSS_DETAILS& layer_det,
                T&& ...args
            );
            /*!
                ensures
                    - #loss_details() == loss_details_type(layer_det)
                    - #subnet()       == subnet_type(args)
            !*/

            template <typename ...T>
            add_loss_layer(
                LOSS_DETAILS&& layer_det,
                T&& ...args
            );
            /*!
                ensures
                    - #loss_details() == loss_details_type(layer_det)
                    - #subnet()       == subnet_type(args)
            !*/

            template <typename ...T>
            add_loss_layer(
                T&& ...args
            );
            /*!
                ensures
                    - This version of the constructor is only called if loss_details_type can't
                      be constructed from the first thing in args.  In this case, the args are
                      simply passed on to the sub layers in their entirety.
                    - #loss_details() == loss_details_type()
                    - #subnet()       == subnet_type(args)
            !*/

            const subnet_type& subnet(
            ) const;
            /*!
                ensures
                    - returns the immediate subnetwork of *this network.
            !*/

            subnet_type& subnet(
            );
            /*!
                ensures
                    - returns the immediate subnetwork of *this network.
            !*/

            const input_layer_type& input_layer(
            ) const;
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

            input_layer_type& input_layer(
            );
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

            const loss_details_type& loss_details(
            ) const;
            /*!
                ensures
                    - returns the loss_details_type instance that defines the behavior of the
                      loss layer used by this network.
            !*/

            loss_details_type& loss_details(
            );
            /*!
                ensures
                    - returns the loss_details_type instance that defines the behavior of the
                      loss layer used by this network.
            !*/

            template <typename forward_iterator>
            void to_tensor (
                forward_iterator ibegin,
                forward_iterator iend,
                resizable_tensor& data
            ) const;
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                ensures
                    - Converts the iterator range into a tensor and stores it into #data.
                    - #data.num_samples()%distance(ibegin,iend) == 0.
                    - #sample_expansion_factor() == #data.num_samples()/distance(ibegin,iend).
                    - #sample_expansion_factor() > 0
                    - The data in the ith sample of #data corresponds to the input_type object
                      *(ibegin+i/sample_expansion_factor()).
                    - Invokes data.async_copy_to_device() so that the data begins transferring
                      to the GPU device, if present.
                    - This function is implemented by calling the to_tensor() routine defined
                      at the input layer of this network.
            !*/

            unsigned int sample_expansion_factor (
            ) const;
            /*!
                ensures
                    - When to_tensor() is invoked on this network's input layer it converts N
                      input objects into M samples, all stored inside a resizable_tensor.  It
                      is always the case that M is some integer multiple of N.
                      sample_expansion_factor() returns the value of this multiplier.  To be
                      very specific, it is always true that M==I*N where I is some integer.
                      This integer I is what is returned by sample_expansion_factor().
            !*/

        // -------------

            const tensor& forward(const tensor& x
            );
            /*!
                requires
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                ensures
                    - Runs x through the network and returns the results as a tensor.  In particular,
                      this function just performs:
                        return subnet().forward(x);
                      So if you want to get the outputs as an output_label_type then call one of the
                      methods below instead, like operator().
                    - The return value from this function is also available in #subnet().get_output().
                      i.e. this function returns #subnet().get_output().
                    - have_same_dimensions(#subnet().get_gradient_input(), #subnet().get_output()) == true
                    - All elements of #subnet().get_gradient_input() are set to 0.
                      i.e. calling this function clears out #subnet().get_gradient_input() and ensures
                      it has the same dimensions as the most recent output.
            !*/

            template <typename output_iterator>
            void operator() (
                const tensor& x,
                output_iterator obegin
            );
            /*!
                requires
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                    - obegin == iterator pointing to the start of a range of
                      x.num_samples()/sample_expansion_factor() output_label_type elements.
                ensures
                    - runs x through the network and writes the output to the range at obegin.
                    - loss_details().to_label() is used to write the network output into
                      obegin.
            !*/

            template <typename forward_iterator, typename label_iterator>
            void operator() (
                forward_iterator ibegin,
                forward_iterator iend,
                label_iterator obegin
            );
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                    - obegin == iterator pointing to the start of a range of
                      std::distance(ibegin,iend) output_label_type elements.
                ensures
                    - runs [ibegin,iend) through the network and writes the output to the range
                      at obegin.
                    - loss_details().to_label() is used to write the network output into
                      obegin.
            !*/

        // -------------

            const output_label_type& operator() (
                const input_type& x
            );
            /*!
                ensures
                    - runs a single object, x, through the network and returns the output.
                    - loss_details().to_label() is used to convert the network output into a
                      output_label_type.
            !*/

            template <typename iterable_type>
            std::vector<output_label_type> operator() (
                const iterable_type& data,
                size_t batch_size = 128
            );
            /*!
                requires
                    - batch_size > 0
                    - data must have a .begin() and .end() that supply iterators over a
                      sequence of input_type elements.  E.g. data could have a type of
                      std::vector<input_type>
                ensures
                    - runs all the objects in data through the network and returns their
                      predicted labels.  This means this function returns a vector V such that:
                        - V.size() == data.size()
                        - for all valid i: V[i] == the predicted label of data[i].
                    - Elements of data are run through the network in batches of batch_size
                      items.  Using a batch_size > 1 can be faster because it better exploits
                      the available hardware parallelism.
                    - loss_details().to_label() is used to convert the network output into a
                      output_label_type.
            !*/

            template <typename ...T>
            const output_label_type& process (
                const input_type& x,
                T&& ...args
            );
            /*!
                ensures
                    - This function is just like (*this)(x), i.e. it runs a single object, x,
                      through the network and returns the output.  But we additionally pass the
                      given args to loss_details().to_label() as the 4th argument (or more,
                      depending on how many things are in args) when converting the network
                      output to an output_label_type.  This is useful, for instance, with loss
                      layers like loss_mmod_ which has an optional adjust_threshold argument to
                      to_label() that adjusts the detection threshold.  Therefore, for such
                      networks you could call them like: net.process(some_image, -0.5), and -0.5
                      would be passed so the adjust_threshold argument of to_tensor().
            !*/

            template <typename iterable_type, typename ...T>
            std::vector<output_label_type> process_batch (
                const iterable_type& data,
                size_t batch_size,
                T&& ...args
            );
            /*!
                requires
                    - batch_size > 0
                    - data must have a .begin() and .end() that supply iterators over a
                      sequence of input_type elements.  E.g. data could have a type of
                      std::vector<input_type>
                ensures
                    - This function is just like (*this)(data,batch_size), i.e. it runs a
                      bunch of objects through the network and returns the outputs.  But we
                      additionally pass the given args to loss_details().to_label() as the 4th
                      argument (or more, depending on how many things are in args) when
                      converting the network output to output_label_types.  This is useful,
                      for instance, with loss layers like loss_mmod_ which has an optional
                      adjust_threshold argument to to_label() that adjusts the detection
                      threshold.  Therefore, for such networks you could call them like:
                      net.process_batch(std::vector<image_type>({some_image, another_image}), 128, -0.5),
                      and -0.5 would be passed so the adjust_threshold argument of to_tensor().
            !*/

        // -------------

            template <typename label_iterator>
            double compute_loss (
                const tensor& x,
                label_iterator lbegin
            );
            /*!
                requires
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                    - lbegin == iterator pointing to the start of a range of
                      x.num_samples()/sample_expansion_factor() training_label_type elements.
                ensures
                    - runs x through the network, compares the output to the expected output
                      pointed to by lbegin, and returns the resulting loss.
                    - for all valid k:
                        - the expected label of the kth sample in x is *(lbegin+k/sample_expansion_factor()).
                    - This function does not update the network parameters.
                    - For sub-layers that are immediate inputs into the loss layer, we also populate the
                      sub-layer's get_gradient_input() tensor with the gradient of the loss with respect
                      to the sub-layer's output.
            !*/

            template <typename forward_iterator, typename label_iterator>
            double compute_loss (
                forward_iterator ibegin,
                forward_iterator iend,
                label_iterator lbegin
            );
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                    - lbegin == iterator pointing to the start of a range of
                      std::distance(ibegin,iend) training_label_type elements.
                ensures
                    - runs [ibegin,iend) through the network, compares the output to the
                      expected output pointed to by lbegin, and returns the resulting loss.
                    - for all valid k:
                        - the expected label of *(ibegin+k) is *(lbegin+k).
                    - This function does not update the network parameters.
                    - For sub-layers that are immediate inputs into the loss layer, we also populate the
                      sub-layer's get_gradient_input() tensor with the gradient of the loss with respect
                      to the sub-layer's output.
            !*/

        // -------------

            double compute_loss (
                const tensor& x
            );
            /*!
                requires
                    - LOSS_DETAILS is an unsupervised loss.  i.e. training_label_type==no_label_type.
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                ensures
                    - runs x through the network and returns the resulting loss.
                    - This function does not update the network parameters.
                    - For sub-layers that are immediate inputs into the loss layer, we also populate the
                      sub-layer's get_gradient_input() tensor with the gradient of the loss with respect
                      to the sub-layer's output.
            !*/

            template <typename forward_iterator>
            double compute_loss (
                forward_iterator ibegin,
                forward_iterator iend,
            );
            /*!
                requires
                    - LOSS_DETAILS is an unsupervised loss.  i.e. training_label_type==no_label_type.
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                ensures
                    - runs [ibegin,iend) through the network and returns the resulting loss.
                    - This function does not update the network parameters.
                    - For sub-layers that are immediate inputs into the loss layer, we also populate the
                      sub-layer's get_gradient_input() tensor with the gradient of the loss with respect
                      to the sub-layer's output.
            !*/

        // -------------

            template <typename label_iterator>
            double compute_parameter_gradients (
                const tensor& x,
                label_iterator lbegin,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                    - lbegin == iterator pointing to the start of a range of
                      x.num_samples()/sample_expansion_factor() training_label_type elements.
                ensures
                    - runs x through the network, compares the output to the expected output
                      pointed to by lbegin, and computes parameter and data gradients with
                      respect to the loss, via backpropagation.  Specifically, this function
                      updates get_final_data_gradient() and also, for each layer, the tensor
                      returned by get_parameter_gradient().
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - for all valid k:
                        - the expected label of the kth sample in x is *(lbegin+k/sample_expansion_factor()).
                    - returns compute_loss(x,lbegin)
            !*/

            template <typename forward_iterator, typename label_iterator>
            double compute_parameter_gradients (
                forward_iterator ibegin,
                forward_iterator iend,
                label_iterator lbegin,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                    - lbegin == iterator pointing to the start of a range of
                      std::distance(ibegin,iend) training_label_type elements.
                ensures
                    - runs [ibegin,iend) through the network, compares the output to the
                      expected output pointed to by lbegin, and computes parameter and data
                      gradients with respect to the loss, via backpropagation.  Specifically,
                      this function updates get_final_data_gradient() and also, for each layer,
                      the tensor returned by get_parameter_gradient().
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - for all valid k:
                        - the expected label of *(ibegin+k) is *(lbegin+k).
                    - returns compute_loss(ibegin,iend,lbegin)
            !*/

            double compute_parameter_gradients (
                const tensor& x,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - LOSS_DETAILS is an unsupervised loss.  i.e. training_label_type==no_label_type.
                    - sample_expansion_factor() != 0
                      (i.e. to_tensor() must have been called to set sample_expansion_factor()
                      to something non-zero.)
                    - x.num_samples()%sample_expansion_factor() == 0
                    - x.num_samples() > 0
                ensures
                    - runs x through the network and computes parameter and data gradients with
                      respect to the loss, via backpropagation.  Specifically, this function
                      updates get_final_data_gradient() and also, for each layer, the tensor
                      returned by get_parameter_gradient().
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - returns compute_loss(x)
            !*/

            template <typename forward_iterator>
            double compute_parameter_gradients (
                forward_iterator ibegin,
                forward_iterator iend,
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - LOSS_DETAILS is an unsupervised loss.  i.e. training_label_type==no_label_type.
                    - [ibegin, iend) is an iterator range over input_type objects.
                    - std::distance(ibegin,iend) > 0
                ensures
                    - runs [ibegin,iend) through the network and computes parameter and data
                      gradients with respect to the loss, via backpropagation.  Specifically,
                      this function updates get_final_data_gradient() and also, for each layer,
                      the tensor returned by get_parameter_gradient().
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - returns compute_loss(ibegin,iend)
            !*/

            template <typename solver_type>
            void update_parameters (
                sstack<solver_type> solvers,
                double learning_rate
            );
            /*!
                requires
                    - solver_type is an implementation of the EXAMPLE_SOLVER interface defined
                      in solvers_abstract.h
                    - compute_parameter_gradients() has been called.
                    - The given solvers have only ever been used with this network.  That
                      is, if you want to call update_parameters() on some other neural network
                      object then you must NOT reuse the same solvers object.
                    - solvers.size() >= num_computational_layers
                    - 0 < learning_rate <= 1
                ensures
                    - Updates all the parameters in the network.  In particular, we pass each
                      layer's parameter gradient (i.e. the tensor returned by the layer's
                      get_parameter_gradient() member) through that layer's corresponding
                      solver object.  This produces a parameter delta vector which we add to
                      the layer's parameters.
                    - The solvers use the given learning rate.
            !*/

            template <typename solver_type>
            void update_parameters(std::vector<solver_type>& solvers, double learning_rate
            ) { update_parameters(make_sstack(solvers), learning_rate); }
            /*!
                Convenience method for calling update_parameters()
            !*/

            void back_propagate_error(
                const tensor& x
                zero_gradients zero_grads = zero_gradients::yes
            );
            /*!
                requires
                    - forward(x) was called to forward propagate x though the network.
                      Moreover, this was the most recent call to forward() and x has not been
                      subsequently modified in any way.
                    - subnet().get_gradient_input() has been set equal to the gradient of this network's
                      output with respect to the loss function (generally this will be done by calling
                      compute_loss()).
                ensures
                    - Back propagates the error gradient, subnet().get_gradient_input(), through this
                      network and computes parameter and data gradients, via backpropagation.
                      Specifically, this function populates get_final_data_gradient() and also,
                      for each layer, the tensor returned by get_parameter_gradient().
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - have_same_dimensions(#get_final_data_gradient(), x) == true.
                    - #get_final_data_gradient() contains the gradient of the network with
                      respect to x.
            !*/

            void back_propagate_error(
                const tensor& x,
                const tensor& gradient_input
            );
            /*!
                requires
                    - forward(x) was called to forward propagate x though the network.
                      Moreover, this was the most recent call to forward() and x has not been
                      subsequently modified in any way.
                    - have_same_dimensions(gradient_input, subnet().get_output()) == true
                ensures
                    - This function is identical to the version of back_propagate_error()
                      defined immediately above except that it back-propagates gradient_input
                      through the network instead of subnet().get_gradient_input().  Therefore, this
                      version of back_propagate_error() is equivalent to performing:
                        subnet().get_gradient_input() = gradient_input;
                        back_propagate_error(x);
                      Except that calling back_propagate_error(x,gradient_input) avoids the
                      copy and is therefore slightly more efficient.
                    - All elements of #subnet().get_gradient_input() are set to 0 if zero_grads == zero_gradients::yes.
                    - have_same_dimensions(#get_final_data_gradient(), x) == true.
                    - #get_final_data_gradient() contains the gradient of the network with
                      respect to x.
            !*/

            const tensor& get_final_data_gradient(
            ) const;
            /*!
                ensures
                    - if back_propagate_error() has been called to back-propagate a gradient
                      through this network then you can call get_final_data_gradient() to
                      obtain the last data gradient computed.  That is, this function returns
                      the gradient of the network with respect to its inputs.
                    - Note that there is only one "final data gradient" for an entire network,
                      not one per layer, since there is only one input to the entire network.
            !*/

            void set_gradient_inputs_to_zero(
            );
            /*!
                ensures
                    - Sets all elements in all gradient inputs in the network to 0.
                    - invokes subnet().set_gradient_inputs_to_zero()
            !*/

        // -------------

            void clean (
            );
            /*!
                ensures
                    - Causes the network to forget about everything but its parameters.
                    - invokes subnet().clean()
            !*/
        };

        template <typename T, typename U>
        std::ostream& operator<<(std::ostream& out, const add_loss_layer<T,U>& item);
        /*!
            prints the network architecture to the given output stream.
        !*/

        template <typename T, typename U>
        void serialize(const add_loss_layer<T,U>& item, std::ostream& out);
        template <typename T, typename U>
        void deserialize(add_loss_layer<T,U>& item, std::istream& in);
        /*!
            provides serialization support
        !*/

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <typename ...T>
        decorator_repeat_group<T...> repeat_group (
            T&& ...args
        );
        /*!
            ensures
                - Decorates a group of variables.  This is essentially like std::make_tuple()
                  except it's only purpose is to group variables together so they can be passed
                  to the repeat object's constructor.
        !*/

        template <
            size_t num,
            template<typename> class REPEATED_LAYER,
            typename SUBNET
            >
        class repeat
        {
            /*!
                REQUIREMENTS ON num
                    - num > 0

                REQUIREMENTS ON REPEATED_LAYER
                    - REPEATED_LAYER must be a template that stacks more layers onto a deep neural
                      network.  For example, if net_type were a network without a loss layer,
                      then it should be legal to create a deeper network with a type of
                      REPEATED_LAYER<net_type>.

                REQUIREMENTS ON SUBNET
                    - One of the following must be true:
                        - SUBNET is an add_layer object.
                        - SUBNET is an add_tag_layer object.
                        - SUBNET is an add_skip_layer object.
                        - SUBNET is a repeat object.

                WHAT THIS OBJECT REPRESENTS
                    This object adds more layers to a deep neural network.  In particular, it
                    adds REPEATED_LAYER on top of SUBNET num times.  So for example, if num were 2 then
                    repeat<2,REPEATED_LAYER,SUBNET> would create a network equivalent to REPEATED_LAYER<REPEATED_LAYER<SUBNET>>.

                    Also, this object provides an interface identical to the one defined by the
                    add_layer object except that we add the num_repetitions() and
                    get_repeated_layer() methods.  These additions are shown below along with
                    some additional explanatory comments.
            !*/

        public:

            typedef SUBNET subnet_type;
            typedef typename SUBNET::input_type input_type;
            typedef typename subnet_type::input_layer_type input_layer_type;
            const static size_t num_computational_layers = (REPEATED_LAYER<SUBNET>::num_computational_layers-SUBNET::num_computational_layers)*num + SUBNET::num_computational_layers;
            const static size_t num_layers = (REPEATED_LAYER<SUBNET>::num_layers-SUBNET::num_layers)*num + SUBNET::num_layers;
            typedef REPEATED_LAYER<an_unspecified_input_type> repeated_layer_type;

            template <typename T, typename ...U>
            repeat(
                T arg1,
                U ...args2
            );
            /*!
                ensures
                    - arg1 is used to initialize the num_repetitions() copies of REPEATED_LAYER inside
                      this object.  That is, all the REPEATED_LAYER elements are initialized identically
                      by being given copies of arg1.
                    - The rest of the arguments to the constructor, i.e. args2, are passed to
                      SUBNET's constructor.
            !*/

            template <typename ...T, typename ...U>
            repeat(
                decorator_repeat_group<T...>&& arg1,
                U ...args2
            );
            /*!
                ensures
                    - arg1 is used to initialize the num_repetitions() copies of REPEATED_LAYER inside
                      this object.  That is, all the REPEATED_LAYER elements are initialized identically
                      by being given copies of an undecorated arg1.
                    - The rest of the arguments to the constructor, i.e. args2, are passed to
                      SUBNET's constructor.
            !*/

            size_t num_repetitions (
            ) const;
            /*!
                ensures
                    - returns num (i.e. the number of times REPEATED_LAYER was stacked on top of SUBNET)
            !*/

            const repeated_layer_type& get_repeated_layer (
                size_t i
            ) const;
            /*!
                requires
                    - i < num_repetitions()
                ensures
                    - returns a reference to the i-th instance of REPEATED_LAYER.  For example,
                      get_repeated_layer(0) returns the instance of REPEATED_LAYER that is on the top of
                      the network while get_repeated_layer(num_repetitions()-1) returns the
                      instance of REPEATED_LAYER that is stacked immediately on top of SUBNET.
            !*/

            repeated_layer_type& get_repeated_layer (
                size_t i
            );
            /*!
                requires
                    - i < num_repetitions()
                ensures
                    - returns a reference to the i-th instance of REPEATED_LAYER.  For example,
                      get_repeated_layer(0) returns the instance of REPEATED_LAYER that is on the top of
                      the network while get_repeated_layer(num_repetitions()-1) returns the
                      instance of REPEATED_LAYER that is stacked immediately on top of SUBNET.
            !*/

            const subnet_type& subnet(
            ) const;
            /*!
                ensures
                    - returns the SUBNET base network that repeat sits on top of.  If you want
                      to access the REPEATED_LAYER components then you must use get_repeated_layer().
            !*/

            subnet_type& subnet(
            );
            /*!
                ensures
                    - returns the SUBNET base network that repeat sits on top of.  If you want
                      to access the REPEATED_LAYER components then you must use get_repeated_layer().
            !*/

            const input_layer_type& input_layer(
            ) const;
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

            input_layer_type& input_layer(
            );
            /*!
                ensures
                    - returns the very first layer in *this network.  It's equivalent to calling
                      subnet() recursively until you get to the first layer.  This means it will return
                      the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
                      in input_abstract.h
            !*/

        };

        template < size_t num, template<typename> class T, typename U >
        std::ostream& operator<<(std::ostream& out, const repeat<num,T,U>& item);
        /*!
            prints the network architecture to the given output stream.
        !*/

        template < size_t num, template<typename> class T, typename U >
        void serialize(const repeat<num,T,U>& item, std::ostream& out);
        template < size_t num, template<typename> class T, typename U >
        void deserialize(repeat<num,T,U>& item, std::istream& in);
        /*!
            provides serialization support
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            unsigned long ID,
            typename SUBNET
            >
        class add_tag_layer
        {
            /*!
                REQUIREMENTS ON SUBNET
                    - One of the following must be true:
                        - SUBNET implements the EXAMPLE_INPUT_LAYER interface defined in
                          input_abstract.h.
                        - SUBNET is an add_layer object.
                        - SUBNET is an add_tag_layer object.
                        - SUBNET is an add_skip_layer object.
                        - SUBNET is a repeat object.

                WHAT THIS OBJECT REPRESENTS
                    This object adds a new layer to a deep neural network.  However, this layer
                    simply performs the identity transform.  This means it is a no-op and its
                    presence does not change the behavior of the network.  It exists solely to
                    be used by add_skip_layer to reference a particular part of a network.

                    Also, this object provides an interface identical to the one defined by the
                    add_layer object.
            !*/
        };

        template <unsigned long ID, typename U>
        std::ostream& operator<<(std::ostream& out, const add_tag_layer<ID,U>& item);
        /*!
            prints the network architecture to the given output stream.
        !*/

        template <unsigned long ID, typename U>
        void serialize(const add_tag_layer<ID,U>& item, std::ostream& out);
        template <unsigned long ID, typename U>
        void deserialize(add_tag_layer<ID,U>& item, std::istream& in);
        /*!
            provides serialization support
        !*/

        template <typename SUBNET> using tag1  = add_tag_layer< 1, SUBNET>;
        template <typename SUBNET> using tag2  = add_tag_layer< 2, SUBNET>;
        template <typename SUBNET> using tag3  = add_tag_layer< 3, SUBNET>;
        template <typename SUBNET> using tag4  = add_tag_layer< 4, SUBNET>;
        template <typename SUBNET> using tag5  = add_tag_layer< 5, SUBNET>;
        template <typename SUBNET> using tag6  = add_tag_layer< 6, SUBNET>;
        template <typename SUBNET> using tag7  = add_tag_layer< 7, SUBNET>;
        template <typename SUBNET> using tag8  = add_tag_layer< 8, SUBNET>;
        template <typename SUBNET> using tag9  = add_tag_layer< 9, SUBNET>;
        template <typename SUBNET> using tag10 = add_tag_layer<10, SUBNET>;

        template <template<typename SUBNET> class tag>
        struct tag_id
        {
            /*!
                REQUIREMENTS ON tag
                    Tag should be an add_tag_layer template such as tag1, tag2, etc.

                WHAT THIS OBJECT REPRESENTS
                    This is a tool for finding the numeric ID of a tag layer.  For example,
                    tag_id<tag3>::id == 3.
            !*/

            const static unsigned long id;
        };

    // ----------------------------------------------------------------------------------------

        template <
            template<typename> class TAG_TYPE,
            typename SUBNET
            >
        class add_skip_layer
        {
            /*!
                REQUIREMENTS ON SUBNET
                    - One of the following must be true:
                        - SUBNET is an add_layer object.
                        - SUBNET is an add_tag_layer object.
                        - SUBNET is an add_skip_layer object.
                        - SUBNET is a repeat object.

                WHAT THIS OBJECT REPRESENTS
                    This object adds a new layer to a deep neural network which draws its
                    inputs from layer<TAG_TYPE>(subnet()) and performs the identity transform.

                    Also, this object provides an interface identical to the one defined by the
                    add_layer object.
            !*/
        };

        template <template<typename> class T, typename U>
        std::ostream& operator<<(std::ostream& out, const add_skip_layer<T,U>& item);
        /*!
            prints the network architecture to the given output stream.
        !*/

        template <template<typename> class T, typename U>
        void serialize(const add_skip_layer<T,U>& item, std::ostream& out);
        template <template<typename> class T, typename U>
        void deserialize(add_skip_layer<T,U>& item, std::istream& in);
        /*!
            provides serialization support
        !*/

        template <typename SUBNET> using skip1  = add_skip_layer< tag1, SUBNET>;
        template <typename SUBNET> using skip2  = add_skip_layer< tag2, SUBNET>;
        template <typename SUBNET> using skip3  = add_skip_layer< tag3, SUBNET>;
        template <typename SUBNET> using skip4  = add_skip_layer< tag4, SUBNET>;
        template <typename SUBNET> using skip5  = add_skip_layer< tag5, SUBNET>;
        template <typename SUBNET> using skip6  = add_skip_layer< tag6, SUBNET>;
        template <typename SUBNET> using skip7  = add_skip_layer< tag7, SUBNET>;
        template <typename SUBNET> using skip8  = add_skip_layer< tag8, SUBNET>;
        template <typename SUBNET> using skip9  = add_skip_layer< tag9, SUBNET>;
        template <typename SUBNET> using skip10 = add_skip_layer<tag10, SUBNET>;

    // ----------------------------------------------------------------------------------------

        template <
            unsigned int i,
            typename net_type
            >
        auto& layer (
            net_type& n
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - i < net_type::num_layers
            ensures
                - This function allows you to access any layer in a network by its layer index
                  i.  Therefore, it will walk i steps down the network and return the layer
                  object there.  Since networks can be big, the best way to find layer index
                  numbers is to print a network to the screen since the print out will include
                  indexes for each layer.
                - In general, this function chains together i calls to n.subnet() and returns
                  the result.  So for example:
                    - if (i == 0)
                        - returns n
                    - else if (i == 1)
                        - returns n.subnet()
                    - else if (i == 2)
                        - returns n.subnet().subnet()
                    - else if (i == 3)
                        - returns n.subnet().subnet().subnet()
                    - else
                        - etc.
                  Except that when it hits a repeat layer it recurses into the repeated layers
                  contained inside.  That is, if the layer index indicates a layer in a repeat
                  object this function will make the appropriate call to get_repeated_layer()
                  and do the right thing.
        !*/

        template <
            template<typename> class Match,
            typename net_type
            >
        auto& layer (
            net_type& n
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
            ensures
                - returns the first layer in n that is of type Match.  E.g. if net_type is
                  fc<relu<fc<input<sample_type>>>> then calling layer<relu>(n) would return
                  layer<1>(n), that is, a reference to the relu layer.
        !*/

        template <
            template<typename> class Match,
            unsigned int i,
            typename net_type
            >
        auto& layer (
            net_type& n
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
            ensures
                - returns layer<i>(layer<Match>(n))
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename net_type>
        auto& input_layer (
            net_type& net
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, repeat, or
                  add_tag_layer.
            ensures
                - returns the input layer of the given network object.  This is the same as just calling
                  net.input_layer().
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename net_type,
            typename visitor
            >
        void visit_layer_parameters(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, tensor& t)
                  or:
                    v(tensor& t)
            ensures
                - Loops over all the computational layers (i.e. layers with parameters, as
                  opposed to loss, tag, or input layers) in net and passes their parameters to
                  v().  To be specific, this function essentially performs the following:

                    size_t computational_layer_idx = 0;
                    for (size_t i = 0; i < net_type::num_layers; ++i)
                    {
                        if (layer<i>(net) is a computational layer)
                        {
                            v(computational_layer_idx, layer<i>(net).layer_details().get_layer_params());
                            ++computational_layer_idx;
                        }
                    }
                - When v() is called, the first argument is always < net_type::num_computational_layers.
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename net_type,
            typename visitor
            >
        void visit_layer_parameter_gradients(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, tensor& t)
                  or:
                    v(tensor& t)
            ensures
                - Loops over all the computational layers (i.e. layers with parameters, as
                  opposed to loss, tag, or input layers) in net and passes their parameter
                  gradients to v().  To be specific, this function essentially performs the
                  following:

                    size_t computational_layer_idx = 0;
                    for (size_t i = 0; i < net_type::num_layers; ++i)
                    {
                        if (layer<i>(net) is a computational layer)
                        {
                            v(computational_layer_idx, layer<i>(net).get_parameter_gradient());
                            ++computational_layer_idx;
                        }
                    }
                - When v() is called, the first argument is always < net_type::num_computational_layers.
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename net_type,
            typename visitor
            >
        void visit_layers(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_net_type& t)
                  or:
                    v(any_net_type& t)
                  That is, it takes an optional size_t and then any of the network types such as
                  add_layer, add_loss_layer, etc.
            ensures
                - Loops over all the layers in net and calls v() on them.  To be specific, this
                  function essentially performs the following:

                    for (size_t i = 0; i < net_type::num_layers; ++i)
                        v(i, layer<i>(net));
        !*/

        template <
            typename net_type,
            typename visitor
            >
        void visit_layers_backwards(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_net_type& t)
                  or:
                    v(any_net_type& t)
                  That is, it takes an optional size_t and then any of the network types such as
                  add_layer, add_loss_layer, etc.
            ensures
                - Loops over all the layers in net and calls v() on them.  The loop happens in
                  the reverse order of visit_layers().  To be specific, this function
                  essentially performs the following:

                    for (size_t i = net_type::num_layers; i != 0; --i)
                        v(i-1, layer<i-1>(net));
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename net_type,
            typename visitor
            >
        void visit_computational_layers(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_computational_layer& t)
                  or:
                    v(any_computational_layer& t)
                  That is, it takes an optional size_t and then any of the computational layers.  E.g.
                  one of the layer types defined in dlib/dnn/layers_abstract.h like fc_ or conv_.
            ensures
                - Loops over all the computational layers in net and calls v() on them.  To be specific, this
                  function essentially performs the following:

                    for (size_t i = 0; i < net_type::num_layers; ++i)
                        if (layer<i>(net) is an add_layer type, i.e. it adds a computational layer)
                            v(i, layer<i>(net).layer_details());
        !*/

        template <
            size_t begin,
            size_t end,
            typename net_type,
            typename visitor
            >
        void visit_computational_layers_range(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_computational_layer& t)
                  or:
                    v(any_computational_layer& t)
                  That is, it takes an optional size_t and then any of the computational layers.  E.g.
                  one of the layer types defined in dlib/dnn/layers_abstract.h like fc_ or conv_.
            ensures
                - Loops over all the computational layers in the range [begin,end) in net and calls v()
                  on them.  To be specific, this function essentially performs the following:

                    for (size_t i = begin; i < end; ++i)
                        if (layer<i>(net) is an add_layer type, i.e. it adds a computational layer)
                            v(i, layer<i>(net).layer_details());
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            size_t begin,
            size_t end,
            typename net_type,
            typename visitor
            >
        void visit_layers_range(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_net_type& t)
                  or:
                    v(any_net_type& t)
                  That is, it takes an optional size_t and then any of the network types such as
                  add_layer, add_loss_layer, etc.
                - begin <= end <= net_type::num_layers
            ensures
                - Loops over the layers in the range [begin,end) in net and calls v() on them.
                  To be specific, this function essentially performs the following:

                    for (size_t i = begin; i < end; ++i)
                        v(i, layer<i>(net));
        !*/

        template <
            size_t begin,
            size_t end,
            typename net_type,
            typename visitor
            >
        void visit_layers_backwards_range(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(size_t idx, any_net_type& t)
                  or:
                    v(any_net_type& t)
                  That is, it takes an optional size_t and then any of the network types such as
                  add_layer, add_loss_layer, etc.
                - begin <= end <= net_type::num_layers
            ensures
                - Loops over the layers in the range [begin,end) in net and calls v() on them.
                  The loop happens in the reverse order of visit_layers_range().  To be specific,
                  this function essentially performs the following:

                    for (size_t i = end; i != begin; --i)
                        v(i-1, layer<i-1>(net));
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            unsigned long tag_id,
            typename net_type,
            typename visitor
            >
        void visit_layers_until_tag(
            net_type& net,
            visitor v
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
                - v is a function object with a signature equivalent to:
                    v(any_net_type& t)
                  That is, it must take any of the network types such as add_layer,
                  add_loss_layer, etc.
            ensures
                - Loops over all the layers in net beginning with layer<0>(net) and going until
                  a tag layer with an ID of tag_id is encountered.  To be specific, this
                  function essentially performs the following:

                    size_t i = 0;
                    while(layer<i>(net) isn't an add_tag_layer with ID == tag_id) {
                        v(layer<i>(net));
                        ++i;
                    }
                    v(layer<i>(net));  // also visits the tag layer itself at the very end.
        !*/

    // ----------------------------------------------------------------------------------------

        struct layer_test_results
        {
            std::string log;
            bool was_good;

            operator bool() const { return was_good; }
        };

        inline std::ostream& operator<< (std::ostream& out, const layer_test_results& item)
        {
            out << item.log;
            return out;
        }

        template <
            typename layer_details_type
            >
        layer_test_results test_layer (
            layer_details_type l
        );
        /*!
            ensures
                - Checks if l correctly implements the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                  defined in layers_abstract.h.  Importantly, it computes numerical approximations
                  to the gradients and compares them to the outputs of the layer.
                - The results of the testing are returned.  In particular, if the returned object
                  is RESULT then we will have:
                    - RESULT.was_good == false if and only if the layer failed the testing.
                    - RESULT.log == a string describing why the testing failed if was_good==false.
                - Note that this function is only capable of checking layers that take
                  arbitrary subnetworks as input.  So if you have designed a layer that expects
                  only a certain restricted type of subnetwork then you might get a compile or
                  runtime error when you call this function.
        !*/

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_DNn_CORE_ABSTRACT_H_