# dlib C++ Library - layers_abstract.h

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

    #include "../cuda/tensor_abstract.h"
    #include "core_abstract.h"

    namespace dlib
    {

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

        class SUBNET
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This object represents a deep neural network.  In particular, it is
                    the simplified interface through which layer objects interact with their
                    subnetworks.  A layer's two important tasks are to (1) take outputs from its
                    subnetwork and forward propagate them through itself and (2) to backwards
                    propagate an error gradient through itself and onto its subnetwork.
                    The idea of a subnetwork is illustrated in the following diagram:

                      +---------------------------------------------------------+
                      | loss <-- layer1 <-- layer2 <-- ... <-- layern <-- input |
                      +---------------------------------------------------------+
                                          ^                            ^
                                          \__ subnetwork for layer1 __/

                    Therefore, by "subnetwork" we mean the part of the network closer to the
                    input.

                    Note that there is no dlib::SUBNET type.  It is shown here purely to
                    document the interface layer objects expect to see when they interact
                    with a network.
            !*/

        public:
            // You aren't allowed to copy subnetworks from inside a layer.
            SUBNET(const SUBNET&) = delete;
            SUBNET& operator=(const SUBNET&) = delete;

            const tensor& get_output(
            ) const;
            /*!
                ensures
                    - returns the output of this subnetwork.  This is the data that the next
                      layer in the network will take as input.
                    - have_same_dimensions(#get_gradient_input(), get_output()) == true
            !*/

            tensor& get_gradient_input(
            );
            /*!
                ensures
                    - returns the error gradient for this subnetwork.  That is, this is the
                      error gradient that this network will use to update itself.  Therefore,
                      when performing back propagation, layers that sit on top of this
                      subnetwork 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 results into their subnetwork's
                      get_gradient_input().
            !*/

            const NEXT_SUBNET& subnet(
            ) const;
            /*!
                ensures
                    - returns the subnetwork of *this network.  With respect to the diagram
                      above, if *this was layer1 then subnet() would return the network that
                      begins with layer2.
            !*/

            NEXT_SUBNET& subnet(
            );
            /*!
                ensures
                    - returns the subnetwork of *this network.  With respect to the diagram
                      above, if *this was layer1 then subnet() would return the network that
                      begins with layer2.
            !*/

            const INPUT_LAYER& 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& 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.  For computational layers, this is the object
                      implementing the EXAMPLE_COMPUTATIONAL_LAYER_ interface that defines the
                      layer's behavior.
            !*/

            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().

                      It should be noted that computational layers likely do not care about the
                      sample expansion factor.  It is only really of concern inside a loss
                      layer where you need to know its value so that tensor samples can be
                      matched against truth objects.  Moreover, in most cases the sample
                      expansion factor is 1.
            !*/

        };

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

        class EXAMPLE_COMPUTATIONAL_LAYER_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    Each computational layer in a deep neural network can be thought of as a
                    function, f(data,parameters), that takes in a data tensor, some parameters,
                    and produces an output tensor.  You create an entire deep network by
                    composing these functions.  Importantly, you are able to use a wide range
                    of different functions to accommodate the task you are trying to
                    accomplish.  Therefore, dlib includes a number of common layer types but if
                    you want to define your own then you simply implement a class with the same
                    interface as EXAMPLE_COMPUTATIONAL_LAYER_.

                    Note that there is no dlib::EXAMPLE_COMPUTATIONAL_LAYER_ type.  It is shown
                    here purely to document the interface that a layer object must implement.

                    The central work of defining a layer is implementing the forward and backward
                    methods.  When you do this you have four options:
                        - Implement the forward() and backward() methods according to the
                          specification shown below.  Do not implement forward_inplace() and
                          backward_inplace().
                        - Implement the forward() and backward() methods according to the
                          specification shown below, except exclude the computed_output
                          parameter from backward().  Doing this will allow dlib to make some
                          layers execute in-place and therefore run a little faster and use
                          less memory. Do not implement forward_inplace() and
                          backward_inplace().
                        - Implement the forward_inplace() and backward_inplace() methods
                          according to the specification shown below.  Do not implement
                          forward() and backward().  These in-place methods allow some types of
                          layers to be implemented more efficiently.
                        - Implement the forward_inplace() and backward_inplace() methods
                          according to the specification shown below, except exclude the
                          computed_output parameter from backward_inplace().  Doing this will
                          allow dlib to make some layers execute in-place and therefore run a
                          little faster and use less memory.  Do not implement forward() and
                          backward().

                    It should also be noted that layers may define additional layer specific
                    fields and the solvers can use these fields as they see fit.  For example,
                    some layers define get_learning_rate_multiplier() and
                    get_weight_decay_multiplier() methods.  The solvers that come with dlib
                    look at these methods, if they exist, and adjust the learning rate or
                    weight decay for that layer according to the multiplier.  Therefore, you
                    can add these methods to your layer types if you want, or even define new
                    fields and new solvers that use those fields in some way.
            !*/

        public:

            EXAMPLE_COMPUTATIONAL_LAYER_(
            );
            /*!
                ensures
                    - Default constructs this object.  This function is not required to do
                      anything in particular but it must exist, that is, it is required that
                      layer objects be default constructable.
            !*/

            EXAMPLE_COMPUTATIONAL_LAYER_ (
                const EXAMPLE_COMPUTATIONAL_LAYER_& item
            );
            /*!
                ensures
                    - EXAMPLE_COMPUTATIONAL_LAYER_ objects are copy constructable
            !*/

            EXAMPLE_COMPUTATIONAL_LAYER_(
                const some_other_layer_type& item
            );
            /*!
                ensures
                    - Constructs this object from item.  This form of constructor is optional
                      but it allows you to provide a conversion from one layer type to another.
                      For example, the following code is valid only if my_layer2 can be
                      constructed from my_layer1:
                        relu<fc<my_layer1<fc<input<matrix<float>>>>>> my_dnn1;
                        relu<fc<my_layer2<fc<input<matrix<float>>>>>> my_dnn2(my_dnn1);
                      This kind of pattern is useful if you want to use one type of layer
                      during training but a different type of layer during testing since it
                      allows you to easily convert between related deep neural network types.

                      Additionally, if you provide a constructor to build a layer from another
                      layer type you should also write your layer's deserialize() routine such
                      that it can read that other layer's serialized data in addition to your
                      own serialized data.
            !*/

            template <typename SUBNET>
            void setup (
                const SUBNET& sub
            );
            /*!
                requires
                    - SUBNET implements the SUBNET interface defined at the top of this file.
                ensures
                    - performs any necessary initial memory allocations and/or sets parameters
                      to their initial values prior to learning.  Therefore, calling setup
                      destroys any previously learned parameters.  Also, typically setup()
                      would look at the dimensions of the outputs of sub and configure the
                      number of parameters in *this accordingly.
            !*/

            template <typename SUBNET>
            void forward(
                const SUBNET& sub,
                resizable_tensor& data_output
            );
            /*!
                requires
                    - SUBNET implements the SUBNET interface defined at the top of this file.
                    - setup() has been called.
                ensures
                    - Runs the output of the subnetwork through this layer and stores the
                      results into #data_output.  In particular, forward() can use any of the
                      outputs in sub (e.g. sub.get_output(), sub.subnet().get_output(), etc.)
                      to compute whatever it wants.
            !*/

            template <typename SUBNET>
            void backward(
                const tensor& computed_output, // this parameter is optional
                const tensor& gradient_input,
                SUBNET& sub,
                tensor& params_grad
            );
            /*!
                requires
                    - SUBNET implements the SUBNET interface defined at the top of this file.
                    - setup() has been called.
                    - computed_output is the tensor resulting from calling forward(sub,computed_output).
                      Moreover, this was the most recent call to forward().  This means that
                      forward() is allowed to cache intermediate results so they can be used
                      during the backward computation.
                    - have_same_dimensions(gradient_input, computed_output) == true
                    - have_same_dimensions(sub.get_gradient_input(), sub.get_output()) == true
                    - have_same_dimensions(params_grad, get_layer_params()) == true
                ensures
                    - This function outputs the gradients of this layer with respect to the
                      input data from sub and also with respect to this layer's parameters.
                      These gradients are stored into #sub and #params_grad, respectively. To be
                      precise, the gradients are taken of a function f(sub,get_layer_params())
                      which is defined thusly:
                        - Recalling that computed_output is a function of both sub and get_layer_params(),
                          since it is the result of calling forward(sub,computed_output):
                          let f(sub,get_layer_params()) == dot(computed_output, gradient_input)
                      Then we define the following gradient vectors:
                        - PARAMETER_GRADIENT == gradient of f(sub,get_layer_params()) with
                          respect to get_layer_params().
                        - for all valid I:
                            - DATA_GRADIENT_I == gradient of f(sub,get_layer_params()) with
                              respect to layer<I>(sub).get_output() (recall that forward() can
                              draw inputs from the immediate sub layer, sub.subnet(), or
                              any earlier layer.  So you must consider the gradients with
                              respect to all inputs drawn from sub)
                      Finally, backward() outputs these gradients by performing:
                        - params_grad = PARAMETER_GRADIENT
                        - for all valid I:
                            - layer<I>(sub).get_gradient_input() += DATA_GRADIENT_I
            !*/

            void forward_inplace(
                const tensor& data_input,
                tensor& data_output
            );
            /*!
                requires
                    - have_same_dimensions(data_input,data_output) == true
                    - setup() has been called.
                ensures
                    - Runs the data_input tensor through this layer and stores the output into
                      #data_output.
                    - This function supports in-place operation, i.e. having
                      is_same_object(data_input, data_output)==true
            !*/

            void backward_inplace(
                const tensor& computed_output, // this parameter is optional
                const tensor& gradient_input,
                tensor& data_grad,
                tensor& params_grad
            );
            /*!
                requires
                    - setup() has been called.
                    - computed_output is the tensor resulting from the most recent call to
                      forward_inplace().  This means that forward_inplace() is allowed to cache
                      intermediate results so they can be used during the backward computation.
                    - have_same_dimensions(gradient_input, data_grad) == true
                    - have_same_dimensions(gradient_input, computed_output) == true
                    - have_same_dimensions(params_grad, get_layer_params()) == true
                ensures
                    - This function supports in-place operation, i.e. having
                      is_same_object(gradient_input, data_grad)==true
                    - This function outputs the gradients of this layer with respect to the
                      input data from a sublayer and also with respect to this layer's parameters.
                      These gradients are stored into #data_grad and #params_grad, respectively. To be
                      precise, the gradients are taken of a function f(data_input,get_layer_params())
                      which is defined thusly:
                        - Recalling that computed_output is a function of both the input to
                          forward_inplace() and get_layer_params(), since it is the result of
                          calling forward_inplace(data_input,computed_output):
                          let f(data_input,get_layer_params()) == dot(computed_output, gradient_input)
                      Then we define the following gradient vectors:
                        - PARAMETER_GRADIENT == gradient of f(data_input,get_layer_params()) with
                          respect to get_layer_params().
                        - DATA_GRADIENT == gradient of f(data_input,get_layer_params()) with respect
                          to data_input.
                      Finally, backward_inplace() outputs these gradients by performing:
                        - params_grad = PARAMETER_GRADIENT
                        - if (is_same_object(gradient_input, data_grad)) then
                            - data_grad = DATA_GRADIENT
                        - else
                            - data_grad += DATA_GRADIENT
            !*/

            const tensor& get_layer_params(
            ) const;
            /*!
                ensures
                    - returns the parameters that define the behavior of forward().
            !*/

            tensor& get_layer_params(
            );
            /*!
                ensures
                    - returns the parameters that define the behavior of forward().
            !*/

            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            /*!
                These two functions are optional.  If provided, they should map between
                (column,row) coordinates in input and output tensors of forward().  Providing
                these functions allows you to use global utility functions like
                input_tensor_to_output_tensor().
            !*/

            void clean (
            );
            /*!
                Implementing this function is optional.  If you don't need it then you don't
                have to provide a clean().  But if you do provide it then it must behave as
                follows:

                ensures
                    - calling clean() causes this object to forget about everything except its
                      parameters.  This is useful if your layer caches information between
                      forward and backward passes and you want to clean out that cache
                      information before saving the network to disk.
            !*/

        };

        std::ostream& operator<<(std::ostream& out, const EXAMPLE_COMPUTATIONAL_LAYER_& item);
        /*!
            print a string describing this layer.
        !*/

        void to_xml(const EXAMPLE_COMPUTATIONAL_LAYER_& item, std::ostream& out);
        /*!
            This function is optional, but required if you want to print your networks with
            net_to_xml().  Therefore, to_xml() prints a layer as XML.
        !*/

        void serialize(const EXAMPLE_COMPUTATIONAL_LAYER_& item, std::ostream& out);
        void deserialize(EXAMPLE_COMPUTATIONAL_LAYER_& item, std::istream& in);
        /*!
            provides serialization support
        !*/

        // For each layer you define, always define an add_layer template so that layers can be
        // easily composed.  Moreover, the convention is that the layer class ends with an _
        // while the add_layer template has the same name but without the trailing _.
        template <typename SUBNET>
        using EXAMPLE_COMPUTATIONAL_LAYER = add_layer<EXAMPLE_COMPUTATIONAL_LAYER_, SUBNET>;

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

        enum fc_bias_mode
        {
            FC_HAS_BIAS = 0,
            FC_NO_BIAS = 1
        };

        struct num_fc_outputs
        {
            num_fc_outputs(unsigned long n) : num_outputs(n) {}
            unsigned long num_outputs;
        };

        template <
            unsigned long num_outputs,
            fc_bias_mode bias_mode
            >
        class fc_
        {
            /*!
                REQUIREMENTS ON num_outputs
                    num_outputs > 0

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a fully connected layer that
                    takes an input tensor and multiplies it by a weight matrix and outputs the
                    results.

                    The dimensions of the tensors output by this layer are as follows (letting
                    IN be the input tensor and OUT the output tensor):
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == get_num_outputs()
                        - OUT.nr() == 1
                        - OUT.nc() == 1
            !*/

        public:

            fc_(
            );
            /*!
                ensures
                    - #get_num_outputs() == num_outputs
                    - #get_bias_mode() == bias_mode
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            fc_(
                num_fc_outputs o
            );
            /*!
                ensures
                    - #get_num_outputs() == o.num_outputs
                    - #get_bias_mode() == bias_mode
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            unsigned long get_num_outputs (
            ) const;
            /*!
                ensures
                    - This layer outputs column vectors that contain get_num_outputs()
                      elements. That is, the output tensor T from forward() will be such that:
                        - T.num_samples() == however many samples were given to forward().
                        - T.k() == get_num_outputs()
                        - The rest of the dimensions of T will be 1.
            !*/

            void set_num_outputs(
                long num
            );
            /*!
                requires
                    - num > 0
                    - get_layer_params().size() == 0 || get_num_outputs() == num
                      (i.e. You can't change the number of outputs in fc_ if the parameter
                      tensor has already been allocated.)
                ensures
                    - #get_num_outputs() == num
            !*/

            fc_bias_mode get_bias_mode (
            ) const;
            /*!
                ensures
                    - returns the bias mode which determines if this layer includes bias terms.
                      That is, if the bias mode is FC_HAS_BIAS then a different constant scalar
                      is added to each of the outputs of this layer.
            !*/

            double get_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its parameters be
                      multiplied by get_learning_rate_multiplier().
            !*/

            double get_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its parameters be
                      multiplied by get_weight_decay_multiplier().
            !*/

            void set_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_learning_rate_multiplier() == val
            !*/

            void set_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_weight_decay_multiplier() == val
            !*/

            double get_bias_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its bias parameters be
                      multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
            !*/

            double get_bias_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its bias parameters be
                      multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
            !*/

            void set_bias_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_learning_rate_multiplier() == val
            !*/

            void set_bias_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_weight_decay_multiplier() == val
            !*/

            void disable_bias(
            );
            /*!
                ensures
                    - bias_is_disabled() returns true
            !*/

            bool bias_is_disabled(
            ) const;
            /*!
                ensures
                    - returns true if bias learning is disabled for this layer.  This means the biases will
                      not be learned during the training and they will not be used in the forward or backward
                      methods either.
            !*/

            alias_tensor_const_instance get_weights(
            ) const;
            /*!
                ensures
                    - returns an alias of get_layer_params(), containing the weights matrix of
                      the fully connected layer.
                    - #get_weights().num_samples() is the number of elements in input sample,
                      i.e. sublayer's output's k * nc * nr.
                    - #get_bias().k() == #get_num_outputs()
                    - if get_bias_mode() == FC_HAS_BIAS:
                        - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
                    - else:
                        - #get_layer_params().size() == #get_weights().size()
            !*/

            alias_tensor_instance get_weights(
            );
            /*!
                ensures
                    - returns an alias of get_layer_params(), containing the weights matrix of
                      the fully connected layer.
                    - #get_weights().num_samples() is the number of elements in input sample,
                      i.e. sublayer's output's k * nc * nr.
                    - #get_bias().k() == #get_num_outputs()
                    - if get_bias_mode() == FC_HAS_BIAS:
                        - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
                    - else:
                        - #get_layer_params().size() == #get_weights().size()
            !*/

            alias_tensor_const_instance get_biases(
            ) const;
            /*!
                requires
                    - #get_bias_mode() == FC_HAS_BIAS
                ensures
                    - returns an alias of get_layer_params(), containing the bias vector of
                      the fully connected layer.
                    - #get_bias().num_samples() == 1
                    - #get_bias().k() == #get_num_outputs()
                    - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
            !*/

            alias_tensor_instance get_biases(
            );
            /*!
                requires
                    - #get_bias_mode() == FC_HAS_BIAS
                ensures
                    - returns an alias of get_layer_params(), containing the bias vector of
                      the fully connected layer.
                    - #get_bias().num_samples() == 1
                    - #get_bias().k() == #get_num_outputs()
                    - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/

        };

        template <
            unsigned long num_outputs,
            typename SUBNET
            >
        using fc = add_layer<fc_<num_outputs,FC_HAS_BIAS>, SUBNET>;

        template <
            unsigned long num_outputs,
            typename SUBNET
            >
        using fc_no_bias = add_layer<fc_<num_outputs,FC_NO_BIAS>, SUBNET>;

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

        struct num_con_outputs
        {
            num_con_outputs(unsigned long n) : num_outputs(n) {}
            unsigned long num_outputs;
        };

        template <
            long _num_filters,
            long _nr,
            long _nc,
            int _stride_y,
            int _stride_x,
            int _padding_y = _stride_y!=1? 0 : _nr/2,
            int _padding_x = _stride_x!=1? 0 : _nc/2
            >
        class con_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    - _num_filters > 0
                    - _nr >= 0
                    - _nc >= 0
                    - _stride_y > 0
                    - _stride_x > 0
                    - _padding_y >= 0
                    - _padding_x >= 0
                    - Also, we require that:
                        - if (_nr == 0) then
                            - _padding_y == 0
                        - else
                            - _padding_y < _nr
                        - if (_nc == 0) then
                            - _padding_x == 0
                        - else
                            - _padding_x < _nc

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a convolution layer that takes an
                    input tensor (nominally representing an image) and convolves it with a set
                    of filters and then outputs the results.

                    The dimensions of the tensors output by this layer are as follows (letting
                    IN be the input tensor and OUT the output tensor):
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == num_filters()
                        - OUT.nr() == 1+(IN.nr() + 2*padding_y() - nr())/stride_y()
                        - OUT.nc() == 1+(IN.nc() + 2*padding_x() - nc())/stride_x()

                    Note also that setting _nr or _nc to 0 has a special meaning of "set the
                    filter size equal to the input image size".  Specifically, it means:
                        - if (_nr == 0) then
                            - nr() == IN.nr()
                            - OUT.nr() == 1
                        - if (_nc == 0) then
                            - nc() == IN.nc()
                            - OUT.nc() == 1
            !*/

        public:
            con_(
            );
            /*!
                ensures
                    - #num_filters() == _num_filters
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            con_(
                num_con_outputs o
            );
            /*!
                ensures
                    - #num_filters() == o.num_outputs
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            long num_filters(
            ) const;
            /*!
                ensures
                    - returns the number of filters contained in this layer.  The k dimension
                      of the output tensors produced by this layer will be equal to the number
                      of filters.
            !*/

            void set_num_filters(
                long num
            );
            /*!
                requires
                    - num > 0
                    - get_layer_params().size() == 0 || num_filters() == num
                      (i.e. You can't change the number of filters in con_ if the parameter
                      tensor has already been allocated.)
                ensures
                    - #num_filters() == num
            !*/

            long nr(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the filters in this layer.  Note that if
                      nr()==0 then it means the size of the filter is not yet assigned, but
                      once setup() is called nr() will be set to the input tensor's nr().
                      Therefore, nr()==0 has the special interpretation of "be the same size as
                      the input tensor".
            !*/

            long nc(
            ) const;
            /*!
                ensures
                    - returns the number of columns in the filters in this layer.  Note that if
                      nc()==0 then it means the size of the filter is not yet assigned, but
                      once setup() is called nc() will be set to the input tensor's nc().
                      Therefore, nc()==0 has the special interpretation of "be the same size as
                      the input tensor".
            !*/

            long stride_y(
            ) const;
            /*!
                ensures
                    - returns the vertical stride used when convolving the filters over an
                      image.  That is, each filter will be moved stride_y() pixels down at a
                      time when it moves over the image.
            !*/

            long stride_x(
            ) const;
            /*!
                ensures
                    - returns the horizontal stride used when convolving the filters over an
                      image.  That is, each filter will be moved stride_x() pixels right at a
                      time when it moves over the image.
            !*/

            long padding_y(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the top and bottom
                      sides of the image.
            !*/

            long padding_x(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the left and right
                      sides of the image.
            !*/

            double get_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its parameters be
                      multiplied by get_learning_rate_multiplier().
            !*/

            double get_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its parameters be
                      multiplied by get_weight_decay_multiplier().
            !*/

            void set_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_learning_rate_multiplier() == val
            !*/

            void set_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_weight_decay_multiplier() == val
            !*/

            double get_bias_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its bias parameters be
                      multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
            !*/

            double get_bias_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its bias parameters be
                      multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
            !*/

            void set_bias_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_learning_rate_multiplier() == val
            !*/

            void set_bias_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_weight_decay_multiplier() == val
            !*/

            void disable_bias(
            );
            /*!
                ensures
                    - bias_is_disabled() returns true
                    - if bias was enabled and allocated, it resizes the layer parameters
                      to accommodate the filter parameters only, and free the bias parameters.
            !*/

            void enable_bias(
            );
            /*!
                ensures
                    - bias_is_disabled() returns false
                    - if bias was disabled and not allocated, it resizes the layer parameters
                      to accommodate the new zero-inizialized biases
            !*/

            bool bias_is_disabled(
            ) const;
            /*!
                ensures
                    - returns true if bias learning is disabled for this layer.  This means the biases will
                      not be learned during the training and they will not be used in the forward or backward
                      methods either.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/

        };

        template <
            long num_filters,
            long nr,
            long nc,
            int stride_y,
            int stride_x,
            typename SUBNET
            >
        using con = add_layer<con_<num_filters,nr,nc,stride_y,stride_x>, SUBNET>;

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

        template <
            long _num_filters,
            long _nr,
            long _nc,
            int _stride_y,
            int _stride_x,
            int _padding_y = _stride_y!=1? 0 : _nr/2,
            int _padding_x = _stride_x!=1? 0 : _nc/2
            >
        class cont_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    All of them must be > 0.
                    Also, we require that:
                        - 0 <= _padding_y && _padding_y < _nr
                        - 0 <= _padding_x && _padding_x < _nc

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a transposed convolution layer
                    that takes an input tensor and transpose convolves (sometimes called
                    "deconvolution") it with a set of filters and then outputs the results.

                    This is essentially a convolutional layer that allows fractional strides.
                    Therefore, you can make output tensors that are larger than the input
                    tensors using this layer type.

                    The dimensions of the tensors output by this layer are as follows (letting
                    IN be the input tensor and OUT the output tensor):
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == num_filters()
                        - OUT.nr() == stride_y()*(IN.nr()-1) + nr() - 2*padding_y()
                        - OUT.nc() == stride_x()*(IN.nc()-1) + nc() - 2*padding_x()
            !*/

        public:
            cont_(
            );
            /*!
                ensures
                    - #num_filters() == _num_filters
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            cont_(
                num_con_outputs o
            );
            /*!
                ensures
                    - #num_filters() == o.num_outputs
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 1
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 0
            !*/

            long num_filters(
            ) const;
            /*!
                ensures
                    - returns the number of filters contained in this layer.  The k dimension
                      of the output tensors produced by this layer will be equal to the number
                      of filters.
            !*/

            void set_num_filters(
                long num
            );
            /*!
                requires
                    - num > 0
                    - get_layer_params().size() == 0 || num_filters() == num
                      (i.e. You can't change the number of filters in cont_ if the parameter
                      tensor has already been allocated.)
                ensures
                    - #num_filters() == num
            !*/

            long nr(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the filters in this layer.
            !*/

            long nc(
            ) const;
            /*!
                ensures
                    - returns the number of columns in the filters in this layer.
            !*/

            long stride_y(
            ) const;
            /*!
                ensures
                    - returns the vertical stride used when convolving the filters over an
                      image.  That is, each filter will be moved 1.0/stride_y() pixels down at
                      a time when it moves over the image.
            !*/

            long stride_x(
            ) const;
            /*!
                ensures
                    - returns the horizontal stride used when convolving the filters over an
                      image.  That is, each filter will be moved 1.0/stride_x() pixels right at
                      a time when it moves over the image.
            !*/

            long padding_y(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the top and bottom
                      sides of the image.
            !*/

            long padding_x(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the left and right
                      sides of the image.
            !*/

            double get_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its parameters be
                      multiplied by get_learning_rate_multiplier().
            !*/

            double get_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its parameters be
                      multiplied by get_weight_decay_multiplier().
            !*/

            void set_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_learning_rate_multiplier() == val
            !*/

            void set_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_weight_decay_multiplier() == val
            !*/

            double get_bias_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its bias parameters be
                      multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
            !*/

            double get_bias_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its bias parameters be
                      multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
            !*/

            void set_bias_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_learning_rate_multiplier() == val
            !*/

            void set_bias_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_weight_decay_multiplier() == val
            !*/

            void disable_bias(
            );
            /*!
                ensures
                    - bias_is_disabled() returns true
            !*/

            bool bias_is_disabled(
            ) const;
            /*!
                ensures
                    - returns true if bias learning is disabled for this layer.  This means the biases will
                      not be learned during the training and they will not be used in the forward or backward
                      methods either.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/

        };

        template <
            long num_filters,
            long nr,
            long nc,
            int stride_y,
            int stride_x,
            typename SUBNET
            >
        using cont = add_layer<cont_<num_filters,nr,nc,stride_y,stride_x>, SUBNET>;

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

        template <
            int scale_y,
            int scale_x
            >
        class upsample_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    All of them must be >= 1.

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it allows you to upsample a layer using
                    bilinear interpolation.  To be very specific, it upsamples each of the
                    channels in an input tensor.  Therefore, if IN is the input tensor to this
                    layer and OUT the output tensor, then we will have:
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == IN.k()
                        - OUT.nr() == IN.nr()*scale_y
                        - OUT.nc() == IN.nc()*scale_x
                        - for all valid i,k:  image_plane(OUT,i,k) is a copy of
                          image_plane(IN,i,k) that has been bilinearly interpolated to fit into
                          the shape of image_plane(OUT,i,k).
            !*/
        public:

            upsample_(
            );
            /*!
                ensures
                    - This object has no state, so the constructor does nothing, aside from
                      providing default constructability.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            int scale,
            typename SUBNET
            >
        using upsample = add_layer<upsample_<scale,scale>, SUBNET>;

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

        template <
            long NR_,
            long NC_
            >
        class resize_to_
        {
            /*!
                REQUIREMENTS ON THE INPUT ARGUMENTS
                    - NR_ >= 1
                    - NC_ >= 1

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it allows you to resize a layer using
                    bilinear interpolation.  To be very specific, it resizes each of the
                    channels in an input tensor.  Therefore, if IN is the input tensor to this
                    layer and OUT the output tensor, then we will have:
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == IN.k()
                        - OUT.nr() == NR_
                        - OUT.nc() == NC_
                        - for all valid i,k:  image_plane(OUT,i,k) is a copy of
                          image_plane(IN,i,k) that has been bilinearly interpolated to fit into
                          the shape of image_plane(OUT,i,k).
            !*/
        public:

            resize_to_(
            );
            /*!
                ensures
                    - This object has no state, so the constructor does nothing, aside from
                      providing default constructability.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            long NR,
            long NC,
            typename SUBNET
            >
        using resize_to = add_layer<resize_to_<NR,NC>, SUBNET>;

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

        class dropout_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a dropout layer.  Therefore, it
                    passes its inputs through the stochastic function f(x) which outputs either
                    0 or x.  The probability of 0 being output is given by the drop_rate
                    argument to this object's constructor.

                    Note that, after you finish training a network with dropout, it is a good
                    idea to replace each dropout_ layer with a multiply_ layer because the
                    multiply_ layer is faster and deterministic.
            !*/

        public:

            explicit dropout_(
                float drop_rate = 0.5
            );
            /*!
                requires
                    - 0 <= drop_rate <= 1
                ensures
                    - #get_drop_rate() == drop_rate
            !*/

            float get_drop_rate (
            ) const;
            /*!
                ensures
                    - returns the probability that an individual input value to this layer will
                      be replaced with 0.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <typename SUBNET>
        using dropout = add_layer<dropout_, SUBNET>;

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

        class multiply_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a basic layer that just
                    multiplies its input tensor with a constant value and returns the result.
                    It therefore has no learnable parameters.
            !*/

        public:
            explicit multiply_(
                float val = 0.5
            );
            /*!
                ensures
                    - #get_multiply_value() == val
            !*/

            multiply_ (
                const dropout_& item
            );
            /*!
                ensures
                    - #get_multiply_value() == 1-item.get_drop_rate()
                      (i.e. We construct the multiply_ layer so that it is essentially a
                      deterministic version of the given dropout_ layer)
            !*/

            float get_multiply_value (
            ) const;
            /*!
                ensures
                    - this layer simply multiplies its input tensor by get_multiply_value() and
                      produces the result as output.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <typename SUBNET>
        using multiply = add_layer<multiply_, SUBNET>;

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

        const double DEFAULT_LAYER_NORM_EPS = 1e-5;

        class layer_norm_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a batch normalization layer that
                    implements the method described in the paper:
                        Layer Normalization by Jimmy Lei Ba, Jamie Ryan Kiros, Geoffrey E. Hinton

                    In particular, this layer produces output tensors with the same
                    dimensionality as the input tensors, except that the mean and variances of
                    the elements in each sample have been standardized to 0 and 1 respectively.
                    This is different from batch normalization, since this layer learns one scaling
                    factor and one bias for each sample in the batch, independently.  As a result,
                    this layer is batch-size independent.
            !*/
        public:
            layer_norm_(
            );
            /*!
                ensures
                    - #get_learning_rate_multiplier()       == 1
                    - #get_weight_decay_multiplier()        == 0
                    - #get_bias_learning_rate_multiplier()  == 1
                    - #get_bias_weight_decay_multiplier()   == 1
                    - #get_eps() == DEFAULT_LAYER_NORM_EPS
            !*/

            explicit layer_norm_(
                double eps_ = DEFAULT_LAYER_NORM_EPS
            )
            /*!
                requires
                    - eps > 0
                ensures
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 0
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 1
                    - #get_eps() == eps
            !*/

            double get_eps(
            ) const;
            /*!
                ensures
                    - When doing layer normalization, we are dividing by the standard
                      deviation.  This epsilon value returned by this function is added to the
                      variance to prevent the division from dividing by zero.
            !*/

            double get_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its parameters be
                      multiplied by get_learning_rate_multiplier().
            !*/

            double get_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its parameters be
                      multiplied by get_weight_decay_multiplier().
            !*/

            void set_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_learning_rate_multiplier() == val
            !*/

            void set_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_weight_decay_multiplier() == val
            !*/

            double get_bias_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its bias parameters be
                      multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
            !*/

            double get_bias_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its bias parameters be
                      multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
            !*/

            void set_bias_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_learning_rate_multiplier() == val
            !*/

            void set_bias_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_weight_decay_multiplier() == val
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

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

        enum layer_mode
        {
            CONV_MODE = 0, // convolutional mode
            FC_MODE = 1    // fully connected mode
        };

        const double DEFAULT_BATCH_NORM_EPS = 0.0001;

        template <
            layer_mode mode
            >
        class bn_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a batch normalization layer that
                    implements the method described in the paper:
                        Batch Normalization: Accelerating Deep Network Training by Reducing
                        Internal Covariate Shift by Sergey Ioffe and Christian Szegedy

                    In particular, this layer produces output tensors with the same
                    dimensionality as the input tensors, except that the mean and variances of
                    the elements have been standardized to 0 and 1 respectively.

                    It should also be noted that when tensors with a num_samples() dimension of
                    1 are passed to this layer it doesn't perform batch normalization.
                    Instead, it runs in "inference mode" where the learned linear normalizing
                    transformation is used to transform the tensor.

                    Finally, after you finish training a batch normalized network, it is a good
                    idea to replace each bn_ layer with an affine_ layer because the affine_
                    layer is faster and will never surprise you by performing batch
                    normalization on tensors that have a num_samples() dimension > 1.  This allows
                    you to run large mini-batches of samples through your final network without
                    batch normalization executing at all.
            !*/

        public:
            bn_(
            );
            /*!
                ensures
                    - #get_mode() == mode
                    - #get_running_stats_window_size()      == 100
                    - #get_learning_rate_multiplier()       == 1
                    - #get_weight_decay_multiplier()        == 0
                    - #get_bias_learning_rate_multiplier()  == 1
                    - #get_bias_weight_decay_multiplier()   == 1
                    - #get_eps() == tt::DEFAULT_BATCH_NORM_EPS
            !*/

            explicit bn_(
                unsigned long window_size,
                double eps = tt::DEFAULT_BATCH_NORM_EPS
            );
            /*!
                requires
                    - eps > 0
                    - window_size > 0
                ensures
                    - #get_mode() == mode
                    - #get_running_stats_window_size()     == window_size
                    - #get_learning_rate_multiplier()      == 1
                    - #get_weight_decay_multiplier()       == 0
                    - #get_bias_learning_rate_multiplier() == 1
                    - #get_bias_weight_decay_multiplier()  == 1
                    - #get_eps() == eps
            !*/

            layer_mode get_mode(
            ) const;
            /*!
                ensures
                    - returns the mode of this layer, either CONV_MODE or FC_MODE.
                      If the mode is FC_MODE then the normalization is applied across the
                      samples in a tensor (i.e. k()*nr()*nc() different things will be
                      normalized).  Otherwise, normalization is applied across everything
                      except for the k() dimension, resulting in there being only k()
                      normalization equations that are applied spatially over the tensor.

                      Therefore, if you are putting batch normalization after a fully connected
                      layer you should use FC_MODE.  Otherwise, if you are putting batch
                      normalization after a convolutional layer you should use CONV_MODE.
            !*/

            double get_eps(
            ) const;
            /*!
                ensures
                    - When doing batch normalization, we are dividing by the standard
                      deviation.  This epsilon value returned by this function is added to the
                      variance to prevent the division from dividing by zero.
            !*/

            unsigned long get_running_stats_window_size (
            ) const;
            /*!
                ensures
                    - Just as recommended in the batch normalization paper, this object keeps a
                      running average of the mean and standard deviations of the features.
                      These averages are used during "inference mode" so you can run a single
                      object through a batch normalized network.  They are also what is used to
                      initialize an affine_ layer that is constructed from a bn_ layer.  This
                      function returns the effective number of recent samples used to compute
                      the running average.
            !*/

            void set_running_stats_window_size (
                unsigned long new_window_size
            );
            /*!
                requires
                    - new_window_size > 0
                ensures
                    - #get_running_stats_window_size() == new_window_size
            !*/

            double get_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its parameters be
                      multiplied by get_learning_rate_multiplier().
            !*/

            double get_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its parameters be
                      multiplied by get_weight_decay_multiplier().
            !*/

            void set_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_learning_rate_multiplier() == val
            !*/

            void set_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_weight_decay_multiplier() == val
            !*/

            double get_bias_learning_rate_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the learning rate used to optimize its bias parameters be
                      multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
            !*/

            double get_bias_weight_decay_multiplier(
            ) const;
            /*!
                ensures
                    - returns a multiplier number.  The interpretation is that this object is
                      requesting that the weight decay used to optimize its bias parameters be
                      multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
            !*/

            void set_bias_learning_rate_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_learning_rate_multiplier() == val
            !*/

            void set_bias_weight_decay_multiplier(
                double val
            );
            /*!
                requires
                    - val >= 0
                ensures
                    - #get_bias_weight_decay_multiplier() == val
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <typename SUBNET>
        using bn_con = add_layer<bn_<CONV_MODE>, SUBNET>;
        template <typename SUBNET>
        using bn_fc = add_layer<bn_<FC_MODE>, SUBNET>;

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

        template <typename net_type>
        void disable_duplicative_biases (
            const net_type& net
        );
        /*!
            requires
                - net_type is an object of type add_layer, add_loss_layer, add_skip_layer, or
                  add_tag_layer.
            ensures
                - Disables bias for all bn_ and layer_norm_ inputs.
                - Sets the get_bias_learning_rate_multiplier() and get_bias_weight_decay_multiplier()
                  to zero of all bn_ and layer_norm_ inputs.
        !*/

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

        class affine_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it applies a simple pointwise linear
                    transformation to an input tensor.  You can think of it as having two
                    parameter tensors, gamma and beta.  If the input tensor is called INPUT
                    then the output of this layer is:
                        gamma*INPUT+beta
                    where all operations are performed element wise and each sample in the
                    INPUT tensor is processed separately.

                    Moreover, this object has two modes that affect the dimensionalities of
                    gamma and beta and how they are applied to compute gamma*INPUT+beta.  If
                    get_mode()==FC_MODE then gamma and beta each have the same dimensionality
                    as the input tensor, except their num_samples() dimensions are 1.  If
                    get_mode()==CONV_MODE then gamma and beta have all their dimensions set
                    to 1 except for k(), which is equal to INPUT.k().

                    In either case, the computation of gamma*INPUT+beta is performed pointwise
                    over all the elements of INPUT using either:
                        OUTPUT(n,k,r,c) == gamma(1,k,r,c)*INPUT(n,k,r,c)+beta(1,k,r,c)
                    or
                        OUTPUT(n,k,r,c) == gamma(1,k,1,1)*INPUT(n,k,r,c)+beta(1,k,1,1)
                    as appropriate.

                    Finally, note that the parameters of this layer are not learnable and
                    therefore not modified during network updates.  Instead, the layer will
                    perform the identity transformation unless it is initialized with a bn_
                    layer, in which case it will perform whatever transformation the bn_ layer
                    has learned.
            !*/

        public:

            affine_(
            );
            /*!
                ensures
                    - #get_mode() == FC_MODE
            !*/

            affine_(
                layer_mode mode
            );
            /*!
                ensures
                    - #get_mode() == mode
            !*/

            template <
                layer_mode mode
                >
            affine_(
                const bn_<mode>& layer
            );
            /*!
                ensures
                    - Constructs affine_ so that it performs the same transformation as the
                      supplied batch normalization layer.  You would want to do this after you
                      finish training a network with bn_ layers because the affine_ layer will
                      execute faster.
                    - #get_mode() == layer.get_mode()
            !*/

            layer_mode get_mode(
            ) const;
            /*!
                ensures
                    - returns the mode of this layer, either CONV_MODE or FC_MODE.
            !*/

            void disable(
            );
            /*!
                ensures
                    - #get_layer_params().size() == 0.
                    - when forward_inplace and backward_inplace are called, they return immediately doing nothing.
                      Causing this layer to trivially perform the an identity transform.
            !*/

            alias_tensor_instance get_gamma();
            /*!
                ensures
                    - returns the gamma parameter that defines the behavior of forward().
            !*/

            alias_tensor_const_instance get_gamma() const;
            /*!
                ensures
                    - returns the gamma parameter that defines the behavior of forward().
            !*/

            alias_tensor_instance get_beta();
            /*!
                ensures
                    - returns the beta parameter that defines the behavior of forward().
            !*/

            alias_tensor_const_instance get_beta() const;
            /*!
                ensures
                    - returns the beta parameter that defines the behavior of forward().
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the
                EXAMPLE_COMPUTATIONAL_LAYER_ interface.  Also note that get_layer_params()
                always returns an empty tensor since there are no learnable parameters in this
                object.
            !*/

        };

        template <typename SUBNET>
        using affine = add_layer<affine_, SUBNET>;

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

        template <
            long _nr,
            long _nc,
            int _stride_y,
            int _stride_x,
            int _padding_y = _stride_y!=1? 0 : _nr/2,
            int _padding_x = _stride_x!=1? 0 : _nc/2
            >
        class max_pool_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    - _nr >= 0
                    - _nc >= 0
                    - _stride_y > 0
                    - _stride_x > 0
                    - _padding_y >= 0
                    - _padding_x >= 0
                    - if (_nr != 0) then
                        - _padding_y < _nr
                    - else
                        - _padding_y == 0
                    - if (_nc != 0) then
                        - _padding_x < _nr
                    - else
                        - _padding_x == 0

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a max pooling layer that takes an
                    input tensor and downsamples it.  It does this by sliding a window over the
                    images in an input tensor and outputting, for each channel, the maximum
                    element within the window.

                    If _nr == 0 then it means the filter size covers all the rows in the input
                    tensor, similarly for the _nc parameter.  To be precise, if we call the
                    input tensor IN and the output tensor OUT, then OUT is defined as follows:
                        - let FILT_NR == (nr()==0) ? IN.nr() : nr()
                        - let FILT_NC == (nc()==0) ? IN.nc() : nc()
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == IN.k()
                        - OUT.nr() == 1+(IN.nr() + 2*padding_y() - FILT_NR)/stride_y()
                        - OUT.nc() == 1+(IN.nc() + 2*padding_x() - FILT_NC)/stride_x()
                        - for all valid s, k, r, and c:
                            - image_plane(OUT,s,k)(r,c) == max(subm_clipped(image_plane(IN,s,k),
                                                                      centered_rect(x*stride_x() + FILT_NC/2 - padding_x(),
                                                                                    y*stride_y() + FILT_NR/2 - padding_y(),
                                                                                    FILT_NC,
                                                                                    FILT_NR)))
            !*/

        public:

            max_pool_ (
            );
            /*!
                ensures
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
            !*/

            long nr(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the pooling window or 0 if the window size
                      is "the entire input tensor".
            !*/

            long nc(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the pooling window or 0 if the window size
                      is "the entire input tensor".
            !*/

            long stride_y(
            ) const;
            /*!
                ensures
                    - returns the vertical stride used when scanning the max pooling window
                      over an image.  That is, each window will be moved stride_y() pixels down
                      at a time when it moves over the image.
            !*/

            long stride_x(
            ) const;
            /*!
                ensures
                    - returns the horizontal stride used when scanning the max pooling window
                      over an image.  That is, each window will be moved stride_x() pixels down
                      at a time when it moves over the image.
            !*/

            long padding_y(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the top and bottom
                      sides of the image.
            !*/

            long padding_x(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the left and right
                      sides of the image.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& computed_output, const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <
            long nr,
            long nc,
            int stride_y,
            int stride_x,
            typename SUBNET
            >
        using max_pool = add_layer<max_pool_<nr,nc,stride_y,stride_x>, SUBNET>;

        template <
            typename SUBNET
            >
        using max_pool_everything = add_layer<max_pool_<0,0,1,1>, SUBNET>;

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

        template <
            long _nr,
            long _nc,
            int _stride_y,
            int _stride_x,
            int _padding_y = _stride_y!=1? 0 : _nr/2,
            int _padding_x = _stride_x!=1? 0 : _nc/2
            >
        class avg_pool_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    - _nr >= 0
                    - _nc >= 0
                    - _stride_y > 0
                    - _stride_x > 0
                    - _padding_y >= 0
                    - _padding_x >= 0
                    - if (_nr != 0) then
                        - _padding_y < _nr
                    - else
                        - _padding_y == 0
                    - if (_nc != 0) then
                        - _padding_x < _nr
                    - else
                        - _padding_x == 0

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines an average pooling layer that
                    takes an input tensor and downsamples it.  It does this by sliding a window
                    over the images in an input tensor and outputting, for each channel, the
                    average element within the window.

                    If _nr == 0 then it means the filter size covers all the rows in the input
                    tensor, similarly for the _nc parameter.  To be precise, if we call the
                    input tensor IN and the output tensor OUT, then OUT is defined as follows:
                        - let FILT_NR == (nr()==0) ? IN.nr() : nr()
                        - let FILT_NC == (nc()==0) ? IN.nc() : nc()
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == IN.k()
                        - OUT.nr() == 1+(IN.nr() + 2*padding_y() - FILT_NR)/stride_y()
                        - OUT.nc() == 1+(IN.nc() + 2*padding_x() - FILT_NC)/stride_x()
                        - for all valid s, k, r, and c:
                            - image_plane(OUT,s,k)(r,c) == mean(subm_clipped(image_plane(IN,s,k),
                                                                      centered_rect(x*stride_x() + FILT_NC/2 - padding_x(),
                                                                                    y*stride_y() + FILT_NR/2 - padding_y(),
                                                                                    FILT_NC,
                                                                                    FILT_NR)))
            !*/

        public:

            avg_pool_ (
            );
            /*!
                ensures
                    - #nr() == _nr
                    - #nc() == _nc
                    - #stride_y() == _stride_y
                    - #stride_x() == _stride_x
                    - #padding_y() == _padding_y
                    - #padding_x() == _padding_x
            !*/

            long nr(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the pooling window or 0 if the window size
                      is "the entire input tensor".
            !*/

            long nc(
            ) const;
            /*!
                ensures
                    - returns the number of rows in the pooling window or 0 if the window size
                      is "the entire input tensor".
            !*/

            long stride_y(
            ) const;
            /*!
                ensures
                    - returns the vertical stride used when scanning the pooling window
                      over an image.  That is, each window will be moved stride_y() pixels down
                      at a time when it moves over the image.
            !*/

            long stride_x(
            ) const;
            /*!
                ensures
                    - returns the horizontal stride used when scanning the pooling window
                      over an image.  That is, each window will be moved stride_x() pixels down
                      at a time when it moves over the image.
            !*/

            long padding_y(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the top and bottom
                      sides of the image.
            !*/

            long padding_x(
            ) const;
            /*!
                ensures
                    - returns the number of pixels of zero padding added to the left and right
                      sides of the image.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& computed_output, const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/

        };

        template <
            long nr,
            long nc,
            int stride_y,
            int stride_x,
            typename SUBNET
            >
        using avg_pool = add_layer<avg_pool_<nr,nc,stride_y,stride_x>, SUBNET>;

        template <
            typename SUBNET
            >
        using avg_pool_everything = add_layer<avg_pool_<0,0,1,1>, SUBNET>;

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

        class relu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a rectified linear layer.
                    Therefore, it passes its inputs through the function
                        f(x)=max(x,0)
                    where f() is applied pointwise across the input tensor.
            !*/

        public:

            relu_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using relu = add_layer<relu_, SUBNET>;

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

        class prelu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a parametric rectified linear
                    layer.  Therefore, it passes its inputs through the function
                        f(x) = x>0 ? x : p*x
                    where f() is applied pointwise across the input tensor and p is a scalar
                    parameter learned by this layer.

                    This is the layer type introduced in the paper:
                        He, Kaiming, et al. "Delving deep into rectifiers: Surpassing
                        human-level performance on imagenet classification." Proceedings of the
                        IEEE International Conference on Computer Vision. 2015.
            !*/

        public:

            explicit prelu_(
                float initial_param_value = 0.25
            );
            /*!
                ensures
                    - The p parameter will be initialized with initial_param_value.
                    - #get_initial_param_value() == initial_param_value.
            !*/

            float get_initial_param_value (
            ) const;
            /*!
                ensures
                    - returns the initial value of the prelu parameter.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <typename SUBNET>
        using prelu = add_layer<prelu_, SUBNET>;

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

        class leaky_relu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a leaky rectified linear
                    layer.  Therefore, it passes its inputs through the function
                        f(x) = x>0 ? x : alpha*x
                    where f() is applied pointwise across the input tensor and alpha is a
                    non-learned scalar.

                    This is the layer type introduced in the paper:
                        A. L. Maas, A. Y. Hannun, and A. Y. Ng. "Rectifier nonlinearities improve
                        neural network acoustic models". In ICML, 2013.
            !*/

        public:
            explicit leaky_relu_(
                float alpha = 0.01f
            );
            /*!
                ensures
                    - the alpha parameter will be initialized with the alpha value
            !*/

            float get_alpha(
            ) const;
            /*!
                ensures
                    - returns the alpha parameter of the leaky_relu
            !*/

            template <typename SUBNET> void setup(const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using leaky_relu = add_layer<prelu_, SUBNET>;

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

        class sig_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a sigmoid layer.  Therefore, it
                    passes its inputs through the function
                        f(x)=1/(1+exp(-x))
                    where f() is applied pointwise across the input tensor.
            !*/

        public:

            sig_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using sig = add_layer<sig_, SUBNET>;

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

        class mish_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a mish layer.  Therefore, it
                    passes its inputs through the function
                        f(x)= x*tanh(log(1+exp(x)))
                    where f() is applied pointwise across the input tensor.

                    This is the layer type introduced in the paper:
                    Diganta Misra. "Mish: A Self Regularized Non-Monotonic Activation Function"
            !*/

        public:

            mish_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& data_output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor&);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using mish = add_layer<mish_, SUBNET>;

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

        class htan_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a hyperbolic tangent layer.
                    Therefore, it passes its inputs through the function
                        f(x)=std::tanh(x)
                    where f() is applied pointwise across the input tensor.
            !*/

        public:

            htan_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using htan = add_layer<htan_, SUBNET>;

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

        class clipped_relu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a clipped version of the relu layer.
                    Therefore, it passes its inputs through the function
                        f(x) = min(max(x, 0), ceiling)
                    where f() is applied pointwise across the input tensor and ceiling is a
                    non-learned scalar.
            !*/

        public:

            clipped_relu_(
                const float ceiling = 6.0f
            );
            /*!
                ensures
                    - the ceiling parameter will be initialized with the ceiling value
            !*/

            float get_ceiling() const;
            /*!
                ensures
                    - returns the celiling parameter of the clipped_relu
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using clipped_relu = add_layer<clipped_relu_, SUBNET>;

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

        class elu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines an exponential linear unit.
                    Therefore, it passes its inputs through the function
                        f(x) = x>0 ? x : alpha*(exp(x)-1)
                    where f() is applied pointwise across the input tensor and alpha is a
                    non-learned scalar.

                    This is the layer type introduced in the paper:
                    Djork-Arné Clevert, Thomas Unterthiner, Sepp Hochreiter.
                    "Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)".
            !*/

        public:

            elu_(
                const float alpha = 1.0f
            );
            /*!
                ensures
                    - the alpha parameter will be initialized with the alpha value
            !*/

            float get_alpha() const;
            /*!
                ensures
                    - returns the alpha parameter of the elu
            !*/
            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using elu = add_layer<elu_, SUBNET>;

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

        class gelu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a gelu layer.  Therefore, it
                    passes its inputs through the function
                            f(x)= x/2 * (1 + erf(x/sqrt(2))
                    where f() is applied pointwise across the input tensor.

                    This is the layer type introduced in the paper:
                    Dan Hendrycks, Kevin Gimpel. "Gaussian Error Linear Units (GELUs)".
            !*/

        public:

            gelu_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& data_output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor&);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using gelu = add_layer<gelu_, SUBNET>;

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

        class smelu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a smooth rectified linear
                    layer.  Therefore, it passes its inputs through the function f(x):
                        - if (x > beta) 1
                        - if (x < -beta) 0
                        - else std::pow(x + beta, 2) / (4 * beta)
                    where f() is applied pointwise across the input tensor and beta is a
                    non-learned scalar.

                    This is the layer type introduced in the paper:
                    "Smooth activations and reproducibility in deep networks" by
                    Gil I. Shamir, Dong Lin, Lorenzo Coviello (https://arxiv.org/abs/2010.09931)
            !*/

        public:
            explicit smelu_(
                float beta = 1
            );
            /*!
                ensures
                    - the beta parameter will be initialized with the beta value
            !*/

            float get_beta(
            ) const;
            /*!
                ensures
                    - returns the beta parameter of the smelu
            !*/

            template <typename SUBNET> void setup(const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using smelu = add_layer<prelu_, SUBNET>;

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

        class silu_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a silu layer.  Therefore, it
                    passes its inputs through the function
                            f(x)= x * sigmoid(x) = x / (1 + exp(-x))
                    where f() is applied pointwise across the input tensor.

                    This is the layer type introduced in the paper:
                    Dan Hendrycks, Kevin Gimpel. "Gaussian Error Linear Units (GELUs)".
            !*/

        public:

            silu_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& data_output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor&);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using silu = add_layer<silu_, SUBNET>;

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

        class softmax_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a softmax layer.  To be precise,
                    we define the softmax function s(x) as:
                        s(x) == exp(x)/sum(exp(x))
                    where x is a vector.  Then this layer treats its input tensor as a
                    collection of multi-channel images and applies s() to each spatial location
                    in each image.  In each application, the tensor::k() channel elements at
                    each position are input to s() and then replaced by the outputs of s().

                    This means that, for example, if you collapsed each output image to a 1
                    channel image by adding the channels then you would end up with images
                    where each pixel value was 1.  This is because the sum of the outputs of
                    s() will always be equal to 1.
            !*/

        public:

            softmax_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using softmax = add_layer<softmax_, SUBNET>;

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

        class softmax_all_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, it defines a softmax layer.  To be precise,
                    we define the softmax function s(x) as:
                        s(x) == exp(x)/sum(exp(x))
                    where x is a vector.  Then this layer treats its input tensor as a
                    collection of tensor::num_samples() vectors and applies s() to each vector
                    in the tensor.  Therefore, there are logically tensor::num_samples()
                    invocations of s().
            !*/

        public:

            softmax_all_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
                interface.  Note that this layer doesn't have any parameters, so the tensor
                returned by get_layer_params() is always empty.
            !*/
        };

        template <typename SUBNET>
        using softmax_all = add_layer<softmax_all_, SUBNET>;

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

        template <
            template<typename> class tag
            >
        class add_prev_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer simply adds the output of two previous layers.
                    In particular, it adds the tensor from its immediate predecessor layer,
                    sub.get_output(), with the tensor from a deeper layer,
                    layer<tag>(sub).get_output().

                    Therefore, you supply a tag via add_prev_'s template argument that tells it
                    what layer to add to the output of the previous layer.  The result of this
                    addition is output by add_prev_.  Finally, the addition happens pointwise
                    according to 4D tensor arithmetic.  If the dimensions don't match then
                    missing elements are presumed to be equal to 0.  Moreover, each dimension
                    of the output tensor is equal to the maximum dimension of either of the
                    inputs.  That is, if the tensors A and B are being added to produce C then:
                        - C.num_samples() == max(A.num_samples(), B.num_samples())
                        - C.k()  == max(A.k(), B.k())
                        - C.nr() == max(A.nr(), B.nr())
                        - C.nc() == max(A.nc(), B.nc())
            !*/

        public:
            add_prev_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            template<typename> class tag,
            typename SUBNET
            >
        using add_prev = add_layer<add_prev_<tag>, SUBNET>;

        // Here we add some convenient aliases for using add_prev_ with the tag layers.
        template <typename SUBNET> using add_prev1  = add_prev<tag1, SUBNET>;
        template <typename SUBNET> using add_prev2  = add_prev<tag2, SUBNET>;
        template <typename SUBNET> using add_prev3  = add_prev<tag3, SUBNET>;
        template <typename SUBNET> using add_prev4  = add_prev<tag4, SUBNET>;
        template <typename SUBNET> using add_prev5  = add_prev<tag5, SUBNET>;
        template <typename SUBNET> using add_prev6  = add_prev<tag6, SUBNET>;
        template <typename SUBNET> using add_prev7  = add_prev<tag7, SUBNET>;
        template <typename SUBNET> using add_prev8  = add_prev<tag8, SUBNET>;
        template <typename SUBNET> using add_prev9  = add_prev<tag9, SUBNET>;
        template <typename SUBNET> using add_prev10 = add_prev<tag10, SUBNET>;
        using add_prev1_  = add_prev_<tag1>;
        using add_prev2_  = add_prev_<tag2>;
        using add_prev3_  = add_prev_<tag3>;
        using add_prev4_  = add_prev_<tag4>;
        using add_prev5_  = add_prev_<tag5>;
        using add_prev6_  = add_prev_<tag6>;
        using add_prev7_  = add_prev_<tag7>;
        using add_prev8_  = add_prev_<tag8>;
        using add_prev9_  = add_prev_<tag9>;
        using add_prev10_ = add_prev_<tag10>;

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

        template <
            template<typename> class tag
            >
        class mult_prev_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer simply multiplies the output of two previous
                    layers.  In particular, it multiplies the tensor from its immediate
                    predecessor layer, sub.get_output(), with the tensor from a deeper layer,
                    layer<tag>(sub).get_output().

                    Therefore, you supply a tag via mult_prev_'s template argument that tells
                    it what layer to multiply with the output of the previous layer.  The
                    result of this multiplication is output by mult_prev_.  Finally, the
                    multiplication happens pointwise according to 4D tensor arithmetic.  If the
                    dimensions don't match then missing elements are presumed to be equal to 0.
                    Moreover, each dimension of the output tensor is equal to the maximum
                    dimension of either of the inputs.  That is, if the tensors A and B are
                    being multiplied to produce C then:
                        - C.num_samples() == max(A.num_samples(), B.num_samples())
                        - C.k()  == max(A.k(), B.k())
                        - C.nr() == max(A.nr(), B.nr())
                        - C.nc() == max(A.nc(), B.nc())
            !*/

        public:
            mult_prev_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            template<typename> class tag,
            typename SUBNET
            >
        using mult_prev = add_layer<mult_prev_<tag>, SUBNET>;

        // Here we add some convenient aliases for using mult_prev_ with the tag layers.
        template <typename SUBNET> using mult_prev1  = mult_prev<tag1, SUBNET>;
        template <typename SUBNET> using mult_prev2  = mult_prev<tag2, SUBNET>;
        template <typename SUBNET> using mult_prev3  = mult_prev<tag3, SUBNET>;
        template <typename SUBNET> using mult_prev4  = mult_prev<tag4, SUBNET>;
        template <typename SUBNET> using mult_prev5  = mult_prev<tag5, SUBNET>;
        template <typename SUBNET> using mult_prev6  = mult_prev<tag6, SUBNET>;
        template <typename SUBNET> using mult_prev7  = mult_prev<tag7, SUBNET>;
        template <typename SUBNET> using mult_prev8  = mult_prev<tag8, SUBNET>;
        template <typename SUBNET> using mult_prev9  = mult_prev<tag9, SUBNET>;
        template <typename SUBNET> using mult_prev10 = mult_prev<tag10, SUBNET>;
        using mult_prev1_  = mult_prev_<tag1>;
        using mult_prev2_  = mult_prev_<tag2>;
        using mult_prev3_  = mult_prev_<tag3>;
        using mult_prev4_  = mult_prev_<tag4>;
        using mult_prev5_  = mult_prev_<tag5>;
        using mult_prev6_  = mult_prev_<tag6>;
        using mult_prev7_  = mult_prev_<tag7>;
        using mult_prev8_  = mult_prev_<tag8>;
        using mult_prev9_  = mult_prev_<tag9>;
        using mult_prev10_ = mult_prev_<tag10>;

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

        template <
            template<typename> class tag
            >
        class resize_prev_to_tagged_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer resizes the output channels of the previous layer
                    to have the same number of rows and columns as the output of the tagged layer.

                    This layer uses bilinear interpolation. If the sizes match already, then it
                    simply copies the data.

                    Therefore, you supply a tag via resize_prev_to_tagged's template argument that
                    tells it what layer to use for the target size.

                    If tensor PREV is resized to size of tensor TAGGED, then a tensor OUT is
                    produced such that:
                        - OUT.num_samples() == PREV.num_samples()
                        - OUT.k()  == PREV.k()
                        - OUT.nr() == TAGGED.nr()
                        - OUT.nc() == TAGGED.nc()
            !*/

        public:
            resize_prev_to_tagged_(
            );

            template <typename SUBNET> void setup(const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            template<typename> class tag,
            typename SUBNET
            >
        using resize_prev_to_tagged = add_layer<resize_prev_to_tagged_<tag>, SUBNET>;

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

        template <
            template<typename> class tag
            >
        class scale_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer scales the output channels of the tagged layer
                    by multiplying it with the output of the previous layer.  To be specific:
                        - Let INPUT  == layer<tag>(sub).get_output()
                        - Let SCALES == sub.get_output()
                        - This layer takes INPUT and SCALES as input.
                        - The output of this layer has the same dimensions as INPUT.
                        - This layer requires:
                            - SCALES.num_samples() == INPUT.num_samples()
                            - SCALES.k()  == INPUT.k()
                            - SCALES.nr() == 1
                            - SCALES.nc() == 1
                        - The output tensor is produced by pointwise multiplying SCALES with
                          INPUT at each spatial location.  Therefore, if OUT is the output of
                          this layer then we would have:
                            OUT(n,k,r,c) == INPUT(n,k,r,c)*SCALES(n,k)
            !*/

        public:
            scale_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            template<typename> class tag,
            typename SUBNET
            >
        using scale = add_layer<scale_<tag>, SUBNET>;

        // Here we add some convenient aliases for using scale_ with the tag layers.
        template <typename SUBNET> using scale1  = scale<tag1, SUBNET>;
        template <typename SUBNET> using scale2  = scale<tag2, SUBNET>;
        template <typename SUBNET> using scale3  = scale<tag3, SUBNET>;
        template <typename SUBNET> using scale4  = scale<tag4, SUBNET>;
        template <typename SUBNET> using scale5  = scale<tag5, SUBNET>;
        template <typename SUBNET> using scale6  = scale<tag6, SUBNET>;
        template <typename SUBNET> using scale7  = scale<tag7, SUBNET>;
        template <typename SUBNET> using scale8  = scale<tag8, SUBNET>;
        template <typename SUBNET> using scale9  = scale<tag9, SUBNET>;
        template <typename SUBNET> using scale10 = scale<tag10, SUBNET>;
        using scale1_  = scale_<tag1>;
        using scale2_  = scale_<tag2>;
        using scale3_  = scale_<tag3>;
        using scale4_  = scale_<tag4>;
        using scale5_  = scale_<tag5>;
        using scale6_  = scale_<tag6>;
        using scale7_  = scale_<tag7>;
        using scale8_  = scale_<tag8>;
        using scale9_  = scale_<tag9>;
        using scale10_ = scale_<tag10>;

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

        template <
            template<typename> class tag
            >
        class scale_prev_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer scales the output channels of the tagged layer
                    by multiplying it with the output of the previous layer.  It is excatly the
                    same as the scale_ layer, but with the inputs swapped, which is useful since
                    it allows mapping between inputs and outputs of this layer.  To be specific:
                        - Let INPUT == sub.get_output()
                        - Let SCALES == layer<tag>(sub).get_output()
                        - This layer takes INPUT and SCALES as input.
                        - The output of this layer has the same dimensions as INPUT.
                        - This layer requires:
                            - SCALES.num_samples() == INPUT.num_samples()
                            - SCALES.k()  == INPUT.k()
                            - SCALES.nr() == 1
                            - SCALES.nc() == 1
                        - The output tensor is produced by pointwise multiplying SCALES with
                          INPUT at each spatial location.  Therefore, if OUT is the output of
                          this layer then we would have:
                            OUT(n,k,r,c) == INPUT(n,k,r,c)*SCALES(n,k)
            !*/

        public:
            scale_prev_(
            );

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            template<typename> class tag,
            typename SUBNET
            >
        using scale_prev = add_layer<scale_prev_<tag>, SUBNET>;

        // Here we add some convenient aliases for using scale_prev_ with the tag layers.
        template <typename SUBNET> using scale_prev1  = scale_prev<tag1, SUBNET>;
        template <typename SUBNET> using scale_prev2  = scale_prev<tag2, SUBNET>;
        template <typename SUBNET> using scale_prev3  = scale_prev<tag3, SUBNET>;
        template <typename SUBNET> using scale_prev4  = scale_prev<tag4, SUBNET>;
        template <typename SUBNET> using scale_prev5  = scale_prev<tag5, SUBNET>;
        template <typename SUBNET> using scale_prev6  = scale_prev<tag6, SUBNET>;
        template <typename SUBNET> using scale_prev7  = scale_prev<tag7, SUBNET>;
        template <typename SUBNET> using scale_prev8  = scale_prev<tag8, SUBNET>;
        template <typename SUBNET> using scale_prev9  = scale_prev<tag9, SUBNET>;
        template <typename SUBNET> using scale_prev10 = scale_prev<tag10, SUBNET>;
        using scale_prev1_  = scale_prev_<tag1>;
        using scale_prev2_  = scale_prev_<tag2>;
        using scale_prev3_  = scale_prev_<tag3>;
        using scale_prev4_  = scale_prev_<tag4>;
        using scale_prev5_  = scale_prev_<tag5>;
        using scale_prev6_  = scale_prev_<tag6>;
        using scale_prev7_  = scale_prev_<tag7>;
        using scale_prev8_  = scale_prev_<tag8>;
        using scale_prev9_  = scale_prev_<tag9>;
        using scale_prev10_ = scale_prev_<tag10>;

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

        template<
            template<typename> class... TAG_TYPES
            >
        class concat_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  This layer simply concatenates the output of tagged layers.
                    Importantly, each input layer must have the same dimensions (i.e.
                    num_samples, nr, and nc) except for the k channel, which may vary.  This is
                    because the concatenation happens along the k dimension.  That is, the
                    output of this network is a tensor, OUT, that is the concatenation of the
                    tensors:
                        for each (tag in TAG_TYPES)
                            layer<tag>(subnet).get_output()
                    Therefore, out.num_samples(), out.nr(), and out.nc() match the dimensions
                    of the input tensors while OUT.k() is the sum of the input layer's k()
                    dimensions.
            !*/

        public:
            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output(dpoint p) const;
            dpoint map_output_to_input(dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        // concat layer definitions
        template <template<typename> class TAG1,
                  template<typename> class TAG2,
                  typename SUBNET>
        using concat2 = add_layer<concat_<TAG1, TAG2>, SUBNET>;

        template <template<typename> class TAG1,
                  template<typename> class TAG2,
                  template<typename> class TAG3,
                  typename SUBNET>
        using concat3 = add_layer<concat_<TAG1, TAG2, TAG3>, SUBNET>;

        template <template<typename> class TAG1,
                  template<typename> class TAG2,
                  template<typename> class TAG3,
                  template<typename> class TAG4,
                  typename SUBNET>
        using concat4 = add_layer<concat_<TAG1, TAG2, TAG3, TAG4>, SUBNET>;

        template <template<typename> class TAG1,
                  template<typename> class TAG2,
                  template<typename> class TAG3,
                  template<typename> class TAG4,
                  template<typename> class TAG5,
                  typename SUBNET>
        using concat5 = add_layer<concat_<TAG1, TAG2, TAG3, TAG4, TAG5>, SUBNET>;

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

        /*!A inception layer definitions !*/

        // Now define inception layer tag types.  These layer aliases allow creating
        // the networks described in the paper:
        //   Szegedy, Christian, et al. "Going deeper with convolutions." Proceedings of
        //   the IEEE Conference on Computer Vision and Pattern Recognition. 2015.
        // See the dnn_inception_ex.cpp example for a complete example of their use.  Note also
        // that we use tag ID numbers >= 1000 to avoid conflict with user's tag layers.
        template <typename SUBNET> using itag0  = add_tag_layer< 1000 + 0, SUBNET>;
        template <typename SUBNET> using itag1  = add_tag_layer< 1000 + 1, SUBNET>;
        template <typename SUBNET> using itag2  = add_tag_layer< 1000 + 2, SUBNET>;
        template <typename SUBNET> using itag3  = add_tag_layer< 1000 + 3, SUBNET>;
        template <typename SUBNET> using itag4  = add_tag_layer< 1000 + 4, SUBNET>;
        template <typename SUBNET> using itag5  = add_tag_layer< 1000 + 5, SUBNET>;
        // skip to inception input
        template <typename SUBNET> using iskip  = add_skip_layer< itag0, SUBNET>;

        // here are some templates to be used for creating inception layer groups
        template <template<typename>class B1,
                  template<typename>class B2,
                  typename SUBNET>
        using inception2 = concat2<itag1, itag2, itag1<B1<iskip< itag2<B2< itag0<SUBNET>>>>>>>;

        template <template<typename>class B1,
                  template<typename>class B2,
                  template<typename>class B3,
                  typename SUBNET>
        using inception3 = concat3<itag1, itag2, itag3, itag1<B1<iskip< itag2<B2<iskip< itag3<B3<  itag0<SUBNET>>>>>>>>>>;

        template <template<typename>class B1,
                  template<typename>class B2,
                  template<typename>class B3,
                  template<typename>class B4,
                  typename SUBNET>
        using inception4 = concat4<itag1, itag2, itag3, itag4,
                    itag1<B1<iskip< itag2<B2<iskip< itag3<B3<iskip<  itag4<B4<  itag0<SUBNET>>>>>>>>>>>>>;

        template <template<typename>class B1,
                  template<typename>class B2,
                  template<typename>class B3,
                  template<typename>class B4,
                  template<typename>class B5,
                  typename SUBNET>
        using inception5 = concat5<itag1, itag2, itag3, itag4, itag5,
                    itag1<B1<iskip< itag2<B2<iskip< itag3<B3<iskip<  itag4<B4<iskip<  itag5<B5<  itag0<SUBNET>>>>>>>>>>>>>>>>;

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

        const double DEFAULT_L2_NORM_EPS = 1e-5;

        class l2normalize_
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  It takes tensors as input and L2 normalizes them.  In particular,
                    it has the following properties:
                        - The output tensors from this layer have the same dimensions as the
                          input tensors.
                        - If you think of each input tensor as a set of tensor::num_samples()
                          vectors, then the output tensor contains the same vectors except they
                          have been length normalized so that their L2 norms are all 1.  I.e.
                          for each vector v we will have ||v||==1.
            !*/

        public:

            explicit l2normalize_(
                double eps = tt::DEFAULT_L2_NORM_EPS
            );
            /*!
                requires
                    - eps > 0
                ensures
                    - #get_eps() == eps
            !*/

            double get_eps(
            ) const;
            /*!
                ensures
                    - When we normalize a vector we divide it by its L2 norm.  However, the
                      get_eps() value is added to the squared norm prior to division to avoid
                      ever dividing by zero.
            !*/

            template <typename SUBNET> void setup (const SUBNET& sub);
            void forward_inplace(const tensor& input, tensor& output);
            void backward_inplace(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

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

        template <
            long _offset,
            long _k,
            long _nr,
            long _nc
            >
        class extract_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    - 0 <= _offset
                    - 0 < _k
                    - 0 < _nr
                    - 0 < _nc

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, the output of this layer is simply a copy of
                    the input tensor.  However, you can configure the extract layer to output
                    only some subset of the input tensor and also to reshape it.  Therefore,
                    the dimensions of the tensor output by this layer are as follows (letting
                    IN be the input tensor and OUT the output tensor):
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == _k
                        - OUT.nr() == _nr
                        - OUT.nc() == _nc

                    So the output will always have the same number of samples as the input, but
                    within each sample (the k,nr,nc part) we will copy only a subset of the
                    values.  Moreover, the _offset parameter controls which part of each sample
                    we take.  To be very precise, we will have:
                        - let IN_SIZE   = IN.k()*IN.nr()*IN.nc()
                        - let OUT_SIZE  = _k*_nr*_nc
                        - for i in range[0,IN.num_samples()) and j in range[0,OUT_SIZE):
                            - OUT.host()[i*OUT_SIZE+j] == IN.host()[i*IN_SIZE+_offset+j]

                    Finally, all this means that the input tensor to this layer must have a big
                    enough size to accommodate taking a _k*_nr*_nc slice from each of its
                    samples.
            !*/

        public:

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <
            long offset,
            long k,
            long nr,
            long nc,
            typename SUBNET
            >
        using extract = add_layer<extract_<offset,k,nr,nc>, SUBNET>;

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

        template <long long row_stride = 2, long long col_stride = 2>
        class reorg_
        {
            /*!
                REQUIREMENTS ON TEMPLATE ARGUMENTS
                    - row_stride >= 1
                    - col_stride >= 1

                WHAT THIS OBJECT REPRESENTS
                    This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
                    defined above.  In particular, the output of this layer is simply a copy of
                    the input tensor.  However, it rearranges spatial information along the
                    channel dimension.  The dimensions of the tensor output by this layer are as
                    follows (letting IN be the input tensor and OUT the output tensor):
                        - OUT.num_samples() == IN.num_samples()
                        - OUT.k()  == IN.k() * row_stride * col_stride
                        - OUT.nr() == IN.nr() / row_stride
                        - OUT.nc() == IN.nc() / col_stride

                    So the output will always have the same number of samples as the input, but
                    within each sample (the k,nr,nc part) we will reorganize the values.  To be
                    very precise, we will have, for all n, k, r, c in OUT:
                    OUT.host[tensor_index(OUT, n, k, r, c)] ==
                    IN.host[tensor_index(IN,
                                          n,
                                          k % IN.k(),
                                          r * row_stride + (k / IN.k()) / row_stride,
                                          c * col_stride + (k / IN.k()) % col_stride)]

                    Finally, you can think of this layer as an alternative to a strided convolutonal
                    layer to downsample a tensor.
            !*/

        public:

            template <typename SUBNET> void setup (const SUBNET& sub);
            template <typename SUBNET> void forward(const SUBNET& sub, resizable_tensor& output);
            template <typename SUBNET> void backward(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
            dpoint map_input_to_output (dpoint p) const;
            dpoint map_output_to_input (dpoint p) const;
            const tensor& get_layer_params() const;
            tensor& get_layer_params();
            /*!
                These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            !*/
        };

        template <typename SUBNET>
        using reorg = add_layer<reorg_<2, 2>, SUBNET>;

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

    }

    #endif // DLIB_DNn_LAYERS_ABSTRACT_H_