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Evaluate deep learning model for custom training loops


Use dlfeval to evaluate custom deep learning models for custom training loops.


For most deep learning tasks, you can use a pretrained network and adapt it to your own data. For an example showing how to use transfer learning to retrain a convolutional neural network to classify a new set of images, see Train Deep Learning Network to Classify New Images. Alternatively, you can create and train networks from scratch using layerGraph objects with the trainNetwork and trainingOptions functions.

If the trainingOptions function does not provide the training options that you need for your task, then you can create a custom training loop using automatic differentiation. To learn more, see Define Deep Learning Network for Custom Training Loops.


[y1,...,yk] = dlfeval(fun,x1,...,xn) evaluates the deep learning array function fun at the input arguments x1,...,xn. Functions passed to dlfeval can contain calls to dlgradient, which compute gradients from the inputs x1,...,xn by using automatic differentiation.


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Rosenbrock's function is a standard test function for optimization. The rosenbrock.m helper function computes the function value and uses automatic differentiation to compute its gradient.

type rosenbrock.m
function [y,dydx] = rosenbrock(x)

y = 100*(x(2) - x(1).^2).^2 + (1 - x(1)).^2;
dydx = dlgradient(y,x);


To evaluate Rosenbrock's function and its gradient at the point [–1,2], create a dlarray of the point and then call dlfeval on the function handle @rosenbrock.

x0 = dlarray([-1,2]);
[fval,gradval] = dlfeval(@rosenbrock,x0)
fval = 
  1x1 dlarray


gradval = 
  1x2 dlarray

   396   200

Alternatively, define Rosenbrock's function as a function of two inputs, x1 and x2.

type rosenbrock2.m
function [y,dydx1,dydx2] = rosenbrock2(x1,x2)

y = 100*(x2 - x1.^2).^2 + (1 - x1).^2;
[dydx1,dydx2] = dlgradient(y,x1,x2);


Call dlfeval to evaluate rosenbrock2 on two dlarray arguments representing the inputs –1 and 2.

x1 = dlarray(-1);
x2 = dlarray(2);
[fval,dydx1,dydx2] = dlfeval(@rosenbrock2,x1,x2)
fval = 
  1x1 dlarray


dydx1 = 
  1x1 dlarray


dydx2 = 
  1x1 dlarray


Plot the gradient of Rosenbrock's function for several points in the unit square. First, initialize the arrays representing the evaluation points and the output of the function.

[X1 X2] = meshgrid(linspace(0,1,10));
X1 = dlarray(X1(:));
X2 = dlarray(X2(:));
Y = dlarray(zeros(size(X1)));
DYDX1 = Y;
DYDX2 = Y;

Evaluate the function in a loop. Plot the result using quiver.

for i = 1:length(X1)
    [Y(i),DYDX1(i),DYDX2(i)] = dlfeval(@rosenbrock2,X1(i),X2(i));

Figure contains an axes object. The axes object contains an object of type quiver.

Use dlgradient and dlfeval to compute the value and gradient of a function that involves complex numbers. You can compute complex gradients, or restrict the gradients to real numbers only.

Define the function complexFun, listed at the end of this example. This function implements the following complex formula:


Define the function gradFun, listed at the end of this example. This function calls complexFun and uses dlgradient to calculate the gradient of the result with respect to the input. For automatic differentiation, the value to differentiate — i.e., the value of the function calculated from the input — must be a real scalar, so the function takes the sum of the real part of the result before calculating the gradient. The function returns the real part of the function value and the gradient, which can be complex.

Define the sample points over the complex plane between -2 and 2 and -2i and 2i and convert to dlarray.

functionRes = linspace(-2,2,100);
x = functionRes + 1i*functionRes.';
x = dlarray(x);

Calculate the function value and gradient at each sample point.

[y, grad] = dlfeval(@gradFun,x);
y = extractdata(y);

Define the sample points at which to display the gradient.

gradientRes = linspace(-2,2,11);
xGrad = gradientRes + 1i*gradientRes.';

Extract the gradient values at these sample points.

[~,gradPlot] = dlfeval(@gradFun,dlarray(xGrad));
gradPlot = extractdata(gradPlot);

Plot the results. Use imagesc to show the value of the function over the complex plane. Use quiver to show the direction and magnitude of the gradient.

axis xy
hold on
title("Real Value and Gradient","Re$(f(x)) = $ Re$((2+3i)x)$","interpreter","latex")

Figure contains an axes object. The axes object with title Real Value and Gradient contains 2 objects of type image, quiver.

The gradient of the function is the same across the entire complex plane. Extract the value of the gradient calculated by automatic differentation.

ans = 
  1x1 dlarray

   2.0000 - 3.0000i

By inspection, the complex derivative of the function has the value


However, the function Re(f(x)) is not analytic, and therefore no complex derivative is defined. For automatic differentiation in MATLAB, the value to differentiate must always be real, and therefore the function can never be complex analytic. Instead, the derivative is computed such that the returned gradient points in the direction of steepest ascent, as seen in the plot. This is done by interpreting the function Re(f(x)): C R as a function Re(f(xR+ixI)): R × R R.

function y = complexFun(x)
    y = (2+3i)*x;    

function [y,grad] = gradFun(x)
    y = complexFun(x);
    y = real(y);

    grad = dlgradient(sum(y,"all"),x);

Input Arguments

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Function to evaluate, specified as a function handle. If fun includes a dlgradient call, then dlfeval evaluates the gradient by using automatic differentiation. In this gradient evaluation, each argument of the dlgradient call must be a dlarray or a cell array, structure, or table containing a dlarray. The number of input arguments to dlfeval must be the same as the number of input arguments to fun.

Example: @rosenbrock

Data Types: function_handle

Function arguments, specified as any MATLAB data type or a dlnetwork object.

An input argument xj that is a variable of differentiation in a dlgradient call must be a traced dlarray or a cell array, structure, or table containing a traced dlarray. An extra variable such as a hyperparameter or constant data array does not have to be a dlarray.

To evaluate gradients for deep learning, you can provide a dlnetwork object as a function argument and evaluate the forward pass of the network inside fun.

Example: dlarray([1 2;3 4])

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | string | struct | table | cell | function_handle | categorical | datetime | duration | calendarDuration | fi
Complex Number Support: Yes

Output Arguments

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Function outputs, returned as any data type. If the output results from a dlgradient call, the output is a dlarray.


Extended Capabilities

Introduced in R2019b