Activation function approximation in deep neural networks using rectified-linear-unit function
A computational apparatus for implementing a neural network model having multiple neurons that evaluate an activation function, the apparatus including a memory and circuitry. The memory is configured to hold values of a difference-function, each value being a respective difference between the activation function and a predefined baseline function. The circuitry is configured to evaluate the neural network model, including, for at least one of the neurons: evaluate the baseline function at the argument, retrieve from the memory one or more values of the difference-function responsively to the argument, and evaluate the activation function at the argument based on the baseline function at the argument and on the one or more values of the difference-function.
1. A computational apparatus for implementing a neural network model having multiple neurons that evaluate an activation function, the apparatus comprising:
a memory, configured to hold values of a difference-function, each value being a respective difference between the activation function and a predefined baseline function; and
circuitry, configured to evaluate the neural network model, including, for at least one of the neurons:
evaluate the baseline function at the argument;
retrieve from the memory one or more values of the difference-function responsively to the argument; and
evaluate the activation function at the argument based on the baseline function at the argument and on the one or more values of the difference-function.
2. The computational apparatus according to claim 1 , wherein the baseline function comprises a Rectified Linear Unit (ReLU) function defined as ReLU(x)=max(0,x).
3. The computational apparatus according to claim 1 , wherein the baseline function comprises a generalized ReLU (GReLU) function defined as GReLU(x)=max(0,ax), where a>0.
4. The computational apparatus according to claim 3 , wherein the baseline function comprises a Leaky GReLU (LeakyGReLU) function defined as LeakyGReLU(x)=max(bx, ax), where 0<b<a.
5. The computational apparatus according to claim 1 , wherein the activation function comprises at least one function, selected from a group of functions consisting of a Gaussian Error Linear Unit (GELU) function, a SWISH function, a Linearly Scaled Hyperbolic Tangent (LISHT) function, and a Symmetrical Gelu (SGELU) function.
6. The computational apparatus according to claim 1 , wherein the difference-function has one of an even symmetry and an odd symmetry.
7. The computational apparatus according to claim 1 , wherein the circuitry is configured to:
retrieve two or more values of the difference-function from the memory;
evaluate the difference-function at the argument by interpolating the two or more values; and
evaluate the activation function at the argument by summing the baseline function at the argument and the difference-function at the argument.
8. The computational apparatus according to claim 1 , wherein the circuitry is further configured to output the evaluated activation function at the argument for use in the neural network model.
9. A computational method for implementing a neural network model having multiple neurons that evaluate an activation function, the method comprising:
holding in a memory values of a difference-function, each value being a respective difference between the activation function and a predefined baseline function; and
evaluating the neural network model, including, for at least one of the neurons:
evaluating the baseline function at the argument;
retrieving from the memory one or more values of the difference-function responsively to the argument; and
evaluating the activation function at the argument based on the baseline function at the argument and on the one or more values of the difference-function.
10. The computational method according to claim 9 , wherein the baseline function comprises a Rectified Linear Unit (ReLU) function defined as ReLU(x)=max(0,x).
11. The computational method according to claim 9 , wherein the baseline function comprises a generalized ReLU (GReLU) function defined as GReLU(x)=max(0,ax), where a>0.
12. The computational method according to claim 11 , wherein the baseline function comprises a Leaky GReLU (LeakyGReLU) function defined as LeakyGReLU(x)=max(bx, ax), where 0<b<a.
13. The computational method according to claim 9 , wherein the activation function comprises at least one function, selected from a group of functions consisting of a Gaussian Error Linear Unit (GELU) function, a SWISH function, a Linearly Scaled Hyperbolic Tangent (LISHT) function, and a Symmetrical Gelu (SGELU) function.
14. The computational method according to claim 9 , wherein the difference-function has one of an even symmetry and an odd symmetry.
15. The computational method according to claim 9 , wherein evaluating the neural network model comprises:
retrieving two or more values of the difference-function from the memory;
evaluating the difference-function at the argument by interpolating the two or more values; and
evaluating the activation function at the argument by summing the baseline function at the argument and the difference-function at the argument.
16. The computational method according to claim 9 , and comprising outputting the evaluated activation function at the argument for use in the neural network model.