Differential equations network
Methods and systems are provided for a differential equations network. In one example, the differential equations network comprises one or more neuron within a single neural layer, where each of the neurons is configured to learn an activation function different or similar to an activation function learned by a different neuron within the same layer.
1 . A method for performing differential equations network (DEN) computations for a DEN having a plurality of DEN layers comprising only one input layer, only one hidden neural network layer, and only one output layer, where there are no other layers in the DEN other than the input layer, the only one hidden neural network layer, and the output layer, the method comprising:
obtaining, from a plurality of input neurons along a plurality of dimensions of the DEN, a plurality of activation functions for a plurality of neurons of the only one hidden neural network layer of the DEN, wherein each of the plurality of activation functions is different;
selecting a single activation function of the plurality of activation functions to teach a neuron of the plurality of neurons, where each neuron of the plurality of neurons learns a different one of the plurality of activation functions independently of other neurons to provide a compact DEN;
presenting a first activation function to a first neuron of the only one hidden neural network layer, wherein the first activation function is a single activation function, and a second activation function to a second neuron of the only one hidden neural network layer;
learning the first activation function via the first neuron of the only one hidden neural network layer and the second activation function via the second neuron of the only one hidden neural network layer independent of the first neuron, wherein the second activation function is different than the first activation function; and
predicting a healthcare outcome via performing DEN computations via a combination of the first and second neurons, the outcome corresponding to a combined output of the first and second neurons relayed to an output DEN layer, wherein each of the input DEN layer, the only one hidden neural network layer, and the output DEN layer constitute a compact DEN.
2 . The method of claim 1 , wherein the only one hidden neural network layer is a single neural layer comprising each of the plurality of neurons.
3 . The method of claim 1 , wherein the selecting is based on at least an error between an actual value and the outcome, where the outcome is based on activation functions learned by each of the plurality of neurons.
4 . The method of claim 3 , wherein the plurality of neurons of the only one hidden neural network layer learn activation functions to decrease the error.
5 . The method of claim 1 , further comprising decreasing an error of the outcome determined by the first and second neurons via adjusting one or more parameters of the first activation function and the second activation function, wherein adjusting the one or more parameters comprises adjusting one or more coefficients and mathematical operators, and wherein the outcome is associated with healthcare.
6 . A system for performing differential equations network (DEN) computations for a DEN having a plurality of DEN layers comprising only one input layer, only one hidden neural network layer, and only one output layer, the system comprising:
a non-transitory computer system comprising one or more controllers with non-transitory memory stored thereon that when executed enable the controller to:
obtain, from a plurality of input neurons along a plurality of dimensions of the DEN, a plurality of activation functions for a plurality of neurons of the only one hidden neural network layer of the DEN, wherein each activation function of the plurality of activation functions is different;
select a first, single activation function of the plurality of activation functions to present to and teach a first neuron of the plurality of neurons;
select a second, single activation function of the plurality of activation functions, different than the first activation function, to present to and teach a second neuron of the plurality of neurons, where each neuron of the plurality of neurons of the only one hidden neural network layer learns a different activation function of the plurality of activation functions independent of the other neurons;
learning the first activation function via the first neuron of the only one hidden neural network layer and the second activation function via the second neuron of the only one hidden neural network layer independent of the first neuron, wherein the second activation function is different than the first activation function; and
predicting an outcome via a combination of the first and second neurons, the outcome corresponding to a combined output of the first and second neurons relayed to an output DEN layer, wherein each of the input DEN layer, the only one hidden neural network layer, and the output DEN layer constitute a compact DEN.
7 . The system of claim 6 , wherein the plurality of activation functions are based on solutions to a second order linear differential equation.
8 . The system of claim 6 , wherein the plurality of activation functions are based on approximations of one or more of a Gauss Hypergeometric function and a polylogarithm function.
9 . The system of claim 6 , wherein the only one input layer comprises the plurality of input neurons, wherein there are no additional layers in the plurality of DEN layers other than the input layer, the output layer, and the only one hidden neural layer, and wherein the only one hidden neural layer comprises more than one neuron and learns more than one activation function.
10 . A non-transitory computer-readable storage medium storing computer executable instructions on non-transitory memory of the computer-readable storage medium, which, when executed by a computer, will cause the computer to perform a method for predicting a healthcare outcome via performing differential equations network (DEN) computations for a DEN having a plurality of DEN layers comprising only one input layer, only one hidden neural network layer, and only one output layer, the method comprising:
obtaining a plurality of activation functions from one or more input neurons of an input DEN layer;
receiving the plurality of activation functions provided by one or more input neurons of the input DEN layer to the only one hidden neural network layer, wherein each activation function of the plurality of activation functions is different, including selecting a single activation function of the plurality of activation functions to teach each neuron of the single hidden neural network layer;
presenting a first activation function to a first neuron of the only one hidden neural network layer, wherein the first activation function is a single activation function, and a second activation function to a second neuron of the only one hidden neural network layer;
learning the first activation function via the first neuron of the only one hidden neural network layer and the second activation function via the second neuron of the only one hidden neural network layer independent of the first neuron, wherein the second activation function is different than the first activation function; and
predicting an outcome via a combination of the first and second neurons, the outcome corresponding to a combined output of the first and second neurons relayed to an output DEN layer, wherein each of the input DEN layer, the single hidden neural network layer, and the output DEN layer constitute a compact DEN.
11 . The non-transitory computer-readable storage medium of claim 10 , wherein the selecting further includes selecting the first activation function and the second activation function based on an error between the combined output of the first and second neurons and an expected output, and wherein the expected output is based on a desired output of the first and second neurons.
12 . The non-transitory computer-readable storage medium of claim 11 , further comprising adjusting one or more coefficients and mathematical operators of the first activation function and the second activation function to decrease the error of the combined output.
13 . The non-transitory computer-readable storage medium of claim 10 , wherein the first and second activation functions are one or more of ReLU and sigmoid functions.
14 . The non-transitory computer-readable storage medium of claim 10 , wherein the only one hidden neural network is a single layer, and wherein the only one hidden neural network is the only layer with neurons configured to learn activation functions.
15 . The non-transitory computer-readable storage medium of claim 10 , wherein the plurality of activation functions from the one or more input neurons are related to one or more healthcare parameters including age, weight, medications, geographic location, diet, current health status, and daily habits.
16 . The non-transitory computer-readable storage medium of claim 15 , wherein the first and second neurons of the hidden neural layer predict healthcare outcomes for one or more of diabetes, acute respiratory disorder, autoimmune diseases, autocrine diseases, neural diseases, mental health disorder, and cancers.
17 . The non-transitory computer-readable storage medium of claim 15 , wherein the plurality of activation functions from the one or more input neurons are adjusted as the one or more healthcare parameters change.