WO2019075267A1

WO2019075267A1 - Self-gating activation neural network layers

Info

Publication number: WO2019075267A1
Application number: PCT/US2018/055504
Authority: WO
Inventors: Barret ZOPH; Prajit RAMACHANDRAN; Quoc V. LE
Original assignee: Google Llc
Priority date: 2017-10-11
Filing date: 2018-10-11
Publication date: 2019-04-18

Abstract

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for processing inputs using a neural network system that includes a self-gating activation layer. One of the methods includes: generating, at a first neural network layer, a first layer output having a plurality of elements, receiving, at a self-gating activation layer, the first layer output generated by the first neural network layer; generating, at the self-gating activation layer, an activation output having a respective activation value for each element of the first layer output, comprising, for each element of the first layer output: generating a gate value from the element; and generating the activation value from the gate value and the element; and providing, from the self-gating activation later, the activation output as an input to a second neural network layer.

Description

SELF-GATING ACTIVATION NEURAL NETWORK LAYERS

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Patent Application No.

62/571,166 filed on October 11, 2017, the entire contents of which are herein

incorporated by reference.

BACKGROUND

[0002] This specification relates to processing inputs through the layers of neural networks to generate outputs.

[0003] Neural networks are machine learning models that employ one or more layers of nonlinear units to predict an output for a received input. Some neural networks include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as input to the next layer in the network, i.e., the next hidden layer or the output layer. Each layer of the network generates an output from a received input in accordance with current values of a respective set of parameters.

SUMMARY

[0004] In general, one innovative aspect of the subject matter described in this specification can be embodied in a neural network system implemented by one or more computers that includes a self-gating activation layer between a first neural network layer and a second neural network layer. The first neural network layer generates first layer outputs having a plurality of elements and the self-gating activation layer is configured to generate an activation output having a respective activation value for each element of the first layer output and provide the activation output as an input to the second neural network layer. To generate the activation output, the self-gating activation layer generates a respective gate value from each element of the first layer output and generates a respective activation value for each particular element from the gate value for the particular element and the particular element. In other words, the activation layer is referred to as "self-gating" in this specification because, for each particular element, only the particular element, i.e., and not any of the other elements in the first layer output, is used to generate the gate value that is then applied to the particular element.

[0005] Particular embodiments of the subject matter described in this specification can be implemented so as to realize one or more of the following advantages. By

incorporating self-gating activation layers as described in this specification into a neural network, the performance of the neural network once trained can be improved over the use of conventional activation functions, e.g., ReLU or other conventionally-used element-wise non-linear functions. This performance improvement is robust to different hyperparameter settings and many different neural network architectures and neural network tasks.

[0006] Because the operations of the self-gated activation layer are bounded below but also unbounded above, gradient saturation is avoided while still providing strong regularization effects during the training of the neural network. This prevents slow down during the training of the neural network while improving generalization after training.

[0007] Because the operations are non-monotonic, the expressivity of the neural network and gradient flow during training are improved. Additionally, the robustness of the training of the neural network to different parameter value initializations and learning rates is improved.

[0008] Because the operations are smooth, optimization and generalization are improved, and sensitivity to learning rates and initializations is reduced.

[0009] Accordingly, self-gating neural network layers result in more accurate and useful updates being applied to the parameters of the neural network at each training iteration, i.e., because gradient saturation is decreased while providing strong regularization effects, gradient flow is improved, and impact of the chosen initialization scheme and learning rate is reduced. Thus, because of the inclusion of the self-gating neural network layers in the neural network, the neural network is easier to train and, once trained, shows improved performance on any of a variety of neural network tasks. In other words, a neural network that replaces conventional activation or transfer functions for at least some of the layers in the neural network with self-gating activation layers requires fewer computational resources and less time to train because it can be trained in fewer training iterations. Such a neural network also achieves improved performance after training.

[0010] The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below.

Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG. 1 shows an example neural network system. [0012] FIG. 2 is a flow diagram of an example process for processing an input using a self-gating activation layer.

[0013] FIG. 3 is a flow diagram of an example process for generating an activation value for a given element of a lower layer output.

[0014] Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

[0015] This specification describes a neural network system implemented as computer programs on one or more computers in one or more locations that includes one or more self-gating activation layers.

[0016] FIG. 1 shows an example neural network system 100. The neural network system 100 is an example of a system implemented as computer programs on one or more computers in one or more locations, in which the systems, components, and techniques described below can be implemented.

[0017] The neural network system 100 can be configured to receive any kind of digital data input and to generate any kind of score, classification, or regression output based on the input.

[0018] For example, if the inputs to the neural network system 100 are images or features that have been extracted from images, the output generated by the neural network system 100 for a given image may be scores for each of a set of object categories, with each score representing an estimated likelihood that the image contains an image of an object belonging to the category. Similarly, if the inputs to the neural network system 100 are videos or features that have been extracted from videos, the output generated by the neural network system 100 for a given video may be scores for each of a set of object categories, with each score representing an estimated likelihood that the video depicts an object belonging to the category.

[0019] As another example, if the inputs to the neural network system 100 are Internet resources (e.g., web pages), documents, or portions of documents or features extracted from Internet resources, documents, or portions of documents, the output generated by the neural network system 100 for a given Internet resource, document, or portion of a document may be a score for each of a set of topics, with each score representing an estimated likelihood that the Internet resource, document, or document portion is about the topic. [0020] As another example, if the inputs to the neural network system 100 are features of an impression context for a particular advertisement, the output generated by the neural network system 100 may be a score that represents an estimated likelihood that the particular advertisement will be clicked on.

[0021] As another example, if the inputs to the neural network system 100 are features of a personalized recommendation for a user, e.g., features characterizing the context for the recommendation, e.g., features characterizing previous actions taken by the user, the output generated by the neural network system 100 may be a score for each of a set of content items, with each score representing an estimated likelihood that the user will respond favorably to being recommended the content item.

[0022] As another example, if the input to the neural network system 100 is text in one language, the output generated by the neural network system 100 may be a score for each of a set of pieces of text in another language, with each score representing an estimated likelihood that the piece of text in the other language is a proper translation of the input text into the other language.

[0023] As another example, if the input to the neural network system 100 is a spoken utterance, a sequence of spoken utterances, or features derived from one of the two, the output generated by the neural network system 100 may be a score for each of a set of pieces of text, e.g., phonemes, characters, or words, each score representing an estimated likelihood that the piece of text is the correct transcript for the utterance or sequence of utterances. Moreover, if the input to the neural network system 100 is audio of this or any other kind, a sequence of spoken utterances, or features derived from one of the two, the output generated by the neural network system 100 may be a score or scores for one or more categories of audio.

[0024] As another example, the neural network system 100 can be part of an autocompletion system or part of a text processing system.

[0025] As another example, the neural network system 100 can be part of a

reinforcement learning system or other control system and can generate outputs used for selecting actions to be performed by an agent interacting with an environment.

[0026] In particular, the neural network system implements a neural network that includes multiple neural network layers. Each of the layers of the neural network is configured to receive an input and generate an output from the input and the neural network layers collectively process neural network inputs 102 received by the neural network system 100 to generate a respective neural network output 114 for each received neural network input 102. For at least one of the layers, the input is the neural network input. Similarly, the output of one of the layers in the neural network is the network output.

[0027] Some of the neural network layers in the neural network generate outputs from inputs in accordance with current values of a set of parameters for the neural network layer. For example, some layers may multiply the received input by a matrix of current parameter values as part of generating an output from the received input.

[0028] The neural network system 100 also includes a self-gating activation layer 108 between a neural network layer A 104 and a neural network layer B 112 in the neural network. That is, during the processing of a neural network input by the neural network, the self-gating activation layer 108 receives an output generated by the neural network layer A 104 and provides outputs to the other neural network layer B 112.

[0029] In many cases, the neural network layer A 104 is a layer that applies a linear transformation to a layer input to generate a layer output, e.g., a linear transformation, e.g., a multiplication or a convolution, that is defined by current values of a set of parameters of the layer. Examples of such layers include fully-connected layers, convolutional layers, and recurrent neural network layers.

[0030] For example, self-gating activation layers can be included in the neural network in place of some or all of the activation functions of the layers in the neural network, i.e., in place of conventional element-wise non-linearities that would be applied by the neural network to outputs of linear transformations. Thus, the neural network layer A 104 and the self-gating activation layer 108 can be considered to be part of the same, larger neural network layer 120, with the activation function or transfer function of the larger neural network layer 120 replaced by the self-gating activation layer 108.

[0031] In other cases, the self-gating activation layer 108 may receive input from a different kind of neural network layer, e.g., a depth concatenation layer, a pooling layer, an element-wise addition layer, or an element-wise multiplication layer.

[0032] The neural network layer B 1 12 can be any appropriate kind of neural network layer, depending on the architecture of the neural network. For example, the neural network layer B 112 can be a layer with parameters, e.g., a fully-connected,

convolutional, or recurrent neural network layer, or a layer without parameters, e.g., a depth concatenation layer, a pooling layer, an element-wise addition layer, or an element- wise multiplication layer. [0033] While not shown in FIG. 1, in some implementations the activation output 110 is provided as output to multiple other layers in the neural network, e.g., through a skip connection or a residual connection.

[0034] Additionally, while only a single self-gating activation layer 108 is shown in FIG. 1, the neural network can include multiple self-gating activation layers at various locations within the architecture of the neural network. For example, as indicated above, the activation or transfer functions of some or all of the layers in the neural network can be replaced with self-gating activation layers.

[0035] More specifically, the self-gating activation layer 108 receives an input, i.e., a layer A output 106, having multiple elements and generates an activation output 110 that has a respective activation value for each of the multiple elements. The self-gating activation layer 108 then provides the activation output 110 as input to the neural network B layer 112.

[0036] To generate the activation value for a given element, the self-gating activation layer 108 generates a gate value from the element, i.e., by applying a bounded non-linear function to the element. The self-gating activation layer 108 then generates the activation value from the gate value and the element, i.e., by multiplying the element, the gate value, and, optionally, a positive constant value.

[0037] The operation of the self-gating activation layer 108 will be described in more detail below with reference to FIGS. 2 and 3.

[0038] To allow the neural network system 100 to effectively be used to generate neural network outputs from neural network inputs, the neural network system 100 is trained on multiple batches of training examples in order to determine trained values of the parameters of the neural network layers in the neural network. A batch of training examples is a set of multiple training examples. For example, during training, the neural network system 100 can process a batch of training examples and generate a respective neural network output for each training example in the batch. The neural network outputs can then be used to adjust the values of the parameters of the neural network layers in the sequence, e.g., through conventional gradient descent and backpropagation neural network training techniques. That is, gradients are backpropagated through the layers in the neural network, including the self-gating activation layer 108, to adjust the values of the parameters of those layers in the neural network that have parameters.

[0039] As will be described in more detail below, by including one or more self-gating activation layer in the neural network, the neural network system 100 can be trained more effectively, resulting in improved performance after the neural network system 100 has been trained, fewer computational resources being consumed during the training, and less time being required for the neural network system 100 to be trained.

[0040] In some implementations, the self-gating activation layers in the neural network can be implemented in special-purpose hardware, e.g., a specially-programmed FPGA or an ASIC, so that the operations of the self-gating activation layers can be performed in hardware. In particular, the self-gating activation layers can be implemented in hardware as part of a neural network accelerator chip. For example, the neural network accelerator chip can include circuitry configured to perform matrix multiplications or convolutions, e.g., a systolic array, as well as circuity configured to perform the operations of a self- gating activation layer.

[0041] FIG. 2 is a flow diagram of an example process 200 for processing an input using a self-gating activation layer. For convenience, the process 200 will be described as being performed by a system of one or more computers located in one or more locations. For example, a self-gating activation layer included in a neural network system, e.g., the self-gating activation layer 108 included in the neural network system 100 of FIG.1 , appropriately programmed, can perform the process 200.

[0042] The self-gating activation layer receives a lower layer output (step 202). The lower layer output includes multiple elements, with each element being a numeric value, e.g., a floating-point or quantized floating-point value. For example, the lower layer output can be a vector, i.e., a one-dimensional array of elements, or a higher-order tensor, i.e., a multi-dimensional array of elements.

[0043] The self-gating activation layer generates an activation output from the lower layer output (step 204). The activation output includes a respective activation value for each element in the lower layer output. Generally, the operations performed by the self- gating activation layer to generate the activation output have one or more, and in some embodiments each, of the following advantageous properties: (i) the operations generate activation values that are bounded below (ii) the operations generate activation values that are unbounded above, (iii) the operations are non-monotonic, and (iv) the operations are smooth.

[0044] Because the operations of the self-gated activation layer are bounded below (e.g. the operations provide an output which always exceeds a lower bound value; in some examples the lower bound may be a small negative number, e.g., a number between zero and negative one) but also unbounded above (e.g. the operations are not constrained to provide an output which is limited by an upper bound value), gradient saturation is avoided while still providing strong regularization effects during the training of the neural network. That is, as described above, gradients are backpropagated through the self-gated activation layer during training to adjust the values of the parameters of the layers before the self-gated activation layer in the neural network. Saturation of these gradients, i.e., compression of the gradients to near-zero values, is avoided because the operations performed by the layer have the above two properties. This prevents slow down during the training of the neural network while improving generalization after training.

[0045] Because the operations are non-monotonic, the expressivity of the neural network and gradient flow during training are improved. Additionally, the robustness of the training of the neural network to different initializations and learning rates is improved.

[0046] Because the operations are smooth, optimization and generalization are improved, and sensitivity to learning rates and initializations is reduced.

[0047] Specific techniques for performing operations that have these properties to generate activation values is described in more detail below with reference to FIG. 3.

[0048] The self-gating activation layer provides the activation output to a layer above the self-gating activation layer in the neural network (step 206). As described above, the above layer can be any appropriate kind of neural network layer.

[0049] FIG. 3 is a flow diagram of an example process 300 for generating an activation value for a given element of a lower layer output. For convenience, the process 300 will be described as being performed by a system of one or more computers located in one or more locations. For example, a self-gating activation layer included in a neural network system, e.g., the self-gating activation layer 108 included in the neural network system

100 of FIG.1 , appropriately programmed, can perform the process 300.

[0050] The self-gating activation layer can perform the process 300 in parallel for each element of the lower layer output to generate an activation output.

[0051] The self-gating activation layer receives a given element of a lower layer output

(step 302).

[0052] The self-gating activation layer generates a gate value for the given element (step 304). In particular, the self-gating activation layer applies a gating function to an input that includes the given element to generate the gate value.

[0053] In some implementations, the gating function is the sigmoid function and the gate value g satisfies:

g = σ(βχ), where σ is the sigmoid function, β is a non-zero scalar value, and x is the given element. The sigmoid function is a function of the form o(a) = (l+exp(-a))^A-l. In some cases, β is a pre-determined fixed value. The pre-determined fixed value can be 1 or some other non-zero, generally positive, scalar. In other cases, however, β is a trainable parameter of the self-gating activation layer.

[0054] The self-gating activation layer generates an activation value from the gate value and the given element (step 306). That is, the self-gating activation layer applies the gate value to the element to generate the activation value. In some implementations, the activation valued satisfies:

A = a*x*g,

where a is a positive constant value, e.g., one or two, x is the given element, and g is the gate value for the given element.

[0055] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non transitory program carrier for execution by, or to control the operation of, data processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0056] The term "data processing apparatus" encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. [0057] A computer program (which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and

interconnected by a communication network.

[0058] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0059] Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data.

Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.

Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0060] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user's client device in response to requests received from the web browser.

[0061] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be

interconnected by any form or medium of digital data communication, e.g., a

communication network. Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), e.g., the Internet.

[0062] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

[0063] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0064] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0065] Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.

Claims

WHAT IS CLAIMED IS:

1. One or more computers and one or more storage devices storing instructions that when executed by the one or more computers cause the one or more computers to implement:

a neural network comprising:

a self-gating activation layer between a first neural network layer and a second neural network layer, wherein the first neural network layer generates first layer outputs having a plurality of elements, and wherein the self-gating activation layer is configured to:

receive a first layer output generated by the first neural network layer; generate an activation output having a respective activation value for each element of the first layer output, comprising, for each element of the first layer output:

generating a gate value from the element; and generating the activation value from the gate value and the element; and

provide the activation output as an input to the second neural network layer.

2. The system of claim 1, wherein the gate value g satisfies:

g = o(Px),

where σ is the sigmoid function, β is a non-zero scalar value, and x is the element of the first layer output.

3. The system of claim 2, wherein β is a pre-determined fixed value.

4. The system of claim 3, wherein β is equal to one.

5. The system of claim 2, wherein β is a trainable parameter of the self-gating activation layer.

6. The system of any one of claims 1-5, wherein the activation value a satisfies:

a = a*x*g,

wherein a is a positive constant value, x is the element of the first layer output, and g is the gate value for the element.

7. The system of claim 6, wherein

8. The system of claim 7, wherein a is two.

9. The system of any one of claims 1-8, wherein the operations performed by the self-gating activation layer (i) generate activation values that are bounded below (ii) generate activation values that are unbounded above, (iii) are non-monotonic, and (iv) are smooth.

10. The system of any one of claims 1-9, wherein the first neural network layer generates the first layer outputs by applying a linear transformation to first layer inputs that is defined by current values of a set of parameters for the first neural network layer.

11. The system of claim 10, wherein the linear transformation is a matrix

multiplication.

12. The system of claim 10, wherein the linear transformation is a convolution.

13. The system of any one of claims 1-12, wherein the second neural network layer generates the second layer outputs by applying a linear transformation to the activation output that is defined by current values of a set of parameters for the second neural network layer.

14. The system of claim 13, wherein the linear transformation is a matrix

multiplication.

15. The system of claim 13, wherein the linear transformation is a convolution.

16. The system of any one of the preceding claims, wherein the neural network is trained to receive a neural network input and generate a particular kind of neural network output from the neural network input.

17. A method comprising the operations performed by the self-gating activation layer of any one of claims 1-16.

18. One or more non-transitory computer storage media encoded with a computer program, the computer program comprising instructions that when executed by one or more computers cause the one or more computers to implement the neural network of any one of claims 1-16.

19. A computer-implemented method for processing a neural network input using a neural network, wherein the neural network comprises a self-gating activation layer between a first neural network layer and a second neural network layer, the method comprising:

generating, at the first neural network layer, a first layer output having a plurality of elements,

receiving, at the self-gating activation layer, the first layer output generated by the first neural network layer;

generating, at the self-gating activation layer, an activation output having a respective activation value for each element of the first layer output, comprising, for each element of the first layer output:

providing, from the self-gating activation later, the activation output as an input to the second neural network layer.

20. The method of claim 19, wherein the gate value g satisfies:

g = o(Px),

21. The method of claim 20, wherein β is a pre-determined fixed value.

22. The method of claim 21, wherein β is equal to one.

23. The method of claim 20, wherein β is a trainable parameter of the self-gating activation layer.

24. The method of any one of claims 19-23, wherein the activation value a satisfies:

a = a*x*g,

25. The method of claim 24, wherein a is one.

26. The method of claim 25, wherein a is two.

27. The method of any one of claims 19-26, wherein the operations performed by the self-gating activation (i) generate activation values that are bounded below (ii) generate activation values that are unbounded above, (iii) are non-monotonic, and (iv) are smooth.

28. The method of any one of claims 19-27, wherein the first neural network layer generates the first layer outputs by applying a linear transformation to first layer inputs that is defined by current values of a set of parameters for the first neural network layer.

29. The method of claim 28, wherein the linear transformation is a matrix multiplication.

30. The method of claim 28, wherein the linear transformation is a convolution.

31. The method of any one of claims 19-30, wherein the second neural network layer generates the second layer outputs by applying a linear transformation to the activation output that is defined by current values of a set of parameters for the second neural network layer.

32. The method of claim 31, wherein the linear transformation is a matrix multiplication.

33. The method of claim 31, wherein the linear transformation is a convolution.

34. The method of any one of claims 19 to 33, wherein the neural network is trained to receive a neural network input and generate a particular kind of neural network output from the neural network input.

35. A method for processing a neural network input for a neural network using a special-purpose neural network accelerator chip, wherein the neural network comprises a self-gating activation layer between a first neural network layer and a second neural network layer, the method comprising:

generating, by first circuitry of the special-purpose neural network accelerator chip, a first layer output for the first neural network layer, the first layer output having a plurality of elements,

receiving, at second circuitry of the special-purpose neural network accelerator configured to perform operations of the self-gating activation layer, the first layer output generated for the first neural network layer;

generating, at the second circuitry, an activation output for the self-gating activation layer, the activation output having a respective activation value for each element of the first layer output, comprising, for each element of the first layer output:

generating a gate value from the element; and

generating the activation value from the gate value and the element; and providing, from the second circuitry, the activation output as an input to third circuitry configured to perform operations of the second neural network layer.

36. One or more non-transitory computer storage media encoded with a computer program, the computer program comprising instructions that when executed by one or more computers cause the one or more computers to implement the method of any one of claims 19-35.

37. A system comprising one or more computers and one or more storage devices storing instructions that when executed by the one or more computers cause the one or more computers to implement the method of any one of claims 19-36.