Batch normalization layer

Abstract

To provide a neural network capable of efficiently performing training.SOLUTION: A neural network system is provided with a batch normalization layer between a neural network layer A and a neural network layer B. The batch normalization layer receives respective layer A outputs for each training example in a batch during training of the neural network system on a batch of the training example, calculates a plurality of normalization statistic values to the batch from the layer A outputs, normalizes each component of each layer A output by using the normalization statistic values, generates respective normalized layer outputs for each training example in the batch, generates the respective batch normalization layer outputs to each of the training examples from the normalized layer outputs, and provides the neural network layer B with the batch normalization layer outputs as an input.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This specification relates to processing inputs through layers of a neural network to produce outputs. [Background technology]

[0002] A neural network is a machine learning model that uses one or more layers of nonlinear units to predict an output for a received input. Some neural networks contain 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 output layer. Each layer of the network generates an output from the received input according to the current values ​​of each set of parameters. Summary of the Invention [Means for solving the problem]

[0003] In general, one inventive aspect of the subject matter described herein can be embodied in a neural network system implemented by one or more computers, including a batch normalization layer between a first neural network layer and a second neural network layer, the first neural network layer generating a first layer output having a plurality of components, the batch normalization layer being configured, during training of the neural network system on a batch of training examples, to receive a respective first layer output for each training example in the batch, calculate a plurality of normalization statistics for the batch from the first layer outputs, normalize each component of each first layer output using the normalization statistics to generate a respective normalized layer output for each training example in the batch, generate a respective batch normalization layer output for each of the training examples from the normalized layer outputs, and provide the batch normalization layer outputs as inputs to the second neural network layer.

[0004] "One or more computer systems are configured to perform particular operations or actions" means that the systems have installed software, firmware, hardware, or a combination thereof that, when in operation, causes the systems to perform those operations or actions. "One or more computer programs are configured to perform particular operations or actions" means that the one or more programs contain instructions that, when executed by a data processing device, cause the device to perform those operations or actions.

[0005] Certain embodiments of the subject matter described herein can be implemented to achieve one or more of the following advantages: A neural network system including one or more batch normalization layers can be trained more quickly than an ideal neural network that does not include any batch normalization layers. For example, including one or more batch normalization layers in the neural network system can mitigate problems caused by changes in the distribution of inputs to a given layer during training. This allows for a higher learning rate to be effectively used during training and can mitigate the effects of how parameters are initialized in the training process. Furthermore, during training, a batch normalization layer can act as a normalizer, reducing the need for other normalization techniques, such as dropout, to be used during training. Once trained, a neural network system including a normalization layer can generate neural network outputs that are as accurate, if not more accurate, than those generated by an ideal neural network system.

[0006] The details of one or more embodiments of the subject matter herein 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, drawings, and claims. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 illustrates an exemplary neural network system. [Figure 2] 1 is a flow diagram of an exemplary process for processing inputs using a batch normalization layer during training of the neural network system. [Figure 3] 1 is a flow diagram of an exemplary process for processing inputs using batch normalization after the neural network system has been trained. DETAILED DESCRIPTION OF THE INVENTION

[0008] Like reference numbers and designations in the various drawings indicate like elements.

[0009] This specification describes a neural network system implemented as a computer program on one or more computers in one or more locations that includes a batch normalization layer.

[0010] Figure 1 illustrates an exemplary neural network system 100. Neural network system 100 is an example of a system implemented as a computer program on one or more computers at one or more locations in which the systems, components, and techniques described below may be implemented.

[0011] The neural network system 100 includes a plurality of neural network layers arranged in order from lowest to highest layer, and generates neural network outputs from neural network inputs by processing the neural network inputs through each of the layers in the sequence.

[0012] Neural network system 100 can be configured to receive any type of digital data input and generate any type of score or classification output based on that input.

[0013] For example, if the input to the neural network system 100 is an image or features being extracted from the image, the output produced by the neural network system 100 for a given image may be a score for each of a set of object categories, each score representing an estimated likelihood that the image contains an image of an object belonging to that category.

[0014] As another example, if the input to neural network system 100 is an Internet resource (e.g., a web page), a document, a portion of a document or features extracted from an Internet resource, a document, or a document portion, the output generated by neural network system 100 for a given Internet resource, document, or document portion may be a score for each of a set of topics, each score representing an estimated likelihood that the Internet resource, document, or document portion is related to that topic.

[0015] As another example, if the input to the neural network system 100 is impression context features for a particular advertisement, the output generated by the neural network system 100 may be a score representing an estimated likelihood that the particular advertisement will be clicked.

[0016] As another example, if the inputs to neural network system 100 are features of a personalized recommendation for a user, such as features that characterize the context for the recommendation, e.g., features that characterize past actions taken by the user, the output generated by neural network system 100 may be a score for each of a set of content items, each score representing an estimated likelihood that the user will respond favorably to that content item being recommended.

[0017] 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 text in another language, each score representing an estimated likelihood that the text in the other language is an accurate translation of the input text into the other language.

[0018] As another example, if the input to the neural network system 100 is an utterance, a sequence of utterances, or features derived from one of these two, the output generated by the neural network system 100 may be a score for each of a set of text, each score representing an estimated likelihood that the text is an accurate transcript for the utterance or sequence of utterances.

[0019] As another example, the neural network system 100 can be part of an automatic input system or part of a text processing system.

[0020] As another example, the neural network system 100 can be part of a reinforcement learning system and can generate outputs that are used to select actions to be taken by an agent interacting with an environment.

[0021] In particular, each of the neural network layers is configured to receive inputs and generate outputs from the inputs, and the neural network layers collectively process the neural network inputs received by neural network system 100 to generate a respective neural network output for each received neural network input. Some or all of the neural network layers in the sequence generate outputs from inputs according to current values ​​of a set of parameters for the neural network layer. For example, some layers may multiply the received inputs by a matrix of current parameter values ​​as part of generating outputs from the received inputs.

[0022] Neural network system 100 also includes a batch normalization layer 108 between neural network layer A 104 and neural network layer B 112 in the sequence of neural network layers. Batch normalization layer 108 is configured to perform one set of operations on inputs received from neural network layer A 104 during training of neural network system 100 and another set of operations on inputs received from neural network layer A 104 after neural network system 100 has been trained.

[0023] In particular, the neural network system 100 can be trained on multiple batches of training examples to determine trained values ​​for the parameters of the neural network layers. A batch of training examples is a set of multiple training examples. For example, during training, the neural network system 100 can process batch 102 of training examples and generate a respective neural network output for each training example in batch 102. The neural network outputs can then be used to adjust the values ​​of the neural network's parameter layers in the sequence, for example, through conventional gradient descent and backpropagation neural network training techniques.

[0024] During training of the neural network system 100 on a given batch of training examples, the batch normalization layer 108 is configured to receive the layer A outputs 106 generated by the neural network layer A 104 for the training examples in the batch, process the layer A outputs 106 to generate respective batch normalization layer outputs 110 for each training example in the batch, and then provide the batch normalization layer outputs 110 as inputs to the neural network layer B 112. The layer A outputs 106 include the respective outputs generated by the neural network layer A 104 for each training example in the batch. Similarly, the batch normalization layer outputs 110 include the respective outputs generated by the batch normalization layer 108 for each training example in the batch.

[0025] Generally, the batch normalization layer 108 computes a set of normalization statistics for the batch from the Layer A outputs 106, normalizes the Layer A outputs 106 to generate a respective normalized output for each training example in the batch, and optionally transforms each of the normalized outputs before providing them as inputs to the neural network layer B 112.

[0026] The normalization statistics computed by the batch normalization layer 108 and the manner in which the batch normalization layer 108 normalizes the layer A outputs 106 during training depend on the nature of the neural network layer A 104 that generates the layer A outputs 106.

[0027] In some cases, neural network layer A104 is a layer that generates an output that includes multiple components indexed by a dimension. For example, neural network layer A104 may be a fully connected neural network layer. In some other cases, however, neural network layer A104 is a convolutional layer or other type of neural network layer that generates an output that includes multiple components that are each indexed by both a feature index and a spatial location index. Generating batch normalization layer outputs during training of neural network system 100 in each of these two cases is described in more detail below with reference to FIG. 2.

[0028] Once neural network system 100 is trained, neural network system 100 may receive new neural network inputs for processing and process the neural network inputs through the neural network layers to generate new neural network outputs for those inputs according to the trained values ​​of the parameters of the components of neural network system 100. The operations performed by batch normalization layer 108 while processing the new neural network inputs also depend on the nature of neural network layer A 104. The processing of new neural network inputs after neural network system 100 has been trained is described in more detail below with reference to FIG. 3.

[0029] Batch normalization layers 108 may be included at various positions within the sequence of neural network layers, and in some implementations, multiple batch normalization layers may be included in the sequence.

[0030] 1 , in some implementations, neural network layer A 104 generates outputs by modifying inputs to that layer according to current values ​​of a set of parameters for the first neural network layer, e.g., by multiplying the inputs to that layer by a matrix of the current parameter values. In these implementations, neural network layer B 112 may receive outputs from batch normalization layer 108 and generate outputs by applying a nonlinear operation, i.e., a nonlinear activation function, to the batch normalization layer outputs. Thus, in these implementations, batch normalization layer 108 is inserted within a conventional neural network layer, and the operation of the conventional neural network layer is split between neural network layer A 104 and neural network layer B 112.

[0031] In some other implementations, neural network layer A 104 generates the output by modifying the layer inputs according to the current values ​​of a set of parameters to generate modified first layer inputs, and then applying a nonlinear operation to the modified first layer inputs before providing the output to batch normalization layer 108. Thus, in these implementations, batch normalization layer 108 is inserted after the conventional neural network layer in the sequence.

[0032] 2 is a flow diagram of an exemplary process 200 for generating batch normalization layer outputs during training of a neural network on a batch of training examples. For convenience, process 200 is described as being performed by one or more computer systems located at one or more locations. For example, a suitably programmed batch normalization layer included in a neural network system, such as batch normalization layer 108 included in neural network system 100 of FIG. 1, can perform process 200.

[0033] The batch normalization layer receives lower layer outputs for a batch of training examples (step 202), which include the respective outputs generated for each training example in the batch by layers below the batch normalization layer in the sequence of neural network layers.

[0034] The batch normalization layer generates a respective normalized output for each training example in the batch (step 204), i.e., the batch normalization layer generates a respective normalized output from each received lower layer output.

[0035] In some cases, the layer below the batch normalization layer is a layer that produces an output that includes multiple components indexed by dimension.

[0036] In these cases, the batch normalization layer calculates, for each dimension, the mean and standard deviation of the components of the lower layer outputs that correspond to that dimension. The batch normalization layer then normalizes each component of each of those lower-level outputs using that mean and standard deviation to generate a respective normalized output for each training example in the batch. In particular, for a given component of a given output, the batch normalization layer normalizes that component using the mean and standard deviation calculated for the dimension that corresponds to that component. For example, in some implementations, the component corresponding to the kth dimension of the i-th lower layer output from batch β is

[0037]

number

[0038] For , the normalized output

[0039]

number

[0040] teeth

[0041]

number

[0042] Satisfies μ B is the mean of the components corresponding to the k-th dimension of the lower layer outputs in batch β, and σ B is the standard deviation of the components corresponding to the k-th dimension of the lower layer outputs in batch β. In some implementations, the standard deviation is

[0043]

number

[0044] is a numerically stable standard deviation equal to , where ε is a constant value,

[0045]

number

[0046] is the variance of the component corresponding to the k-th dimension of the lower layer outputs in batch β.

[0047] In some other cases, however, the neural network layer below the batch normalization layer is a convolutional layer or other kind of neural network layer that produces an output containing multiple components, each indexed by both a feature index and a spatial location index.

[0048] In some of these cases, the batch normalization layer calculates, for each possible combination of feature index and spatial location index, the mean and variance of the components of the lower layer output that have that feature index and spatial location index. The batch normalization layer then calculates, for each feature index, the arithmetic mean of the means over combinations of that feature index and spatial location index that include that feature index. The batch normalization layer also calculates, for each feature index, the arithmetic mean of the variances over combinations of that feature index and spatial location index that include that feature index. Thus, after calculating the arithmetic means, the batch normalization layer calculates mean statistics for each feature across all of that spatial location and variance statistics for each feature across all of that spatial location.

[0049] The batch normalization layer then normalizes each component of each of the lower-level outputs using the mean and arithmetic mean variance to generate a respective normalized output for each of the training examples in the batch. In particular, for a given component of a given output, the batch normalization layer normalizes that component using the mean and arithmetic mean variance for the component's corresponding feature index, e.g., in the same manner as described above when layers below the batch normalization layer generate dimension-indexed outputs.

[0050] In the rest of these cases, the batch normalization layer computes, for each feature index, the mean and variance of the component of the lower layer output that corresponds to, i.e., has, that feature index.

[0051] The batch normalization layer then normalizes each component of each of the lower-level outputs using the mean and variance over the feature index to generate a respective normalized output for each of the training examples in the batch. In particular, for a given component of a given output, the batch normalization layer normalizes that component using the mean and variance over the feature index corresponding to that component, e.g., in the same manner as described above when the layer below the batch normalization layer generates dimensionally indexed outputs.

[0052] Optionally, the batch normalization layer transforms each component of each normalized output (step 206).

[0053] In the case where the layer below the batch normalization layer is a layer that generates an output containing multiple components indexed by dimensions, the batch normalization layer transforms, for each dimension, the components of each normalized output in that dimension according to the current values ​​of a set of parameters for that dimension. That is, the batch normalization layer maintains a separate set of parameters for each dimension and uses these parameters to apply a transformation to the components of the normalized output in that dimension. The values ​​of the set of parameters are adjusted as part of training the neural network system. For example, in some implementations, the normalized output

[0054]

number

[0055] The transformed normalized output generated from

[0056]

number

[0057] teeth

[0058]

number

[0059] Meet the following.

[0060]

number

[0061] is the parameter for the kth dimension.

[0062] In the case where the layer below the batch normalization layer is a convolutional layer, the batch normalization layer transforms each component of the normalized output according to the current values ​​of a set of parameters for the feature index corresponding to that component. That is, the batch normalization layer maintains a separate set of parameters for each feature index and uses these parameters to apply a transformation to the component of the normalized output having that feature index, e.g., in the same manner as described above when the layer below the batch normalization layer generates a dimensionally indexed output. The values ​​of the set of parameters are adjusted as part of training the neural network system.

[0063] The batch normalization layer provides the normalized output or the transformed normalized output as input to the layer above it in the sequence (step 208).

[0064] After the neural network generates neural network outputs for the training examples in a batch, the normalized statistics are backpropagated as part of adjusting the values ​​of the neural network parameters, i.e., as part of implementing the backpropagation training technique.

[0065] 3 is a flow diagram of an example process 300 for generating a batch normalization layer output for a new neural network input after the neural network has been trained. For convenience, process 300 is described as being performed by one or more computer systems located at one or more locations. For example, a suitably programmed batch normalization layer included in a neural network system, such as batch normalization layer 108 included in neural network system 100 of FIG. 1, can perform process 300.

[0066] The batch normalization layer receives lower layer outputs for a new neural network input (step 302), the lower layer outputs being the outputs generated for the new neural network input by layers below the batch normalization layer in the sequence of neural network layers.

[0067] The batch normalization layer generates normalized outputs for the new neural network inputs (step 304).

[0068] If the outputs generated by the layers below the batch normalization layer are indexed by dimension, the batch normalization layer normalizes each component of the lower layer output using a pre-calculated mean and standard deviation for each of those dimensions to generate a normalized output. In some cases, the mean and standard deviation for a given dimension are calculated from the components in all dimensions of the outputs generated by the layers below the batch normalization layer during training of the neural network system.

[0069] In some other cases, however, the mean and standard deviation for a given dimension are calculated from the components within the dimension of lower layer outputs generated by layers below the batch normalization layer after training, e.g., from lower layer outputs generated within the most recent time window of a specified period, or from a specified number of lower layer outputs most recently generated by layers below the batch normalization layer.

[0070] In particular, in some cases, the distribution of network inputs, and therefore the distribution of lower layer outputs, may change between the training examples used during training and the new neural network inputs used after the neural network system is trained, for example, if the new neural network inputs are of a different type than the training examples. For example, a neural network system may be trained on user images and used to process video frames. The user images and video frames may have different distributions in terms of captured class, image properties, composition, etc. Therefore, normalizing lower layer inputs using statistics from training may not accurately capture the statistics of the lower layer outputs being generated for the new inputs. Therefore, in these cases, a batch normalization layer can use normalization statistics calculated from the lower layer outputs generated by layers below the batch normalization layer after training.

[0071] When the outputs generated by the layers below the batch normalization layer are indexed by feature index and spatial location index, the batch normalization layer normalizes each component of the lower layer outputs using the mean and average variance pre-calculated for each of the feature indexes to generate normalized outputs. In some cases, as described above, the mean and average variance for a given feature index are calculated from the outputs generated by the layers below the batch normalization layer for all of the training examples used during training. In some other cases, as described above, the mean and standard deviation for a given feature index are calculated from the lower layer outputs generated by the layers below the batch normalization layer after training.

[0072] Optionally, a batch normalization layer transforms each component of the normalized output (step 306).

[0073] If the outputs generated by the layer below the batch normalization layer are indexed by dimension, the batch normalization layer transforms, for each dimension, the components of the normalized output within that dimension according to the trained values ​​of the set of parameters for that dimension. If the outputs generated by the layer below the batch normalization layer are indexed by feature index and spatial location index, the batch normalization layer transforms each component of the normalized output according to the trained values ​​of the set of parameters for the feature index corresponding to that component. The batch normalization layer provides the normalized output or the transformed normalized output as input to the layer above the batch normalization layer in the sequence (step 308).

[0074] Embodiments of the subject matter described herein and its functional operations can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware containing the structures disclosed herein and their structural equivalents, or in one or more combinations thereof. Embodiments of the subject matter described herein 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 a data processing apparatus. Alternatively, or additionally, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal generated to encode information for transmission to a 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 one or more combinations thereof.

[0075] 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. Such apparatus may include special purpose logic circuitry, such as an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). In addition to hardware, such apparatus may also include code that creates an execution environment for the computer program in question, such as code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or one or more combinations thereof.

[0076] A computer program (which may be referred to or described as a program, software, software application, module, software module, script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, including as a standalone 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 one or more scripts stored in file portions that hold other programs or data, e.g., markup language documents; in a single file dedicated to the program in question; or in multiple coordinated files, e.g., files that store one or more modules, subprograms, or code portions. A computer program can be deployed to be executed on one computer or on multiple computers, located in a single location or distributed across multiple sites and interconnected by a communications network.

[0077] The processes and logic flows described herein can be implemented 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 implemented by an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit), and an apparatus can also be implemented as special purpose logic circuitry, such as an FPGA (Field Programmable Gate Array) or ASIC (Application Specific Integrated Circuit).

[0078] A computer suitable for running a computer program can include, for example, be based on, a general-purpose or special-purpose microprocessor or both, or any other type of central processing unit. Typically, a central processing unit receives 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. Typically, a computer also includes one or more mass storage devices, e.g., magnetic, magneto-optical, or optical disks, for storing data, or is operatively connected to receive data from, transmit data to, or both. However, a computer need not have such devices. Furthermore, a computer can be incorporated into another device, e.g., a mobile phone, 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.

[0079] 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.

[0080] To provide for user interaction, embodiments of the subject matter described herein 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 pointing device, e.g., a mouse or trackball, by which the user can provide input to the computer. Other types of devices can be used to provide for user interaction. For example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, audible feedback, or tactile feedback, and input from the user can be received in any form, including acoustic, speech, or tactile input. Additionally, a computer can interact with a user by sending and receiving documents to a device used by the user, e.g., by sending a web page to a web browser on a user's client device in response to a request received from the web browser.

[0081] Embodiments of the subject matter described herein can be implemented in a computing system that includes a back-end component, e.g., a data server, or a middleware component, e.g., an application server, or a front-end component, e.g., a client computer having a graphical user interface or web browser through which a user can interact with an implementation of the subject matter described herein, 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 communications network. Examples of communications networks include local area networks ("LANs") and wide area networks ("WANs"), e.g., the Internet.

[0082] The computing system may include clients and servers. Clients and servers 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.

[0083] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of a particular invention. Certain features described herein in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, while features may be described above as operating in a particular combination and initially claimed as such, one or more features from a claimed combination can in some cases be implemented from that combination, and the claimed combination may also refer to subcombinations or variations of subcombinations.

[0084] Similarly, although operations are shown in a particular order in the figures, this should not be understood as requiring such operations to be performed in the particular order shown, or in sequential order, or that all of the illustrated operations be performed, to achieve desired results. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems may generally be integrated into a single software product or packaged into multiple software products.

[0085] Certain 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 may 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. [Explanation of symbols]

[0086] 100 Neural Network Systems A batch of 102 training examples 104 Neural Network Layer A 106 Layer A Output 108 batch normalization layers 110 Batch normalization layer output 112 Neural Network Layer B 114 Neural Network Output

Claims

1. A method implemented by one or more computers, comprising: receiving a network input; processing said network inputs with a neural network to generate network outputs for said network inputs; Including, the neural network includes a first neural network layer and a second neural network layer; processing the network input with the neural network includes processing a first layer input to the first neural network layer according to trained values ​​of a set of parameters of the first neural network layer to generate a first layer output having a plurality of components; the trained values ​​of the set of parameters of the first neural network layer are the result of training the neural network with multiple batches of training data; each batch of training data includes a respective plurality of training examples; training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; receiving a respective first layer output generated by the first neural network layer for each of the plurality of training examples in the batch; calculating a plurality of normalized statistics for the batch from the first layer output; For each of a plurality of subsets of the plurality of components of the first layer output, determining an average of the components of the first layer output in the respective subset for each of the plurality of training examples in the batch; For each of the subsets of the components of the first layer output, determining a standard deviation of the components of the first layer output in the respective subset for each of the training examples in the batch; Including, each of the plurality of subsets is indexed by a dimension or feature index; and calculating the plurality of normalized statistics; normalizing each of the plurality of components of each first layer output using the normalization statistic to generate a respective normalized layer output for each training example in the batch; for each first layer output and for each of the plurality of subsets, normalizing the components of the first layer output within each subset using the mean for each subset and the standard deviation for each subset; generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; generating respective normalized layer outputs, including: providing each of the batch normalization layer outputs as inputs to the second neural network layer; A method comprising:

2. training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; generating a respective network output for each network input, the generating comprising processing each batch normalization layer output with the second neural network layer; updating the set of parameters of the first neural network layer using each of the network outputs using a backpropagation technique; The method of claim 1 further comprising:

3. updating the set of parameters of the first neural network layer using each of the network outputs using a backpropagation technique; The method of claim 2 , comprising backpropagating errors through the normalized statistics.

4. the plurality of components of the first layer output are indexed by dimension; Calculating a plurality of normalized statistics for the first layer output includes: For each of the dimensions, calculating an average of the components of the first layer output in that dimension; for each of the dimensions, calculating a standard deviation of the components of the first layer output in that dimension; 2. The method of claim 1, comprising:

5. normalizing each of the plurality of components of each first layer output; normalizing the components using the calculated mean and the calculated standard deviation for the dimension corresponding to the components; 5. The method of claim 4, comprising:

6. generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; For each dimension, transforming the components of the normalized layer output for the training examples in that dimension according to the current values ​​of a set of parameters for that dimension.

5. The method of claim 4, comprising:

7. the first neural network layer is a convolutional layer; the plurality of components of the first layer output are indexed by a feature index and a spatial location index; Calculating a plurality of normalized statistics for the first layer output includes, for each of the feature indexes: calculating an average of the components of the first layer output corresponding to the feature index; calculating the variance of the component of the first layer output corresponding to the feature index; 2. The method of claim 1, comprising:

8. normalizing each of the plurality of components of each layer output, normalizing the components using the mean and the variance for the feature index corresponding to the components; 8. The method of claim 7, comprising:

9. generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; Transforming each of the plurality of components of the normalized layer output according to a current value of a set of parameters for the feature index corresponding to the component.

8. The method of claim 7, comprising:

10. 1. A system comprising: one or more computers and one or more storage devices; the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations; The operation is receiving a network input; processing said network inputs with a neural network to generate network outputs for said network inputs; Including, the neural network includes a first neural network layer and a second neural network layer; processing the network input with the neural network includes processing a first layer input to the first neural network layer according to trained values ​​of a set of parameters of the first neural network layer to generate a first layer output having a plurality of components; the trained values ​​of the set of parameters of the first neural network layer are the result of training the neural network with multiple batches of training data; each batch of training data includes a respective plurality of training examples; training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; receiving a respective first layer output generated by the first neural network layer for each of the plurality of training examples in the batch; calculating a plurality of normalized statistics for the batch from the first layer output; For each of a plurality of subsets of the plurality of components of the first layer output, determining an average of the components of the first layer output in the respective subset for each of the plurality of training examples in the batch; For each of the subsets of the components of the first layer output, determining a standard deviation of the components of the first layer output in the respective subset for each of the training examples in the batch; Including, each of the plurality of subsets is indexed by a dimension or feature index; and calculating the plurality of normalized statistics; normalizing each of the plurality of components of each first layer output using the normalization statistic to generate a respective normalized layer output for each training example in the batch; for each first layer output and for each of the plurality of subsets, normalizing the components of the first layer output within each subset using the mean for each subset and the standard deviation for each subset; generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; generating respective normalized layer outputs, including: providing each of the batch normalization layer outputs as inputs to the second neural network layer; Including, the system.

11. training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; generating a respective network output for each network input, the generating comprising processing each batch normalization layer output with the second neural network layer; updating the set of parameters of the first neural network layer using each of the network outputs using a backpropagation technique; The system of claim 10 further comprising:

12. updating the set of parameters of the first neural network layer using each of the network outputs using a backpropagation technique; The system of claim 11 , further comprising backpropagating errors with the normalized statistics.

13. the plurality of components of the first layer output are indexed by dimension; Calculating a plurality of normalized statistics for the first layer output includes: For each of the dimensions, calculating an average of the components of the first layer output in that dimension; for each of the dimensions, calculating a standard deviation of the components of the first layer output in that dimension; The system of claim 10, comprising:

14. normalizing each of the plurality of components of each first layer output; normalizing the components using the calculated mean and the calculated standard deviation for the dimension corresponding to the components; The system of claim 13, comprising:

15. generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; For each dimension, transforming the components of the normalized layer output for the training examples in that dimension according to the current values ​​of a set of parameters for that dimension. The system of claim 13, comprising:

16. the first neural network layer is a convolutional layer; the plurality of components of the first layer output are indexed by a feature index and a spatial location index; Calculating a plurality of normalized statistics for the first layer output includes, for each of the feature indexes: calculating an average of the components of the first layer output corresponding to the feature index; calculating the variance of the component of the first layer output corresponding to the feature index; The system of claim 10, comprising:

17. normalizing each of the plurality of components of each layer output, normalizing the components using the mean and the variance for the feature index corresponding to the components; 17. The system of claim 16, comprising:

18. generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; Transforming each of the plurality of components of the normalized layer output according to a current value of a set of parameters for the feature index corresponding to the component.

17. The system of claim 16, comprising:

19. one or more non-transitory computer-readable storage media storing instructions, The instructions, when executed by one or more computers, cause the one or more computers to perform operations; The operation is receiving a network input; processing said network inputs with a neural network to generate network outputs for said network inputs; Including, the neural network includes a first neural network layer and a second neural network layer; processing the network input with the neural network includes processing a first layer input to the first neural network layer according to trained values ​​of a set of parameters of the first neural network layer to generate a first layer output having a plurality of components; the trained values ​​of the set of parameters of the first neural network layer are the result of training the neural network with multiple batches of training data; each batch of training data includes a respective plurality of training examples; training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; receiving a respective first layer output generated by the first neural network layer for each of the plurality of training examples in the batch; calculating a plurality of normalized statistics for the batch from the first layer output; For each of a plurality of subsets of the plurality of components of the first layer output, determining an average of the components of the first layer output in the respective subset for each of the plurality of training examples in the batch; For each of the subsets of the components of the first layer output, determining a standard deviation of the components of the first layer output in the respective subset for each of the training examples in the batch; Including, each of the plurality of subsets is indexed by a dimension or feature index; and calculating the plurality of normalized statistics; normalizing each of the plurality of components of each first layer output using the normalization statistic to generate a respective normalized layer output for each training example in the batch; for each first layer output and for each of the plurality of subsets, normalizing the components of the first layer output within each subset using the mean for each subset and the standard deviation for each subset; generating a respective batch normalization layer output for each of the training examples from the normalized layer outputs; generating respective normalized layer outputs, including: providing each of the batch normalization layer outputs as inputs to the second neural network layer; [0023] 1. One or more non-transitory computer-readable storage media,

20. training the neural network to determine the trained values ​​of the set of parameters of the first neural network layer, for each of the plurality of batches; generating a respective network output for each network input, the generating comprising processing each batch normalization layer output with the second neural network layer; updating the set of parameters of the first neural network layer using each of the network outputs using a backpropagation technique; 20. The one or more non-transitory computer-readable storage media of claim 19, further comprising:

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