## Abstract

This cuDNN 8.6.0 Developer Guide provides an overview of the NVIDIA cuDNN features such as customizable data layouts, supporting flexible dimension ordering, striding, and subregions for the 4D tensors used as inputs and outputs to all of its routines. This flexibility allows easy integration into any neural network implementation.

To access the API, refer to the NVIDIA cuDNN API Reference.

For previously released developer documentation, refer to the NVIDIA cuDNN Archives.

## 1. Introduction

NVIDIA® CUDA® Deep Neural Network LIbrary (cuDNN) is a GPU-accelerated library of primitives for deep neural networks. It provides highly tuned implementations of routines arising frequently in DNN applications:
• Convolution forward and backward, including cross-correlation
• Matrix multiplication
• Pooling forward and backward
• Softmax forward and backward
• Neuron activations forward and backward: relu, tanh, sigmoid, elu, gelu, softplus, swish
• Arithmetic, mathematical, relational and logical pointwise operations
• Tensor transformation functions
• LRN, LCN and batch normalization forward and backward

cuDNN convolution routines aim for a performance that is competitive with the fastest GEMM (matrix multiply)-based implementations of such routines while using significantly less memory.

cuDNN features include customizable data layouts, supporting flexible dimension ordering, striding, and subregions for the 4D tensors used as inputs and outputs to all of its routines. This flexibility allows easy integration into any neural network implementation and avoids the input/output transposition steps sometimes necessary with GEMM-based convolutions.

cuDNN offers a context-based API that allows for easy multithreading and (optional) interoperability with NVIDIA® CUDA® streams.

### 1.1. Programming Model

The cuDNN library exposes a host API but assumes that for operations using the GPU, the necessary data is directly accessible from the device.

An application using cuDNN must initialize a handle to the library context by calling cudnnCreate(). This handle is explicitly passed to every subsequent library function that operates on GPU data. Once the application finishes using cuDNN, it can release the resources associated with the library handle using cudnnDestroy(). This approach allows the user to explicitly control the library's functioning when using multiple host threads, GPUs and CUDA streams.

For example, an application can use cudaSetDevice (prior to creating a cuDNN handle) to associate different devices with different host threads, and in each of those host threads, create a unique cuDNN handle that directs the subsequent library calls to the device associated with it. Therefore, the cuDNN library calls made with different handles will automatically run on different devices.

The device associated with a particular cuDNN context is assumed to remain unchanged between the corresponding cudnnCreate() and cudnnDestroy() calls. In order for the cuDNN library to use a different device within the same host thread, the application must set the new device to be used by calling cudaSetDevice() and then create another cuDNN context, which will be associated with the new device, by calling cudnnCreate().

### cuDNN API Compatibility

Beginning in cuDNN 7, the binary compatibility of a patch and minor releases is maintained as follows:
• Any patch release x.y.z is forward or backward-compatible with applications built against another cuDNN patch release x.y.w (meaning, of the same major and minor version number, but having w!=z).

• cuDNN minor releases beginning with cuDNN 7 are binary backward-compatible with applications built against the same or earlier patch release (meaning, an application built against cuDNN 7.x is binary compatible with cuDNN library 7.y, where y>=x).

• Applications compiled with a cuDNN version 7.y are not guaranteed to work with 7.x release when y > x.

### 1.2. GPU And Driver Requirements

For the latest compatibility software versions of the OS, CUDA, the CUDA driver, and the NVIDIA hardware, see the NVIDIA cuDNN Support Matrix.

### 1.3. Backward Compatibility And Deprecation Policy

cuDNN version 8 introduces a new API deprecation policy to enable a faster pace of innovation.

The old deprecation policy required three major library releases to complete an API update. During this process, the original function name was first assigned to the legacy API, and then to the revised API, depending on the library version. The user wishing to migrate to the new API version had to update his or her code twice. In the first update, the original call foo() had to be changed to foo_vN(), where N is the new major cuDNN version. After the next major cuDNN release, the foo_vN() function had to be renamed back as foo(). Clearly, the above process could be difficult for code maintenance, especially when many functions are upgraded.

A streamlined, two-step, deprecation policy will be used for all API changes starting with cuDNN version 8. Let us explain the process using two subsequent, major cuDNN releases, version 8 and 9:
Table 1. Two-step, deprecation policy
cuDNN version Explanation
Major release 8 The updated API is introduced as foo_v8(). The deprecated API foo() is kept unchanged to maintain backward compatibility until the next major release.
Major release 9 The deprecated API foo() is permanently removed and its name is not reused. The foo_v8() function supersedes the retired call foo().

If the existing API needs to be updated, a new function flavor is introduced with the _v tag followed by the current, major cuDNN version. In the next major release, the deprecated function is removed, and its name is never reused. A brand-new API is first introduced without the _v tag.

The revised depreciation scheme allows us to retire the legacy API in just one major release. Similarly to the previous API deprecation policy, the user is able to compile the legacy code without any changes using the next major release of the cuDNN library. The backward compatibility ends when another major cuDNN release is introduced.

The updated function name embeds the information in which the cuDNN version of the API call was modified. As a result, the API changes will be easier to track and document.

The new deprecation policy is applied also to pending API changes from previous cuDNN releases. For example, according to the old deprecation policy, cudnnSetRNNDescriptor_v6() should be removed in cuDNN version 8 and the upgraded call cudnnSetRNNDescriptor() with the same arguments and behavior should be kept. Instead, the new deprecation policy is applied to this case and the tagged function is kept.

Prototypes of deprecated functions will be prepended in cuDNN version 8 headers using the CUDNN_DEPRECATED macro. When the -DCUDNN_WARN_DEPRECATED switch is passed to the compiler, any deprecated function call in the user's code will emit a compiler warning, for example:
warning: ‘cudnnStatus_t cudnnSetRNNMatrixMathType(cudnnRNNDescriptor_t, cudnnMathType_t)’ is deprecated [-Wdeprecated-declarations]
Or
warning C4996: 'cudnnSetRNNMatrixMathType': was declared deprecated

The above warnings are disabled by default to avoid potential build breaks in software setups where compiler warnings are treated as errors.

Note that the simple swapping of older cuDNN version 7 shared library files will not work with the cuDNN version 8 release. The user source code needs to be recompiled from scratch with the cuDNN version 8 headers and linked with the version 8 libraries.

The cuDNN library is thread-safe. Its functions can be called from multiple host threads, so long as the threads do not share the same cuDNN handle simultaneously.

When creating a per-thread cuDNN handle, it is recommended that a single synchronous call of cudnnCreate() be made first before each thread creates its own handle asynchronously.

Per cudnnCreate(), for multi-threaded applications that use the same device from different threads, the recommended programming model is to create one (or a few, as is convenient) cuDNN handles per thread and use that cuDNN handle for the entire life of the thread.

## 2. Tensor Descriptor

The cuDNN library describes data holding images, videos and any other data with contents with a generic n-D tensor defined with the following parameters:
• a dimension nbDims from 3 to 8

• a data type (32-bit floating-point, 64 bit-floating point, 16-bit floating-point...)

• dimA integer array defining the size of each dimension

• strideA integer array defining the stride of each dimension (for example, the number of elements to add to reach the next element from the same dimension)

The first dimension of the tensor defines the batch size n, and the second dimension defines the number of features maps c. This tensor definition allows, for example, to have some dimensions overlapping each other within the same tensor by having the stride of one dimension smaller than the product of the dimension and the stride of the next dimension. In cuDNN, unless specified otherwise, all routines will support tensors with overlapping dimensions for forward-pass input tensors, however, dimensions of the output tensors cannot overlap. Even though this tensor format supports negative strides (which can be useful for data mirroring), cuDNN routines do not support tensors with negative strides unless specified otherwise.

### 2.1. WXYZ Tensor Descriptor

Tensor descriptor formats are identified using acronyms, with each letter referencing a corresponding dimension. In this document, the usage of this terminology implies:
• all the strides are strictly positive

• the dimensions referenced by the letters are sorted in decreasing order of their respective strides

### 2.2. 3-D Tensor Descriptor

A 3-D tensor is commonly used for matrix multiplications, with three letters: B, M, and N. B represents the batch size (for batch GEMM, set to 1 for single GEMM), M represents the number of rows, and N represents the number of columns. Refer to the MatMul operation for more information.

### 2.3. 4-D Tensor Descriptor

A 4-D tensor descriptor is used to define the format for batches of 2D images with 4 letters: N,C,H,W for respectively the batch size, the number of feature maps, the height and the width. The letters are sorted in decreasing order of the strides. The commonly used 4-D tensor formats are:
• NCHW
• NHWC
• CHWN

### 2.4. 5-D Tensor Descriptor

A 5-D tensor descriptor is used to define the format of the batch of 3D images with 5 letters: N,C,D,H,W for respectively the batch size, the number of feature maps, the depth, the height, and the width. The letters are sorted in decreasing order of the strides. The commonly used 5-D tensor formats are called:
• NCDHW
• NDHWC
• CDHWN

### 2.5. Fully-packed Tensors

A tensor is defined as XYZ-fully-packed if and only if:
• the number of tensor dimensions is equal to the number of letters preceding the fully-packed suffix.

• the stride of the i-th dimension is equal to the product of the (i+1)-th dimension by the (i+1)-th stride.

• the stride of the last dimension is 1.

### 2.6. Partially-packed Tensors

The partially XYZ-packed terminology only applies in the context of a tensor format described with a superset of the letters used to define a partially-packed tensor. A WXYZ tensor is defined as XYZ-packed if and only if:
• The strides of all dimensions NOT referenced in the -packed suffix are greater or equal to the product of the next dimension by the next stride.

• The stride of each dimension referenced in the -packed suffix in position i is equal to the product of the (i+1)-st dimension by the (i+1)-st stride.

• If the last tensor's dimension is present in the -packed suffix, its stride is 1.

For example, an NHWC tensor WC-packed means that the c_stride is equal to 1 and w_stride is equal to c_dim x c_stride. In practice, the -packed suffix is usually applied to the minor dimensions of a tensor but can be applied to only the major dimensions; for example, an NCHW tensor that is only N-packed.

### 2.7. Spatially Packed Tensors

Spatially-packed tensors are defined as partially-packed in spatial dimensions. For example, a spatially-packed 4D tensor would mean that the tensor is either NCHW HW-packed or CNHW HW-packed.

### 2.8. Overlapping Tensors

A tensor is defined to be overlapping if iterating over a full range of dimensions produces the same address more than once. In practice an overlapped tensor will have stride[i-1] < stride[i]*dim[i] for some of the i from [1,nbDims] interval.

## 3. Data Layout Formats

This section describes how cuDNN tensors are arranged in memory according to several data layout formats.

The recommended way to specify the layout format of a tensor is by setting its strides accordingly. For compatibility with the v7 API, a subset of the layout formats can also be configured through the cudnnTensorFormat_t enum in the cuDNN API Reference. The enum is only supplied for legacy reasons and is deprecated.

### 3.1. Example Tensor

Consider a batch of images with the following dimensions:
• N is the batch size; 1.
• C is the number of feature maps (i.e., number of channels); 64.
• H is the image height; 5.
• W is the image width; 4.

To keep the example simple, the image pixel elements are expressed as a sequence of integers, 0, 1, 2, 3, and so on. See Figure 1.

Figure 1. Example with N=1, C=64, H=5, W=4.

In the following subsections, we’ll use the above example to demonstrate the different layout formats.

### 3.2.1. NCHW Memory Layout

The above 4D tensor is laid out in the memory in the NCHW format as below:
1. Beginning with the first channel (c=0), the elements are arranged contiguously in row-major order.
2. Continue with second and subsequent channels until the elements of all the channels are laid out. Refer to Figure 2.
3. Proceed to the next batch (if N is > 1).
Figure 2. NCHW Memory Layout

### 3.2.2. NHWC Memory Layout

For the NHWC memory layout, the corresponding elements in all the C channels are laid out first, as below:
1. Begin with the first element of channel 0, then proceed to the first element of channel 1, and so on, until the first elements of all the C channels are laid out.
2. Next, select the second element of channel 0, then proceed to the second element of channel 1, and so on, until the second element of all the channels are laid out.
3. Follow the row-major order of channel 0 and complete all the elements. Refer to Figure 3.
4. Proceed to the next batch (if N is > 1).
Figure 3. NHWC Memory Layout

### 3.2.3. NC/32HW32 Memory Layout

The NC/32HW32 is similar to NHWC, with a key difference. For the NC/32HW32 memory layout, the 64 channels are grouped into two groups of 32 channels each - first group consisting of channels c0 through c31, and the second group consisting of channels c32 through c63. Then each group is laid out using the NHWC format. See Figure 4.
Figure 4. NC/32HW32 Memory Layout

For the generalized NC/xHWx layout format, the following observations apply:
• Only the channel dimension, C, is grouped into x channels each.

• When x = 1, each group has only one channel. Hence, the elements of one channel (i.e, one group) are arranged contiguously (in the row-major order), before proceeding to the next group (i.e., next channel). This is the same as NCHW format.

• When x = C, then NC/xHWx is identical to NHWC, i.e., the entire channel depth C is considered as a single group. The case x = C can be thought of as vectorizing the entire C dimension as one big vector, laying out all the Cs, followed by the remaining dimensions, just like NHWC.

• The tensor format CUDNN_TENSOR_NCHW_VECT_C can also be interpreted in the following way: The NCHW INT8x32 format is really N x (C/32) x H x W x 32 (32 Cs for every W), just as the NCHW INT8x4 format is N x (C/4) x H x W x 4 (4 Cs for every W). Hence the VECT_C name - each W is a vector (4 or 32) of Cs.

### 3.3. MatMul Layouts

As discussed in 3-D Tensor Descriptor, MatMul uses 3D tensors, described using BMN dimensions. The layout can be specified through the following strides. The following are two examples of recommended layouts:
• Packed Row-major: dim [B,M,N] with stride [MN, N, 1], or
• Packed Column-major: dim [B,M,N] with stride [MN, 1, M]

Unpacked layouts for 3-D tensors are supported as well, but their support surface is more ragged.

## 4. Reproducibility (determinism)

By design, most of cuDNN's routines from a given version generate the same bit-wise results across runs when executed on GPUs with the same architecture. There are some exceptions. For example, the following routines do not guarantee reproducibility across runs, even on the same architecture, because they use atomic operations in a way that introduces truly random floating point rounding errors:
• cudnnConvolutionBackwardFilter when CUDNN_CONVOLUTION_BWD_FILTER_ALGO_0 or CUDNN_CONVOLUTION_BWD_FILTER_ALGO_3 is used

• cudnnConvolutionBackwardData when CUDNN_CONVOLUTION_BWD_DATA_ALGO_0 is used

• cudnnPoolingBackward when CUDNN_POOLING_MAX is used

• cudnnSpatialTfSamplerBackward

• cudnnCTCLoss and cudnnCTCLoss_v8 when CUDNN_CTC_LOSS_ALGO_NON_DETERMINSTIC is used

Across different architectures, no cuDNN routines guarantee bit-wise reproducibility. For example, there is no guarantee of bit-wise reproducibility when comparing the same routine run on NVIDIA Volta™ and NVIDIA Turing™, or NVIDIA Turing and NVIDIA Ampere Architecture.

## 5. Scaling Parameters

Many cuDNN routines like cudnnConvolutionForward() accept pointers in host memory to scaling factors alpha and beta. These scaling factors are used to blend the computed values with the prior values in the destination tensor as follows (refer to Figure 5):
dstValue = alpha*computedValue + beta*priorDstValue
Note: The dstValue is written to after being read.
Figure 5. Scaling Parameters for Convolution

When beta is zero, the output is not read and may contain uninitialized data (including NaN).

These parameters are passed using a host memory pointer. The storage data types for alpha and beta are:
• float for HALF and FLOAT tensors, and
• double for DOUBLE tensors.
Note: For improved performance use beta = 0.0. Use a non-zero value for beta only when you need to blend the current output tensor values with the prior values of the output tensor.

## Type Conversion

When the data input x, the filter input w and the output y are all in INT8 data type, the function cudnnConvolutionBiasActivationForward() will perform the type conversion as shown in Figure 6:

Note: Accumulators are 32-bit integers that wrap on overflow.
Figure 6. INT8 for cudnnConvolutionBiasActivationForward

## 6. Tensor Core Operations

The cuDNN v7 library introduced the acceleration of compute-intensive routines using Tensor Core hardware on supported GPU SM versions. Tensor Core operations are supported beginning with the NVIDIA Volta GPU.

### 6.1. Basics

Tensor Core operations accelerate matrix math operations; cuDNN uses Tensor Core operations that accumulate into FP16, FP32, and INT32 values. Setting the math mode to CUDNN_TENSOR_OP_MATH via the cudnnMathType_t enumerator indicates that the library will use Tensor Core operations. This enumerator specifies the available options to enable the Tensor Core and should be applied on a per-routine basis.

The default math mode is CUDNN_DEFAULT_MATH, which indicates that the Tensor Core operations will be avoided by the library. Because the CUDNN_TENSOR_OP_MATH mode uses the Tensor Cores, it is possible that these two modes generate slightly different numerical results due to different sequencing of the floating-point operations.

For example, the result of multiplying two matrices using Tensor Core operations is very close, but not always identical, to the result achieved using a sequence of scalar floating-point operations. For this reason, the cuDNN library requires an explicit user opt-in before enabling the use of Tensor Core operations.

However, experiments with training common deep learning models show negligible differences between using Tensor Core operations and scalar floating point paths, as measured by both the final network accuracy and the iteration count to convergence. Consequently, the cuDNN library treats both modes of operation as functionally indistinguishable and allows for the scalar paths to serve as legitimate fallbacks for cases in which the use of Tensor Core operations is unsuitable.

Kernels using Tensor Core operations are available for:
• Convolutions
• RNNs

### 6.2.1. Prerequisites

For the supported GPUs, the Tensor Core operations will be triggered for convolution functions only when cudnnSetConvolutionMathType() is called on the appropriate convolution descriptor by setting the mathType to CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION.

### 6.2.2. Supported Algorithms

When the prerequisite is met, the below convolution functions can be run as Tensor Core operations:
See the table below for supported algorithms:
Supported Convolution Function Supported Algos
cudnnConvolutionForward

CUDNN_CONVOLUTION_FWD_ALGO_IMPLICIT_PRECOMP_GEMM

cudnnConvolutionBackwardData

CUDNN_CONVOLUTION_BWD_DATA_ALGO_1

cudnnConvolutionBackwardFilter

CUDNN_CONVOLUTION_BWD_FILTER_ALGO_1

### 6.2.3. Data And Filter Formats

The cuDNN library may use padding, folding, and NCHW-to-NHWC transformations to call the Tensor Core operations. See Tensor Transformations.
For algorithms other than *_ALGO_WINOGRAD_NONFUSED, when the following requirements are met, the cuDNN library will trigger the Tensor Core operations:
• Input, filter, and output descriptors (xDesc, yDesc, wDesc, dxDesc, dyDesc and dwDesc as applicable) are of the dataType = CUDNN_DATA_HALF (i.e., FP16). For FP32 dataType see FP32-to-FP16 Conversion.

• The number of input and output feature maps (i.e., channel dimension C) is a multiple of 8. When the channel dimension is not a multiple of 8, see Padding.

• The filter is of type CUDNN_TENSOR_NCHW or CUDNN_TENSOR_NHWC.

• If using a filter of type CUDNN_TENSOR_NHWC, then the input, filter, and output data pointers (X, Y, W, dX, dY, and dW as applicable) are aligned to 128-bit boundaries.

### 6.3.1. Prerequisites

Tensor Core operations are triggered for these RNN functions only when cudnnSetRNNMatrixMathType() is called on the appropriate RNN descriptor setting mathType to CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION.

### 6.3.2. Supported Algorithms

When the above prerequisite is met, the RNN functions below can be run as Tensor Core operations:
See the table below for the supported algorithms:
RNN Function Support Algos
All RNN functions that support Tensor Core operations.

CUDNN_RNN_ALGO_STANDARD

CUDNN_RNN_ALGO_PERSIST_STATIC

### 6.3.3. Data And Filter Formats

When the following requirements are met, then the cuDNN library triggers the Tensor Core operations:
• For algo = CUDNN_RNN_ALGO_STANDARD:
• The hidden state size, input size, and the batch size is a multiple of 8.
• All user-provided tensors, workspace, and reserve space are aligned to 128-bit boundaries.
• For FP16 input/output, the CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION is selected.
• For FP32 input/output, CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION is selected.
• For algo = CUDNN_RNN_ALGO_PERSIST_STATIC:
• The hidden state size and the input size is a multiple of 32.
• The batch size is a multiple of 8.
• If the batch size exceeds 96 (for forward training or inference) or 32 (for backward data), then the batch size constraints may be stricter, and large power-of-two batch sizes may be needed.
• All user-provided tensors, workspace, and reserve space are aligned to 128-bit boundaries.
• For FP16 input/output, CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION is selected.
• For FP32 input/output, CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION is selected.

### 6.4. Tensor Transformations

A few functions in the cuDNN library will perform transformations such as folding, padding, and NCHW-to-NHWC conversion while performing the actual function operation. See below.

### 6.4.1. FP32-to-FP16 Conversion

The cuDNN API allows the user to specify that FP32 input data may be copied and converted to FP16 data internally to use Tensor Core operations for potentially improved performance. This can be achieved by selecting CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION enum for cudnnMathType_t. In this mode, the FP32 tensors are internally down-converted to FP16, the Tensor Op math is performed, and finally up-converted to FP32 as outputs. See Figure 7.
Figure 7. Tensor Operation with FP32 Inputs

#### For Convolutions

For convolutions, the FP32-to-FP16 conversion can be achieved by passing the CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION enum value to the cudnnSetConvolutionMathType() call.
// Set the math type to allow cuDNN to use Tensor Cores:
checkCudnnErr(cudnnSetConvolutionMathType(cudnnConvDesc, CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION));


#### For RNNs

For RNNs, the FP32-to-FP16 conversion can be achieved by passing the CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION enum value to the cudnnSetRNNMatrixMathType() call to allow FP32 data to be converted for use in RNNs.
// Set the math type to allow cuDNN to use Tensor Cores:
checkCudnnErr(cudnnSetRNNMatrixMathType(cudnnRnnDesc, CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION));


For packed NCHW data, when the channel dimension is not a multiple of 8, then the cuDNN library will pad the tensors as needed to enable Tensor Core operations. This padding is automatic for packed NCHW data in both the CUDNN_TENSOR_OP_MATH and the CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION cases.

### 6.4.3. Folding

In the folding operation, the cuDNN library implicitly performs the formatting of input tensors and saves the input tensors in an internal workspace. This can lead to an acceleration of the call to Tensor Cores.

With folding or channel-folding, cuDNN can implicitly format the input tensors within an internal workspace to accelerate the overall calculation. Performing this transformation for the user often allows cuDNN to use kernels with restrictions on convolution stride to support a strided convolution problem.

### 6.4.4. Conversion Between NCHW And NHWC

Tensor Cores require that the tensors be in the NHWC data layout. Conversion between NCHW and NHWC is performed when the user requests Tensor Op math. However, as stated in Basics, a request to use Tensor Cores is just that, a request and Tensor Cores may not be used in some cases. The cuDNN library converts between NCHW and NHWC if and only if Tensor Cores are requested and are actually used.

If your input (and output) are NCHW, then expect a layout change.

Non-Tensor Op convolutions will not perform conversions between NCHW and NHWC.

In very rare and difficult-to-qualify cases that are a complex function of padding and filter sizes, it is possible that Tensor Ops is not enabled. In such cases, users can pre-pad to enable the Tensor Ops path.

### 6.5.1. FP16 Data

For FP16 data, Tensor Cores operate on FP16 input, output in FP16, and may accumulate in FP16 or FP32. The FP16 multiply leads to a full-precision result that is accumulated in FP32 operations with the other products in a given dot product for a matrix with m x n x k dimensions. See Figure 8.

For an FP32 accumulation, with FP16 output, the output of the accumulator is down-converted to FP16. Generally, the accumulation type is of greater or equal precision to the output type.

Figure 8. Tensor operation with FP16 inputs. The accumulation is in FP32, which could be the input for other kernel features (for example, activation/bias, beta blending, etc). The final output in this example would be FP16.

### 6.6. Guidelines For Good Performance On Tensor Cores

For a deep learning compiler, the following are the key guidelines:
• Make sure that the convolution operation is eligible for Tensor Cores by avoiding any combinations of large padding and large filters.
• Transform the inputs and filters to NHWC, pre-pad channel and batch size to be a multiple of 8.
• Make sure that all user-provided tensors, workspace, and reserve space are aligned to 128-bit boundaries. Note that 1024-bit alignment may deliver better performance.

## 7. Convolutions

The convolution functions are:

### 7.1. Convolution Formulas

This section describes the various convolution formulas implemented in convolution functions for the cudnnConvolutionForward() path.
The convolution terms described in the table below apply to all the convolution formulas that follow.
Table 2. Convolution terms
Term Description
$x$ Input (image) Tensor
$w$ Weight Tensor
$y$ Output Tensor
$n$ Current Batch Size
$c$ Current Input Channel
$C$ Total Input Channels
$H$ Input Image Height
$W$ Input Image Width
$k$ Current Output Channel
$K$ Total Output Channels
$p$ Current Output Height Position
$q$ Current Output Width Position
$G$ Group Count
$\mathit{pad}$ Padding Value
$u$ Vertical Subsample Stride (along Height)
$\mathit{v}$ Horizontal Subsample Stride (along Width)
${\mathit{dil}}_{\mathit{h}}$ Vertical Dilation (along Height)
${\mathit{dil}}_{\mathit{w}}$ Horizontal Dilation (along Width)
$r$ Current Filter Height
$R$ Total Filter Height
$s$ Current Filter Width
$S$ Total Filter Width
${C}_{g}$ $\frac{C}{G}$
${K}_{g}$ $\frac{K}{G}$

### Convolution (convolution mode set to CUDNN_CROSS_CORRELATION)

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{C}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, c, p+r, q+s}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k,c,r,s}}$

${x}_{\mathit{<0, <0}}\phantom{\rule{5px}{0ex}}=0$

${x}_{\mathit{>H, >W}}\phantom{\rule{5px}{0ex}}=0$

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{C}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, c, p+r-pad, q+s-pad}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k,c,r,s}}$

### Convolution with Subsample-Striding

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{C}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, c, \left(p*u\right) + r, \left(q*v\right) + s}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k,c,r,s}}$

### Convolution with Dilation

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{C}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, c, p + \left(r*dilh\right), q + \left(s*dilw\right)}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k,c,r,s}}$

### Convolution (convolution mode set to CUDNN_CONVOLUTION)

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{C}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, c, p + r, q + s}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k, c, R-r-1, S-s-1}}$

### Convolution using Grouped Convolution

${C}_{g}=\frac{C}{G}$

${K}_{g}=\frac{K}{G}$

${y}_{\mathit{n, k, p, q}}=\sum _{c}^{{C}_{g}}\phantom{\rule{5px}{0ex}}\sum _{r}^{R}\phantom{\rule{5px}{0ex}}\sum _{s}^{S}\phantom{\rule{10px}{0ex}}{x}_{\mathit{n, Cg*floor\left(k/Kg\right)+c, p+r, q+s}}\phantom{\rule{15px}{0ex}}×\phantom{\rule{15px}{0ex}}{w}_{\mathit{k,c,r,s}}$

### 7.2. Grouped Convolutions

cuDNN supports grouped convolutions by setting groupCount > 1 for the convolution descriptor convDesc, using cudnnSetConvolutionGroupCount().
Note: By default, the convolution descriptor convDesc is set to groupCount of 1.

### Basic Idea

Conceptually, in grouped convolutions, the input channels and the filter channels are split into a groupCount number of independent groups, with each group having a reduced number of channels. The convolution operation is then performed separately on these input and filter groups.

For example, consider the following: if the number of input channels is 4, and the number of filter channels of 12. For a normal, ungrouped convolution, the number of computation operations performed are 12*4.

If the groupCount is set to 2, then there are now two input channel groups of two input channels each, and two filter channel groups of six filter channels each.

As a result, each grouped convolution will now perform 2*6 computation operations, and two such grouped convolutions are performed. Hence the computation savings are 2x: (12*4)/(2*(2*6)) .

### cuDNN Grouped Convolution

• When using groupCount for grouped convolutions, you must still define all tensor descriptors so that they describe the size of the entire convolution, instead of specifying the sizes per group.
• Grouped convolutions are supported for all formats that are currently supported by the functions cudnnConvolutionForward(), cudnnConvolutionBackwardData() and cudnnConvolutionBackwardFilter().
• The tensor stridings that are set for groupCount of 1 are also valid for any group count.
• By default, the convolution descriptor convDesc is set to groupCount of 1.
Note: See Convolution Formulas for the math behind the cuDNN grouped convolution.

### Example

Below is an example showing the dimensions and strides for grouped convolutions for NCHW format, for 2D convolution.
Note: The symbols * and / are used to indicate multiplication and division.
xDesc or dxDesc:
• Dimensions: [batch_size, input_channel, x_height, x_width]
• Strides: [input_channels*x_height*x_width, x_height*x_width, x_width, 1]
wDesc or dwDesc:
• Dimensions: [output_channels, input_channels/groupCount, w_height, w_width]
• Format: NCHW
convDesc:
• Group Count: groupCount

yDesc or dyDesc:
• Dimensions: [batch_size, output_channels, y_height, y_width]
• Strides: [output_channels*y_height*y_width, y_height*y_width, y_width, 1]

### Best Practices For 3D Convolutions

Attention: These guidelines are applicable to 3D convolution and deconvolution functions starting in NVIDIA® CUDA® Deep Neural Network library (cuDNN) v7.6.3.

The following guidelines are for setting the cuDNN library parameters to enhance the performance of 3D convolutions. Specifically, these guidelines are focused on settings such as filter sizes, padding and dilation settings. Additionally, an application-specific use-case, namely, medical imaging, is presented to demonstrate the performance enhancement of 3D convolutions with these recommended settings.

Specifically, these guidelines are applicable to the following functions and their associated data types:

For more information, refer to the NVIDIA cuDNN Developer Guide and the NVIDIA cuDNN API Reference.

### 7.3.1. Recommended Settings

The following table shows the recommended settings while performing 3D convolutions for cuDNN.
Table 3. Recommended settings while performing 3D convolutions for cuDNN
cuDNN 8.6.0
Platform

NVIDIA Hopper Architecture

NVIDIA Ampere Architecture

NVIDIA Turing Architecture

NVIDIA Volta Architecture

Convolution (3D or 2D) 3D and 2D

fprop

Grouped convolution size

C_per_group == K_per_group == {1,4,8,16,32,64,128,256}

Not supported for INT8

Data layout format (NHWC/NCHW)1 NDHWC
Input/output precision (FP16, FP32, INT8, or FP64) FP16, FP322, INT83
Accumulator (compute) precision (FP16, FP32, INT32 or FP64) FP32, INT32
Filter (kernel) sizes No limitation
Image sizes 2 GB limitation for a tensor
Number of channels C

0 mod 8

0 mod 16 (for INT8)

K

0 mod 8

0 mod 16 (for INT8)

Convolution mode Cross-correlation and convolution
Strides No limitation
Dilation No limitation
Data pointer alignment All data pointers are 16-bytes aligned.

### 7.3.2. Limitations

Your application will be functional but could be less performant if the model has channel counts lower than 32 (gets worse the lower it is).

## 8. Features Of RNN Functions

Refer to the table below for a list of features supported by each RNN function:
Note:

For each of these terms, the short-form versions shown in the parenthesis are used in the tables below for brevity: CUDNN_RNN_ALGO_STANDARD (_ALGO_STANDARD), CUDNN_RNN_ALGO_PERSIST_STATIC (_ALGO_PERSIST_STATIC), CUDNN_RNN_ALGO_PERSIST_DYNAMIC (_ALGO_PERSIST_DYNAMIC), and CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION (_ALLOW_CONVERSION).

Functions Input/output layout supported Supports variable sequence length in batch Commonly supported
cudnnRNNForwardInference() Only Sequence major, packed (non-padded)

Only with _ALGO_STANDARD

Require input sequences descending sorted according to length.

Mode (cell type) supported:CUDNN_RNN_RELU, CUDNN_RNN_TANH, CUDNN_LSTM, CUDNN_GRU

Algo supported4 (see the table below for an elaboration on these algorithms):_ALGO_STANDARD, _ALGO_PERSIST_STATIC, _ALGO_PERSIST_DYNAMIC

Math mode supported: CUDNN_DEFAULT_MATH,CUDNN_TENSOR_OP_MATH

(will automatically fall back if run on pre-Volta or if algo doesn’t support Tensor Cores)

_ALLOW_CONVERSION (may do down conversion to utilize Tensor Cores)

Direction mode supported: CUDNN_UNIDIRECTIONAL, CUDNN_BIDIRECTIONAL

RNN input mode: CUDNN_LINEAR_INPUT, CUDNN_SKIP_INPUT

cudnnRNNForwardTraining()
cudnnRNNBackwardData()
cudnnRNNBackwardWeights()
cudnnRNNForwardInferenceEx()

Sequence major unpacked

Batch major unpacked5

Sequence major packed6

Only with _ALGO_STANDARD

For unpacked layout, no input sorting required. 7

For packed layout, require input sequences descending sorted according to length.

cudnnRNNForwardTrainingEx()
cudnnRNNBackwardDataEx()
cudnnRNNBackwardWeightsEx()
The following table provides the features supported by the algorithms referred in the above table: CUDNN_RNN_ALGO_STANDARD, CUDNN_RNN_ALGO_PERSIST_STATIC, and CUDNN_RNN_ALGO_PERSIST_DYNAMIC.
Features _ALGO_STANDARD _ALGO_PERSIST_STATIC CUDNN_RNN_ALGO_PERSIST_STATIC_SMALL_H _ALGO_PERSIST_DYNAMIC
Half input

Single accumulation

Half output

Supported

Half intermediate storage

Single accumulation

Single input

Single accumulation

Single output

Supported

If running on Volta, with CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION*, will down-convert and use half intermediate storage.

Otherwise: Single intermediate storage

Single accumulation

Double input

Double accumulation

Double output

Supported

Double intermediate storage

Double accumulation

Not Supported Not Supported Supported

Double intermediate storage

Double accumulation

LSTM recurrent projection Supported Not Supported Not Supported Not Supported
LSTM cell clipping Supported
Variable sequence length in batch Supported Not Supported Not Supported Not Supported
Tensor Cores

Supported

For half input/output, acceleration requires setting

CUDNN_TENSOR_OP_MATH8 or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION 9

Acceleration requires inputSize and hiddenSize to be a multiple of 8

For single input/output on NVIDIA Volta, NVIDIA Xavier, and NVIDIA Turing, acceleration requires setting

CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION10

Acceleration requires inputSize and hiddenSize to be a multiple of 8

For single input/output on NVIDIA Ampere Architecture, acceleration requires setting

CUDNN_DEFAULT_MATH,CUDNN_TENSOR_OP_MATH,Or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION*

Acceleration requires inputSize and hiddenSize to be a multiple of 4

Not Supported, will execute normally ignoring CUDNN_TENSOR_OP_MATH11 or _ALLOW_CONVERSION12
Other limitations   Max problem size is limited by GPU specifications.
Forward RNN:
• RELU and TANH RNN: hidden_size <= 384
• LSTM and GRU: hidden_size <= 192
BackwardData RNN:
• RELU and TANH RNN: hidden_size <= 256
• LSTM and GRU: hidden_size <= 128
Requires real time compilation through NVRTC

## 9. Mixed Precision Numerical Accuracy

When the computation precision and the output precision are not the same, it is possible that the numerical accuracy will vary from one algorithm to the other.

For example, when the computation is performed in FP32 and the output is in FP16, the CUDNN_CONVOLUTION_BWD_FILTER_ALGO_0 (ALGO_0) has lower accuracy compared to the CUDNN_CONVOLUTION_BWD_FILTER_ALGO_1 (ALGO_1). This is because ALGO_0 does not use extra workspace, and is forced to accumulate the intermediate results in FP16, i.e., half precision float, and this reduces the accuracy. The ALGO_1, on the other hand, uses additional workspace to accumulate the intermediate values in FP32, i.e., full precision float.

## 10. The cuDNN Graph API

The cuDNN library provides a declarative programming model for describing computation as a graph of operations. This graph API was introduced in cuDNN 8.0 to provide a more flexible API, especially with the growing importance of operation fusion.

The user starts by building a graph of operations, like the one pictured in index.html#finalize-op-graph__fig_w12_btl_vlb.

At a high level, the user is describing a dataflow graph of operations on tensors. Given a finalized graph, the user then selects and configures an engine that can execute that graph. There are several methods for selecting and configuring engines, which have tradeoffs with respect to ease-of-use, runtime overhead, and engine performance. The next subsection walks through an example operation graph, covering the process in more detail.

The graph API has two entry points:
We expect that most users prefer the C++ frontend API because:
• It is less verbose without loss of control - all functionality accessible through the backend API is also accessible through the frontend API.
• It adds functionality on top of the backend API, like errata filters and autotuning.
• It is open source.

In either case (i.e. the backend or frontend API), the high level concepts are the same.

### 10.1. Graph API Example with Operation Fusion

In the following example, the user would like to implement a fusion operation of convolution, bias, and activation.

### 10.1.1. Creating Operation and Tensor Descriptors to Specify the Graph Dataflow

First, create three cuDNN backend operation descriptors.

As can be seen in Figure 9, the user specified one forward convolution operation (using CUDNN_BACKEND_OPERATION_CONVOLUTION_FORWARD_DESCRIPTOR), a pointwise operation for the bias addition (using CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_ADD), and a pointwise operation for the ReLU activation (using CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_RELU_FWD). Refer to the backend API for more details on setting the attributes of these descriptors. For an example of how a forward convolution can be set up, refer to the use case in the backend API.

The user should also create tensor descriptors for the inputs and outputs of all of the operations in the graph. The graph dataflow is implied by the assignment of tensors (refer to Figure 9), for example, by specifying the backend tensor Tmp0 as both the output of the convolution operation and the input of the bias operation, cuDNN infers that the dataflow runs from the convolution into the bias. The same applies to tensor Tmp1. If the user doesn’t need the intermediate results Tmp0 and Tmp1 for any other use, then the user can specify them to be virtual tensors, so the memory I/Os can later be optimized out.
• Note that graphs with more than one operation node do not support in-place operations (that is, where any of the input UIDs matches any of the output UIDs). Such in-place operations are considered cyclic in later graph analysis and deemed unsupported. In-place operations are supported for single-node graphs.
• Also note that the operation descriptors can be created and passed into cuDNN in any order, as the tensor UIDs are enough to determine the dependencies in the graph.
Figure 9. A set of operation descriptors the user passes to the operation graph

### 10.1.2. Finalizing The Operation Graph

Second, the user finalizes the operation graph. As part of finalization, cuDNN performs the dataflow analysis to establish the dependency relationship between operations and connect the edges, as illustrated in the following figure. In this step, cuDNN performs various checks to confirm the validity of the graph.
Figure 10. The operation graph after finalization

### 10.1.3. Configuring An Engine That Can Execute The Operation Graph

Third, given the finalized operation graph, the user must select and configure an engine to execute that graph, which results in an execution plan. There are three methods:
1. Heuristics. Users that prefer cuDNN to recommend the best engine and knob choices can query cuDNN’s heuristics to get a list of engine configs, sorted by predicted performance. Typically, the user constructs the execution plan using the top ranked engine config in the list.
2. Auto-tuning. The user can also iterate over a list of engine configs and time each one to choose the best engine config for a particular problem on a particular device. The C++ frontend API provides a convenience function, cudnnFindPlan, which does this. To reduce overhead, a user might only auto-tune over the top N engine configs returned by the heuristics.
3. Manual. Expert users can query for all engines that can support the operation graph. For each engine, the user can then further query the numerical notes and adjustable knobs. Numerical notes inform the user about the numerical behavior of the engine such as whether it does datatype down conversion at the input or during output reduction. The adjustable knobs allow fine grained control of the engine’s behavior and performance. With the engine choice and the knob choice determined, the user can construct the engine, engine config, and execution plan.

### 10.1.4. Executing The Engine

Finally, with the execution plan constructed and when it comes time to run it, the user should construct the backend variant pack by providing the workspace pointer, an array of UIDs, and an array of device pointers. The UIDs and the pointers should be in the corresponding order. With the handle, the execution plan and variant pack, the execution API can be called and the computation is carried out on the GPU.

### 10.2. Supported Graph Patterns

The cuDNN Graph API supports a set of graph patterns. These patterns are supported by a large number of engines, each with their own support surfaces. These engines are grouped into three different classes, as reflected by the following three subsections: pre-compiled single operation engines, runtime fusion engines, and specialized pre-compiled engines.

Since these engines have some overlap in the patterns they support, a given pattern may result in zero, one, or more engines.

### 10.2.1. Pre-compiled Single Operation Engines

One basic class of engines includes pre-compiled engines that support an operation graph with just one operation; specifically: ConvolutionFwd, ConvolutionBwFilter, ConvolutionBwData, or ConvolutionBwBias. Their more precise support surface can be found in the NVIDIA cuDNN API Reference.

### 10.2.1.1. ConvolutionFwd

ConvolutionFwd computes the convolution of X with filter data W. In addition, it uses scaling factors $\mathrm{\alpha }$ and $\mathrm{\beta }$ to blend this result with the previous output. This graph operation is similar to cudnnConvolutionForward().

Figure 11. ConvolutionFwd Engine

### 10.2.1.2. ConvolutionBwFilter

ConvolutionBwFilter computes the convolution filter gradient of the tensor dy. In addition, it uses scaling factors $\mathrm{\alpha }$ and $\mathrm{\beta }$ to blend this result with the previous output. This graph operation is similar to cudnnConvolutionBackwardFilter().
Figure 12. ConvolutionBwFilter Engine

### 10.2.1.3. ConvolutionBwData

ConvolutionBwData computes the convolution data gradient of the tensor dy. In addition, it uses scaling factors $\mathrm{\alpha }$ and $\mathrm{\beta }$ to blend this result with the previous output. This graph operation is similar to cudnnConvolutionBackwardData().
Figure 13. ConvolutionBwData Engine

### 10.2.2. Runtime Fusion Engine

The engines documented in the previous section support single-op patterns. Of course, for fusion to be interesting, the graph needs to support multiple operations. And ideally, we want the supported patterns to be flexible to cover a diverse set of use cases. To accomplish this generality, cuDNN has a runtime fusion engine that generates the kernel (or kernels) at runtime based on the graph pattern. This section outlines the patterns supported by these runtime fusion engines (that is, engines with CUDNN_BEHAVIOR_NOTE_RUNTIME_COMPILATION behavioral note).
We can think of the support surface as covering five generic patterns:
1. ConvolutionFwd fusions

2. ConvolutionBwFilter fusions

3. ConvolutionBwData fusions

4. MatMul fusions

5. Pointwise fusions

${g}_{\text{2}}\left(\text{inputs}\right)$

Figure 14. Graphical Representation of the Five Generic Patterns Supported by the Runtime Fusion Engine

g1 is a directed acyclic graph (DAG) that can consist of zero or any number of the following operation:
• CUDNN_BACKEND_OPERATION_CONCAT_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_SIGNAL_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR
g2 is a DAG that can consist of zero or any number of the following operations:
• CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_RESAMPLE_FWD_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_RESAMPLE_BWD_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_GEN_STATS_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_REDUCTION_DESCRIPTOR
• CUDNN_BACKEND_OPERATION_SIGNAL_DESCRIPTOR
Note:
• The arrow going into g2 can go into any of g2’s nodes and does not necessarily need to feed into a root node.
• The abbreviated notations for operations are used in the diagrams and throughout the text for visualization purposes. The exact mapping with backend descriptors can be found in the Mapping with Backend Descriptors.

### 10.2.2.1. Limitations

While the generic patterns listed previously are widely applicable, there are some cases where we do not have full support.
##### Limitations Common to all Generic Patterns
Limitations to g1:
• Concatenation or signaling operations, if present, should be before any pointwise operations.
• For compute capability < 8.0, g1 is not supported.
Limitations to g2:
• As specified in the previous section, g2 can only include Pointwise operations, ResampleFwd, ResampleBwd, GenStats, and Reduction.
• The I/O (that is, non-virtual) tensor data type can be any of {FP32, FP16, BF16, INT8, packed-BOOLEAN}.
• For pointwise operations, non-virtual tensors need to be either all NCHW (or row-major), or all NHWC (or column-major).
• The intermediate virtual tensor data type can be any of {FP32, FP16, BF16, INT8, BOOLEAN}, and this intermediate storage type is obeyed by the code-generator. Generally, FP32 is recommended.
• The input tensor to a ResampleFwd or ResampleBwd operation should not be produced by another operation within this graph, but should come from global memory. The two operations cannot be used in the ConvolutionBwFilter, ConvolutionBwData, and MatMul fusion patterns.
• There can be at most one reduction operation, and it needs to be at the final node of g2.
• Signaling operations, if present, must be the final nodes in g2. Hence, signaling operations cannot be used in conjunction with reduction operations.
##### Limitations per Generic Pattern
Table 4. Limitations per Generic Pattern
Limitations to g1
ConvolutionFwd fusions
• Fusion operations on input tensors can only be a chain of three specific pointwise operations, in this exact order: Pointwise:mul, Pointwise:add, and Pointwise:ReLU. This specific support is added to realize convolution batch norm fusion use cases.
• All tensors involved can only be FP16.
• Pointwise:mul can only be with a tensor of scalars per channel.
ConvolutionBwFilter fusions Same limitations specified for ConvolutionFwd fusions apply here.
ConvolutionBwData fusions No fusion on input tensors for backward data convolution is supported.
MatMul fusions
• Can be any combination of pointwise operations.
• Only fusible with operand A, not with B.
• Operand A should have an FP16 data type.
• Broadcasted input can have any data type.
• Compute type is FP32 only.
Pointwise fusions Not Applicable
##### Tensor Layout Requirements

Lastly, there are some layout requirements to the I/O tensors involved in fusion graphs. For more information, refer to the Tensor Descriptor and Data Layout Formats sections. The following table describes the requirements per fusion pattern:

Table 5. Layout Requirements per Pattern
Pattern Layout Requirement
ConvolutionFwd, ConvolutionBwFilter, ConvolutionBwData fusions
• All tensors are fully packed NHWC.
MatMul fusions
• Input operands can have either row-major or all column-major.
• In g1, the tensor operating with Matrix A (dim[B, M, K]) can be either a scalar with dim[1, 1, 1], a row vector with dim[B, M, 1], a column vector with dim[B, 1, K], or a full matrix with dim[B, M, K].
• In g2, all I/O tensors should be either all row-major or all column-major.
Pointwise fusions
• If all tensors are 3D, the same layout requirements as MatMul g2.
• If all tensors are 4D or 5D, the same requirements as ConvolutionFwd, ConvolutionBwFilter, ConvolutionBwData layout.

### 10.2.2.2. Examples of Supported Patterns

The following sections provide examples of supported patterns, in order of increasing complexity. We employ the same color scheme as in the overall pattern to aid in identifying the structure of g1 (blue) and g2 (purple).

For illustration purposes, we abbreviated the operations used. For a full mapping to the actual backend descriptors, refer to the Mapping with Backend Descriptors.

### 10.2.2.2.1. Single Operation

The following example illustrates a convolution operation without any operations before or after it. This means, g1 and g2, are empty graphs.
Figure 15. This example illustrates the Runtime Fusion Engine with a Single Operation

### 10.2.2.2.2. Pointwise Operations After Convolution 1

In this example, g2 consists of a sequential set of two pointwise operations after the convolution.
Figure 16. ConvolutionFwd Followed by a DAG with Two Operations

### 10.2.2.2.3. Pointwise Operations After Convolution 2

Similar to the previous example, g2 consists of a sequential set of multiple pointwise operations.
Figure 17. ConvolutionFwd Followed by a DAG with Three Operations

### 10.2.2.2.4. Pointwise Operations Before Matrix Multiplication

Pointwise operations can also precede a convolution or matrix multiplication, that is, g1 is composed of pointwise operations.
Figure 18. MatMul Preceded by a DAG with Two Operations

### 10.2.2.2.5. Convolution Producer Node in Middle of DAG

The following pattern shows g1 as a DAG of pointwise operations feeding into a convolution. In addition, g2 is a DAG consisting of two pointwise operations. Note that the convolution is being consumed in the middle of g2 as opposed to g2’s first node. This is a valid pattern.
Figure 19. This example illustrates fusion of operations before and after the ConvolutionFwd operation. In addition we observe that the output of ConvolutionFwd can feed anywhere in g2.

### 10.2.2.3. Operation specific Constraints for the Runtime Fusion Engine

Every operation in the supported generic patterns of the runtime fusion engine is subject to a few specific constraints regarding their parameter surface. The following subsections document these.

Note that these constraints are in addition to (1) any constraints mentioned in the Backend API, and (2) limitations in relation to other operations in the directed acyclic graph (DAG), as mentioned in the Limitations section.

### 10.2.2.3.1. Convolutions

There are three operation nodes that represent different types of convolutions namely:
ConvolutionFwd
This operation represents forward convolution, that is, computing the response tensor of image tensor convoluted with filter tensor. For complete details on the interface, as well as general constraints, refer to the CUDNN_BACKEND_OPERATION_CONVOLUTION_FORWARD_DESCRIPTOR section.
ConvolutionBwFilter
This operation represents convolution backward filters, that is, computing filter gradients from a response and an image tensor. For complete details on the interface, as well as general constraints, refer to the CUDNN_BACKEND_OPERATION_CONVOLUTION_BACKWARD_FILTER_DESCRIPTOR section.
ConvolutionBwData
This operation represents convolution backward data, that is, computing input data gradients from a response and a filter tensor. For complete details on the interface, as well as general constraints, refer to the CUDNN_BACKEND_OPERATION_CONVOLUTION_BACKWARD_DATA_DESCRIPTOR section.
Table 6. Tensor Attributes for all Three Operations
Input Tensor Attribute Name Output Tensor Attribute Name
ConvolutionFwd

CUDNN_ATTR_OPERATION_CONVOLUTION_FORWARD_X

CUDNN_ATTR_OPERATION_CONVOLUTION_FORWARD_W

CUDNN_ATTR_OPERATION_CONVOLUTION_FORWARD_Y
ConvolutionBwFilter

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_DATA_DX

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_DATA_DY

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_DATA_W
ConvolutionBwData

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_FILTER_DW

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_FILTER_DY

CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_FILTER_X
The following tables list the constraints for all three operations, in addition to any constraints mentioned in the Backend API, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when these operations are used in the runtime fusion engine.
Table 7. Constraints for all Three Operations
Attribute Support
CUDNN_ATTR_CONVOLUTION_MODE CUDNN_CROSS_CORRELATION
CUDNN_ATTR_CONVOLUTION_COMP_TYPE
• For ConvolutionFwdCUDNN_DATA_HALF,CUDNN_DATA_INT32, andCUDNN_DATA_FLOAT
• For ConvolutionBwDataand ConvolutionBwFilter
• Only CUDNN_DATA_FLOAT
CUDNN_ATTR_CONVOLUTION_SPATIAL_DIMS 2 or 3
CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_FILTER_ALPHA 1.0f
CUDNN_ATTR_OPERATION_CONVOLUTION_BWD_FILTER_BETA 0.0f
Table 8. I/O Tensors Alignment Requirements
Tensor Data Type Number of input and output channels for NVIDIA Hopper Architecture and later Number of input and output channels for NVIDIA Ampere Architecture and later Number of input and output channels for NVIDIA Volta/Turing Architecture
INT8 Multiple of 4 Multiple of 4 Multiple of 16
FP8 Multiple of 16 N/A N/A
FP16/BF16 Multiple of 2 Multiple of 2 Multiple of 8
FP32(TF32) Any value Any value Multiple of 4

### 10.2.2.3.2. MatMul

This operation represents matrix-matrix multiplication: A * B = C. For complete details on the interface, refer to the CUDNN_BACKEND_OPERATION_MATMUL_DESCRIPTOR section.

The following two tables list the constraints for MatMul operations, in addition to any general constraints as listed in the Backend API, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when MatMul is used in the runtime fusion engine.

Table 9. Constraints for MatMul Operations
Attribute Support
CUDNN_ATTR_MATMUL_COMP_TYPE CUDNN_DATA_HALF,CUDNN_DATA_INT32, and CUDNN_DATA_FLOAT
Table 10. MatMul Alignment Requirements
Tensor Data Type Innermost dimension for NVIDIA Ampere Architecture and later Innermost dimension for NVIDIA Volta/Turing Architecture
INT8 Multiple of 4 Multiple of 16
FP16/BF16 Multiple of 2 Multiple of 8
FP32(TF32) Any value Multiple of 4

### 10.2.2.3.3. Pointwise

Represents a pointwise operation that implements the equation Y = op (alpha1 * X) or Y = op (alpha1 * X, alpha2 * B). Refer to the CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR and CUDNN_BACKEND_POINTWISE_DESCRIPTOR sections for more information and general constraints.

The following table lists the constraints for pointwise operations, in addition to the general constraints listed above, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when these operations are used in the runtime fusion engine.

Table 11. Constraints for Pointwise Operations
Attribute Requirement
Tensor data type for CUDNN_ATTR_OPERATION_POINTWISE_XDESC, CUDNN_ATTR_OPERATION_POINTWISE_YDESC and, if applicable, CUDNN_ATTR_OPERATION_POINTWISE_BDESC
• For any of the logical operators (CUDNN_POINTWISE_LOGICAL_AND, CUDNN_POINTWISE_LOGICAL_OR, and CUDNN_POINTWISE_LOGICAL_NOT), data type can be any of CUDNN_DATA_INT32, CUDNN_DATA_INT8, or CUDNN_DATA_BOOLEAN.
• For all other operators, all data types are supported.
CUDNN_ATTR_POINTWISE_MATH_PREC
• For any of the logical operators (CUDNN_POINTWISE_LOGICAL_AND, CUDNN_POINTWISE_LOGICAL_OR, and CUDNN_POINTWISE_LOGICAL_NOT), math precision needs to be CUDNN_DATA_BOOLEAN.
• For all other operators, only CUDNN_DATA_FLOAT is supported.
CUDNN_ATTR_OPERATION_POINTWISE_ALPHA1 1.0f
CUDNN_ATTR_OPERATION_POINTWISE_ALPHA2 1.0f

### 10.2.2.3.4. GenStats

Represents an operation that generates per-channel statistics. Refer to the CUDNN_BACKEND_OPERATION_GEN_STATS_DESCRIPTOR section for more information and general constraints.

The following table lists the constraints for GenStats operations, in addition to the general constraints listed above, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when GenStats operations are used in the runtime fusion engine.

Table 12. Constraints for GenStats Operations
Attribute Requirement
Tensor data type for CUDNN_ATTR_OPERATION_GENSTATS_XDESC
• Prior to the NVIDIA Ampere Architecture GPU: CUDNN_DATA_HALF
• On NVIDIA Ampere Architecture and later: CUDNN_DATA_HALF and CUDNN_DATA_FLOAT
Tensor shape for CUDNN_ATTR_OPERATION_GENSTATS_SUMDESC and CUDNN_ATTR_OPERATION_GENSTATS_SQSUMDESC Both should be of shape [1, C, 1, 1] for 2D conv or [1, C, 1, 1, 1] for 3D conv.
Tensor data type for CUDNN_ATTR_OPERATION_GENSTATS_SUMDESC and CUDNN_ATTR_OPERATION_GENSTATS_SQSUMDESC CUDNN_DATA_FLOAT
CUDNN_ATTR_POINTWISE_MATH_PREC CUDNN_DATA_FLOAT
Tensor layout for CUDNN_ATTR_OPERATION_GENSTATS_XDESC, CUDNN_ATTR_OPERATION_GENSTATS_SUMDESC and CUDNN_ATTR_OPERATION_GENSTATS_SQSUMDESC NHWC fully packed

### 10.2.2.3.5. Reduction

This operation represents reducing values of a tensor in one or more dimensions. Refer to the CUDNN_BACKEND_OPERATION_REDUCTION_DESCRIPTOR section for more information and general constraints.

The following two tables are constraints for Reduction forward operations, in addition to the general constraints listed above, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when Reduction operations are used in the runtime fusion engine.

Table 13. Constraints for Reduction Operations
Attribute Requirement
Tensor data type for CUDNN_ATTR_OPERATION_REDUCTION_YDESC CUDNN_DATA_FLOAT
CUDNN_ATTR_REDUCTION_COMP_TYPE CUDNN_DATA_FLOAT
Tensor layout for CUDNN_ATTR_OPERATION_REDUCTION_XDESC and CUDNN_ATTR_OPERATION_REDUCTION_YDESC NHWC/NDHWC/BMN fully packed
Table 14. Supported Reduction Patterns
Reduction Operation Reduction Pattern
Input Output
Standalone reduction operation [N, C, H, W] [N, 1, H, W]
[1, C, 1, 1]
[1, 1, 1, 1]
Reduction fused after convolution backward filter gradient [N, K, P, Q] [N, 1, P, Q]
[1, K, 1, 1]
[1, 1, 1, 1]
Reduction fused after convolution backward data gradient [N, C, H, W] [N, 1, H, W]
[1, C, 1, 1]
[1, 1, 1, 1]
Reduction fused after convolution backward filter gradient [K, C, R, S] [K, 1, 1, 1]
[1, C, R, S]
[1, 1, 1, 1]
Reduction fused after matrix multiplication operation [B, M, N] [B, M, 1]
[B, 1, N]

### 10.2.2.3.6. ResampleFwd

This operation represents resampling of the spatial dimensions of an image to a desired value. Resampling is supported in both directions, upsampling and downsampling. Downsampling represents the standard operation of pooling, commonly used in convolutional neural networks. Refer to the CUDNN_BACKEND_OPERATION_RESAMPLE_FWD_DESCRIPTOR section for more information and general constraints.

The following are constraints for Resample operations, in addition to the general constraints listed above, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when Resample forward operations are used in the runtime fusion engine.

We allow a choice amongst four modes for resample. All modes have the following common support specifications:
• Supported layout: NHWC or NDHWC
• Spatial dimensions supported: 2 or 3
• Input dimensions supported: 4 or 5
• If specified, the index tensor dimension should be equal to the response tensor dimension.

There are some mode specific restrictions also. The following tables list the values that are allowed for particular parameters. For the parameters not listed, we allow any value which is mathematically correct.

The following downsampling modes are supported:
• CUDNN_RESAMPLE_MAXPOOL
Table 15. Specific Restrictions for the Downsampling Modes
Attribute Average Pooling Max Pooling
CUDNN_ATTR_OPERATION_RESAMPLE_FWD_ALPHA 1.0 1.0
CUDNN_ATTR_OPERATION_RESAMPLE_FWD_BETA 0.0 0.0
CUDNN_ATTR_RESAMPLE_COMP_TYPE CUDNN_DATA_FLOAT CUDNN_DATA_FLOAT

For the upsampling modes, CUDNN_RESAMPLE_NEAREST is not supported for any combination of parameters. CUDNN_RESAMPLE_BILINEAR has the following support specifications.

Table 16. Specific Restrictions for Upsampling Mode CUDNN_RESAMPLE_BILINEAR
Attribute Bilinear
Input dimensions Equal to 0.5 x output dimensions
CUDNN_ATTR_RESAMPLE_STRIDES 0.5
CUDNN_ATTR_RESAMPLE_WINDOW_DIMS 2
Data type for CUDNN_ATTR_OPERATION_RESAMPLE_FWD_XDESC and CUDNN_ATTR_OPERATION_RESAMPLE_FWD_YDESC CUDNN_DATA_FLOAT
CUDNN_ATTR_RESAMPLE_COMP_TYPE CUDNN_DATA_FLOAT
CUDNN_ATTR_OPERATION_RESAMPLE_FWD_ALPHA 1.0
CUDNN_ATTR_OPERATION_RESAMPLE_FWD_BETA 0.0

### 10.2.2.3.6.1. Resampling Index Tensor Dump for Training

For max-pooling resampling mode, an index tensor can be provided to be used as a mask for backpropagation.
Values in the index tensors are:
• Zero-indexed row-major position of maximum value of input tensor in the resampling window.
• In case of multiple input pixels with maximum value, the first index in a left-to-right top-to-bottom scan is selected.
Example of index element selection:
Figure 20. Values In the Index Tensors

Select an appropriate element size for the index tensor. As a reference, any element size such that the maximum zero-indexed window position fits should be sufficient.

### 10.2.2.3.7. ResampleBwd

This operation represents backward resampling of the spatial dimensions of an output response to a desired value. Resampling is supported in both directions, upsampling and downsampling. Backwards downsampling represents the standard operation of backward pooling, commonly used in convolutional neural networks. Refer to the CUDNN_BACKEND_OPERATION_RESAMPLE_BWD_DESCRIPTOR section for more information and general constraints.

The following are constraints for Resample backward operations, in addition to the general constraints listed above, and any constraints listed in the Limitations section, in relation to other operations. Note that these additional constraints only apply when Resample backward operations are used in the runtime fusion engine.

We allow a choice amongst four modes for resample. All modes have the following common support specifications:
• Supported layout: NHWC or NDHWC
• Spatial dimensions supported: 2 or 3
• Input dimensions supported: 4 or 5
• The index tensor dimensions should be equal to the input gradient tensor dimensions.

Index tensor should be provided for only max pooling mode, and should adhere to the format described in the resampling forward index dump section.

There are some mode specific restrictions also. The following tables list the values that are allowed for particular parameters. For the parameters not listed, we allow any value which is mathematically correct.

The following backward downsampling modes are supported:
• CUDNN_RESAMPLE_MAXPOOL
Table 17. Specific Restrictions for the Backwards Downsampling Modes
Attribute Average Pooling Max Pooling
CUDNN_ATTR_OPERATION_RESAMPLE_BWD_ALPHA 1.0 1.0
CUDNN_ATTR_OPERATION_RESAMPLE_BWD_BETA 0.0 0.0
CUDNN_ATTR_RESAMPLE_COMP_TYPE CUDNN_DATA_FLOAT CUDNN_DATA_FLOAT

Backward upsampling modes are currently not supported.

### 10.2.3. Pre-compiled Specialized Engines

The pre-compiled specialized engines target and optimize for a specialized graph pattern with a ragged support surface. Because of this targeting, these graphs do not require runtime compilation.

In most cases, the specialized patterns are just special cases of the generic patterns used in the runtime fusion engine, but there are some cases where the specialized pattern does not fit any of the generic patterns. If your graph pattern matches a specialized pattern, you will get at least a pattern matching engine, and you might also get a runtime fusion engine as another option.

Currently, the following patterns are supported by the pattern matching engines. Some nodes are optional. Optional nodes are indicated by dashed outlines.

### 10.2.3.1. ConvBNfprop

In Figure 21, the ConvBNfprop pattern is illustrated. Its restrictions and options include:
1. The three pointwise nodes scale, bias, and ReLU are optional.
2. X, Z, W, s1, b1 must all be of FP16 data type.
3. Z needs to be of shape [N, C, H, W] with NHWC packed layout.
4. W needs to be of shape [K, C, R, S] with KRSC packed layout.
5. s1, b1 need to be of shape [1, C, 1, 1] with NHWC packed layout.
6. Only ReLU activation is supported.
7. All of the intermediate tensors need to be virtual, except, Y needs to be non-virtual.
8. I/O pointers should be 16 bytes aligned.
Figure 21. The pre-compiled ConvBNfprop engine fuses several pointwise operations with ConvolutionFwd and GenStats.

In Figure 22, the ConvBNwgrad pattern is illustrated. Its restrictions and options include:
1. The three pointwise operations are all optional, as indicated by the dashed outlines.
2. Only ReLU activation is supported.
3. X, s1, b1, and dy must all be of FP16 datatype.
4. I/O pointers should be 16 bytes aligned.
Figure 22. The ConvBNwgrad pre-compiled engine fuses several (optional) pointwise operations with ConvolutionBwFilter.

### 10.2.3.3. ConvBiasAct

In the following figure, the ConvBiasAct pattern is illustrated. Its restrictions and options include:
1. ${\alpha }_{\text{1}}$ and ${\alpha }_{\text{2}}$ need to be scalars.
2. The activation node is optional.
3. The size of the bias tensor should be [1, K, 1, 1].
4. Internal conversions are not supported. That is, the virtual output between nodes need to have the same data type as the node’s compute type, which should be the same as the epilog type of the convolution node.
5. There are some restrictions on the supported combination of data types, which can be found in the API Reference (refer to cudnnConvolutionBiasActivationForward()).
Figure 23. ConvBiasAct, another pre-compiled engine, fuses ConvolutionFwd with several pointwise operations.

### 10.2.3.4. ConvScaleBiasAct

In the following figure, the ConvScaleBiasAct pattern is illustrated. Its restrictions and options include:
1. ${\alpha }_{\text{1}}$ and ${\alpha }_{\text{2}}$ and ${b}_{\text{2}}$ should have the same data type/layout and can only be FP32.
2. X, W, and Z can only be int8x4 or int8x32.
3. The size of the bias tensor should be [1, K, 1, 1].
4. Internal conversions are not supported. Meaning, "virtual output" between nodes needs to be the same as their compute type.
5. Currently, Pointwise:ReLU is the only optional pointwise node.
Figure 24. The pre-compiled engine, ConvScaleBiasAct

This pattern is very similar as ConvBiasAct. The difference is that here, the scales ${\alpha }_{\text{1}}$ and ${\alpha }_{\text{2}}$ are tensors, not scalars. If they are scalars, this pattern becomes a normal ConvBiasAct.

### 10.2.3.5. dBNapply

In dBNapply, the dBNapply pattern is illustrated. Its restrictions and options include:
1. One of the inputs to the mul nodes and the input to the final add node must be of FP32 datatype (A, B, C).
2. The other inputs to the mul nodes (X and Y) must be of FP16 data type.
3. X, Y and Z are 4D tensors – [N,C,H,W] with NHWC packed layout.
4. A, B, C are 1D tensors - [1,C,1,1] with NHWC packed layout.
5. Channel C should be a multiple of 16 for all the tensors.
6. Tensors A and B should be attached to the B port of the mul nodes; tensors X and Y should be attached to the X port.
Figure 25. The pre-compiled engine, dBNapply

The pattern implements a simple linear combination:
• Z = A*X + B*Y + C

### 10.2.3.6. DualdBNapply

In Figure 21, the DualdBNapply pattern is illustrated. Its restrictions and options include:
1. One tensor X is shared between the two linear combinations.
2. Five tensors, X, Y1, Y2, Z1, Z2 are 4D tensors [N,C,H,W] with NHWC packed layout.
3. Six tensors A1, A2, B1, B2 ,C1,C2 are 1D tensors [1,C,1,1].
4. Channel C should be a multiple of 16 for all the tensors.

In essence, DualdBNapply runs the previous pattern, dBNapply twice, as two subgraphs. However, both subgraphs share one input tensor, X.

Note that for visibility purposes, the Inputs block is split into Inputs_1 and Inputs_2. This has no semantic meaning.

Figure 26. The DualdBNapply engine

This pattern implements two linear combinations:
• Z1 = A1* X + B1* Y1 + C1
• Z2 = A2* X + B2* Y2 + C2

In Figure 27, the DgradDreluBNBwdWeight pattern is illustrated. Its restrictions and options include:
1. Dgrad input dY_bn and W are of FP16 datatypes.
2. Batch norm fwd inputs, X_bn is of FP16 datatype while the other tensors mean_bn, invstd_dev_bn, scale_bn, and bias_bn are FP32.
3. Outputs: dScale, dBias, A,B,C are of FP32 data type.
4. All pointers are 16 byte aligned.
5. Only supported on NVIDIA Ampere Architecture GPUs.
Figure 27. DgradDreluBNBwdWeight is a pre-compiled engine that can be used in conjunction with the dBNApply pattern to compute the backwards path of batch norm.

The BNBwdWeight operation takes in five inputs: X_bn, mean_bn, invstddev_bn, scale_bn, and dy_bn, and output from the ReLUBwd node.

It produces five outputs: gradients of the batch norm scale and bias params, dScale, dBias, and coefficients A,B,C. Note that for illustration purposes, the inputs are duplicated. The inputs on the left and right are however exactly the same.

This pattern is typically used in the computation of the Batch Norm Backward Pass.

When computing the backward pass of batch norm, dScale, dBias, and dX_bn are needed. The DgradDreluBnBwdWeight pattern computes the former two. Using the generated A, B, and C we can use the dBNApply pattern above to compute dX, the input gradient, as follows dx_bn = A*dy_bn + B*X_bn +C.

Note that this pattern is used in combination with the forward pass, the ConvBNfprop pattern. Because of performance reasons, the output of Batch Norm Y_bn, which was calculated in ConvBNfprop (output of scale-bias), needs to be recalculated by DgradDreluBnBwdWeight. The pointwise add node subtracts mean_bn from X_bn, hence the alpha2 parameter for that node should be set to -1.

### 10.2.4. Mapping with Backend Descriptors

For readability, the operations used in this section are abbreviated. The mapping with the actual backend descriptors can be found in this table:
Table 18. Notations and Backend Descriptors
Notation used in this section Backend descriptor
Pointwise:scale CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_MUL and with operand B broadcasting into operand X
Pointwise:bias CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_ADD and with operand B broadcasting into operand X
Pointwise:add CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_ADD and with operand B with same dimensions as X
Pointwise:mul CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_MUL and with operand B with same dimensions as X
Pointwise:ReLU CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_RELU_FWD
Pointwise:ReLUBwd CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_RELU_BWD
Pointwise:tanh CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_TANH_FWD
Pointwise:sigmoid CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_SIGMOID_FWD
Pointwise:ELU CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with mode CUDNN_POINTWISE_ELU_FWD
Pointwise:{ReLU,tanh,sigmoid,ELU} CUDNN_BACKEND_OPERATION_POINTWISE_DESCRIPTOR with one of the following modes:
CUDNN_POINTWISE_RELU_FWD, CUDNN_POINTWISE_TANH_FWD, CUDNN_POINTWISE_SIGMOID_FWD,
CUDNN_POINTWISE_ELU_FWD
MatMul CUDNN_BACKEND_OPERATION_MATMUL_DESCRIPTOR
ConvolutionFwd CUDNN_BACKEND_OPERATION_CONVOLUTION_FORWARD_DESCRIPTOR
ConvolutionBwFilter CUDNN_BACKEND_OPERATION_CONVOLUTION_BACKWARD_FILTER_DESCRIPTOR
ConvolutionBwData CUDNN_BACKEND_OPERATION_CONVOLUTION_BACKWARD_DATA_DESCRIPTOR
GenStats CUDNN_BACKEND_OPERATION_GEN_STATS_DESCRIPTOR
ResampleFwd CUDNN_BACKEND_OPERATION_RESAMPLE_FWD_DESCRIPTOR
GenStats CUDNN_BACKEND_OPERATION_GEN_STATS_DESCRIPTOR
Reduction CUDNN_BACKEND_OPERATION_REDUCTION_DESCRIPTOR
BnBwdWeight CUDNN_BACKEND_OPERATION_BN_BWD_WEIGHTS_DESCRIPTOR
BOOLEAN/packed-BOOLEAN

CUDNN_DATA_BOOLEAN: As described in the API Reference, this type implies that eight boolean values are packed in a single byte, with the lowest index on the right (that is, least significant bit).

packed-BOOLEAN and BOOLEAN are used interchangeably, where the former is used to emphasize and remind the user about the semantics.

INT8 CUDNN_DATA_INT8
FP8 CUDNN_DATA_FP8_E4M3 or CUDNN_DATA_FP8_E5M2
FP16 CUDNN_DATA_HALF
BF16 CUDNN_DATA_BFLOAT16
FP32 CUDNN_DATA_FLOAT
TF32 A tensor core operation mode used to accelerate floating point convolutions or matmuls. This can be used for an operation with compute type CUDNN_DATA_FLOAT, on Ampere or later and be disabled with NVIDIA_TF32_OVERRIDE=1.

## 11. Troubleshooting

The following sections help answer the most commonly asked questions regarding typical use cases.

### 11.1. Error Reporting And API Logging

The cuDNN error reporting and API logging is a utility for recording the cuDNN API execution and error information. For each cuDNN API function call, all input parameters are reported in the API logging. If errors occur during the execution of the cuDNN API, a traceback of the error conditions can also be reported to help troubleshooting. This functionality is disabled by default, and can be enabled using the methods described in the later part of this section through three logging severity levels: CUDNN_LOGINFO_DBG, CUDNN_LOGWARN_DBG and CUDNN_LOGERR_DBG.

The log output contains variable names, data types, parameter values, device pointers, process ID, thread ID, cuDNN handle, CUDA stream ID, and metadata such as time of the function call in microseconds.

For example, when the severity level CUDNN_LOGINFO_DBG is enabled, the user will receive the API loggings, such as:

cuDNN (v8300) function cudnnSetActivationDescriptor() called:
mode: type=cudnnActivationMode_t; val=CUDNN_ACTIVATION_RELU (1);
reluNanOpt: type=cudnnNanPropagation_t; val=CUDNN_NOT_PROPAGATE_NAN (0);
coef: type=double; val=1000.000000;
Time: 2017-11-21T14:14:21.366171 (0d+0h+1m+5s since start)
Process: 21264, Thread: 21264, cudnn_handle: NULL, cudnn_stream: NULL.

Starting in cuDNN 8.3.0, when the severity level CUDNN_LOGWARN_DBG or CUDNN_LOGERR_DBG are enabled, the log output additionally reports an error traceback such as the example below (currently only cuDNN version 8 graph APIs and legacy convolution APIs are using this error reporting feature). This traceback reports the relevant error/warning conditions, aiming to provide the user hints for troubleshooting purposes. Within the traceback, each message may have their own severity and will only be reported when the respective severity level is enabled. The traceback messages are printed in the reverse order of the execution so the messages at the top will be the root cause and tend to be more helpful for debugging.
cuDNN (v8300) function cudnnBackendFinalize() called:
Info: Traceback contains 5 message(s)
Error: CUDNN_STATUS_BAD_PARAM; reason: out <= 0
Error: CUDNN_STATUS_BAD_PARAM; reason: is_valid_convolution(xDesc, wDesc, cDesc, yDesc)
Error: CUDNN_STATUS_BAD_PARAM; reason: convolution.init(xDesc, wDesc, cDesc, yDesc)
Time: 2021-10-05T17:11:07.935640 (0d+0h+0m+15s since start)


There are two methods, as described below, to enable the error/warning reporting and API logging. For convenience, the log output can be handled by the built-in default callback function, which will direct the output to a log file or the standard I/O as designated by the user. The user may also write their own callback function to handle this information programmably, and use the cudnnSetCallback() to pass in the function pointer of their own callback function.

### Method 1: Using Environment Variables

To enable API logging using environment variables, follow these steps:
• Decide which logging severity levels to include from these three options: CUDNN_LOGINFO_DBG, CUDNN_LOGWARN_DBG, CUDNN_LOGERR_DBG. The logging severity levels are independent of each other. Any combination of them is valid.
• Set the environment variables CUDNN_LOGINFO_DBG or CUDNN_LOGWARN_DBG or CUDNN_LOGERR_DBG to 1, and
• Set the environment variable CUDNN_LOGDEST_DBG to one of the following:
• stdout, stderr, or a user-desired file path, for example, /home/userName1/log.txt.
• Include the conversion specifiers in the file name. For example:
• To include date and time in the file name, use the date and time conversion specifiers: log_%Y_%m_%d_%H_%M_%S.txt. The conversion specifiers will be automatically replaced with the date and time when the program is initiated, resulting in log_2017_11_21_09_41_00.txt.
• To include the process id in the file name, use the %i conversion specifier: log_%Y_%m_%d_%H_%M_%S_%i.txt for the result: log_2017_11_21_09_41_00_21264.txt when the process id is 21264. When you have several processes running, using the process id conversion specifier will prevent these processes from writing to the same file at the same time.
Note: The supported conversion specifiers are similar to the strftime function.

If the file already exists, the log will overwrite the existing file.

Note: These environmental variables are only checked once at the initialization. Any subsequent changes in these environmental variables will not be effective in the current run. Also note that these environment settings can be overridden by Method 2 below.

Refer to Table 19 for the impact on the performance of API logging using environment variables. The CUDNN_LOG{INFO,WARN,ERR}_DBG notation in the table header means the conclusion is applicable to either one of the environment variables.

Table 19. API Logging Using Environment Variables
Environment variables CUDNN_LOG{INFO,WARN,ERR}_DBG=0 CUDNN_LOG{INFO,WARN,ERR}_DBG=1
CUDNN_LOGDEST_DBG not set

No logging output

No performance loss

No logging output

No performance loss

CUDNN_LOGDEST_DBG=NULL

No logging output

No performance loss

No logging output

No performance loss

CUDNN_LOGDEST_DBG=stdout or stderr

No logging output

No performance loss

Logging to stdout or stderr

Some performance loss

CUDNN_LOGDEST_DBG=filename.txt

No logging output

No performance loss

Logging to filename.txt

Some performance loss

### Method 2: Using the API

Method 2: To use API function calls to enable API logging, refer to the API description of cudnnSetCallback() and cudnnGetCallback().

### Q: Where in the software stack does cuDNN sit? What is the interaction between CUDA, cuDNN, and TensorRT?

A: The following graphic shows how cuDNN relates to other software in the stack.
Figure 28. Software stack with cuDNN.

### Q: I’m not sure if I should use cuDNN for inference or training. How does it compare with TensorRT?

A: cuDNN provides the building blocks for common routines such as convolution, pooling, activation and RNN/LSTMs. You can use cuDNN for both training and inference. However, where it differs from TensorRT is that the latter (TensorRT) is a programmable inference accelerator; just like a framework. TensorRT sees the whole graph and optimizes the network by fusing/combining layers and optimizing kernel selection for improved latency, throughout, power efficiency and for reducing memory requirements.

A rule of thumb you can apply is to check out TensorRT, see if it meets your inference needs, if it doesn't, then look at cuDNN for a closer, more in-depth perspective.

### Q: How does heuristics in cuDNN work? How does it know what is the optimal solution for a given problem?

A: NVIDIA actively monitors the Deep Learning space for important problem specifications such as commonly used models. The heuristics are produced by sampling a portion of these problem specifications with available computational choices. Over time, more models are discovered and incorporated into the heuristics.

### Q: Is cuDNN going to support running arbitrary graphs?

A: No, we don’t plan to become a framework and execute the whole graph one op at a time. At this time, we are focused on a subgraph given by the user, where we try to produce an optimized fusion kernel. We will document the rules regarding what can be fused and what cannot. The goal is to support general and flexible fusion, however, it will take time and there will be limits in what it can do in the cuDNN version 8.0.0 launch.

### Q: What’s the difference between TensorRT, TensorFlow/XLA’s fusion, and cuDNN’s fusion?

A: TensorRT and TensorFlow are frameworks; they see the whole graph and can do global optimization, however, they generally only fuse pointwise ops together or pattern match to a limited set of pre-compiled fixed fusion patterns like conv-bias-relu. On the other hand, cuDNN targets a subgraph, but can fuse convolutions with pointwise ops, thus providing potentially better performance. CuDNN fusion kernels can be utilized by TensorRT and TensorFlow/XLA as part of their global graph optimization.

### Q: Can I write an application calling cuDNN directly?

A: Yes, you can call the C/C++ API directly. Usually, data scientists would wait for framework integration and use the Python API which is more convenient. However, if your use case requires better performance, you can target the cuDNN API directly.

### Q: How does mixed precision training work?

A: Several components need to work together to make mixed precision training possible. CuDNN needs to support the layers with the required datatype config and have optimized kernels that run very fast. In addition, there is a module called automatic mixed precision (AMP) in frameworks which intelligently decides which op can run in a lower precision without affecting convergence and minimize the number of type conversions/transposes in the entire graph. These work together to give you speed up. For more information, see Mixed Precision Numerical Accuracy.

### Q: How can I pick the fastest convolution kernels with cuDNN version 8.0.0?

A: In the API introduced in cuDNN v8, convolution kernels are grouped by similar computation and numerical properties into engines. Every engine has a queryable set of performance tuning knobs. A computation case such as a convolution operation graph can be computed using different valid combinations of engines and their knobs, known as an engine configuration. Users can query an array of engine configurations for any given computation case ordered by performance, from fastest to slowest according to cuDNN’s own heuristics. Alternately, users can generate all possible engine configurations by querying the engine count and available knobs for each engine. This generated list could be used for auto-tuning or the user could create their own heuristics.

### Q: Why is cuDNN version 8.0 convolution API call much slower on the first call than subsequent calls?

A: Due to the library split, cuDNN version 8.0 API will only load the necessary kernels on the first API call that requires it. In previous versions, this load would have been observed in the first cuDNN API call that triggers CUDA context initialization, typically cudnnCreate(). In version 8.0, this is delayed until the first sub-library call that triggers CUDA context initialization. Users who desire to have CUDA context preloaded can call the new cudnnCnnInferVersionCheck() API (or its related cousins), which has the side effect of initializing a CUDA context. This will reduce the run time for all subsequent API calls.

### Q: How do I build the cuDNN version 8.0.0 split library?

A: cuDNN v8.0 library is split into multiple sub-libraries. Each library contains a subset of the API. Users can link directly against the individual libraries or link with a dlopen layer which follows a plugin architecture.

To link against an individual library, users can directly specify it and its dependencies on the linker command line. For example, for infer libraries: -lcudnn_adv_infer, -lcudnn_cnn_infer, or -lcudnn_ops_infer.

The dependency order is documented in the cuDNN 8.0.0 Preview Release Notes and the NVIDIA cuDNN API Reference.

Alternatively, the user can continue to link against a shim layer (-libcudnn) which can dlopen the correct library that provides the implementation of the function. When the function is called for the first time, the dynamic loading of the library takes place.

-lcudnn

### Q: What are the new APIs in cuDNN version 8.0.0?

A: The new cuDNN APIs are listed in the cuDNN 8.0.0 Release Notes as well as in the API Changes For cuDNN 8.0.0.

### 11.3. Support

Support, resources, and information about cuDNN can be found online at https://developer.nvidia.com/cudnn. This includes downloads, webinars, NVIDIA Developer Forums, and more.

We appreciate all types of feedback. Consider posting on the forums with questions, comments, and suspected bugs that are appropriate to discuss publicly. cuDNN-related posts are reviewed by the cuDNN engineering team, and internally we will file bugs where appropriate. It’s helpful if you can paste or attach an API log to help us reproduce.

External users can also file bugs directly by following these steps:
1. Register for the NVIDIA Developer website.
3. Click on your name in the upper right corner.
4. Click My account > My Bugs and select Submit a New Bug.
5. Fill out the bug reporting page. Be descriptive and if possible, provide the steps that you are following to help reproduce the problem. If possible, paste or attach an API log.
6. Click Submit a bug.

## 12. Acknowledgments

Some of the cuDNN library routines were derived from code developed by others and are subject to the following:

### 12.1. University of Tennessee

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### 12.2. University of California, Berkeley

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Copyright (c) 2014, The Regents of the University of California (Regents)

All other contributions:
Copyright (c) 2014, the respective contributors

their contributions to Caffe. The project versioning records all such
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### 12.3. Facebook AI Research, New York

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## Notice

1NHWC/NCHW corresponds to NDHWC/NCDHW in 3D convolution.
2 With CUDNN_TENSOROP_MATH_ALLOW_CONVERSION pre-Ampere. Default TF32 math in NVIDIA Ampere Architecture.
3 INT8 does not support dgrad and wgrad. INT8 3D convolutions are only supported in the backend API. Refer to the tables in the cudnnConvolutionForward() section for more information.
4 Do not mix different algos for different steps of training. It’s also not recommended to mix non-extended and extended API for different steps of training.
5 To use an unpacked layout, users need to set CUDNN_RNN_PADDED_IO_ENABLED through cudnnSetRNNPaddingMode().
6 To use an unpacked layout, users need to set CUDNN_RNN_PADDED_IO_ENABLED through cudnnSetRNNPaddingMode().
7 To use an unpacked layout, users need to set CUDNN_RNN_PADDED_IO_ENABLED through cudnnSetRNNPaddingMode().
8CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION can be set through cudnnSetRNNMatrixMathType().
9CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION can be set through cudnnSetRNNMatrixMathType().
10CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION can be set through cudnnSetRNNMatrixMathType().
11CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION can be set through cudnnSetRNNMatrixMathType().
12CUDNN_TENSOR_OP_MATH or CUDNN_TENSOR_OP_MATH_ALLOW_CONVERSION can be set through cudnnSetRNNMatrixMathType().