Deep Neural Network Library (DNNL)  1.2.0
Performance library for Deep Learning
Local Response Normalization (LRN)

API Reference

The LRN primitive performs a forward or backward local response normalization operation defined by the following formulas:

### Forward

LRN across channels:

$dst(n, c, h, w) = \left\{k + \frac{\alpha}{n_{l}} \sum\limits_{i=-(n_{l}-1)/2}^{(n_{l}+1)/2-1} (src(n, c+i, h, w))^2 \right\}^{-\beta} \cdot src(n, c, h, w),$

LRN within channel:

$dst(n, c, h, w) = \left\{k + \frac{\alpha}{n_{l}} \sum\limits_{i=-(n_{l}-1)/2}^{(n_{l}+1)/2-1} \sum\limits_{j=-(n_{l}-1)/2}^{(n_{l}+1)/2-1} (src(n, c, h+i, w+j))^2 \right\}^{-\beta} \cdot src(n, c, h, w),$

where $$n_{l}$$ is the local_size. Formulas are provided for 2D spatial data case.

### Backward

The backward propagation computes $$diff\_src(n, c, h, w)$$, based on $$diff\_dst(n, c, h, w)$$ and $$src(n, c, h, w)$$.

## Implementation Details

### General Notes

1. During training, LRN might or might not require a workspace on forward and backward passes. The behavior is implementation specific. Optimized implementations typically require a workspace and use it to save some intermediate results from the forward pass that accelerate computations on the backward pass. To check whether a workspace is required, query the LRN primitive descriptor for the workspace. Success indicates that the workspace is required and its description will be returned.
2. The memory format and data type for src and dst are assumed to be the same, and in the API are typically referred to as data (e.g., see data_desc in dnnl::lrn_forward::desc::desc()). The same holds for diff_src and diff_dst. The corresponding memory descriptors are referred to as diff_data_desc.

### Data Type Support

The LRN primitive supports the following combinations of data types:

Propagation Source / Destination
forward / backward f32, bf16
forward f16
Warning
There might be hardware and/or implementation specific restrictions. Check the Implementation Limitations section below.

### Data Representation

#### Source, Destination, and Their Gradients

Like most other primitives, the LRN primitive expects the following tensors:

Spatial Source / Destination
0D $$N \times C$$
1D $$N \times C \times W$$
2D $$N \times C \times H \times W$$
3D $$N \times C \times D \times H \times W$$

The LRN primitive is optimized for the following memory formats:

Spatial Logical tensor Implementations optimized for memory formats
2D NCHW dnnl_nchw (dnnl_abcd), dnnl_nhwc (dnnl_acdb), optimized^

Here optimized^ means the format that comes out of any preceding compute-intensive primitive.

### Post-ops and Attributes

The LRN primitive doesn't support any post-ops or attributes.

## Implementation Limitations

1. Refer to Data Types for limitations related to data types support.
2. GPU
• Supports only 2D spatial case.

## Performance Tips

1. For backward propagation, use the same memory format for src, diff_dst, and diff_src (the format of the diff_dst and diff_src are always the same because of the API). Different formats are functionally supported but lead to highly suboptimal performance.