Local Response Normalization (LRN)

API reference: C, C++

The LRN primitive performs a forward or backward local response normalization operation on 2D spatial data and is 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.

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

The LRN primitive supports only 2D spatial data. Like other CNN primitives, the LRN primitive expects data to be \(N \times C \times H \times W\) tensor.

The LRN primitive is optimized for the following memory formats:

Spatial	Logical tensor	Imp
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.

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.