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ThreadingLayer
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ThreadingLayer

[Experimental]

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represents a net layer that takes several input arrays and applies a function f to corresponding array elements.

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ThreadingLayer[f,bspec]

allows array shapes to be conformed according to broadcasting specification bspec.

Details and Options

  • ThreadingLayer is typically used inside NetGraph.
  • In ThreadingLayer[f], the function f can be any one of the following: Plus, Subtract, Times, Divide, Power, Surd, Min, Max, Clip, Mod, ArcTan, Erf.
  • In general, f can be any object that when applied to two arguments gives any combination of Plus, Subtract, etc. together with numbers; all functions supported by ElementwiseLayer; and some logical operations using If, And, Or, Which, Piecewise, Equal, Greater, GreaterEqual, Less, LessEqual, Unequal.
  • The function f can also contain expressions of the form "name"[input], where name is one of the named functions ("ELU", "SELU", "SoftSign", etc.) accepted by ElementwiseLayer.
  • In ThreadingLayer[f,bspec], smaller arrays are implicitly replicated before applying f to match dimensions of larger arrays. The following settings can be given for bspec:
  • Noneno replication
    Automaticreplicate along axis of size 1 (default)
    ninsert dimension(s) with the right size at level n if needed
    -ncount from the end
    {spec1,spec2,…}use specific broadcasting settings for the respective input arrays
  • Option InputPorts can be used to specify the number, names or shapes of input ports. If InputPorts is not specified, the number of ports and their shapes are inferred from NetChain or NetGraph connectivity.
  • Besides input ports, ThreadingLayer exposes the following port for use in NetGraph etc.:
  • "Output"an array
  • Within a NetGraph, a ThreadingLayer can be connected using a single edge of the form {src1,src2,…}threadlayer, where threadlayer is the name or index of the ThreadingLayer, or as multiple separate edges given in the corresponding order, as src1threadlayer,src2threadlayer,…,srcnthreadlayer.
  • If no names are explicitly given for input ports, ThreadingLayer[f,…] exposes input ports named "Input1", "Input2", etc.
  • ThreadingLayer[Function[… #Name1 … #Name2 …], …] exposes input ports named "Name1", "Name2", etc.
  • ThreadingLayer[f,None] forces all input arrays to have the same shape, and the output has this shape. ThreadingLayer[f,Automatic] forces all input arrays to have the same rank, and the respective shapes must be the same or equal to 1. ThreadingLayer[Plus,-1] automatically broadcasts inputs like Plus by inserting dimensions at the deepest level.
  • ThreadingLayer[…][{in1,in2,…}] explicitly computes the output from applying the layer, which is effectively given by f[in1,in2,…].
  • When given NumericArray as inputs, the output will be a NumericArray.
  • Options[ThreadingLayer] gives the list of default options to construct the layer. Options[ThreadingLayer[…]] gives the list of default options to evaluate the layer on some data.
  • Information[ThreadingLayer[…]] gives a report about the layer.
  • Information[ThreadingLayer[…],prop] gives the value of the property prop of ThreadingLayer[…]. Possible properties are the same as for NetGraph.

Examples

open allclose all

Basic Examples  (6)Summary of the most common use cases

Create a ThreadingLayer using Times as the function to be threaded:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-suvpmw
Out[1]=1

Apply the layer to a pair of inputs:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-l4vjnx
Out[2]=2

Create a ThreadingLayer that sums arrays with different dimensions, broadcasting the smallest arrays on the first dimensions:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-hoh3h1
Out[1]=1

Apply the layer to a pair of inputs:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-1mdza2

Create a ThreadingLayer that sums arrays with different dimensions, broadcasting the smallest arrays on the last dimensions:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-weyjno
Out[1]=1

Apply the layer to a pair of inputs:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-0eqsxz

Use ThreadingLayer in a NetGraph:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-jwzxw3
Out[1]=1

Apply the net to two vectors:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-f929t7
Out[2]=2

Create a NetGraph that computes the outer sum of two arrays with ThreadingLayer:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-bfjquh
Out[1]=1

Apply the outer sum to a pair of inputs:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-gqzhga

The names of input ports can be specified using option "Inputs":

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-etg6m9
Out[1]=1

The names of input ports can be specified directly within the function of ThreadingLayer:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-1j1tmi
Out[2]=2

Apply the layer to an association of arrays:

In[3]:=3
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https://wolfram.com/xid/0bnh3jw6cmuf2-g7xhtd
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

Create a ThreadingLayer that takes a specific number of inputs:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-miss03
Out[1]=1

Apply it to data:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-k28wyh
Out[2]=2

Create a ThreadingLayer that uses a custom transformation to compute a spherical Gaussian:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-53c5hd
Out[1]=1

Evaluate the layer on two input vectors to get a vector of outputs:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-txw6
Out[2]=2

Plot the output of the layer:

In[3]:=3
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https://wolfram.com/xid/0bnh3jw6cmuf2-t0axui
Out[3]=3

Applications  (1)Sample problems that can be solved with this function

Define a hinge loss using a ThreadingLayer:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-idugna

Create a net that computes the hinge loss with a margin of 2:

In[2]:=2
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https://wolfram.com/xid/0bnh3jw6cmuf2-jtngzl
Out[2]=2

When the target is within distance 2 of the input, the loss is zero:

In[3]:=3
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https://wolfram.com/xid/0bnh3jw6cmuf2-y63zt7
Out[3]=3

The loss increases linearly beyond a distance of 2:

In[4]:=4
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https://wolfram.com/xid/0bnh3jw6cmuf2-c4hukg
Out[4]=4

Plot the loss as a function of input for a fixed target of 2:

In[5]:=5
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https://wolfram.com/xid/0bnh3jw6cmuf2-jl4pzb
Out[5]=5

Perform linear regression using the hinge loss:

In[6]:=6
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https://wolfram.com/xid/0bnh3jw6cmuf2-1kc6gm
Out[6]=6

Plot the solution:

In[7]:=7
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https://wolfram.com/xid/0bnh3jw6cmuf2-sils2v
Out[7]=7

Compare the solutions obtained using the hinge loss, mean absolute and mean squared error:

In[8]:=8
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https://wolfram.com/xid/0bnh3jw6cmuf2-6thr3m
In[9]:=9
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https://wolfram.com/xid/0bnh3jw6cmuf2-zvitfz
Out[9]=9

Possible Issues  (3)Common pitfalls and unexpected behavior

ThreadingLayer cannot accept symbolic inputs:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-zestcp
Out[1]=1

Certain choices of f can produce failures for inputs outside their domain:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-014g3k
Out[1]=1

Some pure functions are not supported:

In[1]:=1
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https://wolfram.com/xid/0bnh3jw6cmuf2-0xokup
Out[1]=1
Wolfram Research (2017), ThreadingLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/ThreadingLayer.html (updated 2021).
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Wolfram Research (2017), ThreadingLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/ThreadingLayer.html (updated 2021).

Text

Wolfram Research (2017), ThreadingLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/ThreadingLayer.html (updated 2021).

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Wolfram Research (2017), ThreadingLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/ThreadingLayer.html (updated 2021).

CMS

Wolfram Language. 2017. "ThreadingLayer." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ThreadingLayer.html.

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Wolfram Language. 2017. "ThreadingLayer." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ThreadingLayer.html.

APA

Wolfram Language. (2017). ThreadingLayer. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ThreadingLayer.html

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Wolfram Language. (2017). ThreadingLayer. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ThreadingLayer.html

BibTeX

@misc{reference.wolfram_2025_threadinglayer, author="Wolfram Research", title="{ThreadingLayer}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/ThreadingLayer.html}", note=[Accessed: 04-June-2025 ]}

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@misc{reference.wolfram_2025_threadinglayer, author="Wolfram Research", title="{ThreadingLayer}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/ThreadingLayer.html}", note=[Accessed: 04-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_threadinglayer, organization={Wolfram Research}, title={ThreadingLayer}, year={2021}, url={https://reference.wolfram.com/language/ref/ThreadingLayer.html}, note=[Accessed: 04-June-2025 ]}

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@online{reference.wolfram_2025_threadinglayer, organization={Wolfram Research}, title={ThreadingLayer}, year={2021}, url={https://reference.wolfram.com/language/ref/ThreadingLayer.html}, note=[Accessed: 04-June-2025 ]}