Compiles the given anonymous function with the given tensor shapes.

While jit/2 compiles a function just-in time based on the input shapes, this function precompiles the given anonymous function based on the input shapes. This can be beneficial for large numerical definitions, where the cache mechanism in jit/2 may take miliseconds.

For example, take the following definition:

defn softmax(t), do: Nx.exp(t) / Nx.sum(Nx.exp(t))

You can jit and then apply it as:

fun = Nx.Defn.compile(&softmax/1, [Nx.template({3}, {:s, 64})], compiler: EXLA)
fun.(Nx.tensor([1, 2, 3]))

You can also pass a mixture of templates and options when compiling a function. In such cases, you must only pass the inputs when invoking the compiled function, as the options will already be embedded in its compiled value:

fun = Nx.Defn.compile(&Nx.sum/2, [Nx.template({2, 2}, {:s, 64}), [axes: [1]]])
fun.(Nx.iota({2, 2}))

If the input tensors do not match the shape of the tensors given on compilation, it will raise.

Options

• :compiler - the compiler for the JIT compilation

• :hooks - a map of hooks to execute. See Nx.Defn.Kernel.hook/3

Wraps an anonymous function to return its underlying defn expression.

Warning

This function must be invoked for debugging purposes only.

Options

• :hooks - a map of hooks to execute. See Nx.Defn.Kernel.hook/3

Invokes the anonymous function to return its underlying defn expression.

Warning

This function must be invoked for debugging purposes only.

It accepts the same options as debug_expr/2.

Gets the default options for the current process.

Sets the default options for defn in the current process.

The options defined here apply to all future invocations of defn done by the current process. It also applies to calls to the jit/3 and stream/3 functions in this module.

The default options are stored only in the process dictionary and override any global options. This means if you start a separate process, such as Task, the default options must be set on the new process too.

The function returns the values that were previously set as default options.

This function must be used only for scripting and testing.

Examples

iex> Nx.Defn.default_options(compiler: EXLA, client: :cuda)
iex> Nx.Defn.default_options()
[compiler: EXLA, client: :cuda]

Defines a public numerical function.

Defines a private numerical function.

Private numerical functions are always inlined by their callers at compilation time. This happens to all local function calls within defn.

Can be used to define bodiless clauses for multi-clause transforms.

See also: deftransform/2

Examples

deftransform foo(bar, baz \ 1)
deftransform foo(bar, 1), do: bar
deftransform foo(bar, baz), do: bar + baz

Defines a transform that executes the given fun with arg when building defn expressions.

Example

Take the following defn expression:

defn tanh_power(a, b) do
  Nx.tanh(a) + Nx.pow(b, 2)
end

Let's see a trivial example, which is to use IO.inspect/1 to print a tensor expression at definition time:

defn tanh_power(a, b) do
  Nx.tanh(a) + Nx.pow(b, 2) |> my_inspect()
end

deftransformp my_inspect(expr), do: IO.inspect(expr)

Or:

defn tanh_power(a, b) do
  res = Nx.tanh(a) + Nx.pow(b, 2)
  my_inspect(res)
  res
end

When invoked in both cases, it will print the expression being built by defn:

#Nx.Defn.Expr<
  parameter a
  parameter c
  b = tanh [ a ] ()
  d = pow [ c, 2 ] ()
  e = add [ b, d ] ()
>

Although, for convenience, you might use print_expr/2 instead.

Private function version for deftransform/1

Private function version for deftransform/2

Sets the default options globally.

The options defined here apply to all future invocations of defn. It also applies to calls to the jit/3 and stream/3 functions in this module.

You must avoid calling this function at runtime and mostly for testing purposes. You may also set in your test environment using configuration:

config :nx, :default_defn_options, [compiler: EXLA, client: :cuda]

The function returns the values that were previously set as global default options.

Receives an anonymous function and returns a new anonymous function that returns the gradient of the input function when invoked.

Examples

iex> fun = Nx.Defn.grad(fn x -> Nx.sin(x) end)
iex> fun.(Nx.tensor(0))
#Nx.Tensor<
  f32
  1.0
>

Computes the gradient of the given var on fun.

The result of the grad function must be a scalar tensor. If a non-scalar tensor is given, it is assumed the additional dimensions are batch dimensions.

Examples

defn tanh_grad(t) do
  grad(t, &Nx.tanh/&1)
end

To differentiate on multiple vars, pass a tuple as first argument:

defn tanh_power_grad(a, b) do
  grad({a, b}, fn {a, b} -> Nx.tanh(a) + Nx.pow(b, 2) end)
end

var_or_vars can be any Nx.Container with one or multiple tensors.

Wraps an anonymous function with just-in-time compilation.

Once invoked, the wrapped anonymous function will perform just in time compilation with the configured compiler. For example, take the following definition:

defn softmax(t), do: Nx.exp(t) / Nx.sum(Nx.exp(t))

You can jit and then apply it as:

fun = Nx.Defn.jit(&softmax/1, compiler: EXLA)
fun.(Nx.tensor([1, 2, 3]))

Options

• :compiler - the compiler for the JIT compilation

• :hooks - a map of hooks to execute. See Nx.Defn.Kernel.hook/3

• :on_conflict - what to do if a JIT compilation is already in place. It may be :raise (the default), :force (forces a new JIT compilation), or :reuse (reuses the exiting JIT compilation). It is not recommended to set the :compiler option when reusing.

Invokes the anonymous function with just-in-time compilation.

This function is equivalent to calling jit/2 and then applying the given arguments to the anonymous function.

For example, take the following definition:

defn softmax(t), do: Nx.exp(t) / Nx.sum(Nx.exp(t))

You can jit_apply/3 it as:

Nx.Defn.jit_apply(&softmax/1, [Nx.tensor([1, 2, 3])], compiler: EXLA)

It accepts the same options as jit/2.

Starts streaming the given anonymous function with just-in-time compilation.

At least two arguments are expected:

1. The first argument is a tensor template of the data to be streamed in

2. The second argument is a tensor with the stream initial state

The streaming function must return a two element tuple, the first element is the data to be sent and the second is the accumulator.

For each streamed chunk, you must call Nx.Stream.send/2 and Nx.Stream.recv/1. You don't need to call recv immediately after send, but doing so can be a useful mechanism to provide backpressure. Once all chunks are sent, you must use Nx.Stream.done/1 to receive the accumulated result. Let's see an example:

defmodule Streamed do
  import Nx.Defn

  defn sum(tensor, acc) do
    {acc, tensor + acc}
  end
end

Now let's invoke it:

stream = Nx.Defn.stream(&Streamed.sum/2, [Nx.template({}, {:s, 64}), 0])

for i <- 1..5 do
  Nx.Stream.send(stream, i)
  IO.inspect {:chunk, Nx.Stream.recv(stream)}
end

IO.inspect {:result, Nx.Stream.done(stream)}

It will print:

{:chunk, 0}
{:chunk, 1}
{:chunk, 2}
{:chunk, 3}
{:chunk, 4}
{:result, 5}

Options

• :hooks - a map of hooks to execute. See Nx.Defn.Kernel.hook/3

Beware: deadlocks

Some backends (such as XLA) place locks around devices. For example, if you start streaming on the GPU, you cannot perform any other operation on the GPU until streaming is over.

This means if we modify the loop above to the following:

for i <- 1..5 do
  Nx.Stream.send(stream, Nx.tensor(i) |> Nx.multiply(2))
  IO.inspect {:chunk, Nx.Stream.recv(stream)}
end

The loop may deadlock at the time it performs the multiplication. In practice, this means you should perform the streaming on the GPU and the remaining operations on the CPU. If you only have a single device (i.e. only a CPU), then it may not be possible to perform the above and you will have to restructure your code to manipulate the input before streaming starts.

Receives an anonymous function and returns a new anonymous function that returns the value and gradient of the input function when invoked.

Examples

iex> fun = Nx.Defn.value_and_grad(fn x -> Nx.sin(x) end)
iex> {value, grad} = fun.(Nx.tensor(0))
iex> value
#Nx.Tensor<
  f32
  0.0
>
iex> grad
#Nx.Tensor<
  f32
  1.0
>

Computes the value and gradient of the given var on fun with an optional data transformation.

It returns a tuple with the value and the gradient.

Examples

defn tanh_grad(t) do
  value_and_grad(t, &Nx.tanh/&1)
end

To differentiate on multiple vars, pass a tuple as first argument:

defn tanh_power_grad(a, b) do
  value_and_grad({a, b}, fn {a, b} -> Nx.tanh(a) + Nx.pow(b, 2) end)
end

var_or_vars can be any Nx.Container with one or multiple tensors.

transform allows you to transform the expression before the gradient is calculated. This enables optimizations that reuse parts of expressions. As an example, consider the following objective function:

defn objective(predict_fn, loss_fn, params, inputs, targets) do
  preds = predict_fn.(params, inputs)
  loss = loss_fn.(preds, targets)
  {preds, loss}
end

You can compute the gradient with respect to just the loss function by applying a transform:

{{preds, loss}, gradient} = value_and_grad(params, &objective(predict_fn, loss_fn, &1, inputs, targets), &elem(&1, 1))

preds can be re-used to compute other metrics such as accuracy, absolute error, etc. without having to do another forward pass.