/**
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* @license
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* Copyright 2018 Google LLC. All Rights Reserved.
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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* =============================================================================
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*/
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/// <amd-module name="@tensorflow/tfjs-core/dist/gradients" />
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import { CustomGradientFunc } from './engine';
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import { Scalar, Tensor, Variable } from './tensor';
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import { NamedTensorMap } from './tensor_types';
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import { TensorLike } from './types';
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/**
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* Provided `f(x)`, returns another function `g(x, dy?)`, which gives the
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* gradient of `f(x)` with respect to `x`.
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*
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* If `dy` is provided, the gradient of `f(x).mul(dy).sum()` with respect to
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* `x` is computed instead. `f(x)` must take a single tensor `x` and return a
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* single tensor `y`. If `f()` takes multiple inputs, use `tf.grads` instead.
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*
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* ```js
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* // f(x) = x ^ 2
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* const f = x => x.square();
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* // f'(x) = 2x
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* const g = tf.grad(f);
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*
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* const x = tf.tensor1d([2, 3]);
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* g(x).print();
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* ```
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*
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* ```js
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* // f(x) = x ^ 3
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* const f = x => x.pow(tf.scalar(3, 'int32'));
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* // f'(x) = 3x ^ 2
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* const g = tf.grad(f);
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* // f''(x) = 6x
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* const gg = tf.grad(g);
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*
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* const x = tf.tensor1d([2, 3]);
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* gg(x).print();
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* ```
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*
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* @param f The function f(x), to compute gradient for.
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function grad(f: (x: Tensor) => Tensor): (x: TensorLike | Tensor, dy?: TensorLike | Tensor) => Tensor;
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/**
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* Provided `f(x1, x2,...)`, returns another function `g([x1, x2,...], dy?)`,
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* which gives an array of gradients of `f()` with respect to each input
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* [`x1`,`x2`,...].
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*
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* If `dy` is passed when calling `g()`, the gradient of
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* `f(x1,...).mul(dy).sum()` with respect to each input is computed instead.
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* The provided `f` must take one or more tensors and return a single tensor
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* `y`. If `f()` takes a single input, we recommend using `tf.grad` instead.
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*
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* ```js
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* // f(a, b) = a * b
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* const f = (a, b) => a.mul(b);
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* // df / da = b, df / db = a
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* const g = tf.grads(f);
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*
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* const a = tf.tensor1d([2, 3]);
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* const b = tf.tensor1d([-2, -3]);
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* const [da, db] = g([a, b]);
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* console.log('da');
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* da.print();
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* console.log('db');
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* db.print();
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* ```
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*
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* @param f The function `f(x1, x2,...)` to compute gradients for.
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function grads(f: (...args: Tensor[]) => Tensor): (args: Array<Tensor | TensorLike>, dy?: Tensor | TensorLike) => Tensor[];
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/**
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* Like `tf.grad`, but also returns the value of `f()`. Useful when `f()`
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* returns a metric you want to show.
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*
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* The result is a rich object with the following properties:
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* - grad: The gradient of `f(x)` w.r.t. `x` (result of `tf.grad`).
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* - value: The value returned by `f(x)`.
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*
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* ```js
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* // f(x) = x ^ 2
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* const f = x => x.square();
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* // f'(x) = 2x
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* const g = tf.valueAndGrad(f);
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*
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* const x = tf.tensor1d([2, 3]);
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* const {value, grad} = g(x);
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*
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* console.log('value');
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* value.print();
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* console.log('grad');
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* grad.print();
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* ```
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function valueAndGrad<I extends Tensor, O extends Tensor>(f: (x: I) => O): (x: I, dy?: O) => {
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value: O;
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grad: I;
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};
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/**
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* Like `tf.grads`, but returns also the value of `f()`. Useful when `f()`
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* returns a metric you want to show.
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*
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* The result is a rich object with the following properties:
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* - grads: The gradients of `f()` w.r.t. each input (result of `tf.grads`).
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* - value: The value returned by `f(x)`.
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*
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* ```js
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* // f(a, b) = a * b
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* const f = (a, b) => a.mul(b);
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* // df/da = b, df/db = a
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* const g = tf.valueAndGrads(f);
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*
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* const a = tf.tensor1d([2, 3]);
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* const b = tf.tensor1d([-2, -3]);
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* const {value, grads} = g([a, b]);
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*
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* const [da, db] = grads;
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*
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* console.log('value');
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* value.print();
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*
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* console.log('da');
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* da.print();
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* console.log('db');
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* db.print();
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* ```
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function valueAndGrads<O extends Tensor>(f: (...args: Tensor[]) => O): (args: Tensor[], dy?: O) => {
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grads: Tensor[];
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value: O;
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};
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/**
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* Computes and returns the gradient of f(x) with respect to the list of
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* trainable variables provided by `varList`. If no list is provided, it
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* defaults to all trainable variables.
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*
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* ```js
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* const a = tf.variable(tf.tensor1d([3, 4]));
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* const b = tf.variable(tf.tensor1d([5, 6]));
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* const x = tf.tensor1d([1, 2]);
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*
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* // f(a, b) = a * x ^ 2 + b * x
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* const f = () => a.mul(x.square()).add(b.mul(x)).sum();
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* // df/da = x ^ 2, df/db = x
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* const {value, grads} = tf.variableGrads(f);
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*
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* Object.keys(grads).forEach(varName => grads[varName].print());
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* ```
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*
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* @param f The function to execute. f() should return a scalar.
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* @param varList The list of variables to compute the gradients with respect
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* to. Defaults to all trainable variables.
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* @returns An object with the following keys and values:
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* - `value`: The value of the function `f`.
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* - `grads`: A map from the names of the variables to the gradients.
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* If the `varList` argument is provided explicitly and contains a subset of
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* non-trainable variables, this map in the return value will contain keys
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* that map the names of the non-trainable variables to `null`.
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function variableGrads(f: () => Scalar, varList?: Variable[]): {
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value: Scalar;
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grads: NamedTensorMap;
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};
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/**
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* Overrides the gradient computation of a function `f`.
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*
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* Takes a function
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* `f(...inputs, save) => {value: Tensor, gradFunc: (dy, saved) => Tensor[]}`
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* and returns another function `g(...inputs)` which takes the same inputs as
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* `f`. When called, `g` returns `f().value`. In backward mode, custom gradients
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* with respect to each input of `f` are computed using `f().gradFunc`.
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*
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* The `save` function passed to `f` should be used for saving tensors needed
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* in the gradient. And the `saved` passed to the `gradFunc` is a
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* `NamedTensorMap`, which contains those saved tensors.
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*
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* ```js
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* const customOp = tf.customGrad((x, save) => {
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* // Save x to make sure it's available later for the gradient.
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* save([x]);
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* // Override gradient of our custom x ^ 2 op to be dy * abs(x);
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* return {
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* value: x.square(),
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* // Note `saved.x` which points to the `x` we saved earlier.
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* gradFunc: (dy, saved) => [dy.mul(saved[0].abs())]
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* };
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* });
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*
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* const x = tf.tensor1d([-1, -2, 3]);
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* const dx = tf.grad(x => customOp(x));
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*
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* console.log(`f(x):`);
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* customOp(x).print();
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* console.log(`f'(x):`);
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* dx(x).print();
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* ```
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*
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* @param f The function to evaluate in forward mode, which should return
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* `{value: Tensor, gradFunc: (dy, saved) => Tensor[]}`, where `gradFunc`
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* returns the custom gradients of `f` with respect to its inputs.
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*
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* @doc {heading: 'Training', subheading: 'Gradients'}
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*/
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declare function customGrad<T extends Tensor>(f: CustomGradientFunc<T>): (...args: Tensor[]) => T;
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export { customGrad, variableGrads, valueAndGrad, valueAndGrads, grad, grads, };
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