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use crate::element::ElementConversion;
use crate::tensor::{FloatElem, FloatTensor};
use crate::{Backend, TensorMetadata};
use core::f64::consts::SQRT_2;
/// Activation function operations.
///
/// This trait let backend implementations override activation functions for better performance.
pub trait ActivationOps<B: Backend> {
/// Applies the LeakyReLU activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
/// * `negative_slope` - The negative_slope value that values smaller than 0 are multiplied with.
///
/// # Returns
///
/// The output tensor.
fn leaky_relu(tensor: FloatTensor<B>, negative_slope: FloatElem<B>) -> FloatTensor<B> {
let mask = B::float_lower_elem(tensor.clone(), 0.elem());
let scaled_tensor = B::float_mul_scalar(tensor.clone(), negative_slope.elem());
// Update the tensor where the values are `< 0` by `tensor * negative_slope`.
B::float_mask_where(tensor, mask, scaled_tensor)
}
/// Applies the ReLU activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
///
/// # Returns
///
/// The output tensor.
fn relu(tensor: FloatTensor<B>) -> FloatTensor<B> {
let mask = B::float_lower_equal_elem(tensor.clone(), 0.elem());
B::float_mask_fill(tensor, mask, 0.elem())
}
/// Applies the ReLU activation function backward.
///
/// # Arguments
///
/// * `output` - The output tensor.
///
/// # Returns
///
/// The gradient.
fn relu_backward(output: FloatTensor<B>, grad: FloatTensor<B>) -> FloatTensor<B> {
let mask = B::float_lower_equal_elem(output, 0.elem());
B::float_mask_fill(grad, mask, 0.elem())
}
/// Applies the Gelu activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
///
/// # Returns
///
/// The output tensor.
fn gelu(tensor: FloatTensor<B>) -> FloatTensor<B> {
let x = B::float_div_scalar(tensor.clone(), SQRT_2.elem());
let x = B::float_erf(x);
let x = B::float_add_scalar(x, 1i32.elem());
let x = B::float_mul(tensor, x);
B::float_div_scalar(x, 2i32.elem())
}
/// Applies the PReLu activation function.
/// # Arguments
/// * `tensor` - The input tensor
/// * `alpha` - The weight tensor
fn prelu(tensor: FloatTensor<B>, alpha: FloatTensor<B>) -> FloatTensor<B> {
let mask = B::float_lower_elem(tensor.clone(), 0.elem());
let scaled_tensor = B::float_mul(tensor.clone(), alpha);
B::float_mask_where(tensor, mask, scaled_tensor)
}
/// Applies the Gelu activation function backward.
///
/// # Arguments
///
/// * `x` - The tensor.
/// * `grad` - The gradient.
///
/// # Returns
///
/// The output tensor.
fn gelu_backward(x: FloatTensor<B>, grad: FloatTensor<B>) -> FloatTensor<B> {
// Derivative of the approximate gelu implementation based on tanh.
let constant_1 = 0.0356774;
let constant_2 = 0.797885;
let constant_3 = 0.0535161;
let constant_4 = 0.398942;
let x3 = B::float_powi_scalar(x.clone(), 3.elem());
let c1 = B::float_mul_scalar(x3.clone(), constant_1.elem());
let c2 = B::float_mul_scalar(x.clone(), constant_2.elem());
let c3 = B::float_mul_scalar(x3, constant_3.elem());
let c4 = B::float_mul_scalar(x, constant_4.elem());
let inner1 = B::float_add(c1, c2);
let inner2 = B::float_add(c3, c4);
let tanh = B::float_tanh(inner1);
let sech = B::float_powi_scalar(tanh.clone(), 2.elem());
let sech = B::float_neg(sech);
let sech = B::float_add_scalar(sech, 1.elem());
let y1 = B::float_mul_scalar(tanh, 0.5.elem());
let y2 = B::float_mul(inner2, sech);
let y2 = B::float_add_scalar(y2, 0.5.elem());
let y = B::float_add(y1, y2);
B::float_mul(y, grad)
}
/// Applies the Sigmoid activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
///
/// # Returns
///
/// The output tensor.
fn sigmoid(tensor: FloatTensor<B>) -> FloatTensor<B> {
let dtype = tensor.dtype();
let tensor_full = B::float_cast(tensor, burn_std::FloatDType::F32);
let tensor_tmp = B::float_exp(B::float_neg(B::float_log(B::float_add_scalar(
B::float_exp(B::float_neg(tensor_full)),
1.0.elem(),
))));
B::float_cast(tensor_tmp, dtype.into())
}
/// Applies the Sigmoid activation function backward.
///
/// # Arguments
///
/// * `output` - The output tensor of the sigmoid function.
/// * `grad` - The gradient.
///
/// # Returns
///
/// The output tensor.
fn sigmoid_backward(output: FloatTensor<B>, grad: FloatTensor<B>) -> FloatTensor<B> {
let value = B::float_mul(
output.clone(),
B::float_add_scalar(B::float_neg(output), 1.0.elem()),
);
B::float_mul(value, grad)
}
/// Applies the hard Sigmoid activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
/// * `alpha` - The alpha value that the tensor is multiplied with.
/// * `beta` - The beta value that is added to the tensor
///
/// # Returns
///
/// The output tensor.
fn hard_sigmoid(
tensor: FloatTensor<B>,
alpha: FloatElem<B>,
beta: FloatElem<B>,
) -> FloatTensor<B> {
let dtype = tensor.dtype();
let tensor_full = B::float_cast(tensor, burn_std::FloatDType::F32);
let tensor_tmp = B::float_clamp(
B::float_add_scalar(B::float_mul_scalar(tensor_full, alpha.elem()), beta.elem()),
0.0.elem(),
1.0.elem(),
);
B::float_cast(tensor_tmp, dtype.into())
}
/// Applies the LogSigmoid activation function.
///
/// # Arguments
///
/// * `tensor` - The tensor.
///
/// # Returns
///
/// The output tensor.
fn log_sigmoid(tensor: FloatTensor<B>) -> FloatTensor<B> {
// To avoid overflow, we use the log-sum-exp trick.
//
// ```ignore
// log(sigmoid(x)) = log(1/(1 + exp(-x)))
// = log(1) - log(1 + exp(-x))
// = -log(1 + exp(-x))
// = -log(exp(0) + exp(-x))
// ```
// The `exp(t)` of even a moderate-magnitude positive number can be astronomically huge, so we
// subtract the `max(t, 0)` of each value (where `t = -x` in this case). This results in the
// following equivalence:
// ```ignore
// log(sigmoid(x)) = -(max(-x, 0) + log(exp(-max(-x, 0)) + exp(-x - max(-x, 0))))
// ```
//
// This extends the range of values for which we obtain accurate results.
// max(-x, 0)
let tensor_neg = B::float_neg(tensor);
let mask = B::float_lower_elem(tensor_neg.clone(), 0.elem());
let max_elem = B::float_mask_fill(tensor_neg.clone(), mask, 0.elem());
let max_elem_neg = B::float_neg(max_elem.clone());
// z = exp(-max(-x, 0)) + exp(-x - max(-x, 0))
let z = B::float_add(
B::float_exp(max_elem_neg.clone()),
B::float_exp(B::float_sub(tensor_neg, max_elem.clone())),
);
// -max(-x, 0) - log(-z)
B::float_sub(max_elem_neg, B::float_log(z))
}
/// Applies the LogSigmoid activation function backward.
///
/// # Arguments
///
/// * `x` - The input tensor.
/// * `grad` - The gradient.
///
/// # Returns
///
/// The output gradient.
fn log_sigmoid_backward(x: FloatTensor<B>, grad: FloatTensor<B>) -> FloatTensor<B> {
// Derivative of -max(-x, 0) - log(exp(-max(-x, 0)) - exp(-x - max(-x, 0)))) is
// -max_derive - (-max_derive * exp(-max(-x, 0)) + (-1 - max_derive) * exp(-x - max(-x, 0))) / z
// where z = exp(-max(-x, 0)) + exp(-x - max(-x, 0))
//
// This simplifies to:
// -max_derive - (z-1)/z if x is >= 0
// -max_derive + (z-1)/z if x is < 0
let shape = x.shape();
let dtype = x.dtype();
let device = B::float_device(&x);
// max(-x, 0)
let x_neg = B::float_neg(x);
let mask = B::float_lower_elem(x_neg.clone(), 0.elem()); // -x < 0 or x >= 0
let max_elem = B::float_mask_fill(x_neg.clone(), mask.clone(), 0.elem());
// z = exp(-max(-x, 0)) + exp(-x - max(-x, 0))
let z = B::float_add(
B::float_exp(B::float_neg(max_elem.clone())),
B::float_exp(B::float_sub(x_neg, max_elem)),
);
// Derivative of max(-x, 0) is 1 if x < 0 or 0 if x >= 0
let ones = B::float_ones(shape, &device, dtype.into());
let max_derive = B::float_mask_fill(ones.clone(), mask.clone(), 0.elem());
let sign = B::float_mask_fill(ones.clone(), mask, (-1).elem());
// grad * (max_derive - sign * (1 - (1 / z)))
B::float_mul(
grad,
B::float_sub(
max_derive,
B::float_mul(sign, B::float_sub(ones, B::float_recip(z))),
),
)
}
}