Losses#
Collection of Ivy loss functions.
- ivy.binary_cross_entropy(true, pred, /, *, from_logits=False, epsilon=0.0, reduction='mean', pos_weight=None, axis=None, out=None)[source]#
Compute the binary cross entropy loss.
- Parameters:
true (
Union
[Array
,NativeArray
]) – input array containing true labels.pred (
Union
[Array
,NativeArray
]) – input array containing Predicted labels.from_logits (
bool
, default:False
) – Whether pred is expected to be a logits tensor. By default, we assume that pred encodes a probability distribution.epsilon (
float
, default:0.0
) – a float in [0.0, 1.0] specifying the amount of smoothing when calculating the loss. If epsilon is0
, no smoothing will be applied. Default:0
.reduction (
str
, default:'mean'
) –'none'
: No reduction will be applied to the output.'mean'
: The output will be averaged.'sum'
: The output will be summed. Default:'none'
.pos_weight (
Optional
[Union
[Array
,NativeArray
]], default:None
) – a weight for positive examples. Must be an array with length equal to the number of classes.axis (
Optional
[int
], default:None
) – Axis along which to compute crossentropy.out (
Optional
[Array
], default:None
) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.
- Return type:
- Returns:
ret – The binary cross entropy between the given distributions.
Examples
With
ivy.Array
input:>>> x = ivy.array([0, 1, 0, 0]) >>> y = ivy.array([0.2, 0.8, 0.3, 0.8]) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) ivy.array([0.223,0.223,0.357,1.61])
>>> x = ivy.array([[0, 1, 1, 0]]) >>> y = ivy.array([[2.6, 6.2, 3.7, 5.3]]) >>> z = ivy.binary_cross_entropy(x, y, reduction='mean') >>> print(z) ivy.array(7.6666193)
>>> x = ivy.array([[0, 1, 1, 0]]) >>> y = ivy.array([[2.6, 6.2, 3.7, 5.3]]) >>> pos_weight = ivy.array([1, 2, 3, 4]) >>> z = ivy.binary_cross_entropy(x, y, pos_weight=pos_weight, from_logits=True) ivy.array([[2.67164493e+00, 4.05471958e-03, 7.32684899e-02, 5.30496836e+00]])
>>> x = ivy.array([[0, 1, 1, 0]]) >>> y = ivy.array([[2.6, 6.2, 3.7, 5.3]]) >>> pos_weight = ivy.array([1, 2, 3, 4]) >>> z = ivy.binary_cross_entropy(x, y, pos_weight=pos_weight, from_logits=True, reduction='sum', axis=1) # noqa: E501 ivy.array([8.05393649])
>>> x = ivy.array([[0, 1, 1, 0]]) >>> y = ivy.array([[2.6, 6.2, 3.7, 5.3]]) >>> z = ivy.binary_cross_entropy(x, y, reduction='none', epsilon=0.5) ivy.array([[11.49992943, 3.83330965, 3.83330965, 11.49992943]])
>>> x = ivy.array([[0, 1, 0, 0]]) >>> y = ivy.array([[0.6, 0.2, 0.7, 0.3]]) >>> z = ivy.binary_cross_entropy(x, y, epsilon=1e-3) >>> print(z) ivy.array([[0.916,1.61,1.2,0.357]])
With
ivy.NativeArray
input:>>> x = ivy.native_array([0, 1, 0, 1]) >>> y = ivy.native_array([0.2, 0.7, 0.2, 0.6]) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) ivy.array([0.223,0.357,0.223,0.511])
With a mix of
ivy.Array
andivy.NativeArray
inputs:>>> x = ivy.array([0, 0, 1, 1]) >>> y = ivy.native_array([0.1, 0.2, 0.8, 0.6]) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) ivy.array([0.105,0.223,0.223,0.511])
With
ivy.Container
input:>>> x = ivy.Container(a=ivy.array([1, 0, 0]),b=ivy.array([0, 0, 1])) >>> y = ivy.Container(a=ivy.array([0.6, 0.2, 0.3]),b=ivy.array([0.8, 0.2, 0.2])) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) {a:ivy.array([0.511,0.223,0.357]),b:ivy.array([1.61,0.223,1.61])}
With a mix of
ivy.Array
andivy.Container
inputs:>>> x = ivy.array([1 , 1, 0]) >>> y = ivy.Container(a=ivy.array([0.7, 0.8, 0.2])) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) { a: ivy.array([0.357, 0.223, 0.223]) }
Instance Method Examples
Using
ivy.Array
instance method:>>> x = ivy.array([1, 0, 0, 0]) >>> y = ivy.array([0.8, 0.2, 0.2, 0.2]) >>> z = ivy.binary_cross_entropy(x, y) >>> print(z) ivy.array([0.223, 0.223, 0.223, 0.223])
- ivy.cross_entropy(true, pred, /, *, axis=-1, epsilon=1e-07, reduction='mean', out=None)[source]#
Compute cross-entropy between predicted and true discrete distributions.
- Parameters:
true (
Union
[Array
,NativeArray
]) – input array containing true labels.pred (
Union
[Array
,NativeArray
]) – input array containing the predicted labels.axis (
int
, default:-1
) – the axis along which to compute the cross-entropy. If axis is-1
, the cross-entropy will be computed along the last dimension. Default:-1
.epsilon (
float
, default:1e-07
) – a float in [0.0, 1.0] specifying the amount of smoothing when calculating the loss. If epsilon is0
, no smoothing will be applied. Default:1e-7
.out (
Optional
[Array
], default:None
) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.
- Return type:
- Returns:
ret – The cross-entropy loss between the given distributions
Examples
>>> x = ivy.array([0, 0, 1, 0]) >>> y = ivy.array([0.25, 0.25, 0.25, 0.25]) >>> print(ivy.cross_entropy(x, y)) ivy.array(1.3862944)
>>> z = ivy.array([0.1, 0.1, 0.7, 0.1]) >>> print(ivy.cross_entropy(x, z)) ivy.array(0.35667497)
- ivy.sparse_cross_entropy(true, pred, /, *, axis=-1, epsilon=1e-07, reduction='mean', out=None)[source]#
Compute sparse cross entropy between logits and labels.
- Parameters:
true (
Union
[Array
,NativeArray
]) – input array containing the true labels as logits.pred (
Union
[Array
,NativeArray
]) – input array containing the predicted labels as logits.axis (
int
, default:-1
) – the axis along which to compute the cross-entropy. If axis is-1
, the cross-entropy will be computed along the last dimension. Default:-1
.epsilon (
float
, default:1e-07
) – a float in [0.0, 1.0] specifying the amount of smoothing when calculating the loss. If epsilon is0
, no smoothing will be applied. Default:1e-7
.out (
Optional
[Array
], default:None
) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.
- Return type:
- Returns:
ret – The sparse cross-entropy loss between the given distributions
Examples
With
ivy.Array
input:>> x = ivy.array([2]) >> y = ivy.array([0.1, 0.1, 0.7, 0.1]) >> print(ivy.sparse_cross_entropy(x, y)) ivy.array([0.35667494])
>>> x = ivy.array([3]) >>> y = ivy.array([0.1, 0.1, 0.7, 0.1]) >>> print(ivy.cross_entropy(x, y)) ivy.array(21.79329094)
>>> x = ivy.array([2,3]) >>> y = ivy.array([0.1, 0.1]) >>> print(ivy.cross_entropy(x, y)) ivy.array(11.512926)
With
ivy.NativeArray
input:>>> x = ivy.native_array([4]) >>> y = ivy.native_array([0.1, 0.2, 0.1, 0.1, 0.5]) >>> print(ivy.sparse_cross_entropy(x, y)) ivy.array([0.693])
With
ivy.Container
input:>>> x = ivy.Container(a=ivy.array([4])) >>> y = ivy.Container(a=ivy.array([0.1, 0.2, 0.1, 0.1, 0.5])) >>> print(ivy.sparse_cross_entropy(x, y)) { a: ivy.array([0.693]) }
With a mix of
ivy.Array
andivy.NativeArray
inputs:>>> x = ivy.array([0]) >>> y = ivy.native_array([0.1, 0.2, 0.6, 0.1]) >>> print(ivy.sparse_cross_entropy(x,y)) ivy.array([2.3])
With a mix of
ivy.Array
andivy.Container
inputs:>>> x = ivy.array([0]) >>> y = ivy.Container(a=ivy.array([0.1, 0.2, 0.6, 0.1])) >>> print(ivy.sparse_cross_entropy(x,y)) { a: ivy.array([2.3]) }
Instance Method Examples
With
ivy.Array
input:>>> x = ivy.array([2]) >>> y = ivy.array([0.1, 0.1, 0.7, 0.1]) >>> print(x.sparse_cross_entropy(y)) ivy.array([0.357])
With
ivy.Container
input:>>> x = ivy.Container(a=ivy.array([2])) >>> y = ivy.Container(a=ivy.array([0.1, 0.1, 0.7, 0.1])) >>> print(x.sparse_cross_entropy(y)) { a: ivy.array([0.357]) }
This should have hopefully given you an overview of the losses submodule, if you have any questions, please feel free to reach out on our discord in the losses channel!