js_divergence: Jensen-Shannon divergence

js_divergence

hypercoil.loss.js_divergence(P: Tensor, Q: Tensor, *, axis: int | Sequence[int] = -1, keepdims: bool = True, reduce: bool = True, key: PRNGKey | None = None) → Tensor

Jensen-Shannon divergence between two categorical distributions.

This function operates on probability tensors. For a version that operates on logits, see js_divergence_logit().

\[JS(P || Q) = \frac{1}{2} KL(P || M) + \frac{1}{2} KL(Q || M)\]

Parameters:

PTensor

Input tensor parameterising the first categorical distribution.

QTensor

Input tensor parameterising the second categorical distribution.

axisint or sequence of ints, optional (default: -1)

Axis or axes over which to compute the JS divergence.

keepdimsbool, optional (default: True)

As in jax.numpy.sum.

reducebool, optional (default: True)

If this is False, then the unsummed JS divergence is computed for each element of the input tensor. Otherwise, the JS divergence is computed over the specified axis or axes.

Returns:

Tensor

JS divergence between the two distributions.

hypercoil.loss.js_divergence_logit(P: Tensor, Q: Tensor, *, axis: int | Sequence[int] = -1, keepdims: bool = True, reduce: bool = True, key: PRNGKey | None = None) → Tensor

Jensen-Shannon divergence between two categorical distributions.

This function operates on logits. For a version that operates on probabilities, see js_divergence().

\[JS(P || Q) = \frac{1}{2} KL(P || M) + \frac{1}{2} KL(Q || M)\]

Parameters:

PTensor

Input tensor parameterising the first categorical distribution.

QTensor

Input tensor parameterising the second categorical distribution.

axisint or sequence of ints, optional (default: -1)

Axis or axes over which to compute the JS divergence.

keepdimsbool, optional (default: True)

As in jax.numpy.sum.

reducebool, optional (default: True)

If this is False, then the unsummed JS divergence is computed for each element of the input tensor. Otherwise, the JS divergence is computed over the specified axis or axes.

Returns:

Tensor

JS divergence between the two distributions.

JSDivergenceLoss

class hypercoil.loss.JSDivergenceLoss(nu: float = 1.0, name: str | None = None, *, axis: int | Tuple[int, ...] = -1, keepdims: bool = False, reduce: bool = True, scalarisation: Callable | None = None, key: 'jax.random.PRNGKey' | None = None)

Loss based on the Jensen-Shannon divergence between two categorical distributions.

This operates on probability tensors. For a version that operates on logits, see JSDivergenceLogitLoss.

\[JS(P || Q) = \frac{1}{2} KL(P || M) + \frac{1}{2} KL(Q || M)\]

Parameters:

name: str

Designated name of the loss function. It is not required that this be specified, but it is recommended to ensure that the loss function can be identified in the context of a reporting utilities. If not explicitly specified, the name will be inferred from the class name and the name of the scoring function.

nu: float

Loss strength multiplier. This is a scalar multiplier that is applied to the loss value before it is returned. This can be used to modulate the relative contributions of different loss functions to the overall loss value. It can also be used to implement a schedule for the loss function, by dynamically adjusting the multiplier over the course of training.

axisint or sequence of ints, optional (default: -1)

Axis or axes over which to compute the JS divergence.

keepdimsbool, optional (default: True)

As in jax.numpy.sum.

reducebool, optional (default: True)

If this is False, then the unsummed JS divergence is computed for each element of the input tensor. Otherwise, the JS divergence is computed over the specified axis or axes.

scalarisation: Callable

The scalarisation function to be used to aggregate the values returned by the scoring function. This function should take a single argument, which is a tensor of arbitrary shape, and return a single scalar value. By default, the mean scalarisation is used.

class hypercoil.loss.JSDivergenceLogitLoss(nu: float = 1.0, name: str | None = None, *, axis: int | Tuple[int, ...] = -1, keepdims: bool = False, reduce: bool = True, scalarisation: Callable | None = None, key: 'jax.random.PRNGKey' | None = None)

Loss based on the Jensen-Shannon divergence between two categorical distributions.

This operates on logit tensors. For a version that operates on probabilities, see JSDivergenceLoss.

\[JS(P || Q) = \frac{1}{2} KL(P || M) + \frac{1}{2} KL(Q || M)\]

Parameters:

name: str

Designated name of the loss function. It is not required that this be specified, but it is recommended to ensure that the loss function can be identified in the context of a reporting utilities. If not explicitly specified, the name will be inferred from the class name and the name of the scoring function.

nu: float

Loss strength multiplier. This is a scalar multiplier that is applied to the loss value before it is returned. This can be used to modulate the relative contributions of different loss functions to the overall loss value. It can also be used to implement a schedule for the loss function, by dynamically adjusting the multiplier over the course of training.

axisint or sequence of ints, optional (default: -1)

Axis or axes over which to compute the JS divergence.

keepdimsbool, optional (default: True)

As in jax.numpy.sum.

reducebool, optional (default: True)

If this is False, then the unsummed JS divergence is computed for each element of the input tensor. Otherwise, the JS divergence is computed over the specified axis or axes.

scalarisation: Callable

The scalarisation function to be used to aggregate the values returned by the scoring function. This function should take a single argument, which is a tensor of arbitrary shape, and return a single scalar value. By default, the mean scalarisation is used.