class

PoissonNLLLoss

extendsModule

PoissonNLLLoss(log_input: bool = True, full: bool = False, eps: float = 1e-08, reduction: str = 'mean')

source

Poisson negative log-likelihood loss for count data.

Models the negative log-likelihood under a Poisson observation model. Two modes are supported, controlled by log_input:

log_input=True — the input x is the natural logarithm of the Poisson rate $\lambda$ (i.e. $x = \log\lambda$ ):

\ell(x, y) = e^{x} - y \cdot x

log_input=False — the input x is the Poisson rate $\lambda$ directly:

\ell(x, y) = x - y \cdot \log(x + \varepsilon)

where $\varepsilon$ is added for numerical stability.

When full=True, the Stirling approximation term $y\log y - y + 0.5\log(2\pi y)$ is added to approximate the full log-likelihood including the factorial term.

Parameters

log_inputbool= True

If True, the input is

\log\lambda

. Default True.

fullbool= False

If True, adds the Stirling approximation term. Default False.

epsfloat= 1e-08

Small constant for numerical stability when log_input=False. Default 1e-8.

reductionstr= 'mean'

'none' | 'mean' (default) | 'sum'.

Attributes

log_inputbool

Whether the input is in log-space.

fullbool

Whether the full approximation is applied.

epsfloat

Numerical stability constant.

reductionstr

The reduction mode.

Notes

Input x : $(*)$ .
Target y : $(*)$ — non-negative counts.
Output : scalar for 'mean' / 'sum'; $(*)$ for 'none'.

Commonly used for count-valued outputs such as word counts in language modelling or photon counts in imaging.
The log_input=True variant is the standard form for neural network outputs because it guarantees $\lambda > 0$ and simplifies the gradient.

Examples

Log-input mode (standard neural network output):
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.PoissonNLLLoss(log_input=True)
>>> log_rates = lucid.tensor([1.5, 0.3, -0.5, 2.0])
>>> counts    = lucid.tensor([4.0, 1.0,  0.0, 7.0])
>>> loss = criterion(log_rates, counts)
Direct rate mode with full approximation:
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.PoissonNLLLoss(log_input=False, full=True)
>>> rates  = lucid.tensor([4.5, 1.0, 0.5, 7.5])
>>> counts = lucid.tensor([4.0, 1.0, 0.0, 7.0])
>>> loss = criterion(rates, counts)

Methods (3)

dunder

init

→None

__init__(log_input: bool = True, full: bool = False, eps: float = 1e-08, reduction: str = 'mean')

source

Initialise the PoissonNLLLoss module. See the class docstring for parameter semantics.

forward

→Tensor

forward(x: Tensor, target: Tensor)

source

Compute the loss between predictions and targets.

Parameters

xTensor

Input tensor.

targetTensor

Input tensor.

Returns

Tensor

Scalar loss (or unreduced tensor depending on reduction).

extra_repr

→str

extra_repr()

source

Return a string representation of the layer's configuration.