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Merge pull request #309 from f-dangel/development
Update master with code for `1.6.0` release
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| Original file line number | Diff line number | Diff line change |
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| """NLL extention for BCEWithLogits Loss.""" | ||
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| from math import sqrt | ||
| from typing import List, Tuple | ||
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| from torch import Size, Tensor, sigmoid | ||
| from torch.distributions import Binomial | ||
| from torch.nn import BCEWithLogitsLoss | ||
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| from backpack.core.derivatives.nll_base import NLLLossDerivatives | ||
| from backpack.utils.subsampling import subsample | ||
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| class BCELossWithLogitsDerivatives(NLLLossDerivatives): | ||
| """Derivatives of the BCEWithLogits Loss.""" | ||
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| def __init__(self, use_autograd: bool = False): | ||
| """Initialization for BCEWithLogitsLoss derivative. | ||
| Args: | ||
| use_autograd: Compute gradients with autograd (rather than manual) | ||
| Defaults to ``False`` (manual computation). | ||
| """ | ||
| super().__init__(use_autograd=use_autograd) | ||
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| def _verify_support(self, module: BCEWithLogitsLoss): | ||
| """Verification of module support for BCEWithLogitsLoss. | ||
| Currently BCEWithLogitsLoss only supports binary target tensors, | ||
| 2D inputs, and default parameters. | ||
| Args: | ||
| module: BCEWithLogitsLoss module | ||
| """ | ||
| self._check_binary(module) | ||
| self._check_is_default(module) | ||
| self._check_input_dims(module) | ||
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| def _check_binary(self, module: BCEWithLogitsLoss): | ||
| """Raises exception if labels are not binary. | ||
| Args: | ||
| module: BCEWithLogitsLoss module | ||
| Raises: | ||
| NotImplementedError: if labels are non-binary. | ||
| """ | ||
| if any(x not in [0, 1] for x in module.input1.flatten()): | ||
| raise NotImplementedError( | ||
| "Only binary targets (0 and 1) are currently supported." | ||
| ) | ||
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| def _check_is_default(self, module: BCEWithLogitsLoss): | ||
| """Raises exception if module parameters are not default. | ||
| Args: | ||
| module: BCEWithLogitsLoss module | ||
| Raises: | ||
| NotImplementedError: if module parameters non-default. | ||
| """ | ||
| if module.weight is not None: | ||
| raise NotImplementedError("Only None weight is currently supported.") | ||
| if module.pos_weight is not None: | ||
| raise NotImplementedError("Only None pos_weight is currently supported.") | ||
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| def _check_input_dims(self, module: BCEWithLogitsLoss): | ||
| """Raises an exception if the shapes of the input are not supported. | ||
| Args: | ||
| module: BCEWithLogitsLoss module | ||
| Raises: | ||
| NotImplementedError: if input is not a batch of scalars. | ||
| """ | ||
| if module.input0.dim() != 2: | ||
| raise NotImplementedError("Only 2D inputs are currently supported.") | ||
| if module.input0.shape[1] != 1: | ||
| raise NotImplementedError( | ||
| "Only scalar-valued predictions are currently supported." | ||
| ) | ||
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| def _make_distribution(self, subsampled_input: Tensor) -> Binomial: | ||
| """Make the sampling distribution for the NLL loss form of BCEWithLogits. | ||
| The BCEWithLogitsLoss ∝ ∑ᵢ₌₁ⁿ Yᵢ log 𝜎(xᵢ) + (1 − Yᵢ) log(1− 𝜎(xᵢ)). | ||
| The log likelihood of the Binomial distribution is | ||
| Yᵢ log p(xᵢ) + (1 − Yᵢ) log(1 − p(xᵢ)), so these are equivalent if | ||
| p(xᵢ) = 𝜎(xᵢ). | ||
| Args: | ||
| subsampled_input: input after subsampling | ||
| Returns: | ||
| Binomial distribution with sigmoid probabilities from the subsampled_input. | ||
| """ | ||
| return Binomial(probs=subsampled_input.sigmoid()) | ||
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| def _compute_sampled_grads_manual( | ||
| self, subsampled_input: Tensor, mc_samples: int | ||
| ) -> Tensor: | ||
| """Manually compute gradients from sampled targets. | ||
| Let fₙ ∈ ℝ and yₙ ∈ {0, 1} ∼ p(y | fₙ) and σ(fₙ) the softmax probability. | ||
| Then the gradient is ∇ℓ(fₙ, yₙ) = σ(fₙ) - fₙ. | ||
| Args: | ||
| subsampled_input: input after subsampling | ||
| mc_samples: number of samples | ||
| Returns: | ||
| Gradient samples | ||
| """ | ||
| probs = subsampled_input.sigmoid() | ||
| expand_dims = [mc_samples] + probs.dim() * [-1] | ||
| probs_unsqeezed = probs.unsqueeze(0).expand(*expand_dims) # [V N 1] | ||
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| distribution = self._make_distribution(subsampled_input) | ||
| samples = distribution.sample(Size([mc_samples])) # [V N 1] | ||
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| return probs_unsqeezed - samples | ||
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| @staticmethod | ||
| def _get_mean_normalization(input: Tensor) -> int: | ||
| return input.shape[0] | ||
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| def _sqrt_hessian( | ||
| self, | ||
| module: BCEWithLogitsLoss, | ||
| g_inp: Tuple[Tensor], | ||
| g_out: Tuple[Tensor], | ||
| subsampling: List[int], | ||
| ) -> Tensor: # noqa: D102 | ||
| """Return a symmetric factorization of the loss Hessian. | ||
| # noqa: DAR101 | ||
| Let fₙ ∈ ℝ be the input and yₙ ∈ [0; 1] be the label, and σ(fₙ) ∈ (0; | ||
| 1) be the sigmoid probability. Then, the gradient ∇ℓ(fₙ, yₙ) w.r.t. fₙ | ||
| is ∇ℓ(fₙ, yₙ) = σ(fₙ) - yₙ, and the Hessian ∇²ℓ(fₙ, yₙ) w.r.t. fₙ is | ||
| ∇²ℓ(fₙ, yₙ) = σ'(fₙ) = σ(fₙ) (1 - σ(fₙ)). Consequently, the (scalar) | ||
| Hessian square root is √(σ(fₙ) (1 - σ(fₙ))). | ||
| Returns: | ||
| Hessian square root factorization of shape ``[1, N, 1]`` where ``N`` | ||
| corresponds to the (subsampled) batch size. | ||
| """ | ||
| self._check_is_default(module) | ||
| self._check_input_dims(module) | ||
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| input0 = subsample(module.input0, subsampling=subsampling) | ||
| sigma = sigmoid(input0).unsqueeze(0) | ||
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| sqrt_H = (sigma * (1 - sigma)).sqrt() | ||
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| if module.reduction == "mean": | ||
| sqrt_H /= sqrt(self._get_mean_normalization(module.input0)) | ||
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| return sqrt_H | ||
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| def hessian_is_psd(self) -> bool: | ||
| """Return whether the Hessian is PSD. | ||
| Let fₙ ∈ ℝ be the input and yₙ ∈ [0; 1] be the label, and σ(fₙ) ∈ (0; | ||
| 1) be the sigmoid probability. The Hessian ∇²ℓ(fₙ, yₙ) w.r.t. fₙ is | ||
| ∇²ℓ(fₙ, yₙ) = σ'(fₙ) = σ(fₙ) (1 - σ(fₙ)) > 0. Hence, the Hessian is PSD. | ||
| Returns: | ||
| True | ||
| """ | ||
| return True |
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