Foundations

Masked Log Softmax

EasyRaw PyTorchAbout 10 min1 public example plus private tests

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Your task

Return the natural logarithm of each included score’s softmax probability along dim. Each valid entry is its score minus the log of the included exponential sum; excluded entries use the finite sentinel.

Function signature

masked_log_softmax(
    logits: torch.Tensor,
    mask: torch.Tensor,
    dim: int = -1,
    sentinel: float = 0.0,
) -> torch.Tensor

Worked example

Unequal included scores

Take logits=[0,1,100], mask=[True,True,False] and dim=0. Only exponential weights 1 and e participate; the masked score 100 is excluded even from the denominator. With sentinel=-9, the log probabilities are [-log(1+e), 1-log(1+e), -9] ≈ [-1.313262, -0.313262, -9]. Exponentiating just the two valid entries gives probabilities that add to one.

Parameters

Parameter	Shape and meaning
`logits`torch.Tensor	$[d_0,\ldots,d_{R-1}]$ Finite scores to normalize along dim.
`mask`torch.Tensor	Any shape broadcastable to logits.shape.True includes an entry in both the probability mass and normalizer.
`dim`intDefault `-1`	One integer normalization axis; negative indices count from the end. The output retains this axis and has the same shape as logits.
`sentinel`floatDefault `0.0`	Finite reporting value for excluded log-probability entries, including every entry of an entirely masked slice along dim; it is not log(0).

Return

torch.Tensor · Exactly logits.shape.

A tensor with exactly logits.shape. Each slice along dim contains log probabilities at included entries and sentinel at excluded entries; an entirely masked slice is filled with sentinel.

Required behavior

logits has rank at least one; mask is Boolean and must broadcast to exactly logits.shape. True includes a score. dim is one integer axis (default -1); negative axes count from the end. A slice fixes every index except dim.
For a nonempty included set V, let a be its largest score and Z = sum(exp(logits[i]-a) for i in V). Subtract this included maximum before exponentiating; masked scores contribute neither exponential weight nor normalizer.
Return logits[i]-a-log(Z) at included entries. Fill excluded entries, including all-masked slices, with sentinel (default 0). A zero-length normalization axis returns an empty tensor with logits.shape. The sentinel is a reporting value, not log(0).
Use no epsilon, probability clipping or probability floor. Empty-support outputs have zero gradients. Preserve the shared CPU float32/float64 dtype and device, accept noncontiguous inputs, and do not mutate inputs.
Use raw tensor operations, not a ready-made implementation of the requested primitive. Supplied parameters and random variates must not be reinitialized.

Why this matters

Subtracting a valid maximum controls exponent size; an explicit empty-row branch prevents an all-masked input from becoming NaN or a uniform distribution.

Starter code

You write the body of this function in the BioTorch workspace. Your code runs in an isolated PyTorch sandbox; Run checks the public examples and Submit grades the full test suite, including gradients.

import torch


def masked_log_softmax(
    logits: torch.Tensor,  # (d_0,...,d_{R-1})
    mask: torch.Tensor,  # Any shape broadcastable to logits.shape.
    dim: int = -1,
    sentinel: float = 0.0,
) -> torch.Tensor:
    """Return a tensor with shape logits.shape."""
    # Implement the operation. Inputs and test setup are supplied by BioTorch.
    raise NotImplementedError("Implement masked_log_softmax")

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3 progressive hints, a solution walkthrough, and grading that checks values, shapes and gradients are waiting in the workspace.

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Sources and further reading

A primitive exercise, not an end-to-end reproduction of the named models. No affiliation or endorsement is implied.