question about _likelihood

[Hanawh]

I am a beginner in image compression. I don’t understand why lower, upper and sign are calculated for this step.

[jbegaint]

Upper and lower are the estimated CDF bounds for the current input, from there the densities can be derived.

You can find more information in Ballé et al. papers: End-to-end Optimized Image Compression, Variational image compression with a scale hyperprior

The sign is used for floating point optimization, this had been directly ported from the tensorflow/compression project, you can find some explanations in the comments.

[Hanawh]

Thanks for your reply!

[Freed-Wu]

    @torch.jit.unused
    def _likelihood(self, inputs: Tensor) -> Tensor:
        half = float(0.5)
        v0 = inputs - half
        v1 = inputs + half
        lower = self._logits_cumulative(v0, stop_gradient=False)
        upper = self._logits_cumulative(v1, stop_gradient=False)
        sign = -torch.sign(lower + upper)
        sign = sign.detach()
        likelihood = torch.abs(
            torch.sigmoid(sign * upper) - torch.sigmoid(sign * lower)
        )
        return likelihood

Why not

    @torch.jit.unused
    def _likelihood(self, inputs: Tensor) -> Tensor:
        half = float(0.5)
        v0 = inputs - half
        v1 = inputs + half
        lower = self._logits_cumulative(v0, stop_gradient=False)
        upper = self._logits_cumulative(v1, stop_gradient=False)
        likelihood = torch.sigmoid(upper) - torch.sigmoid(lower)
        return likelihood

I debug found

> ll = torch.sigmoid(upper) - torch.sigmoid(lower)
> likelihood.isclose(ll).all()
True
> (likelihood == ll).all()
False

Why?!