[Cassian433]

Checklist before merging this PR:

• Mentioned all issues that this PR fixes or addresses.
• Summarized the updates of this PR under Summary.
• Added an entry under Unreleased in the Changelog.

Fixes #2743.

Summary

io_processor runs RINorm.inverse on the raw likelihood outputs, before the likelihood applies its softplus. For the location-scale likelihoods that turns the scale channel into raw * std + mean, so the predicted sigma tracks the level of the series instead of its spread. With DLinearModel + GaussianLikelihood + RIN, predict_likelihood_parameters gives sigma 0.62 on the base series, 999.85 when the input is shifted by 1000, and 0.0 when it is multiplied by 100.

This is option 2 from my comment on the issue: undo RIN on the distribution parameters instead of on the raw outputs.

• TorchLikelihood._rin_parameters names what each output channel is. Gaussian, Laplace, Cauchy and Gumbel are ("loc", "scale"), QuantileRegression is all "loc", everything else is None.
• "loc" channels keep the existing full inverse. "scale" channels go through the new RINorm.inverse_scale: softplus, times std (divided by |affine_weight + eps**2| when affine), clamped, then the inverse softplus, so the likelihood's own softplus lands on the right value. No shift, since a scale has no affine bias or mean.
• QuantileRegression and models without a likelihood take the same path as before.
• With use_reversible_instance_norm=True, any other likelihood (Poisson, Beta, NegativeBinomial, ...) now raises a ValueError at model creation. Poisson is in that list even though you thought it might be fine: its rate comes out as softplus(raw * std + mean), which only holds up while the series stays well above 0. I can let the mean-only likelihoods through if you'd rather. Models saved before this change with one of them still load and predict as before.

Same setup after the change: sigma 0.580 on the base series, 0.580 shifted by 1000, 57.955 multiplied by 100.

Models already trained with RIN and one of the four location-scale likelihoods still load, but the scale they predict changes (a saved DLinear + Gaussian model went from sigma 4.93 to 0.62 with the same weights), so they need retraining. That's why the changelog entry is marked as breaking.

Other Information

#3175 (RIN for covariates) rewrites io_processor too, and its _rin_denormalize_output still inverts the raw likelihood output, so it has the same scale problem. If it lands first I'll move the per-channel split into that function.

If you'd rather have option 1 (raise for every likelihood except QuantileRegression), the model-creation check is already here and I can cut the PR down to it.

Tests: 32 new cases in test_layer_norm_variants.py and test_torch_forecasting_model.py.

• inverse_scale at extreme scales, float32 and float64, with and without affine, gradients finite
• shift/scale equivariance of the predicted parameters for the four likelihoods and QuantileRegression
• the raw-output inverse per likelihood with no affine and with affine weights 2.5 and -0.5, including Poisson, which keeps the old full inverse (that's the path a model saved before this change takes after load())
• the ValueError for an unsupported likelihood

22 of them fail on master. The 10 that pass there are the QuantileRegression, no-likelihood and Poisson cases, which shouldn't change. A DLinear + Poisson + RIN model saved on master loads and predicts the same values on this branch. test_layer_norm_variants.py, test_torch_forecasting_model.py and darts/tests/utils/test_likelihood_models/: 443 passed. ruff 0.7.2 (the pre-commit pin) check and format are clean.