Torchjd

Added

- PyTorch Lightning integration example.
- Explanation about Jacobian descent in the README.

Fixed

- Made the dependency on [ecos](https://github.com/embotech/ecos-python) explicit in pyproject.toml
(before `cvxpy` 1.16.0, it was installed automatically when installing `cvxpy`).

Changed

- Removed upper cap on `numpy` version in the dependencies. This makes `torchjd` compatible with
the most recent numpy versions too.

Fixed

- Prevented `IMTLG` from dividing by zero during its weight rescaling step. If the input matrix
consists only of zeros, it will now return a vector of zeros instead of a vector of `nan`.

Added

- `autojac` package containing the backward pass functions and their dependencies.
- `mtl_backward` function to make a backward pass for multi-task learning.
- Multi-task learning example.

Changed

- **BREAKING**: Moved the `backward` module to the `autojac` package. Some imports may have to be
adapted.
- Improved documentation of `backward`.

Fixed

- Fixed wrong tensor device with `IMTLG` in some rare cases.
- **BREAKING**: Removed the possibility of populating the `.grad` field of a tensor that does not
expect it when calling `backward`. If an input `t` provided to backward does not satisfy
`t.requires_grad and (t.is_leaf or t.retains_grad)`, an error is now raised.
- **BREAKING**: When using `backward`, aggregations are now accumulated into the `.grad` fields
of the inputs rather than replacing those fields if they already existed. This is in line with the
behavior of `torch.autograd.backward`.

Added

- Basic project structure.
- `aggregation` package:
- `Aggregator` base class to aggregate Jacobian matrices.
- `AlignedMTL` from [Independent Component
Alignment for Multi-Task Learning](
https://openaccess.thecvf.com/content/CVPR2023/papers/Senushkin_Independent_Component_Alignment_for_Multi-Task_Learning_CVPR_2023_paper.pdf>).
- `CAGrad` from [Conflict-Averse Gradient Descent for Multi-task
Learning](https://arxiv.org/pdf/2110.14048.pdf).
- `Constant` to aggregate with constant weights.
- `DualProj` adapted from [Gradient Episodic
Memory for Continual Learning](https://proceedings.neurips.cc/paper/2017/file/f87522788a2be2d171666752f97ddebb-Paper.pdf).
- `GradDrop` from [Just Pick a Sign: Optimizing Deep
Multitask Models with Gradient Sign Dropout](https://arxiv.org/pdf/2010.06808.pdf).
- `IMTLG` from [Towards Impartial Multi-task Learning](https://discovery.ucl.ac.uk/id/eprint/10120667/).
- `Krum` from [Machine Learning with Adversaries: Byzantine
Tolerant Gradient Descent](https://proceedings.neurips.cc/paper/2017/file/f4b9ec30ad9f68f89b29639786cb62ef-Paper.pdf).
- `Mean` to average the rows of the matrix.
- `MGDA` from [Multiple-gradient descent algorithm (MGDA) for multiobjective optimization](https://www.sciencedirect.com/science/article/pii/S1631073X12000738/pdf?md5=2622857e4abde98b6f7ddc8a13a337e1&pid=1-s2.0-S1631073X12000738-main.pdf>).
- `NashMTL` from [Multi-Task Learning as a Bargaining Game](https://arxiv.org/pdf/2202.01017.pdf).
- `PCGrad` from [Gradient Surgery for Multi-Task Learning](https://arxiv.org/pdf/2001.06782.pdf).
- `Random` from [Reasonable Effectiveness of Random Weighting: A
Litmus Test for Multi-Task Learning](https://arxiv.org/pdf/2111.10603.pdf).
- `Sum` to sum the rows of the matrix.
- `TrimmedMean` from [Byzantine-Robust Distributed Learning: Towards
Optimal Statistical Rates](https://proceedings.mlr.press/v80/yin18a/yin18a.pdf).
- `UPGrad` from [Jacobian Descent for Multi-Objective Optimization](https://arxiv.org/pdf/2406.16232).
- `backward` function to perform a step of Jacobian descent.
- Documentation of the public API and of some usage examples.
- Tests:
- Unit tests.
- Documentation tests.
- Plotting utilities to verify qualitatively that aggregators work as expected.