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        "author": "Floris Laporte",
        "author_email": "floris.laporte@gmail.com",
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        "description": "# torch_eunn\n\nThis repository contains a simple PyTorch implementation of a Tunable Efficient\nUnitary Neural Network (EUNN) Cell.\n\nThe implementation is loosely based on the tunable EUNN presented in this\npaper: [https://arxiv.org/abs/1612.05231](https://arxiv.org/abs/1612.05231).\n\n\n## Installation\n\n```\n    pip install torch_eunn\n```\n\n\n## Usage\n\n```python\n    from torch_eunn import EUNN # feed forward layer\n    from torch_eunn import EURNN # recurrent unit\n```\n\n#### Note\nThe `hidden_size` ***and*** the `capacity` of the EUNN need to be ***even***, as explained in the section *\"Difference with original implementation\"*.\n\n## Examples\n\n* 00: [Simple Tests](examples/00_simple_tests.ipynb)\n* 01: [Copying Task](examples/01_copying_task.ipynb)\n* 02: [MNIST Task](examples/02_mnist.ipynb)\n\n\n## Requirements\n\n* [PyTorch](http://pytorch.org) >= 0.4.0: `conda install pytorch -c pytorch`\n\n\n## Difference with original implementation\n\n\nThis implementation of the EUNN has a major difference with the original\nimplementation proposed in\n[https://arxiv.org/abs/1612.05231](https://arxiv.org/abs/1612.05231), which is\noutlined below.\n\nIn the original implementation, the first output of the top directional coupler\nof a capacity-2 sublayer skips the second layer of directional couplers\n(indicated with dots in the ascii figure below) to connect to the next\ncapacity-2 sublayer of the EUNN. The reverse happens at the bottom, where the\nfirst layer of the capacity-2 sublayer is skipped. This way, a\n`(2*n+1)`-dimensional unitary matrix representation is created, with `n` the\nnumber of mixing units in each capacity-1 sublayer.\n```\n  __  __......\n    \\/\n  __/\\____  __\n          \\/\n  __  ____/\\__\n    \\/\n  __/\\____  __\n          \\/\n  ......__/\\__\n```\nFor each capacity-1 sublayer with `N=2*n+1` inputs (`N` odd), we thus have `N-1`\nparameters (each mixing unit has 2 parameters). Thus to have a unitary matrix\nrepresentation that spans the full unitary space, one needs `N` capacity-1\nlayers ***and*** `N` *extra* phases appended to the back of the capacity-`N`\nsublayer to bring the total number of parameters in the unitary-matrix\nrepresentation to `N**2` (the total number of independent parameters in a\nunitary matrix).\n\nIn the implementation proposed here, the dots in each capacity-2 sublayer are\nconnected onto themselves (periodic boundaries). This has the implication that\nfor each capacity-1 sublayer with `n` directional couplers, there are `N=2*n`\ninputs and as many independent parameters. This means that we just need `N`\ncapacity-1 sublayers and **no** *extra* phases to span the full unitary space\nwith `N**2` parameters.\n\nThis, however, has the implication that the `hidden_size = N = 2*n` of the\nunitary matrix should always be *even*. Also, because the forward pass is\ndefined per capacity-**2** sublayer (as opposed per capacity-1 sublayer in the\noriginal implementation) the capacity has to be *even* as well.\n\n\n## License\n\n\u00a9 Floris Laporte, 2018-2019.\n\nMade available under the MIT license.\n\n\n",
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