Backpropagation through combinatorial algorithms: identity with projection works
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| Year of publication | 2023 |
| Type | Appeared in Conference without Proceedings |
| MU Faculty or unit | |
| Citation | |
| Description | The result is a paper (27 pages) at the International Conference on Learning Representations. Although this is one of the very best conferences in CS, the proceedings do not have an ISBN or ISSN, so the result cannot be added to the RIV database as a type D result. The original abstract is as follows: Embedding discrete solvers as differentiable layers has given modern deep learning architectures combinatorial expressivity and discrete reasoning capabilities. The derivative of these solvers is zero or undefined, therefore a meaningful replacement is crucial for effective gradient-based learning. Prior works rely on smoothing the solver with input perturbations, relaxing the solver to continuous problems, or interpolating the loss landscape with techniques that typically require additional solver calls, introduce extra hyper-parameters, or compromise performance. We propose a principled approach to exploit the geometry of the discrete solution space to treat the solver as a negative identity on the backward pass and further provide a theoretical justification. Our experiments demonstrate that such a straightforward hyper-parameter-free approach is able to compete with previous more complex methods on numerous experiments such as backpropagation through discrete samplers, deep graph matching, and image retrieval. Furthermore, we substitute the previously proposed problem-specific and label-dependent margin with a generic regularization procedure that prevents cost collapse and increases robustness. |
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