Eric Dolores-Cuenca

Susana Lopez-Moreno, Eric Dolores-Cuenca, Sangil Kim

Reproducibility remains a challenge in machine learning research. While code and data availability requirements have become increasingly common, post-publication verification in journals is still limited and unformalized. This position paper argues that it is plausible for journals and conference proceedings to implement post-publication verification. We propose a modification to ACM pre-publication verification badges that allows independent researchers to submit post-publication code replications to the journal, leading to visible verification badges included in the article metadata. Each article may earn up to two badges, each linked to verified code in its corresponding public repository. We describe the motivation, related initiatives, a formal framework, the potential impact, possible limitations, and alternative views.

Eric Dolores-Cuenca, Aldo Guzman-Saenz, Sangil Kim et al.

The paper ``Tropical Geometry of Deep Neural Networks'' by L. Zhang et al. introduces an equivalence between integer-valued neural networks (IVNN) with $\text{ReLU}_{t}$ and tropical rational functions, which come with a map to polytopes. Here, IVNN refers to a network with integer weights but real biases, and $\text{ReLU}_{t}$ is defined as $\text{ReLU}_{t}(x)=\max(x,t)$ for $t\in\mathbb{R}\cup\{-\infty\}$. For every poset with $n$ points, there exists a corresponding order polytope, i.e., a convex polytope in the unit cube $[0,1]^n$ whose coordinates obey the inequalities of the poset. We study neural networks whose associated polytope is an order polytope. We then explain how posets with four points induce neural networks that can be interpreted as $2\times 2$ convolutional filters. These poset filters can be added to any neural network, not only IVNN. Similarly to maxout, poset pooling filters update the weights of the neural network during backpropagation with more precision than average pooling, max pooling, or mixed pooling, without the need to train extra parameters. We report experiments that support our statements. We also define the structure of algebra over the operad of posets on poset neural networks and tropical polynomials. This formalism allows us to study the composition of poset neural network arquitectures and the effect on their corresponding Newton polytopes, via the introduction of the generalization of two operations on polytopes: the Minkowski sum and the convex envelope.