Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete

Authors: Daniel Bertschinger, Christoph Hertrich, Paul Jungeblut, Tillmann Miltzow, Simon Weber

NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We show that the problem is R-complete. This complexity class can be defined as the set of algorithmic problems that are polynomial-time equivalent to finding real roots of a multivariate polynomial with integer coefficients.
Researcher Affiliation Academia Daniel Bertschinger Department of Computer Science ETH Zurich Zurich, Switzerland daniel.bertschinger@inf.ethz.ch; Christoph Hertrich Department of Mathematics London School of Economics and Political Science London, United Kingdom c.hertrich@lse.ac.uk; Paul Jungeblut Institute of Theoretical Informatics Karlsruhe Institute of Technology Karlsruhe, Germany paul.jungeblut@kit.edu; Tillmann Miltzow Department of Information and Computing Sciences Utrecht University Utrecht, The Netherlands t.miltzow@uu.nl; Simon Weber Department of Computer Science ETH Zurich Zurich, Switzerland simon.weber@inf.ethz.ch
Pseudocode No The paper provides high-level descriptions of its proof strategy and 'gadgets' in Section 6 'Proof Ideas' but does not include formal pseudocode or algorithm blocks.
Open Source Code No The paper is theoretical and does not describe software implementations or release source code.
Open Datasets No The paper is theoretical and does not conduct experiments with actual datasets. It refers to 'data points' in the context of defining the theoretical problem TRAIN-F2NN, but does not use or provide a public dataset for empirical training.
Dataset Splits No The paper is theoretical and does not involve empirical data splits (training, validation, test sets).
Hardware Specification No The paper is theoretical and does not describe any empirical experiments or the hardware used to conduct them.
Software Dependencies No The paper is theoretical and does not describe any software implementations or their dependencies.
Experiment Setup No The paper is theoretical and does not describe empirical experiments, therefore no experimental setup details like hyperparameters or training configurations are provided.