Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
The Real Tropical Geometry of Neural Networks for Binary Classification
Authors: Marie-Charlotte Brandenburg, Georg Loho, Guido Montufar
TMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. In particular, the set of functions represented by a ReLU neural network can be regarded as a subset in the parameter space of tropical rational functions, specifically, it is contained as a semialgebraic set. We initiate the study of two different subdivisions of the parameter space of tropical rational functions... Our findings extend and refine the connection between neural networks and tropical geometry by observing structures established in real tropical geometry... This project has been supported by DFG grant 464109215 Combinatorial and implicit approaches to deep learning within the priority programme SPP 2298 Theoretical Foundations of Deep Learning. |
| Researcher Affiliation | Academia | Marie-Charlotte Brandenburg EMAIL KTH Royal Institute of Technology Georg Loho EMAIL University of Twente & Freie Universität Berlin Guido Montúfar EMAIL University of California, Los Angeles & Max Planck Institute Mi S |
| Pseudocode | No | The paper describes methods and concepts using mathematical definitions, theorems, and proofs. It does not include any sections or blocks explicitly labeled as 'Pseudocode' or 'Algorithm'. |
| Open Source Code | No | The paper mentions 'We computed the 12-dimensional fan Σ 2 D (2, 2) using the software Sage Math (Sage Developers, 2021)', which refers to a third-party software package, not original code released by the authors for their methodology. There is no explicit statement about releasing code or a link to a code repository for the work described in the paper. |
| Open Datasets | No | The paper primarily uses abstract data sets (e.g., 'Let D Rd be a finite set of data points') or small, manually defined point configurations for examples (e.g., 'Consider the data set D = {p1, p2, p3, p4} with p1 = (0, 0), p2 = (1, 1), p3 = (2, 2), p4 = (3, 3)...'). These are illustrative examples for theoretical concepts, and no publicly available datasets with access information (links, DOIs, formal citations) are provided or used for empirical evaluation. |
| Dataset Splits | No | The paper does not describe empirical experiments involving large datasets, therefore, no information regarding training, testing, or validation dataset splits is provided. |
| Hardware Specification | No | The paper focuses on theoretical mathematical concepts and does not present empirical experiments that would require specific hardware. Therefore, no hardware specifications (such as GPU models, CPU types, or cloud resources) are mentioned. |
| Software Dependencies | No | The paper mentions 'We computed the 12-dimensional fan Σ 2 D (2, 2) using the software Sage Math (Sage Developers, 2021)'. While Sage Math is a software, it is a general tool used for mathematical computation, and no specific versions of other libraries or dependencies used for their methodology are detailed beyond this single mention. The version of Sage Math is provided, but this is not sufficient to qualify for 'Yes' given the lack of other software components and versions for experimental replication. |
| Experiment Setup | No | The paper presents theoretical work, including definitions, theorems, and proofs, without conducting empirical experiments. Consequently, there are no details provided regarding experimental setup, hyperparameters, model initialization, or training schedules. |