Position: Algebra Unveils Deep Learning - An Invitation to Neuroalgebraic Geometry
Authors: Giovanni Luca Marchetti, Vahid Shahverdi, Stefano Mereta, Matthew Trager, Kathlén Kohn
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations, whose associated function spaces are semialgebraic varieties. We outline a dictionary between algebro-geometric invariants of these varieties, such as dimension, degree, and singularities, and fundamental aspects of machine learning, such as sample complexity, expressivity, training dynamics, and implicit bias. Along the way, we review the literature and discuss ideas beyond the algebraic domain. This work lays the foundations of a research direction bridging algebraic geometry and deep learning, that we refer to as neuroalgebraic geometry. |
| Researcher Affiliation | Collaboration | 1Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden 2AWS AI Labs, New York, USA (Work done outside Amazon). |
| Pseudocode | No | The paper does not contain any sections explicitly labeled as "Pseudocode" or "Algorithm", nor does it present any structured, code-like blocks describing a procedure. It primarily focuses on theoretical discussions and frameworks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories. As a position paper, its focus is theoretical discussion rather than implementation. |
| Open Datasets | No | The paper is a position paper outlining a theoretical framework and does not present experimental results based on specific datasets. While it discusses general concepts like 'dataset D' in theoretical contexts, it does not provide access information for any particular dataset. |
| Dataset Splits | No | The paper does not describe experiments using specific datasets and therefore does not provide any information about training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not mention any specific hardware used for computations or experiments. This is consistent with its nature as a theoretical position paper. |
| Software Dependencies | No | The paper does not specify any software tools, libraries, or programming languages with version numbers. This is expected for a theoretical position paper that does not present computational experiments. |
| Experiment Setup | No | The paper does not provide details about an experimental setup, such as hyperparameter values, training configurations, or system-level settings. This is consistent with the paper being a theoretical position paper rather than an empirical study. |