On the Expressive Power of Deep Polynomial Neural Networks
Authors: Joe Kileel, Matthew Trager, Joan Bruna
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also present computational evidence that it is profitable in terms of expressiveness for layer widths to increase monotonically and then decrease monotonically. ... We have written code2 in the mathematical software Sage Math [12] that computes the dimension of Vd,r for a general architecture d and activation degree r. Our approach is based on randomly selecting parameters = (Wh, . . . , W1) and computing the rank of the Jacobian of Φd,r( ) in (1). ... We present examples of some of our computations in Tables 1 and 2. |
| Researcher Affiliation | Academia | Joe Kileel Princeton University Matthew Trager New York University Joan Bruna New York University |
| Pseudocode | No | The paper describes the steps taken for computational investigation of dimensions but does not present them in pseudocode or an algorithm block format. |
| Open Source Code | Yes | We have written code2 in the mathematical software Sage Math [12]... Available at https://github.com/mtrager/polynomial_networks. |
| Open Datasets | No | The paper conducts computational investigations rather than empirical studies on publicly available datasets for training models. The data used for the computations are generated based on the theoretical framework, not external datasets. |
| Dataset Splits | No | The paper conducts computational investigations of theoretical properties, not empirical studies involving training, validation, and test splits on datasets. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for their computational investigations. |
| Software Dependencies | No | The paper mentions 'Sage Math [12]' but does not provide a specific version number or list other software dependencies with versions. |
| Experiment Setup | No | The paper describes the general approach for its computational investigations (e.g., 'randomly selecting parameters', 'leveraging backpropagation', 'finite field F = Z/p Z'), but it does not specify concrete hyperparameters, training configurations, or system-level settings typically found in experimental setups for machine learning models. |