Polynomial Implicit Neural Framework for Promoting Shape Awareness in Generative Models

Abstract

Polynomial functions have been employed to represent shape-related information in 2D and 3D computer vision, even from the very early days of the field. In this paper, we present a framework using polynomial-type basis functions to promote shape awareness in contemporary generative architectures. The benefits of using a learnable form of polynomial basis functions as drop-in modules into generative architectures are several—including promoting shape awareness, a noticeable disentanglement of shape from texture, and high quality generation. To enable the architectures to have a small number of parameters, we further use implicit neural representations (INR) as the base architecture. Most INR architectures rely on sinusoidal positional encoding, which accounts for high-frequency information in data. However, the finite encoding size restricts the model’s representational power. Higher representational power is critically needed to transition from representing a single given image to effectively representing large and diverse datasets. Our approach addresses this gap by representing an image with a polynomial function and eliminates the need for positional encodings. Therefore, to achieve a progressively higher degree of polynomial representation, we use element-wise multiplications between features and affine-transformed coordinate locations after every ReLU layer. The proposed method is evaluated qualitatively and quantitatively on large datasets such as ImageNet. The proposed Poly-INR model performs comparably to state-of-the-art generative models without any convolution, normalization, or self-attention layers, and with significantly fewer trainable parameters. With substantially fewer training parameters and higher representative power, our approach paves the way for broader adoption of INR models for generative modeling tasks in complex domains. The code is publicly available at https://github.com/Rajhans0/Poly_INR.