Generative Models as Distributions of Functions (2102.04776v4)

Abstract: Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead parameterize individual data points by continuous functions. We then build generative models by learning distributions over such functions. By treating data points as functions, we can abstract away from the specific type of data we train on and construct models that are agnostic to discretization. To train our model, we use an adversarial approach with a discriminator that acts on continuous signals. Through experiments on a wide variety of data modalities including images, 3D shapes and climate data, we demonstrate that our model can learn rich distributions of functions independently of data type and resolution.

• The paper introduces a novel generative model that represents data as continuous functions via implicit neural representations and hypernetworks.
• It employs an adversarial training framework with discriminators operating on continuous signals to bypass grid-based resolution limits.
• Experimental results show robust super-resolution in images, 3D shapes, and climate data, highlighting the model's broad applicability.

Analyzing "Generative Models as Distributions of Functions"

The paper "Generative Models as Distributions of Functions" by Dupont et al. presents a novel methodology in the field of generative modeling by transitioning from traditional grid-based data representation to viewing data as continuous functions. This methodological shift allows for the construction of generative models that are independent of signal resolution and discretization.

Core Contributions

The authors propose using implicit neural representations, where data is parameterized as a neural network that learns a mapping from continuous coordinate space to feature space. This approach abstracts away the dependencies associated with data discretization prevalent in conventional generative models. By employing hypernetworks for parameterizing the weights of these neural networks, the researchers develop generative models that function as distributions over these weights.

To train these models, Dupont et al. employ an adversarial training approach, specifically citing the Generative Adversarial Network (GAN) framework. A key feature lies in using discriminators that operate on continuous signals, diverging from standard convolutional networks tied to resolution constraints.

Technical Approach

The paper extensively explores how implicit neural representations operate. For example, in image generation, a two-dimensional input space is transformed into an RGB feature space using multi-layer perceptrons (MLPs). Furthermore, the research explores modeling high-frequency functions by incorporating random Fourier feature encodings, which mitigate the low-frequency bias typically observed in coordinate-based mappings.

Additionally, the authors introduce a novel point cloud-based discriminator design leveraging the PointConv framework. This method takes advantage of the metric properties inherent in coordinate spaces, overcoming the limitations of set-based discriminators which fail to adequately capture complex distributions in high-dimensional data scenarios.

Experimental Validation

Experimental results demonstrate the robustness of this model across a diverse set of datasets comprising images, 3D shapes, and even climate data on spherical manifolds. Critically, the model is shown to generate coherent and high-resolution images from lower-resolution training data, reflecting its ability to generalize beyond trained discretization. Similarly, when applied to 3D shapes, the continuous nature of the representation allows for seamless super-resolution.

Critical Analysis and Implications

The paper presents an interesting convergence of neural implicit representation and adversarial training for generative modeling. By abstracting away from grids, the method allows training models that possess greater flexibility and can operate in a higher dimensional feature space without resolution-specific constraints. This is particularly advantageous in domains like 3D modeling and geographical data, where high-resolution grid sampling is computationally expensive or impractical.

However, the paper admits to the wider performance gap when comparing against state-of-the-art convolutional GANs specialized in 2D image generation, suggesting that integration with more sophisticated GAN training strategies might enhance performance. Moreover, while promoting broad applicability, the paper indicates potential instability in training, particularly linked to irregular sampling, thereby encouraging future exploration toward refined methods of training stability.

Conclusion and Prospects

This paper contributes significantly to the field by presenting a model structure that could lead the way to more flexible and scalable generative models. Future work may deepen the integration of such continuous methods with other advanced AI components to achieve parity in performance with specialized discrete models. As such, this line of research holds promise for gaining deeper insights into building and utilizing generative function models across diverse and complex data modalities.