Learning Signal-Agnostic Manifolds of Neural Fields

Abstract: Deep neural networks have been used widely to learn the latent structure of datasets, across modalities such as images, shapes, and audio signals. However, existing models are generally modality-dependent, requiring custom architectures and objectives to process different classes of signals. We leverage neural fields to capture the underlying structure in image, shape, audio and cross-modal audiovisual domains in a modality-independent manner. We cast our task as one of learning a manifold, where we aim to infer a low-dimensional, locally linear subspace in which our data resides. By enforcing coverage of the manifold, local linearity, and local isometry, our model -- dubbed GEM -- learns to capture the underlying structure of datasets across modalities. We can then travel along linear regions of our manifold to obtain perceptually consistent interpolations between samples, and can further use GEM to recover points on our manifold and glean not only diverse completions of input images, but cross-modal hallucinations of audio or image signals. Finally, we show that by walking across the underlying manifold of GEM, we may generate new samples in our signal domains. Code and additional results are available at https://yilundu.github.io/gem/.

• The paper introduces GEM, which learns a low-dimensional, locally linear manifold of neural fields for signal-agnostic reconstruction.
• It enforces data coverage, local linearity, and local isometry, achieving lower MSE and higher PSNR than competing models.
• The approach supports cross-modal tasks such as generating auditory outputs from images, paving the way for versatile and responsible AI applications.

Overview of "Learning Signal-Agnostic Manifolds of Neural Fields"

The paper "Learning Signal-Agnostic Manifolds of Neural Fields" by Yilun Du et al. proposes a novel approach for learning the latent structures of datasets across various modalities such as images, shapes, and audio without relying on modality-specific architectures. The paper introduces a model named GEM, which leverages the concept of neural fields to capture the underlying manifold of data in a modality-agnostic manner.

Core Contributions and Methodology

The researchers cast the task as one of learning a manifold and propose the use of neural fields—continuous functions parameterized by neural networks—to model signals across different domains. The central idea is to infer a low-dimensional, locally linear subspace where the data resides. The model focuses on ensuring three key properties of manifolds: data coverage, local linearity, and local isometry.

1. Data Coverage: Achieved through an auto-decoding framework, where individual latents are learned for each training signal, ensuring the manifold encompasses all data instances.
2. Local Linearity: The manifold is structured into local convex linear regions, allowing for coherent interpolation between nearby latent codes.
3. Local Isometry: Ensures perceptual consistency, maintaining that similar signals map to proximate points on the manifold.

The model employs hypernetworks to regress individual neural fields from the latent space, allowing it to represent various signal types without altering the architecture.

Results and Implications

GEM demonstrates impressive capabilities in several tasks, including interpolation between samples, completion of partial inputs, and generation of new samples in diverse modalities. The model successfully reconstructs test signals across images, audio, 3D shapes, and multi-modal audio-visual setups with higher accuracy than competing methods such as VAEs and GANS.

Quantitative Performance: The model achieves lower mean squared error (MSE) and higher peak signal-to-noise ratio (PSNR) in test reconstructions, indicating better data coverage and reconstruction fidelity.

Qualitative Insights: GEM shows robustness in generating perceptually smooth interpolations and completing missing segments of signals with diversity and consistency.

The paper also explores the potential of cross-modal applications, where the model can generate auditory outputs from visual inputs and vice versa, showcasing a flexible application across domains without needing specialized processing frameworks.

Future Directions

This research opens several avenues for future exploration. It highlights the possibility of further refining neural field parameterizations and incorporating additional constraints to enhance fidelity in capturing complex signal manifolds. Additionally, the implications for cross-modal generative modeling are vast, facilitating enhanced synthesis of coherent multi-sensory data.

The work illustrates potential risks inherent to synthetic media generation, such as the creation of "deep fakes," thus emphasizing the need for responsible deployment practices. Future research could focus on ethical frameworks and control mechanisms in generative modeling, ensuring that these advancements benefit societal needs without exacerbating challenges related to misinformation or bias.

Overall, the paper makes a substantial contribution to the field of manifold learning and generative modeling; it offers a pathway towards signal-agnostic solutions with broad applicability across various domains of machine learning and artificial intelligence.