Learned Initializations for Optimizing Coordinate-Based Neural Representations (2012.02189v2)

Abstract: Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

• The paper introduces meta-learning strategies that dramatically reduce the gradient descent steps needed to optimize neural representations.
• It employs frameworks like MAML and Reptile to outperform random initializations in diverse tasks such as 2D image regression and 3D scene reconstruction.
• Learned initializations act as robust priors, improving convergence speed and generalization especially when handling incomplete data.

Learned Initializations for Optimizing Coordinate-Based Neural Representations

The paper "Learned Initializations for Optimizing Coordinate-Based Neural Representations" explores the effectiveness of using meta-learning to improve the initial weight settings of fully-connected neural networks, known as coordinate-based neural representations. This research is partly motivated by the inefficiencies associated with optimizing such networks from random initializations for each new signal, a common scenario when dealing with low-dimensional signals like 2D images or 3D scenes. The authors propose that leveraging standard meta-learning algorithms can significantly enhance the convergence speed of these neural networks and also serve as a robust prior for signal representation, improving the network's generalization capabilities in scenarios with incomplete data.

Key Concepts

Coordinate-based neural representations (often implemented as multilayer perceptrons or MLPs) offer continuous signal representations and avoid fixed spatial resolution constraints typical of discrete representations. Despite their potential, these neural representations usually demand solving intensive optimization problems to derive network parameters that accurately encode a specific signal, posing a computational burden. The paper investigates the potential benefits of using meta-learning techniques, specifically Model-Agnostic Meta-Learning (MAML) and Reptile, to determine optimal initialization weights for these networks. These learned initial weights are expected to improve convergence efficiency and act as a strong prior for representing an entire signal class.

Methodology

The research utilizes well-established meta-learning frameworks like MAML and Reptile. MAML aims to derive an initialization that minimizes the number of gradient descent steps needed to optimize new signal representations at test time. Reptile offers a more computationally light alternative by using an update rule that foregoes second-order gradient calculations. The experimental setup consists of a meta-learning phase to determine optimal initial weights and a test-time optimization phase applied to a new signal using standard gradient-based optimization.

The empirical analysis encompasses several tasks: 2D image regression, CT reconstruction, 3D object and scene reconstruction, and view synthesis for landmark scenes. Each of these tasks showcases the advantages of a learned initialization across different signal types and sizes both in terms of speed and quality of convergence.

Results and Discussion

The findings indicate substantial improvements in convergence speed and signal representation quality with learned initializations compared to traditional methods. For instance, in 2D image regression, the meta-learned weights enabled an MLP to converge significantly faster, achieving high-fidelity image representations in about one-tenth of the typical number of optimization steps. The research illustrates competitive performance in reconstructing 3D objects from single or sparse views, crucial for applications such as CT scans or neRF-based view synthesis.

The benefit of learned initial weights is also prominent in scenarios with partial signal observations. These weights help in extracting more information from limited data, acting as a class-specific prior and enhancing generalization capabilities across unseen signals from the same class. This behavior is notably beneficial when optimizing neural representations under data-constrained environments.

Implications and Future Work

The research opens discussions about the uses of meta-learned initializations in various fields, potentially reducing the computational expense and incrementally improving signal reconstructive capabilities. Future developments could investigate more sophisticated meta-learning frameworks, aim to diminish the quantity of data required for effective meta-learning, and explore other domains where coordinate-based neural representations could be beneficial. Furthermore, understanding the precise geometry and dynamics within weight space that these learned initializations harness could yield insights into developing more efficient neural representations across diverse applications.

Overall, the research presents a linchpin for future efforts in refining the process of neural representation learning, highlighting the importance of initialization strategies in optimizing gradient-based methodologies across complex signal classes.