Meta-Learning Symmetries by Reparameterization (2007.02933v3)

Abstract: Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only works when practitioners know the symmetries of the task and can manually construct an architecture with the corresponding equivariances. Our goal is an approach for learning equivariances from data, without needing to design custom task-specific architectures. We present a method for learning and encoding equivariances into networks by learning corresponding parameter sharing patterns from data. Our method can provably represent equivariance-inducing parameter sharing for any finite group of symmetry transformations. Our experiments suggest that it can automatically learn to encode equivariances to common transformations used in image processing tasks. We provide our experiment code at https://github.com/AllanYangZhou/metalearning-symmetries.

• The paper introduces a novel reparameterization framework to automatically learn equivariances in neural networks.
• It demonstrates that encoding symmetry through parameter sharing improves model generalization and reduces architectural complexity.
• Theoretical validation and experiments confirm the method’s ability to recover convolutional architectures and learn robust invariances.

Overview of "Meta-learning Symmetries by Reparameterization"

The paper "Meta-learning Symmetries by Reparameterization" addresses the challenge of automatically learning equivariances in neural network architectures, aiming to optimize parameters and improve generalization without the necessity of designing custom task-specific architectures. The authors propose a novel approach to achieve this by embedding equivariance-inducing parameter sharing patterns directly into networks through a process of meta-learning.

Core Contributions

1. Equivariance Learning Framework: The paper introduces a method capable of representing equivariance-inducing parameter sharing for any finite symmetry group of transformations. This eliminates the need for manually constructing layers with built-in symmetries, such as conventional convolutional layers for translation.
2. Reparameterization Mechanism: The method utilizes reparameterization of network layers to represent sharing patterns, effectively encoding and learning symmetries from data. By doing so, practitioners are freed from designing specific architectures for each task and can transfer learned symmetries across tasks.
3. Theoretical Validation: The authors provide theoretical evidence that their approach can represent networks equivariant to any finite symmetry group. This is achieved through constructing symmetry matrices that transform filter parameters into shared weights that exhibit desired symmetries.
4. Experiments and Results: Empirical evaluations demonstrate that the approach can automatically recover convolutional architectures from data and learn invariances to transformations commonly utilized in image processing tasks. The meta-learned models showed improved performance on synthetic problems and few-shot classification benchmarks, particularly when augmented datasets introduced transformations such as rotations, reflections, and rescaling.

Numerical and Empirical Insights

In synthetic experiments, the proposed method outperformed conventional meta-learning techniques, such as MAML, by more effectively learning symmetries from data. Notably, MSR models learn rotation, reflection, and scaling equivariances from augmented data, exemplifying their capacity for encoding data-augmented invariances without requiring augmented datasets at meta-test time. By restructuring layer parameters with symmetry matrices, the method achieves competitive results with architectures specifically designed for certain transformations, demonstrating robustness across diverse task distributions.

Implications and Future Directions

The theoretical premise that all linear equivariant layers are generalized convolutions implies that leveraging group theory in neural network design can be immensely beneficial. Practically, this enables architectures to adapt to varied transformations, allowing for efficient model design and application across numerous domains, including robotics and simulation-to-real transfer.

Moving forward, further research could examine the computational efficiency of learned equivariances, striving for implementations that maximize inference speed while maintaining high performance. Extending the reparameterization to accommodate continuous symmetry groups or optimizing the complexity of symmetry matrices could widen the applicability of these methods. Additionally, exploring rapid discovery of task-specific symmetries could further enhance model adaptability in real-world scenarios.

In summary, "Meta-learning Symmetries by Reparameterization" presents a compelling strategy for automating the learning of architectural equivariances, setting the stage for more versatile and efficient deep learning models capable of exploiting inherent data symmetries.