Stabilizing Backpropagation Through Time to Effectively Learn Complex Physics-Based Tasks

Core Concepts

Modifying the backpropagation step to create a more balanced vector field for optimization can significantly improve the learning of complex physics-based tasks compared to the regular gradient.

Abstract

The paper addresses the challenges of optimizing long unrolled sequences in training setups that combine neural networks and physics simulators. The key issue is the unbalanced gradient field resulting from repeatedly applying the same operator, leading to exploding and vanishing gradients.
The authors propose modifying the backpropagation step to create an alternative vector field for optimization. Specifically, they stop the feedback propagation through the neural network inputs while keeping the full temporal trajectory through the physics simulator. This results in a more balanced gradient flow, as physical systems typically have inherent constraints on the rate of change.
However, this modification also introduces rotation in the vector field, which can cause issues for optimization algorithms like Adam. To address this, the authors introduce a combined update that selectively uses the original gradient direction near minima while leveraging the balanced updates elsewhere.
The authors evaluate their method on three control tasks of increasing complexity: a guidance-by-repulsion model, a cart pole swing-up, and a quantum control problem. The results show that the proposed combined update consistently outperforms the regular gradient, especially as the tasks become more challenging. This demonstrates the benefits of the authors' approach in effectively learning complex physics-based behaviors.

Stats

The cart pole system has 1 to 4 poles.
The quantum control task has target states of 2, 3, and 4.

Quotes

"Of all the vector fields surrounding the minima of recurrent learning setups, the gradient field with its exploding and vanishing updates appears a poor choice for optimization, offering little beyond efficient computability."
"Backpropagating only along this path improves the situation of the gradient sizes as most physics simulators come with a well-behaved gradient flow; the key lies in separately considering the partial derivatives for x and c."
"Any modifications of the backpropagation pass decouple it from the corresponding forward pass and can destroy the rotation-free character of the gradient field, an unfamiliar situation in optimization."

Key Insights Distilled From

Stabilizing Backpropagation Through Time to Learn Complex Physics

by Patrick Schn... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2405.02041.pdf

Deeper Inquiries

How could the proposed method be extended to handle contact-rich scenarios, where the gradient flow of the physics simulator may not be as well-behaved

To extend the proposed method to handle contact-rich scenarios where the gradient flow of the physics simulator may not be as well-behaved, several adjustments can be considered. One approach could involve incorporating constraints or penalties in the optimization process to ensure that the simulator's dynamics are respected. This could involve introducing regularization terms that penalize unrealistic behaviors or enforcing physical constraints during training. Additionally, techniques such as adaptive learning rates or gradient clipping could be employed to stabilize the training process in the presence of discontinuities or non-smooth dynamics. Another strategy could involve incorporating domain-specific knowledge or heuristics to guide the optimization process in contact-rich scenarios, leveraging insights from physics or engineering principles to inform the learning process.

What other modifications to the backpropagation pass could be explored to create alternative vector fields for optimization, and how would they compare to the approach presented in this work

Several other modifications to the backpropagation pass could be explored to create alternative vector fields for optimization. One approach could involve introducing additional constraints or regularization terms to the backpropagation process to encourage the emergence of specific vector field properties. For example, incorporating constraints that enforce rotation-free or balanced gradient flows could help address the challenges associated with unbalanced updates in recurrent learning setups. Another approach could involve exploring different update rules or optimization algorithms that are specifically designed to handle the characteristics of the modified vector fields. Techniques such as adaptive momentum methods or second-order optimization algorithms could be investigated to improve convergence and stability in the presence of rotation or other non-ideal vector field properties. Additionally, exploring the use of meta-learning or reinforcement learning techniques to adaptively adjust the backpropagation process based on the characteristics of the vector field could offer further improvements in optimization performance.

Given the insights gained about the importance of the vector field structure in optimization, how could these principles be applied to improve the training of other types of neural network architectures beyond recurrent setups with physics simulators

The insights gained about the importance of the vector field structure in optimization can be applied to improve the training of other types of neural network architectures beyond recurrent setups with physics simulators. For example, in convolutional neural networks (CNNs), understanding the structure of the gradient field could lead to the development of more efficient optimization algorithms tailored to the specific characteristics of image data. By considering the spatial relationships in the data and the corresponding gradient flows, novel optimization techniques could be designed to enhance the training of CNNs for tasks such as image classification or object detection. Similarly, in graph neural networks (GNNs), insights about the vector field structure could inform the development of optimization methods that leverage the graph structure to improve learning and inference. By incorporating principles of vector field analysis into the optimization process, researchers can potentially unlock new avenues for enhancing the training of a wide range of neural network architectures across various domains and applications.