Highway and Residual Networks learn Unrolled Iterative Estimation (1612.07771v3)

Abstract: The past year saw the introduction of new architectures such as Highway networks and Residual networks which, for the first time, enabled the training of feedforward networks with dozens to hundreds of layers using simple gradient descent. While depth of representation has been posited as a primary reason for their success, there are indications that these architectures defy a popular view of deep learning as a hierarchical computation of increasingly abstract features at each layer. In this report, we argue that this view is incomplete and does not adequately explain several recent findings. We propose an alternative viewpoint based on unrolled iterative estimation -- a group of successive layers iteratively refine their estimates of the same features instead of computing an entirely new representation. We demonstrate that this viewpoint directly leads to the construction of Highway and Residual networks. Finally we provide preliminary experiments to discuss the similarities and differences between the two architectures.

• The paper reveals that Highway and Residual Networks iteratively refine features through unrolled estimation instead of building new representations each layer.
• It demonstrates that successive layers preserve feature identities, with mean square error analyses confirming minimal output differences.
• Layer lesioning and reshuffling experiments underline the robustness and interchangeability of layers within the iterative estimation framework.

Overview of "Highway and Residual Networks Learn Unrolled Iterative Estimation"

"Highway and Residual Networks Learn Unrolled Iterative Estimation" by Klaus Greff, Rupesh K. Srivastava, and Jürgen Schmidhuber presents a significant re-evaluation of the conventional understanding of deep neural architectures, specifically Highway Networks and Residual Networks (ResNets). While these networks have achieved remarkable success in various applications, their operational mechanics have defied the representation-centric view traditionally espoused in deep learning. The authors propose an alternative interpretative framework: these networks function through unrolled iterative estimation rather than merely computing novel representations at each layer. This paper elucidates this framework and critically examines its implications for network design and operation.

Key Findings

The paper challenges the conventional representation view, which holds that each layer in a neural network computes higher abstractions of the input data. The authors provide evidence that Highway and ResNet models actually refine the same features through successive layers rather than computing new representations. From this perspective, a finite group of layers works collectively to iteratively enhance initial feature estimates.

The authors present empirical evidence and theoretical justifications to substantiate this perspective:

• Preservation of Feature Identity: Through mean square error analyses, they show that the expected difference between outputs of succeeding layers in a stage is negligible, suggesting feature identity preservation over architectural depth.
• Analysis of Lesioning and Reshuffling: Experimentation with layer removal and order reshuffling manifests minimal degradation in network performance. This indicates that layers are more interchangeable and less critical individually than previously assumed.

Theoretical Contributions

The manuscript derives the functional forms of ResNets and Highway Networks under the paradigm of iterative estimation:

• Residual Networks: Modelling the difference between layer outputs and latent representations as zero-mean residuals aligns ResNets closely with iterative refinement ideology.
• Highway Networks: Here, the architecture optimally integrates previous and current layer outputs to refine latent features. The gating mechanisms act as probabilistic interpolators balancing new estimates against inherited representations.

Furthermore, the paper justifies the usage of certain design elements within these architectures—such as batch normalization—by arguing for their roles in maintaining the integrity of the iterative estimation process.

Implications and Potential Directions

The unrolled iterative estimation view elucidates several operational insights:

• Resiliency to Lesioning: It explains why individual layer removal scarcely impacts overall network performance; robustness stems from the interdependency of iterative refinement processes.
• Layer Shuffling: It rationalizes the layers' fungibility within a competent estimation stage, given their collective maintenance of feature identities.

Several applications, including but not limited to deep architectures in image processing and natural language processing, are considered in light of this framework. The paper explores practical comparisons between various Highway and Residual network configurations, recommending architectures attuned with task-specific refinements.

Future Developments

While the paper offers a substantive exploration of alternative interpretations, it sets the stage for ensuing research into deeper architectural modifications and optimizations. Future work could delve into embedding explicit iterative mechanisms or further integration with non-conventional neural forms that benefit from iterative estimation principles.

In conclusion, this work invites researchers to reconceptualize very deep networks not as mere feedforward aggregators of representations but as sophisticated estimative frameworks capable of nuanced feature refinement. This approach holds promise for enhancing our understanding and the performance efficacy of future neural models.