Residual Connections Encourage Iterative Inference (1710.04773v2)

Abstract: Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is still a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of features. We attempt to further expose properties of this aspect. To this end, we study Resnets both analytically and empirically. We formalize the notion of iterative refinement in Resnets by showing that residual connections naturally encourage features of residual blocks to move along the negative gradient of loss as we go from one block to the next. In addition, our empirical analysis suggests that Resnets are able to perform both representation learning and iterative refinement. In general, a Resnet block tends to concentrate representation learning behavior in the first few layers while higher layers perform iterative refinement of features. Finally we observe that sharing residual layers naively leads to representation explosion and counterintuitively, overfitting, and we show that simple existing strategies can help alleviating this problem.

• The paper shows residual connections encourage iterative inference, where blocks refine feature representations iteratively as if performing optimization steps.
• Empirical analysis shows lower Resnet blocks learn initial representations, while higher blocks iteratively refine features to improve predictions for challenging examples.
• Experiments show Resnets can be unrolled beyond training depth, confirming their intrinsic iterative nature, and explore challenges and solutions for parameter sharing.

Iterative Inference in Residual Networks: A Detailed Examination

Residual networks (Resnets) have gained significant traction in deep learning primarily due to their ability to effectively train very deep architectures with remarkable performance. The work of Jastrzębski et al. explores the iterative refinement characteristics of Resnets by providing a comprehensive analysis that combines both theoretical constructs and empirical findings.

Analytical Insights

The authors provide a formal framework to understand the iterative refinement capabilities of Resnets through the lens of gradient descent in the activation space. They argue that each residual block naturally propels the hidden representations to shift along the direction of the negative gradient of the loss function, effectively implementing an iterative optimization scheme. This is substantiated through the application of Taylor's series expansion, which suggests that the alignment of the residual block's output with the negative loss gradient is a key driver for the block's optimization. The authors empirically validate this by measuring cosine similarity between the residual block outputs and the negative gradient, finding a consistent negative value, particularly in higher blocks.

Empirical Characterization

Through a variety of architectures and datasets, the paper meticulously explores the behavior of Resnets to discern how these networks balance representation learning with iterative refinement. The authors highlight that lower residual blocks play a crucial role in representation learning by substantially altering the representation, while higher blocks fine-tune these changes via iterative refinement. This dichotomy is showcased through $\ell^2$ ratios and experiments involving block removal, which demonstrate the sensitivity of network performance to lower block functionality and the roles fulfilled by higher blocks.

Additionally, the paper of borderline examples reveals that higher blocks enhance predictions by focusing on ambiguous samples near decision boundaries, thereby underscoring the iterative refinement concept. Specifically, these blocks cater to samples incorrectly classified by marginal probabilities, thus confirming their function as fine-tuners of feature representations.

Challenges of Parameter Sharing and Unrolling

The authors explore the sharing and unrolling of residual blocks as potential methods of resource optimization in deep networks. They note challenges such as representation explosion and unintended overfitting when sharing blocks naively across different layers. To mitigate this, a variant of batch normalization is proposed, which unshares batch statistics and parameters effectively. When analyzing iterative inference in the context of unrolling, they find that Resnets can be unrolled beyond their training configuration, maintaining effective performance and demonstrating the intrinsic iterative capacity of residual blocks.

Implications and Future Directions

The findings of this paper extend our understanding of Resnets by crystallizing the dual roles played by different block layers in advancing both representation learning and iterative feature refinement. This has profound implications for optimizing deep network architectures, highlighting the potential for refined block utilization that adapts to network depth and task complexity.

Moreover, the paper elucidates potential avenues for further research in residual network optimization, such as improving sharing strategies and identifying how recurrent neural network techniques might be innovatively applied to enhance Resnets' efficiency.

In conclusion, Jastrzębski et al.'s work provides a pivotal step toward demystifying the mechanics underlying Resnets, offering detailed insights that pave the way for both theoretical advancements and practical implementations in the ongoing evolution of neural networks.