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Abstract Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss. In this letter, we study the dynamics of such implicit nonlinear representation learning. We identify a pair of a new assumption and a novel condition, called the on-model structure assumption and the data architecture alignment condition. Under the on-model structure assumption, the data architecture alignment condition is shown to be sufficient for the global convergence and necessary for global optimality. Moreover, our theory explains how and when increasing network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure; for example, the on-model structure assumption can be used as a justification for using a particular model structure instead of others. As an application, we then derive a new training framework, which satisfies the data architecture alignment condition without assuming it by automatically modifying any given training algorithm dependent on data and architecture. Given a standard training algorithm, the framework running its modified version is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark data sets, including MNIST, CIFAR-10, CIFAR-100, Semeion, KMNIST, and SVHN.
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This content will become publicly available on June 3, 2026
What Makes Freezing Layers in Deep Neural Networks Effective? A Linear Separability Perspective
Freezing layers in deep neural networks has been shown to enhance generalization and accelerate training, yet the underlying mechanisms remain unclear. This paper investigates the impact of frozen layers from the perspective of linear separability, examining how untrained, randomly initialized layers influence feature representations and model performance. Using multilayer perceptrons trained on MNIST, CIFAR-10, and CIFAR-100, we systematically analyze the effects freezing layers and network architecture. While prior work attributes the benefits of frozen layers to Cover’s theorem, which suggests that nonlinear transformations improve linear separability, we find that this explanation is insufficient. Instead, our results indicate that the observed improvements in generalization and convergence stem from other mechanisms. We hypothesize that freezing may have similar effects to other regularization techniques and that it may smooth the loss landscape to facilitate training. Furthermore, we identify key architectural factors---such as network overparameterization and use of skip connections---that modulate the effectiveness of frozen layers. These findings offer new insights into the conditions under which freezing layers can optimize deep learning performance, informing future work on neural architecture search.
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- PAR ID:
- 10634221
- Publisher / Repository:
- AutoML Conference 2025
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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