Is double descent a myth or reality in ML?

The phenomenon of double descent has sparked significant interest and debate within the machine learning community. As machine learning models become increasingly complex, understanding the intricacies of double descent is crucial for practitioners and researchers alike. This article explores the reality of double descent, its phases, and its implications for model design and training.

Defining double descent

Double descent is a phenomenon observed in machine learning where the test error of a model initially decreases, then increases, and finally decreases again as the model complexity increases. This non-monotonic behavior challenges the traditional bias-variance trade-off, which suggests that increasing model complexity should always lead to overfitting and higher test error.

According to Wikipedia, double descent occurs when a model with a small number of parameters and a model with an extremely large number of parameters both exhibit low test error, while a model with an intermediate number of parameters shows high test error.

Historical context and discovery

Researchers such as Mikhail Belkin and his colleagues first discovered the concept of double descent. Their work, published in the Proceedings of the National Academy of Sciences, highlighted modern machine learning models' unexpected test error patterns. This discovery has since prompted a reevaluation of established theories regarding model complexity and generalization.

Phases of double descent

Underfitting phase

In the early stages of model training, the model is underparameterized, meaning it lacks the complexity to capture the underlying patterns in the data. This phase is characterized by high bias and low variance, resulting in high test error. As described by Data Science Dojo, the model struggles to fit the training data adequately, leading to underfitting.

Overfitting phase

As the model's complexity increases, it begins to capture noise in the training data as if it were signal, leading to overfitting. This phase is marked by low bias but high variance, causing the test error to rise. The model's performance degrades because it becomes too tailored to the training data.

Second descent

Surprisingly, as the model complexity grows even further into the highly overparameterized regime, the test error begins to decrease once again. This phase, known as the second descent, challenges traditional views on overfitting. The model's ability to generalize improves despite its increased complexity, a phenomenon observed in various deep learning architectures, including CNNs and Transformers.

Types of double descent

Model-wise double descent

Model-wise double descent occurs when the model's performance is evaluated as a function of its size. The test error peaks around the interpolation threshold, where the model is just barely able to fit the training set.

Sample-wise non-monotonicity

This phenomenon occurs when increasing the number of training samples can temporarily degrade model performance. As more samples require larger models to fit, the interpolation threshold shifts, leading to a regime where more data can hurt performance before eventually improving it.

Epoch-wise double descent

Double descent can also manifest across training epochs. As training proceeds, the test error may decrease, increase, and then decrease again, even for a fixed model size.

Implications for model design and training

The reality of double descent has significant implications for model design and training strategies. Traditional approaches that focus solely on avoiding overfitting may need to be reconsidered.

Instead, practitioners might benefit from embracing higher model complexity and longer training times to achieve better generalization. Understanding the phases and types of double descent can help design more robust models that perform well across a range of complexities.

Practical considerations

• Model complexity: Balancing model complexity is crucial. Overly simplistic models may underfit, while moderately complex models may overfit. Highly complex models, however, might achieve better generalization.
• Training data: The quantity and quality of training data play a significant role. More data can sometimes temporarily degrade performance.
• Training epochs: Monitoring test error across training epochs can provide insights into the model's performance and help identify the second descent phase.

Real-world applications and examples

Double descent has been observed in various deep learning architectures, including Convolutional Neural Networks (CNNs), Residual Networks (ResNets), and Transformers. Studies of deep learning models have revealed double descent patterns across different architectures, highlighting its widespread relevance.

Key insights on double descent

Double descent is a real and significant phenomenon in machine learning, challenging traditional views on model complexity and generalization. Understanding its phases—underfitting, overfitting, and second descent—is crucial for designing robust models. Practical considerations include balancing model complexity, managing training data, and monitoring training epochs. By accounting for these aspects, practitioners can build models that perform well across various complexities and achieve better generalization.

Double descent is a nuanced and complex phenomenon that continues to shape our understanding of machine learning models. As research progresses, our strategies for model design and training will undoubtedly evolve, incorporating the lessons learned from this intriguing behavior.

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Sources cited

• Belkin, Mikhail, et al. "Reconciling Modern Machine-Learning Practice and the Classical Bias–Variance Trade-Off." Proceedings of the National Academy of Sciences, vol. 116, no. 32, 2019, pp. 15849-15854. https://www.pnas.org/content/116/32/15849.

• Data Science Dojo. "Deep Double Descent—Understanding the Phenomenon." https://datasciencedojo.com/blog/deep-double-descent/.

• Hastie, Trevor, et al. "Surprises in High-Dimensional Ridgeless Least Squares Interpolation." arXiv, 2019. https://arxiv.org/abs/1903.08560.

• Nakkiran, Preetum, et al. "Deep Double Descent: Where Bigger Models and More Data Hurt." arXiv, 2019. https://arxiv.org/abs/1912.02292.

• Telnyx. "Double Descent: A Phenomenon in Deep Learning." https://telnyx.com/learn-ai/double-descent-deep-learning/.

• Wikipedia. "Double Descent." Wikipedia, https://en.wikipedia.org/wiki/Double_descent.