Double descent: understanding deep learning's curve

Double descent is an intriguing phenomenon in deep learning that challenges traditional views on model complexity and generalization. This concept has gained significant attention due to its counterintuitive behavior, where test error does not monotonically decrease with increasing model complexity. Instead, it exhibits a double descent curve, which has profound implications for designing and training deep learning models.

Understanding double descent

Double descent refers to the non-monotonic behavior of test error as a function of model complexity. Initially, as the model complexity increases, the test error decreases. However, as the model continues to grow in complexity, the test error increases, reaching a peak before decreasing again in the highly overparameterized regime. This behavior has been observed in various deep learning architectures, including Convolutional Neural Networks (CNNs), Residual Networks (ResNets), and Transformers.

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 results in high bias and high test error. As the model complexity increases, the test error decreases.

Overfitting phase

As the model becomes more complex relative to the amount of training data, it starts to capture noise as if it were signal, leading to high variance and an increase in test error. This phase is characterized by the model being too complex for the available 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 defies traditional expectations about overfitting and is a key aspect of the double descent phenomenon.

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. Changes in the number of training samples, optimization algorithm, or label noise can affect the location of this peak.

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. This behavior is influenced by the duration of training and the presence of noise in the data.

Mechanisms behind double descent

The exact mechanisms behind double descent are still under research, but several factors are identified:

• Overparameterization: Models with a high parameter-to-data point ratio enter the overparameterized regime, where the second descent becomes observable.
• Inductive biases: The implicit bias of stochastic gradient descent (SGD) leads to selecting smooth empirical risk minimizers among multiple interpolating solutions, which contributes to the second descent.
• Noise and label quality: The presence of label noise amplifies the double descent phenomenon, making it easier to investigate).

Mitigating double descent

To avoid the negative effects of double descent, several strategies can be employed:

• Regularization: Careful regularization can help avoid the peak in test error associated with the interpolation threshold.
• Early stopping: Stopping training before the model fully interpolates the training set can prevent overfitting.
• Smaller models: Using smaller models with fewer parameters can avoid the complexities and potential degradations associated with double descent.

Implications for deep learning

The double descent phenomenon challenges traditional learning theory and underscores the importance of exploring a wide range of model architectures, sizes, and training durations. It suggests that very large overparameterized models can achieve great generalization performance, contrary to classical expectations.

Understanding and addressing double descent is an important step in optimizing deep learning models and achieving better performance. As research continues, more insights are expected to emerge, further refining our approach to model training and complexity.

Contact our team of experts to discover how Telnyx can power your AI solutions.

___________________________________________________________________________________

Sources cited

• "Deep Double Descent." OpenAI, https://openai.com/index/deep-double-descent/.
• "Deep Double Descent." Data Science Dojo, https://datasciencedojo.com/blog/deep-double-descent/.
• "Double Descent." ICLR, https://openreview.net/forum?id=r1g0dJ3KvB.
• Belkin, Mikhail, et al. "Reconciling Modern Machine-Learning Practice and the Classical Bias–Variance Trade-Off." PNAS, 2019, https://www.pnas.org/doi/10.1073/pnas.1903070116.
• "Double Descent." Deepgram, https://deepgram.com/ai-glossary/double-descent.
• Nakkiran, Preetum, et al. "The Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers." arXiv, 2023, https://arxiv.org/abs/2303.14151.
• "The Role of Overparameterization in Double Descent." arXiv, https://arxiv.org/abs/2403.10459.