[Paper Review] Can Pretext-Based Self-Supervised Learning Be Boosted by Downstream Data? A Theoretical Analysis

Jiaye Teng, Weiran Huang+1 more|arXiv (Cornell University)|Mar 5, 2021

Domain Adaptation and Few-Shot Learning28 references4 citations

TL;DR

This paper investigates whether downstream data can improve pretext-based self-supervised learning by refining input data to satisfy conditional independence ($f(\mathbf{x}) \perp \mathbf{z} \mid \mathbf{y}$), a condition that minimizes downstream sample complexity. It proves that using insufficient downstream data to train a data processor $f$ can hurt performance, establishing both model-free and model-dependent lower bounds on required downstream samples, thus validating standard self-supervised learning as optimal under data scarcity.

ABSTRACT

Pretext-based self-supervised learning learns the semantic representation via a handcrafted pretext task over unlabeled data and then uses the learned representation for downstream tasks, which effectively reduces the sample complexity of downstream tasks under Conditional Independence (CI) condition. However, the downstream sample complexity gets much worse if the CI condition does not hold. One interesting question is whether we can make the CI condition hold by using downstream data to refine the unlabeled data to boost self-supervised learning. At first glance, one might think that seeing downstream data in advance would always boost the downstream performance. However, we show that it is not intuitively true and point out that in some cases, it hurts the final performance instead. In particular, we prove both model-free and model-dependent lower bounds of the number of downstream samples used for data refinement. Moreover, we conduct various experiments on both synthetic and real-world datasets to verify our theoretical results.

Motivation & Objective

• To investigate whether downstream data can improve pretext-based self-supervised learning by enforcing conditional independence between refined inputs and pretext labels given downstream labels.
• To identify conditions under which using downstream data for data refinement fails or harms downstream performance, challenging the intuition that more data always helps.
• To derive theoretical lower bounds on the number of downstream samples required to successfully refine representations and achieve improved sample complexity.
• To validate the theoretical findings through experiments on synthetic and real-world datasets, including CIFAR-10.

Proposed method

• Proposes a learnable data processor $f$ that transforms input $\mathbf{x}$ to improve conditional independence $f(\mathbf{x}) \perp \mathbf{z} \mid \mathbf{y}$, where $\mathbf{z}$ is the pretext label and $\mathbf{y}$ the downstream label.
• Introduces a novel loss function to train $f$ such that the resulting representation satisfies both conditional independence and predictive capacity for $\mathbf{y}$.
• Derives a model-free lower bound on the number of downstream samples needed to avoid performance degradation during representation learning.
• Establishes a model-dependent lower bound that increases with model capacity, showing that more complex models require proportionally more downstream data for effective refinement.
• Empirically validates theoretical claims using synthetic data and real-world datasets like CIFAR-10, varying $\lambda$, model size, and downstream sample size.

Experimental results

Research questions

• RQ1 Can using downstream data to refine unlabeled data via a learnable function $f$ improve the sample complexity of pretext-based self-supervised learning?
• RQ2 Under what conditions does using downstream data fail or degrade performance in self-supervised representation learning?
• RQ3 What is the minimum number of downstream samples required to successfully refine representations and achieve performance gains?
• RQ4 How does model capacity affect the required number of downstream samples for effective data refinement?

Key findings

• Using insufficient downstream data to train the data processor $f$ provably degrades downstream performance, contradicting the intuitive expectation that more data always helps.
• A model-free lower bound on downstream samples is derived, showing that limited data cannot improve representation learning and may harm it.
• A model-dependent lower bound is established, indicating that higher model capacity requires proportionally more downstream samples to achieve performance gains.
• Experiments on CIFAR-10 show that increasing $\lambda$ in the proposed loss function hurts performance, validating Theorem 1.
• Performance degrades when using fewer downstream samples for processor training, confirming the theoretical lower bound in Table 2.
• Doubling model capacity without sufficient downstream data leads to significantly worse performance, validating Theorem 4.