Quantifying Representation Reliability in Self-Supervised Learning Models

TL;DR

The paper tackles the problem of quantifying reliability of self-supervised representations when downstream task data are unavailable or private. It introduces a formal definition of representation reliability based on downstream performance and shows standard supervised UQ tools cannot directly assess SSL representations. To estimate reliability without task labels, it develops Neighborhood Consistency (NC): an ensemble-based approach that aligns representation spaces via consistent neighbors across multiple embedding functions, quantified by NC$_k$(x*) = (1/$M^2$) sum_{i<j} Sim(k-NN_i(x*), k-NN_j(x*)). Through extensive experiments across CIFAR variants, transfer tasks, and model types (SimCLR, BYOL, MoCo), NC demonstrates robust correlation with actual downstream performance, enabling model ranking and reliability assessment in privacy-preserving settings. The work provides theoretical and empirical evidence that anchor-based alignment of representation spaces can bound downstream uncertainty, offering a practical tool for safer deployment of SSL foundation models.

Abstract

Self-supervised learning models extract general-purpose representations from data. Quantifying the reliability of these representations is crucial, as many downstream models rely on them as input for their own tasks. To this end, we introduce a formal definition of representation reliability: the representation for a given test point is considered to be reliable if the downstream models built on top of that representation can consistently generate accurate predictions for that test point. However, accessing downstream data to quantify the representation reliability is often infeasible or restricted due to privacy concerns. We propose an ensemble-based method for estimating the representation reliability without knowing the downstream tasks a priori. Our method is based on the concept of neighborhood consistency across distinct pre-trained representation spaces. The key insight is to find shared neighboring points as anchors to align these representation spaces before comparing them. We demonstrate through comprehensive numerical experiments that our method effectively captures the representation reliability with a high degree of correlation, achieving robust and favorable performance compared with baseline methods.

Figures (5)

• Figure 1: Illustration of representation reliability ($\mathsf{Reli}$) and neighborhood consistency ($\mathsf{NC}$). For a test point $\bm{x}^*$ and a class of pre-trained backbone models $\mathcal{H} = \{h_1, \cdots, h_M\}$, the representation reliability is defined as the average performance of downstream models when using the representations of $\bm{x}^*$ provided by the backbones in $\mathcal{H}$. Our $\mathsf{NC}$ estimates $\mathsf{Reli}$ without requiring any prior knowledge of the downstream tasks. It operates by measuring the number of consistent neighbors of $\bm{x}^*$ among reference points across different representation spaces.
• Figure 2: Ablation studies on the ensemble size ($M$) and the number of neighbors ($k$) for $\mathsf{NC}_k$ (ours) and baselines. Brier score is used for the downstream performance metric. The comprehensive results can be found in Appendix \ref{['app:suppl']}.
• Figure 3: Graphical visualization of the sketch for the proof of Theorem \ref{['thm::nb_consistency']}. Let $\mathcal{Z}i$ and $\mathcal{Z}j$ denote the representation spaces defined by the embedding functions $h_i$ and $h_j$, respectively. Suppose that there is a reliable neighboring point $\bm{x}^r$ that is located close to the test point $\bm{x}^*$ in each representation space. For any downstream task $t$, a reliable neighboring point $\bm{x}^r$ serves as an anchor for comparing different representations $\bm{z}_i^* = h_i(\bm{x}^*)$ and $\bm{z}_j^* = h_j(\bm{x}^*)$ of the test point $\bm{x}^*$. The key idea is that $y_{i,t}^*$ and $y_{j,t}^*$ --- the downstream predictions on the test point using the two different embedding functions --- should be similar because the predictions $y_{i,t}^*$ and $y_{i,t}^r$ as well as $y_{j,t}^r$ and $y_{j,t}^*$ are similar due to the Lipschitz continuity of the downstream predictors. Additionally, since $\bm{x}^r$ is a reliable point, the predictions $y_{i,t}^r$ and $y_{j,t}^r$ are similar. Thus, it follows that $y_{i,t}^*$ and $y_{j,t}^*$ are similar as well.
• Figure 4: Ablation over the ensemble size ($M$) for $\mathsf{NC}_k$ (ours) and baselines. Brier score is used for the downstream performance metric.
• Figure 5: Ablation over the number of neighbors ($k$) for $\mathsf{NC}_k$ (ours) and baselines. Brier score is used for the downstream performance metric.

Theorems & Definitions (10)

• Definition 1
• Theorem 1
• Theorem 2
• Remark 1
• Theorem 3
• proof
• proof
• Lemma 1
• proof
• Corollary 1