Beyond Scalars: Concept-Based Alignment Analysis in Vision Transformers

Vision transformers (ViTs) can be trained using various learning paradigms, from fully supervised to self-supervised. Diverse training protocols often result in significantly different feature spaces, which are usually compared through alignment analysis. However, current alignment measures quantify this relationship in terms of a single scalar value, obscuring the distinctions between common and unique features in pairs of representations that share the same scalar alignment. We address this limitation by combining alignment analysis with concept discovery, which enables a breakdown of alignment into single concepts encoded in feature space. This fine-grained comparison reveals both universal and unique concepts across different representations, as well as the internal structure of concepts within each of them. Our methodological contributions address two key prerequisites for concept-based alignment: 1) For a description of the representation in terms of concepts that faithfully capture the geometry of the feature space, we define concepts as the most general structure they can possibly form - arbitrary manifolds, allowing hidden features to be described by their proximity to these manifolds. 2) To measure distances between concept proximity scores of two representations, we use a generalized Rand index and partition it for alignment between pairs of concepts. We confirm the superiority of our novel concept definition for alignment analysis over existing linear baselines in a sanity check. The concept-based alignment analysis of representations from four different ViTs reveals that increased supervision correlates with a reduction in the semantic structure of learned representations.

Layer-wise Feedback Propagation

In this paper, we present Layer-wise Feedback Propagation (LFP), a novel training approach for neural-network-like predictors that utilizes explainability, specifically Layer-wise Relevance Propagation(LRP), to assign rewards to individual connections based on their respective contributions to solving a given task. This differs from traditional gradient descent, which updates parameters towards anestimated loss minimum. LFP distributes a reward signal throughout the model without the need for gradient computations. It then strengthens structures that receive positive feedback while reducingthe influence of structures that receive negative feedback. We establish the convergence of LFP theoretically and empirically, and demonstrate its effectiveness in achieving comparable performance to gradient descent on various models and datasets. Notably, LFP overcomes certain limitations associated with gradient-based methods, such as reliance on meaningful derivatives. We further investigate how the different LRP-rules can be extended to LFP, what their effects are on training, as well as potential applications, such as training models with no meaningful derivatives, e.g., step-function activated Spiking Neural Networks (SNNs), or for transfer learning, to efficiently utilize existing knowledge.