Empirical evidence shows that deep vision networks often represent concepts as directions in latent space with concept information written along directional components in the vector representation of the input. However, the mechanism to encode (write) and decode (read) concept information to and from vector representations is not directly accessible as it constitutes a latent mechanism that naturally emerges from the training process of the network. Recovering this mechanism unlocks significant potential to open the black-box nature of deep networks, enabling understanding, debugging, and improving deep learning models. In this work, we propose an unsupervised method to recover this mechanism. For each concept, we explain that under the hypothesis of linear concept representations, this mechanism can be implemented with the help of two directions: the first facilitating encoding of concept information and the second facilitating decoding. Unlike prior matrix decomposition, autoencoder, or dictionary learning methods that rely on feature reconstruction, we propose a new perspective: decoding directions are identified via directional clustering of activations, and encoding directions are estimated with signal vectors under a probabilistic view. We further leverage network weights through a novel technique, Uncertainty Region Alignment, which reveals interpretable directions affecting predictions. Our analysis shows that (a) on synthetic data, our method recovers ground-truth direction pairs; (b) on real data, decoding directions map to monosemantic, interpretable concepts and outperform unsupervised baselines; and (c) signal vectors faithfully estimate encoding directions, validated via activation maximization. Finally, we demonstrate applications in understanding global model behavior, explaining individual predictions, and intervening to produce counterfactuals or correct errors.