Inner interpretability is a promising field focused on uncovering the internal mechanisms of AI systems and developing scalable, automated methods to understand these systems at a mechanistic level. While significant research has explored top-down approaches starting from high-level problems or algorithmic hypotheses and bottom-up approaches building higher-level abstractions from low-level or circuit-level descriptions, most efforts have concentrated on analyzing large language models. Moreover, limited attention has been given to applying inner interpretability to large-scale image tasks, primarily focusing on architectural and functional levels to visualize learned concepts. In this paper, we first present a conceptual framework that supports inner interpretability and multilevel analysis for large-scale image classification tasks. We introduce the Bi-directional Interaction between Concept and Input Embeddings (Bi-ICE) module, which facilitates interpretability across the computational, algorithmic, and implementation levels. This module enhances transparency by generating predictions based on human-understandable concepts, quantifying their contributions, and localizing them within the inputs. Finally, we showcase enhanced transparency in image classification, measuring concept contributions and pinpointing their locations within the inputs. Our approach highlights algorithmic interpretability by demonstrating the process of concept learning and its convergence.