Minimal Sufficient Representations for Self-interpretable Deep Neural Networks

Deep neural networks (DNNs) are widely used, but interpreting what they actually learn remains difficult. A major obstacle is that individual neurons often encode multiple unrelated concepts, obscuring the decision process of the network. While prior work, such as sparse autoencoders, can separate these mixed signals into more meaningful, "monosemantic" features, this typically requires altering the model in ways that can degrade downstream performance. To overcome this, we introduce ELUDe (explicit, lossless, unsupervised disentanglement), a method for improving the interpretability of DNNs while preserving their functional equivalence. ELUDe breaks latent representations into clear, inspectable sub-units that behave like interpretable features, while guaranteeing that the model's outputs remain exactly the same. It requires no explicit training, no labels, and can be applied to pretrained models. ELUDe works by reorganizing how information flows between layers, re-routing concept-specific contributions while preserving the original computation by construction. Across several vision models, including DINOv2 and supervised ViT-B/16, ELUDe improves interpretability, keeps downstream accuracy unchanged, runs efficiently, and supports practical uses such as steering model representations. In short, ELUDe offers interpretability (almost) without a tradeoff: clearer, scalable, and actionable model insights with no loss in performance.

In the current era of deep learning and especially generative models, there is significant investment in training very large deep neural networks. Thus far, such models have been "black boxes" that are difficult to understand in the sense that they have opaque internal mechanisms, leading to difficulties in interpretability, reliability, and control. Naturally, this lack of understanding has led to both hype and fear. This book is an attempt to "open the black box" and understand the mechanisms of large deep networks, through the perspective of representation learning, which is a major factor - arguably the single most important one - in the empirical power of deep learning models. A brief outline of this book is as follows. Chapter 1 will summarize the threads that underlie the whole text. Chapters 2, 3, 4, 5, and 6 will explain the design principles of modern neural network architectures through optimization and information theory, reducing the process of architecture development (long having been described as a sort of "alchemy") to undergraduate-level linear algebra and calculus exercises once the underlying principles are introduced. Chapters 7 and 8 will discuss applications of these principles to solve problems in more paradigmatic ways, obtaining new methods and models which are efficient, interpretable, and controllable by design, and yet no less - sometimes even more - powerful than the black-box models they resemble. Chapter 9 will discuss potential future directions for deep learning, the role of representation learning, as well as some open problems.

Interpretable Mesomorphic Neural Networks (IMNs) offer a promising framework that combines the predictive power of deep neural networks with the interpretability of linear models. However, the original formulation lacks safeguards to ensure that the learned interpretations are in fact reliable. In particular, the network is free to concentrate all explanatory variance into a single weight of the linear output layer, achieving strong predictive performance while producing interpretations that are largely meaningless. Paradoxically, the L1 penalty proposed to encourage sparse solutions exacerbates this problem by further incentivizing such degenerate configurations. To address this vulnerability, we introduce Local Fidelity Regularization (LFR), a novel penalty term that prevents degenerate weight collapse by aligning the linear output weights with local data variations. This structural constraint guarantees faithful explanations and substantially improves the reliability of model interpretations. Furthermore, empirical evaluations across the OpenML benchmark suite demonstrate that LFR does not compromise accuracy for explainability; rather, it achieved improved AUROC over the unregularized IMN. By yielding results highly competitive with state-of-the-art black-box models, LFR provides the dual benefit of reliable interpretability and superior predictive performance. Source code and usage instructions are available at https://github.com/hugohammer/LFR-IMN.git.