Neural Network Interpretability

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural networks (BNNs) address the latter by representing weights as probability distributions, allowing for predictive uncertainty evaluation. Latent binary Bayesian neural networks (LBBNNs) further handle structural uncertainty and sparsify models by removing redundant weights. This article advances LBBNNs by enabling covariates to skip to any succeeding layer or be excluded, simplifying networks and clarifying input impacts on predictions. This further allows us to learn simpler structures (e.g., linear or even constant intercept only models) when appropriate. Furthermore, the input-skip LBBNN (ISLaB) approach reduces network density significantly compared to standard LBBNNs, achieving over 99% reduction for small networks and over 99.9% for larger ones, while still maintaining high predictive accuracy and uncertainty quantification. For example, on MNIST, we reached 97% accuracy and great calibration with just 935 weights, reaching state-of-the-art for compression of neural networks. Furthermore, the proposed method accurately identifies the true covariates and adjusts for system non-linearity. The main contribution is the introduction of active paths, enhancing directly designed global and local explanations within the LBBNN framework. The latter are exact with theoretical guarantees and do not require post hoc external tools.

Deep reinforcement learning (DRL) has successfully addressed many complex control problems. However, the neural networks representing policies or values remain opaque, undermining trust in high-stakes applications. While concept-based methods have shown promise in deciphering internal representations in computer vision, applying them to DRL is impeded by the absence of pre-defined semantic concepts in continuous state spaces. In this work, we propose a novel concept-based explanation framework designed to provide fine-grained, neuron-level insights into DRL models. Unlike previous approaches that rely on manual feature engineering, our framework automatically aligns neuron activations with logical formulas composed of semantic predicates. To bridge the gap between continuous signals and symbolic reasoning, we introduce a value-sensitive discretization mechanism that transforms raw state features into interpretable atomic concepts. This ensures that the vocabulary used for explanation captures strategic decision boundaries relevant to the agent's value assessment. By composing these interpretable concepts and matching them with neuron behaviors, we derive explicit explanations for the network's internal representations. Experimental results on both continuous and discrete environments demonstrate that our method effectively identifies meaningful decision-making patterns, offering faithful explanations that align with human intuition.

We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations. We show that gradient descent corresponds to a dynamical process in the input layer, whereby clusters of data are progressively reduced in complexity ("truncated") at an exponential rate that increases with the number of data points that have already been truncated. We provide a detailed discussion of several types of solutions to the gradient flow equations. A main motivation for this work is to shed light on the interpretability question in supervised learning.