The emerging field of eXplainable Artificial Intelligence (XAI) aims to bring transparency to today’s powerful but opaque deep learning models. While local XAI methods explain individual predictions in form of attribution maps, thereby identifying where important features occur (but not providing information about what they represent), global explanation techniques visualize what concepts a model has generally learned to encode. Both types of methods thus only provide partial insights and leave the burden of interpreting the model’s reasoning to the user. Only few contemporary techniques aim at combining the principles behind both local and global XAI for obtaining more informative explanations. Those methods, however, are often limited to specific model architectures or impose additional requirements on training regimes or data and label availability, which renders the post-hoc application to arbitrarily pre-trained models practically impossible. In this work we introduce the Concept Relevance Propagation (CRP) approach, which combines the local and global perspectives of XAI and thus allows answering both the “where” and “what” questions for individual predictions, without additional constraints imposed. We further introduce the principle of Relevance Maximization for finding representative examples of encoded concepts based on their usefulness to the model. We thereby lift the dependency on the common practice of Activation Maximization and its limitations. We demonstrate the capabilities of our methods in various settings, showcasing that Concept Relevance Propagation and Relevance Maximization lead to more human interpretable explanations and provide deep insights into the model’s representations and reasoning through concept atlases, concept composition analyses, and quantitative investigations of concept subspaces and their role in fine-grained decision making.

From "Where" to "What": Towards Human-Understandable Explanations through Concept Relevance Propagation

Explainable AI transforms opaque decision strategies of ML models into explanations that are interpretable by the user, for example, identifying the contribution of each input feature to the prediction at hand. Such explanations, however, entangle the potentially multiple factors that enter into the overall complex decision strategy. We propose to disentangle explanations by finding relevant subspaces in activation space that can be mapped to more abstract human-understandable concepts and enable a joint attribution on concepts and input features. To automatically extract the desired representation, we propose new subspace analysis formulations that extend the principle of PCA and subspace analysis to explanations. These novel analyses, which we call principal relevant component analysis (PRCA) and disentangled relevant subspace analysis (DRSA), optimize relevance of projected activations rather than the more traditional variance or kurtosis. This enables a much stronger focus on subspaces that are truly relevant for the prediction and the explanation, in particular, ignoring activations or concepts to which the prediction model is invariant. Our approach is general enough to work alongside common attribution techniques such as Shapley Value, Integrated Gradients, or LRP. Our proposed methods show to be practically useful and compare favorably to the state of the art as demonstrated on benchmarks and three use cases.

Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces

The completeness axiom renders the explanation of a post-hoc XAI method only locally faithful to the model, i.e. for a single decision. For the trustworthy application of XAI, in particular for high-stake decisions, a more global model understanding is required. Recently, concept-based methods have been proposed, which are however not guaranteed to be bound to the actual model reasoning. To circumvent this problem, we propose Multi-dimensional Concept Discovery (MCD) as an extension of previous approaches that fulfills a completeness relation on the level of concepts. Our method starts from general linear subspaces as concepts and does neither require reinforcing concept interpretability nor re-training of model parts. We propose sparse subspace clustering to discover improved concepts and fully leverage the potential of multi-dimensional subspaces. MCD offers two complementary analysis tools for concepts in input space: (1) concept activation maps, that show where a concept is expressed within a sample, allowing for concept characterization through prototypical samples, and (2) concept relevance heatmaps, that decompose the model decision into concept contributions. Both tools together enable a detailed understanding of the model reasoning, which is guaranteed to relate to the model via a completeness relation. This paves the way towards more trustworthy concept-based XAI. We empirically demonstrate the superiority of MCD against more constrained concept definitions.

Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees

Applying traditional post-hoc attribution methods to segmentation or object detection predictors offers only limited insights, as the obtained feature attribution maps at input level typically resemble the models' predicted segmentation mask or bounding box. In this work, we address the need for more informative explanations for these predictors by proposing the post-hoc eXplainable Artificial Intelligence method L-CRP to generate explanations that automatically identify and visualize relevant concepts learned, recognized and used by the model during inference as well as precisely locate them in input space. Our method therefore goes beyond singular input-level attribution maps and, as an approach based on the recently published Concept Relevance Propagation technique, is efficiently applicable to state-of-the-art black-box architectures in segmentation and object detection, such as DeepLabV3+ and YOLOv6, among others. We verify the faithfulness of our proposed technique by quantitatively comparing different concept attribution methods, and discuss the effect on explanation complexity on popular datasets such as CityScapes, Pascal VOC and MS COCO 2017. The ability to precisely locate and communicate concepts is used to reveal and verify the use of background features, thereby highlighting possible biases of the model.

Revealing Hidden Context Bias in Segmentation and Object Detection through Concept-specific Explanations

This paper introduces two randomized preconditioning techniques for robustly solving kernel ridge regression (KRR) problems with a medium to large number of data points ($10^4 \leq N \leq 10^7$). The first method, RPCholesky preconditioning, is capable of accurately solving the full-data KRR problem in $O(N^2)$ arithmetic operations, assuming sufficiently rapid polynomial decay of the kernel matrix eigenvalues. The second method, KRILL preconditioning, offers an accurate solution to a restricted version of the KRR problem involving $k \ll N$ selected data centers at a cost of $O((N + k^2) k \log k)$ operations. The proposed methods solve a broad range of KRR problems and overcome the failure modes of previous KRR preconditioners, making them ideal for practical applications.

Robust, randomized preconditioning for kernel ridge regression

Concepts are key building blocks of higher level human understanding. Explainable AI (XAI) methods have shown tremendous progress in recent years, however, local attribution methods do not allow to identify coherent model behavior across samples and therefore miss this essential component. In this work, we study concept-based explanations and put forward a new definition of concepts as low-dimensional subspaces of hidden feature layers. We novelly apply sparse subspace clustering to discover these concept subspaces. Moving forward, we derive insights from concept subspaces in terms of localized input (concept) maps, show how to quantify concept relevances and lastly, evaluate similarities and transferability between concepts. We empirically demonstrate the soundness of the proposed Sparse Subspace Clustering for Concept Discovery (SSCCD) method for a variety of different image classification tasks. This approach allows for deeper insights into the actual model behavior that would remain hidden from conventional input-level heatmaps.

Sparse Subspace Clustering for Concept Discovery (SSCCD)

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances due to physical symmetries can be incorporated into the kernel function to compensate for much larger data sets. So far, the scalability of kernel machines has however been hindered by its quadratic memory and cubical runtime complexity in the number of training points. While it is known that iterative Krylov subspace solvers can overcome these burdens, their convergence crucially relies on effective preconditioners, which are elusive in practice. Effective preconditioners need to partially presolve the learning problem in a computationally cheap and numerically robust manner. Here, we consider the broad class of Nyström-type methods to construct preconditioners based on successively more sophisticated low-rank approximations of the original kernel matrix, each of which provides a different set of computational trade-offs. All considered methods aim to identify a representative subset of inducing (kernel) columns to approximate the dominant kernel spectrum.

https://pubs.acs.org/doi/pdf/10.1021/acs.jctc.2c01304

Stefan Blücher

Papers

Sparse Subspace Clustering for Concept Discovery (SSCCD)

Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees

Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence