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Grégoire Montavon

Grégoire Montavon appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine LearningArtificial IntelligenceComputer VisionNeural and Evolutionary Computingphysics.chem-phastro-ph.EPComputation and LanguageInformation Retrieval

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Published work

22 published item(s)

preprint2026arXiv

Distilling Lightweight Domain Experts from Large ML Models by Identifying Relevant Subspaces

Knowledge distillation involves transferring the predictive capabilities of large, high-performing AI models (teachers) to smaller models (students) that can operate in environments with limited computing power. In this paper, we address the scenario in which only a few classes and their associated intermediate concepts are relevant to distill. This scenario is common in practice, yet few existing distillation methods explicitly focus on the relevant subtask. To address this gap, we introduce 'SubDistill', a new distillation algorithm with improved numerical properties that only distills the relevant components of the teacher model at each layer. Experiments on CIFAR-100 and ImageNet with Convolutional and Transformer models demonstrate that SubDistill outperforms existing layer-wise distillation techniques on a representative set of subtasks. Our benchmark evaluations are complemented by Explainable AI analyses showing that our distilled student models more closely match the decision structure of the original teacher model.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport

Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not violate the true geometry of change. We propose Displacement-Reshaped Optimal Transport (ReshapeOT), a method that reshapes the ground metric by integrating observed sample displacements as an additional source of knowledge. Technically, ReshapeOT replaces the Euclidean metric with a Mahalanobis distance estimated from displacement second moments. This effectively carves expressways through the input space, inviting transport solutions that better align with observed displacements. Our method is computationally lightweight, integrates seamlessly into any OT solver that operates on a cost matrix, and can be kernelized for further flexibility. Experiments on synthetic and real-world data show that ReshapeOT achieves substantial gains in transport reliability. We further demonstrate our method's usefulness in two practical use cases.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Towards Desiderata-Driven Design of Visual Counterfactual Explainers

Visual counterfactual explainers (VCEs) are a straightforward and promising approach to enhancing the transparency of image classifiers. VCEs complement other types of explanations, such as feature attribution, by revealing the specific data transformations to which a machine learning model responds most strongly. In this paper, we argue that existing VCEs focus too narrowly on optimizing sample quality or change minimality; they fail to consider the more holistic desiderata for an explanation, such as fidelity, understandability, and sufficiency. To address this shortcoming, we explore new mechanisms for counterfactual generation and investigate how they can help fulfill these desiderata. We combine these mechanisms into a novel 'smooth counterfactual explorer' (SCE) algorithm and demonstrate its effectiveness through systematic evaluations on synthetic and real data.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Analyzing Atomic Interactions in Molecules as Learned by Neural Networks

While machine learning (ML) models have been able to achieve unprecedented accuracies across various prediction tasks in quantum chemistry, it is now apparent that accuracy on a test set alone is not a guarantee for robust chemical modeling such as stable molecular dynamics (MD). To go beyond accuracy, we use explainable artificial intelligence (XAI) techniques to develop a general analysis framework for atomic interactions and apply it to the SchNet and PaiNN neural network models. We compare these interactions with a set of fundamental chemical principles to understand how well the models have learned the underlying physicochemical concepts from the data. We focus on the strength of the interactions for different atomic species, how predictions for intensive and extensive quantum molecular properties are made, and analyze the decay and many-body nature of the interactions with interatomic distance. Models that deviate too far from known physical principles produce unstable MD trajectories, even when they have very high energy and force prediction accuracy. We also suggest further improvements to the ML architectures to better account for the polynomial decay of atomic interactions.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features

Explainable Artificial Intelligence (XAI) plays a crucial role in fostering transparency and trust in AI systems, where traditional XAI approaches typically offer one level of abstraction for explanations, often in the form of heatmaps highlighting single or multiple input features. However, we ask whether abstract reasoning or problem-solving strategies of a model may also be relevant, as these align more closely with how humans approach solutions to problems. We propose a framework, called Symbolic XAI, that attributes relevance to symbolic queries expressing logical relationships between input features, thereby capturing the abstract reasoning behind a model's predictions. The methodology is built upon a simple yet general multi-order decomposition of model predictions. This decomposition can be specified using higher-order propagation-based relevance methods, such as GNN-LRP, or perturbation-based explanation methods commonly used in XAI. The effectiveness of our framework is demonstrated in the domains of natural language processing (NLP), vision, and quantum chemistry (QC), where abstract symbolic domain knowledge is abundant and of significant interest to users. The Symbolic XAI framework provides an understanding of the model's decision-making process that is both flexible for customization by the user and human-readable through logical formulas.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

XAI for Transformers: Better Explanations through Conservative Propagation

Transformers have become an important workhorse of machine learning, with numerous applications. This necessitates the development of reliable methods for increasing their transparency. Multiple interpretability methods, often based on gradient information, have been proposed. We show that the gradient in a Transformer reflects the function only locally, and thus fails to reliably identify the contribution of input features to the prediction. We identify Attention Heads and LayerNorm as main reasons for such unreliable explanations and propose a more stable way for propagation through these layers. Our proposal, which can be seen as a proper extension of the well-established LRP method to Transformers, is shown both theoretically and empirically to overcome the deficiency of a simple gradient-based approach, and achieves state-of-the-art explanation performance on a broad range of Transformer models and datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Unifying Review of Deep and Shallow Anomaly Detection

Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly detection problem and led to the introduction of a great variety of new methods. With the emergence of numerous such methods, including approaches based on generative models, one-class classification, and reconstruction, there is a growing need to bring methods of this field into a systematic and unified perspective. In this review we aim to identify the common underlying principles as well as the assumptions that are often made implicitly by various methods. In particular, we draw connections between classic 'shallow' and novel deep approaches and show how this relation might cross-fertilize or extend both directions. We further provide an empirical assessment of major existing methods that is enriched by the use of recent explainability techniques, and present specific worked-through examples together with practical advice. Finally, we outline critical open challenges and identify specific paths for future research in anomaly detection.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications

With the broader and highly successful usage of machine learning in industry and the sciences, there has been a growing demand for Explainable AI. Interpretability and explanation methods for gaining a better understanding about the problem solving abilities and strategies of nonlinear Machine Learning, in particular, deep neural networks, are therefore receiving increased attention. In this work we aim to (1) provide a timely overview of this active emerging field, with a focus on 'post-hoc' explanations, and explain its theoretical foundations, (2) put interpretability algorithms to a test both from a theory and comparative evaluation perspective using extensive simulations, (3) outline best practice aspects i.e. how to best include interpretation methods into the standard usage of machine learning and (4) demonstrate successful usage of explainable AI in a representative selection of application scenarios. Finally, we discuss challenges and possible future directions of this exciting foundational field of machine learning.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

From Clustering to Cluster Explanations via Neural Networks

A recent trend in machine learning has been to enrich learned models with the ability to explain their own predictions. The emerging field of Explainable AI (XAI) has so far mainly focused on supervised learning, in particular, deep neural network classifiers. In many practical problems however, label information is not given and the goal is instead to discover the underlying structure of the data, for example, its clusters. While powerful methods exist for extracting the cluster structure in data, they typically do not answer the question why a certain data point has been assigned to a given cluster. We propose a new framework that can, for the first time, explain cluster assignments in terms of input features in an efficient and reliable manner. It is based on the novel insight that clustering models can be rewritten as neural networks - or 'neuralized'. Cluster predictions of the obtained networks can then be quickly and accurately attributed to the input features. Several showcases demonstrate the ability of our method to assess the quality of learned clusters and to extract novel insights from the analyzed data and representations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Building and Interpreting Deep Similarity Models

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation in terms of input features. We develop BiLRP, a scalable and theoretically founded method to systematically decompose similarity scores on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear functions. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Clever Hans Effect in Anomaly Detection

The 'Clever Hans' effect occurs when the learned model produces correct predictions based on the 'wrong' features. This effect which undermines the generalization capability of an ML model and goes undetected by standard validation techniques has been frequently observed for supervised learning where the training algorithm leverages spurious correlations in the data. The question whether Clever Hans also occurs in unsupervised learning, and in which form, has received so far almost no attention. Therefore, this paper will contribute an explainable AI (XAI) procedure that can highlight the relevant features used by popular anomaly detection models of different type. Our analysis reveals that the Clever Hans effect is widespread in anomaly detection and occurs in many (unexpected) forms. Interestingly, the observed Clever Hans effects are in this case not so much due to the data, but due to the anomaly detection models themselves whose structure makes them unable to detect the truly relevant features, even though vast amounts of data points are available. Overall, our work contributes a warning against an unrestrained use of existing anomaly detection models in practical applications, but it also points at a possible way out of the Clever Hans dilemma, specifically, by allowing multiple anomaly models to mutually cancel their individual structural weaknesses to jointly produce a better and more trustworthy anomaly detector.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Machine learning inference of the interior structure of low-mass exoplanets

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Towards Explaining Anomalies: A Deep Taylor Decomposition of One-Class Models

A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been predicted in a certain way. We present a new principled approach for one-class SVMs that decomposes outlier predictions in terms of input variables. The method first recomposes the one-class model as a neural network with distance functions and min-pooling, and then performs a deep Taylor decomposition (DTD) of the model output. The proposed One-Class DTD is applicable to a number of common distance-based SVM kernels and is able to reliably explain a wide set of data anomalies. Furthermore, it outperforms baselines such as sensitivity analysis, nearest neighbor, or simple edge detection.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Explaining Predictions of Non-Linear Classifiers in NLP

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional neural network (CNN) trained on a topic categorization task. Our analysis highlights which words are relevant for a specific prediction of the CNN. We compare our technique to standard sensitivity analysis, both qualitatively and quantitatively, using a "word deleting" perturbation experiment, a PCA analysis, and various visualizations. All experiments validate the suitability of LRP for explaining the CNN predictions, which is also in line with results reported in recent image classification studies.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Identifying individual facial expressions by deconstructing a neural network

This paper focuses on the problem of explaining predictions of psychological attributes such as attractiveness, happiness, confidence and intelligence from face photographs using deep neural networks. Since psychological attribute datasets typically suffer from small sample sizes, we apply transfer learning with two base models to avoid overfitting. These models were trained on an age and gender prediction task, respectively. Using a novel explanation method we extract heatmaps that highlight the parts of the image most responsible for the prediction. We further observe that the explanation method provides important insights into the nature of features of the base model, which allow one to assess the aptitude of the base model for a given transfer learning task. Finally, we observe that the multiclass model is more feature rich than its binary counterpart. The experimental evaluation is performed on the 2222 images from the 10k US faces dataset containing psychological attribute labels as well as on a subset of KDEF images.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Interpreting the Predictions of Complex ML Models by Layer-wise Relevance Propagation

Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack transparency due to their complex nonlinear structure and to the complex data distributions to which they typically apply. As a result, it is difficult to fully characterize what makes these models reach a particular decision for a given input. This lack of transparency can be a drawback, especially in the context of sensitive applications such as medical analysis or security. In this short paper, we summarize a recent technique introduced by Bach et al. [1] that explains predictions by decomposing the classification decision of DNN models in terms of input variables.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers

Layer-wise relevance propagation is a framework which allows to decompose the prediction of a deep neural network computed over a sample, e.g. an image, down to relevance scores for the single input dimensions of the sample such as subpixels of an image. While this approach can be applied directly to generalized linear mappings, product type non-linearities are not covered. This paper proposes an approach to extend layer-wise relevance propagation to neural networks with local renormalization layers, which is a very common product-type non-linearity in convolutional neural networks. We evaluate the proposed method for local renormalization layers on the CIFAR-10, Imagenet and MIT Places datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Analyzing Classifiers: Fisher Vectors and Deep Neural Networks

Fisher Vector classifiers and Deep Neural Networks (DNNs) are popular and successful algorithms for solving image classification problems. However, both are generally considered `black box' predictors as the non-linear transformations involved have so far prevented transparent and interpretable reasoning. Recently, a principled technique, Layer-wise Relevance Propagation (LRP), has been developed in order to better comprehend the inherent structured reasoning of complex nonlinear classification models such as Bag of Feature models or DNNs. In this paper we (1) extend the LRP framework also for Fisher Vector classifiers and then use it as analysis tool to (2) quantify the importance of context for classification, (3) qualitatively compare DNNs against FV classifiers in terms of important image regions and (4) detect potential flaws and biases in data. All experiments are performed on the PASCAL VOC 2007 data set.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Evaluating the visualization of what a Deep Neural Network has learned

Deep Neural Networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multi-layer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the ''importance'' of individual pixels wrt the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three different methods on the SUN397, ILSVRC2012 and MIT Places data sets. Our main result is that the recently proposed Layer-wise Relevance Propagation (LRP) algorithm qualitatively and quantitatively provides a better explanation of what made a DNN arrive at a particular classification decision than the sensitivity-based approach or the deconvolution method. We provide theoretical arguments to explain this result and discuss its practical implications. Finally, we investigate the use of heatmaps for unsupervised assessment of neural network performance.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Wasserstein Training of Boltzmann Machines

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from training samples to the Boltzmann model. We propose in this work a novel approach for Boltzmann training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model parameters. Minimization of this new Wasserstein objective leads to generative models that are better when considering the metric and that have a cluster-like structure. We demonstrate the practical potential of these models for data completion and denoising, for which the metric between observations plays a crucial role.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Learning Feature Hierarchies with Centered Deep Boltzmann Machines

Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of the activation functions to zero. This modification leads to a better conditioned Hessian and thus makes learning easier. We test the algorithm on real data and demonstrate that our suggestion, the centered deep Boltzmann machine, learns a hierarchy of increasingly abstract representations and a better generative model of data.

0 citations0 reviewsNo code linkedOpen access