Laurent Najman

Transforming gradient-based techniques into interpretable methods

Abstract

The explication of Convolutional Neural Networks (CNN) through xAI techniques often poses challenges in interpretation. The inherent complexity of input features, notably pixels extracted from images, engenders complex correlations. Gradient-based methodologies, exemplified by Integrated Gradients (IG), effectively demonstrate the significance of these features. Nevertheless, the conversion of these explanations into images frequently yields considerable noise. Presently, we introduce GAD (Gradient Artificial Distancing) as a supportive framework for gradient-based techniques. Its primary objective is to accentuate influential regions by establishing distinctions between classes. The essence of GAD is to limit the scope of analysis during visualization and, consequently reduce image noise. Empirical investigations involving occluded images have demonstrated that the identified regions through this methodology indeed play a pivotal role in facilitating class differentiation.

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Unsupervised discovery of interpretable visual concepts

Abstract

Providing interpretability of deep-learning models to non-experts, while fundamental for a responsible real-world usage, is challenging. Attribution maps from xAI techniques, such as Integrated Gradients, are a typical example of a visualization technique containing a high level of information, but with difficult interpretation. In this paper, we propose two methods, Maximum Activation Groups Extraction (MAGE) and Multiscale Interpretable Visualization (Ms-IV), to explain the model’s decision, enhancing global interpretability. MAGE finds, for a given CNN, combinations of features which, globally, form a semantic meaning, that we call concepts. We group these similar feature patterns by clustering in concepts, that we visualize through Ms-IV. This last method is inspired by Occlusion and Sensitivity analysis (incorporating causality) and uses a novel metric, called Class-aware Order Correlation (CAOC), to globally evaluate the most important image regions according to the model’s decision space. We compare our approach to xAI methods such as LIME and Integrated Gradients. Experimental results evince the Ms-IV higher localization and faithfulness values. Finally, qualitative evaluation of combined MAGE and Ms-IV demonstrates humans’ ability to agree, based on the visualization, with the decision of clusters’ concepts; and, to detect, among a given set of networks, the existence of bias.

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Bridging human concepts and computer vision for explainable face verification

Abstract

With Artificial Intelligence (AI) influencing the decision-making process of sensitive applications such as Face Verification, it is fundamental to ensure the transparency, fairness, and accountability of decisions. Although Explainable Artificial Intelligence (XAI) techniques exist to clarify AI decisions, it is equally important to provide interpretability of these decisions to humans. In this paper, we present an approach to combine computer and human vision to increase the explanation’s interpretability of a face verification algorithm. In particular, we are inspired by the human perceptual process to understand how machines perceive face’s human-semantic areas during face comparison tasks. We use Mediapipe, which provides a segmentation technique that identifies distinct human-semantic facial regions, enabling the machine’s perception analysis. Additionally, we adapted two model-agnostic algorithms to provide human-interpretable insights into the decision-making processes.

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Discrete Morse functions and watersheds

Abstract

Any watershed, when defined on a stack on a normal pseudomanifold of dimension $d$, is a pure $(d-1)$-subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined, and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.

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Gradients intégrés renforcés

Abstract

Les visualisations fournies par les techniques d’Intelligence Artificielle Explicable xAI) pour expliquer les réseaux de neurones convolutionnels (CNN’s) sont parfois difficile á interpréter. La richesse des motifs d’une image qui sont fournis en entrées (les pix l d’une image) entraîne des corrélations complexes entre les classes. Les techniques basées sur les gradients, telles que les gradients intégrés, mettent en évidence l’import nce de ces caractéristiques. Cependant, lorsqu’on les visualise sous forme d’images, on peut e retrouver avec un bruit excessif et donc une difficulté á interpréter les explic tions fournies. Nous proposons la méthode intitulée Gradients Intégrés Renforcés (RI ), une variation des gradients intégrés, qui vise á mettre en évidence les régions nfluentes des images dans la décision des réseaux. Cette méthode vise á réduire la sur ace des zones á analyser lors de la visualisation des résultats, générant ainsi moins e bruit apparent. Des expériences á base d’occlusions démontrent que les régions chois es par notre méthode jouent effectivement un rôle important en terme de classification.

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Some equivalence relation between persistent homology and morphological dynamics

Abstract

In Mathematical Morphology (MM), connected filters based on dynamics are used to filter the extrema of an image. Similarly, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) that represents the stability of the extrema of a Morse function. Since these two concepts seem to be closely related, in this paper we examine their relationship, and we prove that they are equal on $n$-D Morse functions, $n\geq 1$. More exactly, pairing a minimum with a $1$-saddle by dynamics or pairing the same $1$-saddle with a minimum by persistence leads exactly to the same pairing, assuming that the critical values of the studied Morse function are unique. This result is a step further to show how much topological data analysis and mathematical morphology are related, paving the way for a more in-depth study of the relations between these two research fields.

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Gradient vector fields of discrete morse functions and watershed-cuts

Abstract

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Continuous well-composedness implies digital well-composedness in $n$-D

Abstract

In this paper, we prove that when a $n$-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological $(n-1)$-manifold, then it is digitally well-composed (DWC), which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D.

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An equivalence relation between morphological dynamics and persistent homology in $n$-D

Abstract

In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to $n$-D, $n \geq 2$, showing that this equality can be applied to $n$-D images and not only to 1D functions. This is a step further to show how much MM and MT are related.

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Equivalence between digital well-composedness and well-composedness in the sense of Alexandrov on $n$-D cubical grids

Abstract

Among the different flavors of well-composednesses on cubical grids, two of them, called respectively Digital Well-Composedness (DWCness) and Well-Composedness in the sens of Alexandrov (AWCness), are known to be equivalent in 2D and in 3D. The former means that a cubical set does not contain critical configurations when the latter means that the boundary of a cubical set is made of a disjoint union of discrete surfaces. In this paper, we prove that this equivalence holds in $n$-D, which is of interest because today images are not only 2D or 3D but also 4D and beyond. The main benefit of this proof is that the topological properties available for AWC sets, mainly their separation properties, are also true for DWC sets, and the properties of DWC sets are also true for AWC sets: an Euler number locally computable, equivalent connectivities from a local or global point of view… This result is also true for gray-level images thanks to cross-section topology, which means that the sets of shapes of DWC gray-level images make a tree like the ones of AWC gray-level images.

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