Source: French to English Tester Published on: 2026-04-23
Source: The Conversation – in French– By Guillaume Guérard, Teacher-Researcher, Artificial Intelligence, ESILV, Léonard de Vinci Campus
Most of today’s efficient algorithms – notably deep learning (deep learning) and its neural networks – function as black boxes. We know they deliver good results, but it is impossible to understand their internal logic. This poses a problem for many application areas (medicine, justice…), which prompts regulators to demand “explainable” systems. Several avenues toward explainability exist. Focus on “pretopology.”
Let’s imagine a patient whose blood test results show a hemoglobin level of 12.5 grams per deciliter of blood. An early cancer detection algorithm analyzes these numbers, as well as his family history (present or absent), his smoking status (yes or no), and his physical activity level (low, medium, high). The algorithm classifies him into a moderate risk group. But when his doctor asks why, the system cannot respond: it is a black box.
And this is obviously a problem for the patient, the doctor, health insurance, etc. That is why the European AI Act, adopted in March 2024, imposes strict obligations on organizations and companies operating in Europe. By 2026-2027, all so-called high-risk AI systems will have to be “transparent” and “explainable,” that is, ones whose logic a human can understand. Thesanctionsmay reach 35 million euros or 7% of the global annual turnover, as the concerned areas can have significant effects.
For example, in human resources, resume screening software that analyzes both diploma levels, years of experience, and technical skills must be able to justify why one candidate is selected and another is rejected. In the energy industry, predictive maintenance systems that combine sensor data (temperature, vibrations), maintenance history, and equipment type must explain why a wind turbine or other equipment is flagged as “at risk of failure.”
To counter the“black box effect” of current AI systems, we propose a method derived from a discipline little known to the general public, “pre-topology,” which makes it possible to render explicit the reasoning made on mixed data (the hemoglobin rate is a number while the presence or absence of family history is not quantified).
What is pretopology?
- Pretopology is the art of drawing “zones of influence” around each person or object in a network — like friend circles on social networks, where influence is not necessarily reciprocal.
- To describe a complex area, it uses a recipe called disjunctive normal form, which assembles basic blocks, then automatically calculates everything that “adheres” to this assembly, that is to say everything that naturally revolves around it.
The limits of current methods for making AI systems “explainable”
Thehierarchical clusteringis today the reference method for automatically grouping similar observations and thus making data more interpretable: by organizing observations into a hierarchy of nested groups (a dendrogram), it allows an expert to navigate between levels of granularity, identify typical profiles, and explain why two individuals are grouped together without having to open the “black box” of a predictive model.
Its operation is simple and transparent. First, the distance between each pair of observations is measured. Then, the closest observations are progressively grouped together. Finally, a tree (called a dendrogram) is obtained, which can be cut at different levels to form groups.
Let’s take the example ofpenguins of the Palmer Archipelago in Antarctica. If we measure the length of their beak and their body mass, hierarchical clustering automatically identifies three groups that correspond to the three biological species present: Adélie, Chinstrap, and Gentoo. The major advantage is its transparency: we visualize the tree, follow the successive groupings, easily understand how the groups were formed, and the branching height gives an idea of the “difference” between two groups.
The challenge arises when mixing numbers and categories. Measuring a distance between two numbers is easy: if a patient has a blood glucose level of 5.5 millimoles per liter (a concentration unit) and another has 6.2 millimoles per liter, the difference is 0.7. But how do you measure the distance between two “categories” that cannot be quantified, such as a yes or no response (smoker or non-smoker), or even the color of a biological tissue?
For example, in our early cancer detection example, if patient A has a hemoglobin concentration of 12.5 grams per deciliter (number), a family history (category “yes”), and does not smoke (category “no”); while patient B has a hemoglobin concentration of 13.1 grams per deciliter, no family history, and smokes… how to say if these two patients are “close” or “distant” in terms of risks?
Existing solutions, such ask-means, HDBSCAN and DIANAall have limitations. Transforming categories into artificial numbers (“yes” = 1, “no” = 0) is arbitrary and causes loss of meaning. More precisely, this means that one introduces an order relation and a distance that do not exist: coding “cat” = 1, “dog” = 2, “bird” = 3 implicitly suggests that dog is “between” cat and bird, or that the distance cat-dog is equal to dog-bird, which can bias all downstream similarity calculations.
Ignoring categories to keep only the numbers, as in the methods previously mentioned, results in the loss of crucial information such as family history. More complex statistical methods are often opaque or require strong assumptions about the structure of the data. This is the case withGower distanceor of theanalysis of latent factors– the kind of structure that can be hidden behind large language models (LLM).
It is precisely in the definition of these neighborhoods – how to measure that a patient “resembles” a group despite heterogeneous data – that pretopology offers a natural framework: it allows the construction of flexible areas of influence, without imposing artificial distances or hypotheses about the data structure.
A solution in development: measuring similarity differently
For this, instead of trying to measure distances, we propose to change perspective by defining “neighborhoods,” built using disjunctive normal forms, or DNF. Behind this name lie simple logical rules of the type: “A patient belongs to the neighborhood of a group if (they are diabetic AND over 60 years old) OR (they have a family history AND are hypertensive).” Each condition in parentheses is a block; the neighborhood is the union of these blocks. No numbers, no distances: only combinations of features, like readable decision rules.
Once the neighborhoods are defined, for each group, we calculate the set of all patients who “adhere” to it — that is, who fall into at least one of these DNF blocks. This adherence calculation is iterative: at each step, patients join or leave a group until stabilization is reached. The result is similar to a dendrogram: we obtain a hierarchy of successive groupings, from the most local (fine blocks, few patients) to the most global (large stable groups), without ever having imposed an artificial distance between categories and numbers.
An analogy helps to understand. On a geographical map, the distance between Paris and Lyon is measured in kilometers. But one can also say that Dijon is a neighbor of Lyon because they share characteristics: similar region, comparable climate, close economy. This notion of “neighborhood” by common characteristics does not require calculating a precise distance.
Our algorithm in open access for pilot studies
This is the basic principle of PretopoMD, our algorithm that automatically classifies mixed data (numbers and categories) while making its grouping logic explicit. For numbers, two values are neighbors if they fall within the same window: all blood glucose levels between 5 and 7 mmol/L are neighbors. For categories, two observations are neighbors if they share the same modality: two patients are neighbors if they are both smokers, or if both have family medical history.
PretopoMD is alreadyavailable in open accessto enable health, HR or maintenance teams to use it for pilot studies. In the medium term, we hope that this approach can help European organizations meet the requirements of the AI Act by offering classifications that are explainable by design.
The key advantage is traceability. For our medical example, we can say:
“Patients A and C are in the same group because they share a blood glucose level in the 5-7 millimoles per liter range (step 1), both have a family history (step 1), and both have a BMI between 25-30 (step 2). Patient B joins them at step 3 via a similar BMI, despite the absence of family history.”
This step-by-step explanation directly meets the requirements of theAI Act. Furthermore, the hierarchical structure is preserved, allowing the identification of major groups and relevant subgroups.
Nevertheless, our algorithm has limitations, since the size of the windows and the similarity thresholds must be chosen, currently requiring an expert in the field. We are working on methods to automate these choices.
Thus, the question remains open: how far can we push performance while maintaining explainability? In sensitive fields such as healthcare or law, is this compromise acceptable? Our work shows that at least this path can be explored.
Guillaume Guérard does not work for, advise, own shares in, or receive funds from any organization that might benefit from this article, and has declared no affiliation other than his research institution.
–ref. Penguins from Antarctica to explainability in AI. Welcome to pretopology!https://theconversation.com/antarctic-penguins-and-explainability-in-ai-welcome-to-pretology-278007