arXiv subjects

Olivier Laurent

Publications and source records attributed to Olivier Laurent.

14 recordsLinked to original sources

arXiv2026

Yeo's Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic

We revisit sequentialization proofs associated with the Danos-Regnier correctness criterion in the theory of proof nets of linear logic. Our approach relies on a generalization of Yeo's theorem for graphs, based on colorings of half-edges. This happens to be the appropriate level of abstraction to extract sequentiality information from a proof net without modifying its graph structure. We thus obtain different ways of recovering a sequent calculus derivation from a proof net inductively, by relying on a splitting vertex, which we can impose to be a par-vertex, or a terminal vertex, or a non-axiom vertex, etc., in a modular way. This approach applies in presence of the mix-rules as well as for proof nets of unit-free multiplicative-additive linear logic (through an appropriate further generalization of Yeo's theorem). The proof of our Yeo-style theorem relies on a key lemma that we call cusp minimization. Given a coloring of half-edges, a cusp in a path is a vertex whose adjacent half-edges in the path have the same color. And, given a cycle with at least one cusp and subject to suitable hypotheses, cusp minimization constructs a cycle with strictly less cusps. In the absence of cusp-free cycles, cusp minimization is then enough to ensure the existence of a splitting vertex, i.e. a vertex that is a cusp of any cycle it belongs to. Our theorem subsumes several graph-theoretical results, including some known to be equivalent to Yeo's theorem. The novelty is that they can be derived in a straightforward way, just by defining a dedicated coloring, again without any modification of the underlying graph structure (vertices and edges) -- similar results from the literature required more involved encodings.

cs.LO↗

arXiv2025

Type Isomorphisms for Multiplicative-Additive Linear Logic

We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This yields a much richer equational theory involving distributivity and cancellation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by Hughes and Van Glabbeek. We use the sequent calculus to extend our results to full MALL, including all units, thanks to a study of cut-elimination and rule commutations.

cs.LO↗

arXiv2025

Torch-Uncertainty: A Deep Learning Framework for Uncertainty Quantification

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify the uncertainty of their predictions, limiting their broader adoption in critical real-world applications. Uncertainty Quantification (UQ) for Deep Learning seeks to address this challenge by providing methods to improve the reliability of uncertainty estimates. Although numerous techniques have been proposed, a unified tool offering a seamless workflow to evaluate and integrate these methods remains lacking. To bridge this gap, we introduce Torch-Uncertainty, a PyTorch and Lightning-based framework designed to streamline DNN training and evaluation with UQ techniques and metrics. In this paper, we outline the foundational principles of our library and present comprehensive experimental results that benchmark a diverse set of UQ methods across classification, segmentation, and regression tasks. Our library is available at https://github.com/ENSTA-U2IS-AI/Torch-Uncertainty

cs.LG↗

arXiv2025

Packed-Ensembles for Efficient Uncertainty Estimation

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems constrain to smaller ensembles and lower-capacity networks, significantly deteriorating their performance and properties. We introduce Packed-Ensembles (PE), a strategy to design and train lightweight structured ensembles by carefully modulating the dimension of their encoding space. We leverage grouped convolutions to parallelize the ensemble into a single shared backbone and forward pass to improve training and inference speeds. PE is designed to operate within the memory limits of a standard neural network. Our extensive research indicates that PE accurately preserves the properties of DE, such as diversity, and performs equally well in terms of accuracy, calibration, out-of-distribution detection, and robustness to distribution shift. We make our code available at https://github.com/ENSTA-U2IS/torch-uncertainty.

cs.LG↗

arXiv2025

Towards Understanding Why Label Smoothing Degrades Selective Classification and How to Fix It

Label smoothing (LS) is a popular regularisation method for training neural networks as it is effective in improving test accuracy and is simple to implement. ``Hard'' one-hot labels are ``smoothed'' by uniformly distributing probability mass to other classes, reducing overfitting. Prior work has suggested that in some cases LS can degrade selective classification (SC) -- where the aim is to reject misclassifications using a model's uncertainty. In this work, we first demonstrate empirically across an extended range of large-scale tasks and architectures that LS consistently degrades SC. We then address a gap in existing knowledge, providing an explanation for this behaviour by analysing logit-level gradients: LS degrades the uncertainty rank ordering of correct vs incorrect predictions by suppressing the max logit more when a prediction is likely to be correct, and less when it is likely to be wrong. This elucidates previously reported experimental results where strong classifiers underperform in SC. We then demonstrate the empirical effectiveness of post-hoc logit normalisation for recovering lost SC performance caused by LS. Furthermore, linking back to our gradient analysis, we again provide an explanation for why such normalisation is effective.

cs.LG↗

arXiv2024

Learning to Generate Training Datasets for Robust Semantic Segmentation

Semantic segmentation methods have advanced significantly. Still, their robustness to real-world perturbations and object types not seen during training remains a challenge, particularly in safety-critical applications. We propose a novel approach to improve the robustness of semantic segmentation techniques by leveraging the synergy between label-to-image generators and image-to-label segmentation models. Specifically, we design Robusta, a novel robust conditional generative adversarial network to generate realistic and plausible perturbed images that can be used to train reliable segmentation models. We conduct in-depth studies of the proposed generative model, assess the performance and robustness of the downstream segmentation network, and demonstrate that our approach can significantly enhance the robustness in the face of real-world perturbations, distribution shifts, and out-of-distribution samples. Our results suggest that this approach could be valuable in safety-critical applications, where the reliability of perception modules such as semantic segmentation is of utmost importance and comes with a limited computational budget in inference. We release our code at https://github.com/ENSTA-U2IS-AI/robusta.

cs.CV↗

arXiv2023

Make Me a BNN: A Simple Strategy for Estimating Bayesian Uncertainty from Pre-trained Models

Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are equipped for uncertainty estimation but cannot scale to large DNNs that are highly unstable to train. To address this challenge, we introduce the Adaptable Bayesian Neural Network (ABNN), a simple and scalable strategy to seamlessly transform DNNs into BNNs in a post-hoc manner with minimal computational and training overheads. ABNN preserves the main predictive properties of DNNs while enhancing their uncertainty quantification abilities through simple BNN adaptation layers (attached to normalization layers) and a few fine-tuning steps on pre-trained models. We conduct extensive experiments across multiple datasets for image classification and semantic segmentation tasks, and our results demonstrate that ABNN achieves state-of-the-art performance without the computational budget typically associated with ensemble methods.

cs.LG↗

arXiv2023

A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors

The distribution of the weights of modern deep neural networks (DNNs) - crucial for uncertainty quantification and robustness - is an eminently complex object due to its extremely high dimensionality. This paper proposes one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we will shortly release the first large-scale checkpoint dataset, including thousands of real-world models and our codes.

stat.ML↗

arXiv2021

Super Exponentials in Linear Logic

Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules. We call this system Superexponential Linear Logic (superLL). Assuming some appropriate constraints on the parameters of superLL, we give a generic proof of cut elimination. This implies that each variant of Linear Logic which appears as a valid instance of superLL also satisfies cut elimination.

cs.LO↗

arXiv2019

Intersection Subtyping with Constructors

We study the question of extending the BCD intersection type system with additional type constructors. On the typing side, we focus on adding the usual rules for product types. On the subtyping side, we consider a generic way of defining a subtyping relation on families of types which include intersection types. We find back the BCD subtyping relation by considering the particular case where the type constructors are intersection, omega and arrow. We obtain an extension of BCD subtyping to product types as another instance. We show how the preservation of typing by both reduction and expansion is satisfied in all the considered cases. Our approach takes benefits from a "subformula property" of the proposed presentation of the subtyping relation.

cs.LO↗

arXiv2017

Focusing in Orthologic

We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one incorporates the notion of focusing (coming from linear logic) to add constraints on proofs and to optimise proof search. We demonstrate how to take benefits from the new systems in automatic proof search for orthologic.

cs.LO↗

arXiv2010

Game semantics for first-order logic

We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of first-order classical logic. We present some relations with Krivine's classical realizability and applications to type isomorphisms.

cs.LO↗

arXiv2010

Acyclic Solos and Differential Interaction Nets

We present a restriction of the solos calculus which is stable under reduction and expressive enough to contain an encoding of the pi-calculus. As a consequence, it is shown that equalizing names that are already equal is not required by the encoding of the pi-calculus. In particular, the induced solo diagrams bear an acyclicity property that induces a faithful encoding into differential interaction nets. This gives a (new) proof that differential interaction nets are expressive enough to contain an encoding of the pi-calculus. All this is worked out in the case of finitary (replication free) systems without sum, match nor mismatch.

cs.LO↗

arXiv2009

Parametric mixed sequent calculus

In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.

math.LO↗