11 Search Results for "Paquet, Hugo"

Document
DOI: 10.4230/LIPIcs.FSCD.2026.23
Universal Properties of Petri Net Unfoldings

Authors: Serge Lechenne and Hugo Paquet

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
It is an established idea in concurrency theory that every Petri net admits an unfolding semantics. This is a denotational object that represents its domain of possible executions. Unfoldings play an important role in practical analysis and verification. This paper is concerned with the following well-known problem: while the unfolding resembles a universal construction in the category of Petri nets, it generally fails to satisfy the expected universal property. This is because the unfolding construction overlooks the net’s internal symmetries. There are two solutions: make these symmetries explicit to obtain a weak universal property (one that holds only "up to symmetry"); or break the symmetries by assigning individual identities to components of the net. We review these two solutions and establish, in each case, a universal unfolding of Petri nets to event structures. This paper demonstrates a 2-categorical approach to Petri net unfoldings. We show that each unfolding semantics determines a 2-categorical relative adjunction involving Petri nets and event structures. Viewed in this way, the above two constructions can be related formally via an appropriate morphism of adjunctions. We exhibit a 2-density property of event structures which implies that unfolding functors are essentially unique.
Cite as

Serge Lechenne and Hugo Paquet. Universal Properties of Petri Net Unfoldings. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lechenne_et_al:LIPIcs.FSCD.2026.23,
  author =	{Lechenne, Serge and Paquet, Hugo},
  title =	{{Universal Properties of Petri Net Unfoldings}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.23},
  URN =		{urn:nbn:de:0030-drops-263734},
  doi =		{10.4230/LIPIcs.FSCD.2026.23},
  annote =	{Keywords: Petri nets, Event structures, Symmetry, Unfolding, 2-Categories}
}
Document
DOI: 10.4230/LIPIcs.LICS.2026.25
Lazy Intermediate Representations for Algebraic Effects

Authors: Simon Castellan and Hugo Paquet

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
A lazy program interpreter postpones computation until the result is actually needed. This is typically more efficient than an eager (or call-by-value) interpreter, but a concern is that the semantics is not generally preserved. We propose a new semantic analysis of lazy evaluation that relies on a subtle combination of name generation and read-only state. Our perspective is that laziness arises from a hybrid evaluation strategy, in which only the name generation follows call-by-value. This semantic model suggests better intermediate representations of sum and product types in a lazy interpreter, along with equations that justify further optimizations. We illustrate this with an implementation in OCaml. Our motivation is practical: the origin of this work is a real-world application of discrete probabilistic programming, in which large algebraic data types cause significant performance issues with a call-by-value interpreter. Our lazy semantics justifies better optimized representations, and provides principled foundations for other methods involving laziness in probabilistic programming.
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Simon Castellan and Hugo Paquet. Lazy Intermediate Representations for Algebraic Effects. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 25:1-25:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{castellan_et_al:LIPIcs.LICS.2026.25,
  author =	{Castellan, Simon and Paquet, Hugo},
  title =	{{Lazy Intermediate Representations for Algebraic Effects}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{25:1--25:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.25},
  URN =		{urn:nbn:de:0030-drops-268124},
  doi =		{10.4230/LIPIcs.LICS.2026.25},
  annote =	{Keywords: Categorical semantics, lazy evaluation, interpreter, probabilistic programming}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.19
Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means

Authors: Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is equipped with a protected attribute, and a number k, the goal is to partition P into k clusters with a designated center each, such that a center-based objective function is minimized and the attributes are fairly distributed with respect to the following two fairness concepts: 1) group fairness: We aim for clusters with balanced numbers of attributes by specifying lower and upper bounds for the desired attribute proportions. 2) diverse center selection: Clusters have natural representatives, i.e., their centers. We ask for a balanced set of representatives by specifying the desired number of centers to choose from each attribute. Dickerson, Esmaeili, Morgenstern, and Pena [John P. Dickerson et al., 2023] denote the combination of these two constraints as doubly constrained fair clustering. They present algorithms whose guarantees depend on the best known approximation factors for either of these problems. Currently, this implies an 8-approximation with a small additive violation on the group fairness constraint. For k-center, we improve this approximation factor to 4 with a small additive violation. This guarantee also depends on the currently best algorithm for DS-fair k-center given by Jones, Nguyen and Nguyen [Matthew Jones et al., 2020]. For k-median and k-means, we propose the first constant-factor approximation algorithms. Our algorithms transform a solution that satisfies diverse center selection into a doubly constrained fair clustering using an LP-based approach. Furthermore, our results are generalizable to other center-selection constraints, such as matroid k-clustering and knapsack constraints.
Cite as

Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm. Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{funk_et_al:LIPIcs.SWAT.2026.19,
  author =	{Funk, Nicole and Hennes, Annika and Hillebrand, Johanna and Sturm, Sarah},
  title =	{{Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.19},
  URN =		{urn:nbn:de:0030-drops-260551},
  doi =		{10.4230/LIPIcs.SWAT.2026.19},
  annote =	{Keywords: Clustering, Fairness, Approximation Algorithms, k-center, k-median, k-means}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.12
String Diagrams for Closed Symmetric Monoidal Categories

Authors: Callum Reader and Alessandro Di Giorgio

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics.
Cite as

Callum Reader and Alessandro Di Giorgio. String Diagrams for Closed Symmetric Monoidal Categories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{reader_et_al:LIPIcs.CSL.2026.12,
  author =	{Reader, Callum and Di Giorgio, Alessandro},
  title =	{{String Diagrams for Closed Symmetric Monoidal Categories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.12},
  URN =		{urn:nbn:de:0030-drops-254369},
  doi =		{10.4230/LIPIcs.CSL.2026.12},
  annote =	{Keywords: diagrammatic languages, logic, lambda calculi}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2026.4
Towards A Rosetta Stone of Interactive and Quantitative Semantics (Invited Talk)

Authors: Pierre Clairambault

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Quantitative semantics are those denotational semantics that inherit from linear logic [Jean-Yves Girard, 1987] a sensitivity to the multiplicity of resources involved in computation. Those include the relational model [Jean-Yves Girard, 1987] and its numerous variations (such as finiteness spaces [Thomas Ehrhard, 2005], weighted relational models [Jim Laird et al., 2013] and their extensions [Thomas Ehrhard et al., 2011; Thomas Ehrhard, 2002], generalized species of structure [Fiore et al., 2008], span models [Paul-André Melliès, 2019; Pierre Clairambault and Simon Forest, 2023], etc), as well as related syntactic methods such as non-idempotent intersection types [Daniel de Carvalho, 2018] and Taylor expansion of lambda-terms [Thomas Ehrhard and Laurent Regnier, 2003]. Interactive semantics are usually also quantitative, but in addition they present the interactive behaviour of proofs and programs, generally organized chronologically - those include the many variants of game semantics (starting with [J. M. E. Hyland and C.-H. Luke Ong, 2000; Samson Abramsky et al., 2000]), and other frameworks such as Geometry of Interaction [Girard, 1989] or ludics [Jean-Yves Girard, 2001]. Both families are cornerstones of modern denotational semantics, and both have associated Alonzo Church awards: game semantics in 2017, and quantitative semantics (in particular, differential linear logic and the differential λ-calculus) in 2024. It has more or less always been clear to the experts that the two, sharing an origin in linear logic, are conceptually related. Yet there are differences, which seem fundamental: in particular, while quantitative models compose relationally, the composition of strategies follows an intricate "parallel interaction plus hiding" process inspired from concurrency theory [Abramsky, 1997]. The two families of models have also historically targeted different kinds of languages: whereas quantitative semantics focused on theoretical calculi (and the λ-calculus in particular), game semantics is known for fully abstract models for languages with elaborate combinations of effects including local state [Samson Abramsky and Guy McCusker, 1996], control operators [James Laird, 1997], and concurrent primitives [Dan R. Ghica and Andrzej S. Murawski, 2008]. Early on, researchers have explored the relationship between the two [Thomas Ehrhard, 1996; Patrick Baillot et al., 1997], and investigations on this question have spanned decades [Pierre Boudes, 2009; Ana C. Calderon and Guy McCusker, 2010; Takeshi Tsukada and C.-H. Luke Ong, 2016; C.-H. Luke Ong, 2017]. In particular, Melliès' work on asynchronous games [Paul-André Melliès, 2006; Paul-André Melliès, 2005] made significant conceptual contributions, showing that the issue was enlightened by adopting a positional formulation of game semantics, where points in the relational model simply arise as certain positions. This talk surveys recent developments in this line of work, shedding light on the connection between those two families. Our work is set in so-called "thin concurrent games" [Simon Castellan et al., 2019; Pierre Clairambault, 2024], an extension with symmetry of Rideau and Winskel’s concurrent games on event structures [Silvain Rideau and Glynn Winskel, 2011]. Event structures being one of the main "truly concurrent" models of concurrency [Glynn Winskel, 1986], it is perhaps expected that thin concurrent games can model concurrent languages: they provide a truly concurrent refinement of Ghica and Murawski’s fully abstract model of Idealized Concurrent Algol [Simon Castellan and Pierre Clairambault, 2024; Pierre Clairambault, 2024]. But beyond the semantics of concurrency, thin concurrent games are also a deep reworking on game semantics built from causal principles, inheriting from asynchronous games a positional flavour. In thin concurrent games, strategies have a dual nature: an event-based nature where they appear as certain event structures composed via parallel interaction plus hiding; or a positional nature where they appear as certain spans of groupoids, composed by pullback (modulo a technical condition on strategies called visibility) - they can be regarded both as a games and a relational model! Leveraging this dual nature, in a sequence of papers with Castellan, de Visme, Olimpieri and Paquet, we have been able to link the single framework of thin concurrent games with numerous other models. This includes various traditional alternating or non-alternating games models [Simon Castellan and Pierre Clairambault, 2024; Pierre Clairambault, 2024], the weighted relational model [Pierre Clairambault and Hugo Paquet, 2021], the quantum relational model [Pierre Clairambault and Marc de Visme, 2020], generalized species of structure [Pierre Clairambault et al., 2023], and - going beyond quantitative semantics - the linear Scott model [Clairambault, 2025], a linear decomposition of standard Scott domain semantics [Thomas Ehrhard, 2012]. All these distinct models are obtained by projecting away certain aspects of thin concurrent games, giving some support to the claim that thin concurrent games are a Rosetta stone for interactive and quantitative semantics.
Cite as

Pierre Clairambault. Towards A Rosetta Stone of Interactive and Quantitative Semantics (Invited Talk). In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clairambault:LIPIcs.CSL.2026.4,
  author =	{Clairambault, Pierre},
  title =	{{Towards A Rosetta Stone of Interactive and Quantitative Semantics}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{4:1--4:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.4},
  URN =		{urn:nbn:de:0030-drops-254286},
  doi =		{10.4230/LIPIcs.CSL.2026.4},
  annote =	{Keywords: Denotational semantics, Game semantics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.10
Categorical Continuation Semantics for Concurrency

Authors: Flavien Breuvart and Hugo Paquet

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Continuation semantics for simple programming languages can be axiomatized as a dialogue category: a symmetric monoidal category equipped with a negation operation. This axiomatization makes clear the relationship between game semantics, CPS transformations, and continuation monads. In this paper we extend dialogue categories with 2-categorical structure and concurrent primitives. This is inspired by a recent analysis of concurrency based on 2-categorical monads. We show that the fine-grained structure of dialogue categories, not generally available in other semantic models, can be exploited to give a type to concurrent primitives join and fork. Our main theorem is that this simple axiomatization induces a concurrent continuation 2-monad. We also show that this framework is expressive beyond call-by-value monadic programming. The definitions in this paper are illustrated by concrete constructions in concurrent game semantics, and our results give a formal categorical basis for concurrent strategies. From a more practical perspective, our approach suggests a candidate target language for linear CPS transformations of concurrent programming languages.
Cite as

Flavien Breuvart and Hugo Paquet. Categorical Continuation Semantics for Concurrency. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{breuvart_et_al:LIPIcs.FSCD.2025.10,
  author =	{Breuvart, Flavien and Paquet, Hugo},
  title =	{{Categorical Continuation Semantics for Concurrency}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.10},
  URN =		{urn:nbn:de:0030-drops-236251},
  doi =		{10.4230/LIPIcs.FSCD.2025.10},
  annote =	{Keywords: denotational semantics, 2-categories, concurrency, continuations, game semantics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
Cite as

Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.1
Privacy-Computation Trade-Offs in Private Repetition and Metaselection

Authors: Kunal Talwar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
A Private Repetition algorithm takes as input a differentially private algorithm with constant success probability and boosts it to one that succeeds with high probability. These algorithms are closely related to private metaselection algorithms that compete with the best of many private algorithms, and private hyperparameter tuning algorithms that compete with the best hyperparameter settings for a private learning algorithm. Existing algorithms for these tasks pay either a large overhead in privacy cost, or a large overhead in computational cost. In this work, we show strong lower bounds for problems of this kind, showing in particular that for any algorithm that preserves the privacy cost up to a constant factor, the failure probability can only fall polynomially in the computational overhead. This is in stark contrast with the non-private setting, where the failure probability falls exponentially in the computational overhead. By carefully combining existing algorithms for metaselection, we prove computation-privacy tradeoffs that nearly match our lower bounds.
Cite as

Kunal Talwar. Privacy-Computation Trade-Offs in Private Repetition and Metaselection. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{talwar:LIPIcs.FORC.2025.1,
  author =	{Talwar, Kunal},
  title =	{{Privacy-Computation Trade-Offs in Private Repetition and Metaselection}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.1},
  URN =		{urn:nbn:de:0030-drops-231282},
  doi =		{10.4230/LIPIcs.FORC.2025.1},
  annote =	{Keywords: Differential Privacy, Hyperparameter Tuning, Metaselection}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.23
The Correlated Gaussian Sparse Histogram Mechanism

Authors: Christian Janos Lebeda and Lukas Retschmeier

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the problem of releasing a sparse histogram under (ε, δ)-differential privacy. The stability histogram independently adds noise from a Laplace or Gaussian distribution to the non-zero entries and removes those noisy counts below a threshold. Thereby, the introduction of new non-zero values between neighboring histograms is only revealed with probability at most δ, and typically, the value of the threshold dominates the error of the mechanism. We consider the variant of the stability histogram with Gaussian noise. Recent works ([Joseph and Yu, COLT '24] and [Lebeda, SOSA '25]) reduced the error for private histograms using correlated Gaussian noise. However, these techniques can not be directly applied in the very sparse setting. Instead, we adopt Lebeda’s technique and show that adding correlated noise to the non-zero counts only allows us to reduce the magnitude of noise when we have a sparsity bound. This, in turn, allows us to use a lower threshold by up to a factor of 1/2 compared to the non-correlated noise mechanism. We then extend our mechanism to a setting without a known bound on sparsity. Additionally, we show that correlated noise can give a similar improvement for the more practical discrete Gaussian mechanism.
Cite as

Christian Janos Lebeda and Lukas Retschmeier. The Correlated Gaussian Sparse Histogram Mechanism. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lebeda_et_al:LIPIcs.FORC.2025.23,
  author =	{Lebeda, Christian Janos and Retschmeier, Lukas},
  title =	{{The Correlated Gaussian Sparse Histogram Mechanism}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.23},
  URN =		{urn:nbn:de:0030-drops-231503},
  doi =		{10.4230/LIPIcs.FORC.2025.23},
  annote =	{Keywords: differential privacy, correlated noise, sparse gaussian histograms}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.31
A Combinatorial Approach to Higher-Order Structure for Polynomial Functors

Authors: Marcelo Fiore, Zeinab Galal, and Hugo Paquet

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Polynomial functors are categorical structures used in a variety of applications across theoretical computer science; for instance, in database theory, denotational semantics, functional programming, and type theory. A well-known problem is that the bicategory of finitary polynomial functors between categories of indexed sets is not cartesian closed, despite its success and influence on denotational models and linear logic. This paper introduces a formal bridge between the model of finitary polynomial functors and the combinatorial theory of generalised species of structures. Our approach consists in viewing finitary polynomial functors as free analytic functors, which correspond to free generalised species. In order to systematically consider finitary polynomial functors from this combinatorial perspective, we study a model of groupoids with additional logical structure; this is used to constrain the generalised species between them. The result is a new cartesian closed bicategory that embeds finitary polynomial functors.
Cite as

Marcelo Fiore, Zeinab Galal, and Hugo Paquet. A Combinatorial Approach to Higher-Order Structure for Polynomial Functors. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{fiore_et_al:LIPIcs.FSCD.2022.31,
  author =	{Fiore, Marcelo and Galal, Zeinab and Paquet, Hugo},
  title =	{{A Combinatorial Approach to Higher-Order Structure for Polynomial Functors}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.31},
  URN =		{urn:nbn:de:0030-drops-163129},
  doi =		{10.4230/LIPIcs.FSCD.2022.31},
  annote =	{Keywords: Bicategorical models, denotational semantics, stable domain theory, linear logic, polynomial functors, species of structures, groupoids}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.16
Fully Abstract Models of the Probabilistic lambda-calculus

Authors: Pierre Clairambault and Hugo Paquet

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We compare three models of the probabilistic lambda-calculus: the probabilistic Böhm trees of Leventis, the probabilistic concurrent games of Winskel et al., and the weighted relational model of Ehrhard et al. Probabilistic Böhm trees and probabilistic strategies are shown to be related by a precise correspondence theorem, in the spirit of existing work for the pure lambda-calculus. Using Leventis' theorem (probabilistic Böhm trees characterise observational equivalence), we derive a full abstraction result for the games model. Then, we relate probabilistic strategies to the weighted relational model, using an interpretation-preserving functor from the former to the latter. We obtain that the relational model is also fully abstract.
Cite as

Pierre Clairambault and Hugo Paquet. Fully Abstract Models of the Probabilistic lambda-calculus. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{clairambault_et_al:LIPIcs.CSL.2018.16,
  author =	{Clairambault, Pierre and Paquet, Hugo},
  title =	{{Fully Abstract Models of the Probabilistic lambda-calculus}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.16},
  URN =		{urn:nbn:de:0030-drops-96835},
  doi =		{10.4230/LIPIcs.CSL.2018.16},
  annote =	{Keywords: Game Semantics, Lambda-calculus, Probabilistic programming, Relational model, Full abstraction}
}
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