arXiv research

Researchers show how to secretly train models with hidden data, detect usage with high confidence.

Improved canary crafting for one-run privacy auditing reduces leakage estimates.

Fine-tuning LLMs on privacy-sensitive data introduces privacy risk, and synthetic data audits can quantify this risk.

Canary optimizes VaR-constrained RL problems with a conservative bound using Cantelli's inequality.

We present a new proof of the bi-Lipschitz model theorem, which occupies the main part of the Ending Lamination Conjecture proved by Minsky and Brock-Canary-Minsky. Our proof is done by using techniques of standard hyperbolic geometry as much as possible.

This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler & Shalen [ACCS96]. It generalizes a result by Hou [Hou01] and its proof is rather straightforward once we know the work by Lim [Lim08] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the …

Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into PSL(2,C) does not contain parabolics, then it is also the sequence's geometric limit. We construct examples that demonstrate the failure of this theorem for certain sequences…

We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $\log (2k-1)$ Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as …

In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary. Thus we obtain a complete description of th…

We present examples of hyperbolizable 3-manifolds $M$ with the following property. Let $CC(π_1(M))$ denote the space of convex co-compact representations of $π_1(M)$. We show that for every $K\geq 1$ there exists a representation $ρ$ in $\bar {CC(π_1(M))}$ so that every $K$-quasiconformal deformation of $ρ$ lies in the…

In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for the associated quasiconformal homogeneity constants across all closed hyperbolic…

A privacy-preserving synthetic data generation framework that distinguishes between true and phantom data disclosures.

In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of Euclidean space. Their motivation was to provide a characterization of quasi-disks, i.e. domains which are quasiconformally homeomorphic to the unit disk. As a gener…

We refine the recent local rigidity result for the marked length spectrum obtained by the first and third author in \cite{Guillarmou-Lefeuvre-18} and give an alternative proof using the geodesic stretch between two Anosov flows and some uniform estimate on the variance appearing in the central limit theorem for Anosov …

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian group…

We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space o…

The hitting measure is singular and has dimension less than 1 for cocompact Fuchsian groups.

Online monitor detects classifier drift and adapts predictions.

Paper proves finite BMS measure for SPR groups in higher rank Lie groups.

The paper defines a path metric on a stable component of polynomial families.

We survey recent work on the dynamics of the outer automorphism group of a word hyperbolic group on spaces of (conjugacy classes of) representations ofthe group into a semi-simple Lie group G. All these results are motivated by the fact that the mapping class group of a closed surface acts properly discontinuously on t…

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly degenerate hyperbolic 3-manifolds developed by Brock, Canary, and Minsky during …

The paper bounds eigenvalues of hyperbolic manifolds with infinite volume.

The study classifies weakly almost Fuchsian manifolds and proves geometric properties.

This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of…

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that π_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at least 4g-1 then M contains a closed incompressible surface of genus at most g. Thi…

In this article, we apply the forward variance modeling approach by L.Bergomi to the co-terminal swap market model. We build an interest rate model for which all the market price changes of hedging instruments, interest rate swaps and European swaptions, are interpreted as the state variable variations, and no diffusio…

Study shows exact dimensionality and regularity of manifolds for specific groups.

Consider a geometrically finite Kleinian group $G$ without parabolic or elliptic elements, with its Kleinian manifold $M=(\H^3\cup Ω_G)/G$. Suppose that for each boundary component of $M$, either a maximal and connected measured lamination in the Masur domain or a marked conformal structure is given. In this setting, w…

RBM models reveal how hidden unit tail behavior affects pattern reconstruction.

Expands Hidden Markov Model to include Markov chain observations.

This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian non…

Supervised learning frequently boils down to determining hidden and bright parameters in a parameterized hypothesis space based on finite input-output samples. The hidden parameters determine the attributions of hidden predictors or the nonlinear mechanism of an estimator, while the bright parameters characterize how h…

New attacks improve privacy audits by analyzing model updates.

Randomly chosen primary hidden units and derived secondary units reduce neural network complexity.

New MBL hidden Born machine learns various tasks.

Unified framework analyzes privacy risks from gradients in distributed learning.

New insights into hidden minima in neural networks.

Paper tackles hidden game problem in AI alignment and language games.

Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…

We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain Monte Carlo to move between solutions. In contrast, we assume that the number of hi…

Hidden Markov Neural Networks balance adaptation and forgetting in time-series data.

The paper introduces FMCI and hybrid decoding for hidden Markov models.

This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into the learning process of the network. But this strategy can not be applied for E…

A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the relations to other variables in the model and determining the number of states of …

The paper proves limitations on hyperbolic knot complements with hidden symmetries.

This paper tackles hidden state inference for HMMs using particle filtering.

Extends causal inference to hidden mediators with proxies.