Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
problem Improving the mixing time of Gibbs sampler under strong log-concavity.
method Analyzing Gibbs sampler contraction under strong log-concavity, providing sharp contraction rate.
result Gibbs sampler contracts entropy linearly with condition number and independent of dimension under strong log-concavity.
Nonnegative sectional curvature linked to matrix displacement convexity.
problem Nonnegative sectional curvature in Riemannian manifolds.
method Matrix displacement convexity as a criterion for nonnegative sectional curvature.
result Entropy functional matrix displacement convexity implies nonnegative sectional curvature.
Study non-negative curvature Markov chains, proving entropy contraction.
problem Prove entropy contraction for Markov chains with non-negative curvature.
method Prove 1-step contraction in Wasserstein distance implies 1-step contraction in relative entropy.
result Prove MLSI with constant equal to minimal rate increment for mean-field zero-range process.
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.
The paper introduces a new intrinsic reward method for exploration in reinforcement learning.
problem Improving exploration in reinforcement learning agents.
method Intrinsic rewards proportional to the entropy of future state-action features.
result The new objective leads to improved visitation of features within individual trajectories.
New RL approach uses future state and action visitation measures for better exploration.
problem Improving exploration in reinforcement learning.
method Intrinsic reward based on future state and action visitation measures, using contraction operators.
result Policies achieve good state-action space coverage and high performance.
The paper examines robustness of topological entropy in geodesic flows.
problem Entropy robustness in geodesic flows under C0 perturbations. method Study of topological entropy on Riemannian metrics with C0 topology. result Metrics with contractible closed geodesics have robust entropy.
Holomorphic automorphisms on hyperkähler manifolds with high entropy are Kummer examples.
problem Characterizing holomorphic automorphisms with high entropy on hyperkähler manifolds.
method Using Jensen's inequality and properties of stable and unstable distributions, the authors show uniform contraction and expansion, leading to the conclusion that the manifold is birational to a torus quotient.
result Holomorphic automorphisms with high entropy on hyperkähler manifolds are Kummer examples.
The paper categorizes and analyzes various event-linked perpetual futures contracts.
problem Developing a risk-design framework for complex event-linked perpetual futures.
method Formal taxonomy of seven pure-form canonical variants, organized along four design axes.
result Detailed analysis of microstructure properties and limitations of various variants.
Study introduces new curvature conditions for Lorentzian spaces using Rényi entropy.
problem Developing synthetic curvature conditions for Lorentzian spaces.
method Introducing timelike curvature-dimension conditions and measure-contraction properties using Rényi entropy.
result Equivalence of new curvature conditions to entropic counterparts.
Quantum channels' contraction under privacy constraints studied.
problem Understanding the privacy constraints on quantum channel contractions.
method Established upper bounds on contraction coefficients for specific divergences under QLDP constraints.
result Upper bounds and full characterization of contraction coefficients for specific quantum distances.
The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.
problem Developing a mathematical framework for denoising diffusion models in noncommutative settings.
method Formulating diffusion and reverse processes governed by operator-valued stochastic dynamics, using tools from free stochastic analysis.
result Establishing an information-geometric link between entropy production, transport, and deconvolution.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
Locally private mechanisms' output divergence bounds derived.
problem Bounding divergence between locally private mechanisms' outputs.
method Sharp upper bounds on divergence between input and output distributions.
result Established locally private versions of estimation risk bounds.
We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality, gradient estimates and Wa…
We prove the equivalence of the curvature-dimension bounds of Lott-Sturm-Villani (via entropy and optimal transport) and of Bakry--Émery (via energy and Γ_2$-calculus) in complete generality for infinitesimally Hilbertian metric measure spaces. In particular, we establish the full Bochner inequality on such metric meas…
For the first time ever, we analyze a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40,000 public procurements in the Czech Republic between 2006…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value o…
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed…
Large deviations theory applied to policy gradient methods.
problem Understanding convergence of policy gradient methods in reinforcement learning.
method Large deviation rate function and contraction principle from large deviations theory.
result Convergence properties of policy gradient methods can be extended to various policy parametrizations.
Maximizes coding rate difference for robust, discriminative features.
problem Learning robust, discriminative features from high-dimensional data.
method Maximal Coding Rate Reduction (MCR^2) principle.
result Significantly more robust to label corruptions in classification.
We show under weak hypotheses that ∂X, the Roller boundary of a finite dimensional CAT(0) cube complex X is the Furstenberg-Poisson boundary of a sufficiently nice random walk on an acting group Γ. In particular, we show that if Γ admits a nonelementary proper action on X, and μ is a generating prob…
We provide a framework for incorporating robustness -- to perturbations in the transition dynamics which we refer to as model misspecification -- into continuous control Reinforcement Learning (RL) algorithms. We specifically focus on incorporating robustness into a state-of-the-art continuous control RL algorithm call…
Geodesics found in spacetime satisfy curvature conditions.
problem Finding geodesics in spacetime satisfying specific curvature conditions.
method Proving existence of geodesics with entropic semiconvexity and uniform L∞ densities. result Existence of geodesics satisfying the timelike curvature-dimension condition.
The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.
The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topolog…
Computable contracts simplify financial transactions and reduce legal costs.
problem Difficulty in querying, executing, and analyzing text-based financial contracts.
method Develop a Contract Definition Language and illustrate use cases.
result Substantial improvements in customer experience and cost reduction.
The condition number predicts efficient information encoding in neural units, aiding model fine-tuning.
problem Efficient information encoding in neural units for various tasks and input modalities.
method Linking the condition number to the log-volume scaling factor and entropy of the output distribution.
result High condition number indicates efficient encoding, reducing overall information transfer.
In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any c…
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms of an enforcement of the Lott, Sturm and Villani geodesic convexity condition for t…
Optimal execution strategy for merger & acquisition contracts with price impact.
problem Optimal execution and pricing of financial derivatives in M&A deals.
method Indifference utility arguments, considering linear and nonlinear contracts.
result Linear contracts are more expensive and vulnerable to manipulation.
This paper develops a method to select a reference contract for multi-contract quoting to minimize execution risk.
problem Minimizing execution risk in multi-contract quoting sequences.
method Develops a diagnostic framework using order-flow Hawkes forecasts and CLF to select a stable reference contract.
result Event-history and LOB-state signals offer complementary views for reference-contract selection.
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the L2-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together with a square integrable 1-form in the sense of \cite{giglinonsmooth}. This ex…
We consider a general framework of optimal mechanism design under adverse selection and ambiguity about the type distribution of agents. We prove the existence of optimal mechanisms under minimal assumptions on the contract space and prove that centralized contracting implemented via mechanisms is equivalent to delegat…
Improved security of smart contracts by classifying them into four categories.
problem Detecting and classifying vulnerabilities in smart contracts efficiently.
method Used AWD-LSTM for multi-class classification, addressing class imbalance.
result Achieved a weighted average Fbeta score of 90.0%.
Study on contracting maps and their rigidity under curvature constraints.
problem Rigidity of contracting maps between manifolds with positive curvature.
method Analysis of curvature pinching and contracting conditions involving singular values.
result Established the relation between curvature pinching and contracting conditions.
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…
Study shows some contractible complexes can't have certain immersions.
problem Understanding non-positive immersions in contractible complexes.
method Provided counterexamples to a conjecture by Wise.
result Some contractible complexes do not have non-positive immersions.
This paper presents some partial answers to the following question. QUESTION. If a normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, must X be contractible? The main results of the paper are: THEOREM 1. If a normal space X is the union…
The simplicial volume of non-R^3 contractible 3-manifolds is infinite.
problem Characterizing contractible 3-manifolds based on their simplicial volume.
method Analyzing the simplicial volume of contractible 3-manifolds and open 3-manifolds.
result The Euclidean space is the unique contractible 3-manifold with vanishing minimal volume.
New family of measurable pseudo-Anosov maps on spheres.
problem Generalizing pseudo-Anosov maps to measurable ones.
method Continuous family of homeomorphisms on sphere, semi-conjugate to core tent map.
result Measurable pseudo-Anosov maps have invariant dense streamlines with uniform measures.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
Optimal contracts help principals delegate data collection in decentralized ML.
problem Dealing with information asymmetries in decentralized ML.
method Design of optimal and near-optimal contracts addressing uncertainty in model quality and performance.
result Simple linear contracts achieve 1-1/e fraction of optimal utility.
Optimal contracts are found for agents with quadratic effort costs.
problem Finding optimal contracts in principal-agent problems with quadratic effort costs.
method Modeling the problem using Hamilton-Jacobi-Bellman (HJB) equations and proving the existence of classical solutions.
result Existence of optimal contracts for agents with quadratic effort costs is proven.
Fair insurance contracts are designed to handle default risk using cooperative game theory.
problem Designing fair insurance contracts in the presence of default risk.
method Cooperative game theory to specify premiums and participation in benefit.
result Fair benefit participation emerges as a game outcome involving residual risks.