New mechanism for pure differential privacy on functional summaries using Laplace-like process.
problem Challenges in achieving differential privacy for complex, structured functional summaries.
method Independent Component Laplace Process (ICLP) mechanism for infinite-dimensional Hilbert space.
result Effective enhancement of utility of private summaries through oversmoothing.
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…
Study spider mechanism configuration spaces using squared distance function.
problem Understand configuration spaces of spider mechanisms.
method Use Morse theory of squared distance function from body to fixed point.
result List and describe critical manifolds of squared distance function as products of polygon spaces.
Optimal DP mechanisms for vector queries are found to be staircase distributions.
problem Designing optimal additive mechanisms for vector-valued queries under differential privacy.
method Reduction to radially symmetric distributions and convex rearrangement theory.
result Staircase mechanisms are optimal for any norm and cost function.
Algorithm learns optimal dynamic mechanisms from data.
problem Designing optimal mechanisms for dynamic settings with unknown reward functions.
method Offline reinforcement learning with pessimism principle.
result Learned mechanisms are efficient, individually rational, and truthful.
Proves a theorem for mechanical systems with reflections.
problem Action functionals on paths with reflections.
method Proves a Morse index theorem for action functionals on paths that can reflect.
result Action functionals on paths with reflections have a well-defined Morse index.
New mechanisms improve differential privacy for scalar queries.
problem Improving differential privacy for scalar, real-valued query functions.
method Mixing multiple Gaussian distributions to satisfy differential privacy.
result Mechanisms yield lower noise amplitudes and variances compared to the analytic Gaussian mechanism.
Human decision-makers often receive assistance from data-driven algorithmic systems that provide a score for evaluating objects, including individuals. The scores are generated by a function (mechanism) that takes a set of features as input and generates a score.The scoring functions are either machine-learned or human…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
The exponential mechanism is a fundamental tool of Differential Privacy (DP) due to its strong privacy guarantees and flexibility. We study its extension to settings with summaries based on infinite dimensional outputs such as with functional data analysis, shape analysis, and nonparametric statistics. We show that one…
This paper presents a new mechanism for producing sanitized statistical summaries that achieve \emph{differential privacy}, called the \emph{K-Norm Gradient} Mechanism, or KNG. This new approach maintains the strong flexibility of the exponential mechanism, while achieving the powerful utility performance of objective …
Develops new instance-optimality concepts in differential privacy.
problem Improving privacy guarantees in statistical estimation.
method Introduces local minimax risk and unbiased mechanisms, and develops inverse sensitivity mechanisms.
result Inverse sensitivity mechanisms are nearly instance optimal for a wide range of functions.
New RL approach learns dynamic VCG mechanisms in unknown MDP environments.
problem Learning dynamic VCG mechanisms in unknown MDP environments.
method Reward-free online RL for exploration, combined with function approximation.
result Regret bound of O~(T2/3) for dynamic VCG mechanism learning. This study approximates neural network features for modeling relations and attention mechanisms.
problem Approximating neural network features for modeling relations and attention mechanisms.
method Analyzes inner products of multi-layer perceptrons for universal approximation of symmetric and asymmetric relation functions.
result Universal approximation of relation functions and attention mechanisms using inner products of neural networks.
In this paper we study dynamic pricing mechanism of contingent claims. A typical model of such pricing mechanism is the so-called g-expectation Es,tg[X] defined by the solution of the backward stochastic differential equation with generator g and with the contingent claim X as terminal condition. The generating f…
Geometrically decomposes Kähler functions on toric manifolds.
problem Decomposing Kähler functions on Kähler toric manifolds.
method Defining spectrum of Kähler functions and proving spectral decomposition theorem.
result Geometric spectral theory for Kähler functions established.
This paper analyzes and compares different Automated Market Maker mechanisms.
problem Impermanent loss in Constant Function Market Makers.
method Mean-Variance analysis of liquidity providers' profit and loss, comparison of different mechanisms.
result Optimized oracle-based mechanisms outperform Constant Function Market Makers.
Single-head attention approximates any function under various norms.
problem Universal approximation of functions using attention mechanisms.
method Interpreting attention as partitioning and summing linear transformations.
result Single-head attention can approximate any continuous function under L∞-norm and Lebesgue integrable functions under Lp-norm. A new privacy-preserving mechanism for shapes on manifolds.
problem Privacy-preserving sanitization of shapes on curved manifolds.
method Developed a K-norm gradient mechanism on Riemannian manifolds.
result The K-norm gradient mechanism offers better control over sensitivity than the Laplace mechanism on positively curved manifolds.
This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.
problem Designing efficient exchange mechanisms between assets.
method Formalizes a complexity-approximation trade-off for CFMMs and LOBs, introducing an exchange complexity measure.
result Optimally expressive mechanisms can be designed with minimal complexity, allowing for arbitrary demand curves.
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Study reveals attention mechanism's similarity computation parallels traditional machine learning.
problem Understanding the essence and principles of attention mechanism in deep learning.
method Examined classic metrics and vector space properties in manifold learning, clustering, and supervised learning to identify key characteristics of similarity computation and information propagation.
result Self-attention mechanism in deep learning adheres to the same principles but operates more flexibly and adaptively.
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics …
New method uses quantum annealing and VAN for better statistical mechanics calculations.
problem Difficulty in computing partition function in statistical mechanics.
method Combines quantum annealing samples with variational autoregressive networks.
result Enhanced accuracy in finite-size Sherrington-Kirkpatrick model.
In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a differential form which only upon integration over a cycle provides a conserved real number…
This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
New method uncovers bias mechanisms in observational studies.
problem Understanding the sources of bias in observational studies.
method Analyzing the relationship between bias magnitude and nuisance function estimators' performance.
result Method can distinguish between common sources of causal bias.
Paper introduces a new deep-learning method for quantum mechanics.
problem Simulating time-evolving Schrödinger equations efficiently.
method Generative diffusion models and stochastic mechanics.
result Significantly lower computational complexity compared to existing methods.
POSCMs extend SCMs for causal modeling with latent contexts.
problem Causal modeling with latent contexts and endogenous mechanisms.
method Kolmogorov-Arnold-Sprecher edge-functional decomposition for explicit parametrization.
result Identifiability of structure and mechanisms under latent context.
Proposes an iterative algorithm for optimizing attention mechanisms in large language models.
problem Optimizing attention mechanisms in large language models.
method Iterative algorithm for rescaled hyperbolic functions regression.
result Efficiency and generalizability of the rescaled softmax regression framework.
Extends PoS proof-of-stake transaction fee mechanism with miner utility model.
problem Designing a transaction fee mechanism for PoS protocol that incorporates miner utility.
method Introduced a new mechanism (BSP(θ)) incorporating a parameter θ to ensure user and miner incentives.
result The new mechanism (BSP(θ)) satisfies user and miner incentives and contract proofness.
Prediction markets show considerable promise for developing flexible mechanisms for machine learning. Here, machine learning markets for multivariate systems are defined, and a utility-based framework is established for their analysis. This differs from the usual approach of defining static betting functions. It is sho…
A new method for semi-supervised learning with missing data using GMM and margin confidence.
problem Handling missing data in semi-supervised learning with classification uncertainty.
method Explicitly models missingness mechanism, uses margin confidence and Aranda Ordaz function, develops ECM algorithm.
result Effective reduction of bias and robustness in semi-supervised learning with substantial missing labels.
The Madelung transform connects quantum mechanics and hydrodynamics.
problem Quantum mechanics and hydrodynamics equivalence for generic wave functions.
method Poisson geometry and coadjoint orbits of semidirect extensions of diffeomorphism groups.
result The Madelung transform provides a natural infinite-dimensional version of convexity results.
We study the problem of what causes prices to change. We define the mechanical impact of a trading order as the change in future prices in the absence of any future changes in decision making, and its it informational impact as the remainder of the total impact once mechanical impact is removed. We introduce a method o…
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is …
Unified framework for subsampling mechanisms with tighter privacy guarantees.
problem Improving privacy in machine learning models through subsampling.
method Conditional optimal transport for deriving mechanism-specific subsampling guarantees.
result Tighter privacy bounds for subsampled mechanisms compared to traditional methods.
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
The Dirichlet mechanism protects privacy while minimizing KL divergence.
problem Minimizing KL divergence while protecting sensitive data privacy.
method Using the exponential mechanism with the KL divergence loss function, resulting in the Dirichlet mechanism.
result Proved a probability tail bound on KL divergence and derived a lower bound for sample complexity.
The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We study the variation of the energy and Lagrangian functions along the evolution and…
Popular approaches to differential privacy, such as the Laplace and exponential mechanisms, calibrate randomised smoothing through global sensitivity of the target non-private function. Bounding such sensitivity is often a prohibitively complex analytic calculation. As an alternative, we propose a straightforward sampl…
IMA improves representation learning even when assumptions are violated.
problem Recovering true latent codes from mixed data.
method IMA, which assumes independent causal mechanisms.
result IMA's benefits extend to violations of its assumptions.
A new Dirac algebroid approach for nonholonomic systems.
problem Nonholonomic constraints in mechanical systems.
method Developed a Dirac algebroid to generate phase equations for systems with linear nonholonomic constraints.
result Unified approach to describe systems with different potentials.
The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems [S. Vacaru: J. Math. Phys. \textbf{49} (2008) 043504 \& Rep. Math. Phys. \textbf{63} (2009) 95] is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometri…
Differentially private log-location-scale regression models improve privacy in statistical analysis.
problem Ensuring privacy in statistical regression models while maintaining accuracy.
method Integrates differential privacy into LLS regression using the functional mechanism.
result Proposed DP-LLS models satisfy ε-differential privacy and perform well under various conditions.
Investigates the fundamental components of attention mechanisms.
problem Understanding the building blocks of attention in deep learning.
method Classified and studied three key mechanisms: additive, multiplicative output, and synaptic attention.
result Additive activation attention is central in proofs of lower bounds.