Comparison Lift uses bandit algorithms to optimize online ad testing.
problem Optimizing online ad testing to maximize click-through rates.
method Bandit-based experimentation algorithm that adapts to test results.
result Ad click-through rates increased by 46% on average.
Paper improves privacy-preserving measurement of advertising incrementality.
problem Privacy degradation in randomized lift tests for advertising measurement.
method Formulates a robust causal decision problem under signal losses, projecting clean worlds onto incrementality.
result Sharp decision frontier shows valid certification or rejection outside the frontier.
Two-sample tests improve on existing methods for microtubule data.
problem Testing differences between two groups of filament data.
method Optimal lifts and manifold stability theorem applied to microtubule data.
result New tests outperform existing methods on simulated and real data.
The paper optimizes A/B tests by balancing lift and cost in large-scale settings.
problem Balancing lift and cost in A/B tests for large-scale experimentation.
method Empirical Bayes approach using a greedy knapsack algorithm to rank experiments based on lift-to-cost ratio, incorporating local false discovery rate (lfdr).
result The proposed method maximizes expected profit while controlling false discovery rate, demonstrating superior performance in large-scale settings.
Invariance principle proved for lifted geodesic walks on Riemannian submersions.
problem Proving convergence to horizontal Brownian motion for lifted geodesic walks.
method Appropriate conditions on geodesic random walks' speed; proving invariance principle.
result Convergence to horizontal Brownian motion for lifted geodesic walks.
Study large deviation in stationarized fully lifted blirp interpolation.
problem Understanding atypical solutions in random optimization problems.
method Large deviation theory applied to fully lifted blirp interpolation.
result Elegant relations uncovered for fundamental interpolating parameters.
New method lowers spherical perceptron capacity using fully lifted random duality theory.
problem Tackles the negative spherical perceptron capacity, a long-standing open problem.
method Develops fully lifted random duality theory (fl RDT) to characterize capacity.
result Shows remarkable closed-form analytical relations for practical capacity values.
Study binary perceptrons' capacity using random duality theory.
problem Characterize the capacity of binary perceptrons with general thresholds.
method Utilized fully lifted random duality theory (fl RDT) to characterize the capacity.
result Characterizations match replica symmetry breaking predictions and uncover the capacity for zero-threshold scenario.
The study calculates the injectivity capacity of ReLU networks using a novel mathematical approach.
problem Determining the injectivity capacity of ReLU networks layers.
method Employing fully lifted random duality theory (fl RDT) to handle the ℓ0 spherical perceptron and implicitly the ReLU layers injectivity. result The lifting mechanism converges remarkably fast with relative corrections not exceeding 0.1%.
New method improves statistical interpolation for analyzing complex random structures.
problem Analyzing atypical random structures in statistical models.
method Introduces a large deviation upgrade to fully lifted interpolation.
result Allows for easier analysis of atypical random structures.
Develops a new bidding system to maximize advertiser profit.
problem Inaccurate prediction of ad lift-effect due to biased log data.
method Unbiased Lift-based Bidding System that predicts lift-effect from biased log data.
result Demonstrates superior and practical high-performing lift-based bidding strategy.
In sequential anytime-valid inference, any admissible procedure must be based on e-processes: generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any stopping time. This paper proposes a method for combining e-processes constructed in different filtrations b…
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
problem Creating a differential geometry for infinite dimensional spaces without topology or local coordinates.
method Introduces a general algebraic framework for lifted geometry applicable to various infinite dimensional spaces.
result Stokes' Theorem appears as a form of differentiability in the lifted geometry of spaces of submanifolds.
The paper explores conditions for lifting maps between graphs to embeddings.
problem Conditions for embedding maps between graphs.
method Combinatorial techniques and satisfiability of 3-CNF formulas.
result Established necessary and sufficient conditions for lifting.
Path signatures adapted for Lie groups improve action recognition in computer vision.
problem Improving action recognition in computer vision with geometric constraints.
method Lifting path signatures to Lie groups and proving universality and characteristic property.
result Path signatures on Lie groups provide comparable performance to shallow learning approaches in action recognition.
Exploratory analysis over network data is often limited by the ability to efficiently calculate graph statistics, which can provide a model-free understanding of the macroscopic properties of a network. We introduce a framework for estimating the graphlet count---the number of occurrences of a small subgraph motif (e.g…
Wide hidden layer TCM nets capacity analyzed using RDT and fl RDT.
problem Capacity analysis of wide hidden layer TCM nets.
method Employed Fully Lifted Random Duality Theory (fl RDT) for capacity characterization.
result Explicit, closed form capacity characterizations for a generic class of hidden layer activations.
The paper finds lower bounds for volumes of complex geometric structures.
problem Estimating the volume of complex geometric structures.
method Reduction to a counting problem in the unit tangent bundle, solved using exponential multiple mixing for the geodesic flow.
result First known lower bound for the volume of these manifolds in terms of curve length.
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general expone…
We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on Out(FN). In both cases, we relate the asymptotics of the stretching factor of the diffeomorphism/automorphism obtained at time n of the random walk to the Lyapunov exponent of …
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
Framework combines random features with CDEs for efficient time-series learning.
problem Efficient training of time-series models with strong inductive bias.
method Random Fourier CDEs and Random Rough DEs using continuous-time reservoirs and log-ODE discretization.
result Unified perspective on random-feature reservoirs and path-signature theory.
A new method to rescale ReLU neural networks based on path-lifting.
problem Lack of principled ways to leverage rescaling symmetries in ReLU neural networks.
method Introduces a geometrically motivated criterion to rescale neural network parameters, aligning a kernel in the path-lifting space with a chosen reference.
result Proposed method can speed up training and aligns a kernel in the path-lifting space with a chosen reference.
This paper develops a path-first theory using signatures and jump lifts for self-exiting processes.
problem Developing a universal coordinate system for various types of paths and processes.
method Using signatures, jump lifts, and expected signatures, the paper presents a geometricity framework with algebraic properties and obstructions.
result The framework links various mathematical concepts and offers four main contributions to understanding and modeling self-exiting processes.
Mining association rules is an important technique for discovering meaningful patterns in transaction databases. Many different measures of interestingness have been proposed for association rules. However, these measures fail to take the probabilistic properties of the mined data into account. In this paper, we start …
Random curves on surfaces have predictable properties as they grow.
problem Characterizing topological properties of random curves on surfaces.
method Analyzing a simple random walk on the Cayley graph of surface groups.
result The properties of random curves are generic and predictable as they grow.
A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.
problem Noise-robustness vs. data-consistency in Cryo-EM 3D map reconstruction.
method Ellipsoidal support lifting (ESL) for regularizing and approximating the global minimizer over Riemannian manifolds.
result The induced bias due to regularizing effect of ESL estimates better rotations than global optimisation.
The study revisits Hopfield's associative memory model and calculates its capacity for two specific pattern basins.
problem Determining the capacity of a Hebbian-Hopfield network for storing binary patterns.
method Using fully lifted random duality theory and numerical analysis, the study calculates the capacity for two specific pattern basins.
result Explicit characterizations of the capacity for the AGS and NLT pattern basins, with remarkable fast lifting convergence.
For a specific class of 4-manifolds, random isometries cannot lift to orientation-preserving diffeomorphisms.
problem When does a finite group of isometries of a specific 4-manifold lift to orientation-preserving diffeomorphisms?
method Combination of equivariant connected-sum constructions, fixed-point theory, finite group actions on surfaces, analytic combinatorics, and previous work.
result Random subgroups of isometries are asymptotically almost never realizable in orientation-preserving diffeomorphisms.
Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is limited by GPU memory and data size. To overcome this issue, we introduce a netwo…
When solving consensus optimization problems over a graph, there is often an explicit characterization of the convergence rate of Gradient Descent (GD) using the spectrum of the graph Laplacian. The same type of problems under the Alternating Direction Method of Multipliers (ADMM) are, however, poorly understood. For i…
New framework for neural networks converging to low loss without overparameterization.
problem Training deep neural networks without overparameterization assumptions.
method Construction of random sparse lifts and analysis using algebraic topology and random graph theory.
result Provable convergence to low loss for large sparse neural networks.
CLuP achieves near optimal ground state energies for positive and negative Hopfield models.
problem Finding near optimal ground state energies for positive and negative Hopfield models.
method Controlled Loosening-up (CLuP) algorithm with fully lifted random duality theory (fl RDT).
result Achieves ground state free energies of 1.77 and 0.33 for positive and negative Hopfield models respectively. Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invari…
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.
Study potential computational gaps in symmetric binary perceptrons using fl-RDT.
problem Potential statistical-computational gaps in symmetric binary perceptrons.
method Parametric utilization of fully lifted random duality theory (fl-RDT).
result Observation of a computational gap SCG=αc−αa in SBP. We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup H. We further assume that H is not consisting only of lifts with respect to any one covering. Then w…
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based on an ensemble approach that uses the sum of squared symmetry statistics and di…
New method combines randomization tests and flexible models for valid inference without splitting data.
problem Valid inference in randomized panel experiments with complex effect heterogeneity.
method Model-assisted randomization tests that estimate unsigned CATE from residualized outcomes.
result CATE-assisted tests control Type I error and achieve higher power than alternatives.
Existence and rigidity results for lifts in Carnot groups.
problem Existence and properties of lifts for maps between Carnot groups.
method Use central extensions to define lifts and prove existence and rigidity results for Lipschitz, Sobolev, and quasiconformal maps.
result Quasiconformal maps admit contact lifts that are bi-Lipschitz.
Study lift metrics and connections on tangent bundles of Riemannian manifolds.
problem Investigate geometric properties of tangent bundles and their lifts.
method Analyze lift metrics and connections on TM of (M,g), and study statistical and Codazzi couples. result Prove a result on 1-Stein and Osserman structures on TM. Improved neural network capacity analysis using simplified RDT.
problem Analyzing the memorization capabilities of sign perceptron neural networks.
method Developed a simplified, partially lifted Random Duality Theory (fl RDT) approach.
result Concrete capacity bounds universally improve over previous best known ones.
LLMs optimize quantum circuits by iteratively improving proposals with feedback and memory traces.
problem Optimizing quantum circuits using large language models (LLMs) under black-box evaluation.
method Closed-loop, test-time optimization with LLMs, score-difference feedback, and restart-from-the-best sampling.
result The approach improves circuit synthesis performance and success rate, especially for larger qubit settings.
Improved MMD test for two-sample testing with random Fourier features.
problem Quadratic-time complexity of MMD test for large-scale analysis.
method Approximated MMD test using random Fourier features, investigating time-power trade-off.
result Sub-quadratic time complexity with same minimax separation rates as MMD test.
We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with random slipping and twisting. The system is modelled by a stochastic differential equation of Stratonovich-type driven by semimartingales, on…
Develops tests for conditional symmetry under group actions.
problem Testing conditional symmetry in distributions under group actions.
method Nonparametric randomization tests with kernel methods and asymptotic consistency.
result Tests achieve finite-sample Type I error control and power.
New test detects sparse alternatives in Gaussian random fields.
problem Detecting sparse alternatives in Gaussian random fields.
method Ad-hoc Kac Rice formula for second maximum distribution, exact spacing test.
result Exact t-spacing test for high power in detecting sparse alternatives. A new test for IRG models using KSD for small networks.
problem Testing goodness-of-fit for inhomogeneous random graph models.
method Kernelised Stein Discrepancy (KSD) test for IRG models.
result The test is effective for small networks and provides theoretical guarantees.