Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
This paper uses QUBO to train machine learning models on quantum computers.
problem Efficiently training machine learning models on quantum computers.
method Formulated three machine learning models (linear regression, SVM, k-means) as QUBO problems.
result Formulations are more efficient or equivalent in time and space complexity to classical methods.
Quantum machine learns to clean up blurry images.
problem Cleaning up blurry images using quantum computing.
method Uses Boltzmann machines, QUBO, and quantum annealing to balance image quality and noise.
result Quantum method produces cleaner images than noisy originals on average.
Quantum algorithm improves sparse vector recovery from noisy measurements.
problem Accurately recover sparse vectors from noisy linear measurements.
method Formulated as a QUBO task, solved using quantum technology.
result Quantum approach outperforms classical methods in sparse coding.
This paper uses quantum computing to solve sparse linear regression problems efficiently.
problem Sparse linear regression to identify important features from a large set of variables.
method Formulates the ℓ0 optimization problem as a QUBO problem and solves it using the D-Wave adiabatic quantum computer. result The QUBO solution matches the optimal solution for a wide range of sparsity penalty values across datasets.
Quantum computing improves feature selection in machine learning.
problem Optimizing feature selection in machine learning problems.
method Formulated feature selection as a QUBO problem and compared quantum and classical methods.
result Quantum computing can outperform classical methods in feature selection, depending on data set.
Quantum computing speeds up linear regression training.
problem Reducing training time for machine learning models.
method Formulated regression problem as QUBO, used D-Wave 2000Q for adiabatic optimization.
result Quantum approach achieves up to 2.8x speedup on larger datasets.
Hybrid classical-quantum framework optimizes portfolio rebalancing with reduced transaction costs.
problem Optimizing portfolio rebalancing with reduced transaction costs and lookahead bias.
method Combining Ledoit-Wolf shrinkage covariance estimation, hierarchical correlation clustering, entropy-regularised Genetic Algorithm, minimum-variance and equal-weight benchmarks, QUBO formulation, and QAOA for solving the combinatorial optimisation problem.
result GA + QAOA strategy outperforms classical methods with reduced rebalances and transaction costs.
End-to-end portfolio optimization using quantum annealing for financial decision problems.
problem Optimizing financial portfolios with quantum computing constraints.
method Hybrid pipeline combining quantum and classical optimization.
result Quantum-assisted portfolio optimization can achieve competitive returns.
Optimizes train schedules and maintenance using CP and QA.
problem Optimizing train schedules and maintenance considering constraints.
method Used Constraint Programming and Quantum Annealing to model and solve the problem.
result Both CP and QA approaches produce comparable results on real quantum computers.
Quantum annealing solves matrix factorization for large datasets.
problem Finding low-rank approximations of large real-valued matrices.
method Transformed real optimization into QUBO problems, solved on D-Wave quantum annealer.
result Quantum approach outperforms classical methods and finds better results.
The 2008 mortgage crisis is an example of an extreme event. Extreme value theory tries to estimate such tail risks. Modern finance practitioners prefer Expected Shortfall based risk metrics (which capture tail risk) over traditional approaches like volatility or even Value-at-Risk. This paper provides a quantum anneali…
A new reinforcement learning method improves Max-Cut solutions without needing training data.
problem Max-Cut problem is NP-hard, and existing methods struggle with generalizability and scalability.
method Training-data-free reinforcement learning approach to hyperplane rounding for Max-Cut optimization.
result Our method consistently achieves better Max-Cut solutions across various graph types.
Simulated Bifurcation outperforms quantum machines in community detection.
problem Community detection in complex networks
method Quantum-inspired Simulated Bifurcation algorithm for QUBO formulation
result Simulated Bifurcation achieves highest modularity in community detection
Quantum Annealing Enhanced Reinforcement Learning for Accurate RUL Prediction
problem RUL estimation in predictive maintenance
method QAQL framework combining quantum annealing and Q-learning
result Outperforms classical and quantum baselines
Hybrid LLM and quantum optimization improve CSA collateral management by 9-10%.
problem Finance-native collateral optimization under ISDA CSAs with legal constraints.
method Hybrid pipeline combining LLM, quantum-inspired exploration, and CP-SAT.
result Improves a strong classical baseline by 9.1-10.7% across different scenarios.
A new penalty-free method optimizes portfolios without quantum annealing penalties.
problem Optimizing portfolios with quantum annealing penalties.
method Removing the penalty term and using a classical feasibility projector.
result Significant reduction in chain-break fractions and post-processed regret.
Quantum algorithm finds extrema in discrete optimisation problems.
problem Finding extrema in discrete optimisation functions.
method Quantum unstructured search algorithm (QSERA) to map and find extrema.
result Quadratic speed-up over classical algorithms for discrete optimisation.
Quantum-inspired method optimizes portfolio selection.
problem Optimizing asset allocation in finance.
method Combining quantum-inspired and conventional optimization methods.
result Faster and more accurate portfolio optimization solutions.
A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator whic…
Proposes a quantum-inspired algorithm for selecting representative data subsets.
problem Selecting the most representative subset of data from a larger dataset.
method Uses a Quadratic Unconstrained Binary Optimization (QUBO) problem approach.
result Demonstrates the effectiveness of the selector algorithm in finance applications.
Quantum optimization for portfolios with risk and diversification constraints.
problem Implementing complex constraints in portfolio optimization for financial applications.
method Transformed portfolio optimization into a quadratic binary optimization problem suitable for quantum annealers.
result Demonstrated practical implementation of daily constraints in real data using quantum processors.
A quantum framework optimizes collateral allocation for derivatives.
problem Legal constraints and operational rules in collateral allocation for derivatives.
method Certified higher-order quantum framework that normalizes margin requirements and builds a bounded neighborhood of actions.
result Quantum framework improves certified sample quality compared to classical methods.
Optimal data-driven formulations are found for learning and decision-making with historical data.
problem Designing optimal learning and decision-making formulations from historical data.
method Define a yardstick for measuring formulation quality, then construct an optimal formulation that is uniformly closer to the true cost.
result Existence of three distinct out-of-sample performance regimes with corresponding optimal formulations.
A new DR formulation improves metric learning for faster and more stable performance.
problem Learning embeddings for class separation in metric learning.
method Distance-ratio (DR) formulation for metric learning.
result DR formulation achieves improved or comparable generalization performances.
New formulations for Ricci flows without smoothness.
problem Characterize Ricci flows without smooth solutions.
method Weak formulations of super Ricci flows with saturation condition.
result Generalized formulations for singular settings.
Defines a metric and form for a bundle moduli space, leading to a zero-curvature formulation.
problem Formulating a metric and form for a bundle moduli space.
method Defines an algebraic metric and closed 3-form on a subspace of the moduli of G-bundles. result Shows a zero-curvature formulation for a σ-model with target the moduli space. We study ranking quantilized mean-field games to select top-performing agents.
problem Selecting top-performing agents in competitive scenarios.
method Developed two formulations: target-based and threshold-based, and provided analytic and semi-explicit solutions.
result Analytic and semi-explicit solutions for quantilized mean-field consistency conditions.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Equivalent formulations for low-rank matrix optimization are proven.
problem Low-rank matrix optimization with rank constraints.
method Established geometric landscape connections between manifold and factorization formulations.
result Equivalence between manifold and factorization formulations at FOSPs, SOSPs, and strict saddles.
A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
problem Formulating the Raychaudhuri equation in non-Riemannian geometries.
method Established a formal connection between the expansion scalar and the cross-sectional volume of the congruence. Derived a Lagrangian and Hamiltonian formulation.
result The expansion scalar equals the fractional rate of change of volume, weighted by a scalar factor.
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the ℓ1- and ℓ2-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
The paper tackles robust statistical methods using Wasserstein DRO formulations.
problem Distributional uncertainty in learning from limited samples.
method Min-max distributionally robust optimization with Wasserstein DRO formulations.
result Error bounds free from the curse of dimensionality.
Genetic algorithms are a well-known method for tackling the problem of variable selection. As they are non-parametric and can use a large variety of fitness functions, they are well-suited as a variable selection wrapper that can be applied to many different models. In almost all cases, the chromosome formulation used …
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…
Bayesian optimization identifies optimal alloy formulations.
problem Accelerated discovery in materials science with autonomous systems.
method Bayesian optimization over problem formulation space.
result Framework converges on optimal alloy formulations.
New formulations capture aversion to ambiguity about volatility.
problem Capturing aversion to ambiguity about unknown and time-varying volatility.
method Introduces novel preference formulations and compares them with existing models.
result Illustrates the impact of ambiguity aversion in static and dynamic models.
ROCK method generalizes MOCK for learning dynamical systems efficiently.
problem Learning dynamical systems from data efficiently.
method Variational formulation in Reproducing Kernel Hilbert Spaces.
result ROCK method is more computationally efficient and performs better on benchmarks.
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard do…
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the f…
We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…
Current pharmaceutical formulation development still strongly relies on the traditional trial-and-error approach by individual experiences of pharmaceutical scientists, which is laborious, time-consuming and costly. Recently, deep learning has been widely applied in many challenging domains because of its important cap…
Oral Disintegrating Tablets (ODTs) is a novel dosage form that can be dissolved on the tongue within 3min or less especially for geriatric and pediatric patients. Current ODT formulation studies usually rely on the personal experience of pharmaceutical experts and trial-and-error in the laboratory, which is inefficient…
The paper proves an index theorem for loop spaces of compact manifolds.
problem Defining an index theorem for loop spaces of compact manifolds.
method Formulated and proved an equivariant index theorem for non-compact manifolds with S1-actions, using a ring of formal power series. result Found an appropriate form of the index theorem for loop spaces.