Quantum machine learning uses superposition to create a large ensemble of classifiers.
problem Improving machine learning efficiency on quantum computers.
method Using superposition to create an exponentially large ensemble of classifiers, trained with an optimization-free learning algorithm.
result Adding an optimization step improves the performance of quantum ensembles of classifiers.
Quantum computing speeds up asset pricing models exponentially.
problem Solving dynamic nonlinear asset pricing models efficiently.
method Utilizes quantum superposition and entanglement to solve models exponentially faster than classical methods.
result Exponential computational speed-up for solving asset pricing models.
Quantum variational circuits improve reinforcement learning efficiency.
problem Improving reinforcement learning algorithms using quantum computing.
method Investigation of quantum variational circuits for DQN and Double DQN, encoding classical data for quantum circuits.
result Quantum variational circuits can solve reinforcement learning tasks with a smaller parameter space.
New methods combine model predictions to avoid linear mixtures' limitations.
problem Combining predictions from different models to avoid linear mixtures' limitations.
method Log-linear pooling (locking) and quantum superposition (quacking) to optimise model weights.
result Demonstrated locking method with illustrative example and practical application.
Quantum algorithms for multi-armed bandits are explored with limited reward access.
problem Exploring quantum speed-ups in multi-armed bandit problems with limited reward information.
method Introduced new bandit models and showed query complexity equivalence with classical algorithms.
result No quadratic speed-up is possible for multi-armed bandits with limited reward access.
Quantum computing improves training of binary neural networks.
problem Training binary neural networks (BiNNs) is challenging.
method Employing a Variational Quantum Algorithm to generate binary weights using quantum circuit measurements.
result The proposed methods improve trainability and generalization of BiNNs.
Quantum computing speeds up multi-period asset allocation.
problem High computational complexity in classic computing for multi-period asset allocation.
method Applied quantum computing to simulate multi-asset portfolio using historic data.
result Quantum computing offers significant advantages over classical computing in finance.
Classical clients can verify quantum learning tasks efficiently.
problem Making quantum learning accessible to classical clients.
method Developed a framework for classical verification of quantum learning.
result Quantum learning tasks can be efficiently verified by classical verifiers.
Quantum algorithm improves ensemble classification with reduced memory and time requirements.
problem High memory and computational time requirements in ensemble methods.
method Quantum superposition, entanglement, and interference to build an ensemble of classification models.
result Exponential growth of ensemble size with linear increase in depth of circuit.
Improved PQM for pattern classification on quantum computers.
problem Pattern classification in quantum computing.
method Parametric Probabilistic Quantum Memory (PQM) with quantum circuit.
result Classical evaluation and quantum experiments validate PQM viability.
In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit interference effects, by…
This paper applies quantum theory to cost accounting, focusing on WIP valuation.
problem Uncertainties in WIP valuation in cost accounting.
method Quantum theory applied to WIP valuation in cost accounting.
result More nuanced understanding of uncertainties in managerial accounting.
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges. A principal opportunity is that a large number of computations can be carried ou…
Quantum mechanics applied to credit loans for better repayment schedules.
problem Improving repayment schedules for credit loans.
method Introducing quantum mechanics concepts to credit loans, defining operators for debt, amortization, interest, and installments, and using SO(M) symmetry to optimize periodic payments.
result Optimized repayment schedules for borrowers without altering lender's earnings.
This study compares feature importance and explainability in quantum vs classical ML models.
problem Lack of transparency in ML models, especially in sensitive fields.
method Comparison of classical ML (SVM, Random Forest) and hybrid quantum ML (VQC, QSVC) models using feature importance and explainability methods.
result Quantum ML models provide insights similar to classical models but with unique quantum features.
Quantum computing improves Monte Carlo option pricing for complex derivatives.
problem Complex financial derivatives require extensive computations in high-dimensional spaces.
method Developed a quantum algorithm for simulating many potential asset paths in parallel.
result Quantum algorithm provides highly accurate option pricing and risk analysis.
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quant…
Quantum Fourier Transform aids machine learning inference.
problem Generalizing from finite data samples to ground truth.
method Inspired by quantum algorithms, uses Quantum Fourier Transform to expose invariant subspace for data comparison.
result Proposes a concrete implementation for machine learning applications leveraging symmetries.
Superposition accelerates training to a universal power-law exponent.
problem Training dynamics in neural networks.
method Teacher-student framework and analytic theory.
result Superposition leads to a universal power-law exponent of ~1, independent of data and channel statistics.
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
problem Efficiently extracting linearly separable components from complex data.
method Eigen component analysis (ECA) incorporates quantum mechanics principles into linear learning models.
result ECA outperforms classical linear models and can be integrated with deep neural networks.
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the "quantu…
We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the parti…
Quantum algorithms improve VaR and CVaR estimation for financial derivatives.
problem Quantum advantage in financial risk analysis of derivatives.
method Two quantum algorithms: QSP and QSP-based approach.
result QSP-based approach requires fewer quantum resources for the same accuracy.
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be related with equations on a Lie group and with some connections in fiber bundles. We …
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
problem Understanding the underlying mechanism of distribution formation in complex quantum entanglement.
method Exploring the logical relationship between Schrödinger's wave equation and Shi's trading volume-price wave equation in finance.
result A non-localized wave equation in quantum mechanics reveals the invariance of interaction as a universal law.
Study harmonic surfaces in 3D space, proving superposition principle.
problem Understanding harmonic surfaces in R3. method Using harmonic Enneper immersions and superposition principle.
result Minimal and maximal surfaces can be decomposed into harmonic components.
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this notion and other related ones to systems of higher-order differential equations …
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement is a generalization of the celebrated Lie-Scheffers Theorem, char…
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Skq(S), which is spanned by links in the surface which are allowed to have endpoints at the marked points, modulo several locally defined relations. The product…
In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where mul…
The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
We consider the class of integer rectifiable currents without boundary satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.
Formulae for Bäcklund transformations of hyperbolic and elliptic sine-Gordon/sinh-Gordon equations.
problem Finding solutions for specific types of equations.
method Providing superposition formulae for Bäcklund transformations.
result Algebraically obtain infinitely many solutions after first integration.
New algorithm extracts features from superpositions in machine learning models.
problem Challenges in extracting interpretable features from complex models in superposition.
method An efficient query algorithm that identifies non-degenerate feature directions and reconstructs the function.
result Identifies all feature directions whose responses are non-degenerate and reconstructs the function \( f \) in a general superposition setting.
Observing a linear superposition principle, a family of new minimal hypersurfaces in Euclidean space is found, as well as that linear combinations of generalized helicoids induce new algebraic minimal cones of arbitrarily high degree.
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models …
Superposition in autoencoders leads to loss in simple models.
problem Mechanistic interpretability of neural networks
method Analyzing mathematical basis for superposition and providing bounds for reconstruction loss
result Upper and lower bounds for L2 reconstruction loss in the sparse regime
Paper introduces Manifold Probe for discovering representation manifolds in superposition.
problem Discovering representation manifolds in complex superposition representations.
method Generalizes linear regression probes to learn feature spaces and directions in superposition representations.
result Demonstrates Manifold Probe on Llama 2-7b representations, finding causally involved manifolds in model behaviour.
We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood estimation, we explore the associated risk bound. Further, we consider the superposition o…
The study examines Euclid's Book I, focusing on area applications and construction methods.
problem Exploring Euclid's geometric constructions and proofs, particularly those involving area calculations.
method Summarizing medieval editions and ancient commentaries, comparing constructions and proofs.
result Medieval editions often avoid Euclid's use of superposition in area proofs, offering alternative constructions.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords are sparse linear combinations of columns of the matrix. In this paper, we prop…
MIMONets speed up neural network inference by processing multiple inputs in parallel.
problem Reducing computational cost in neural network inference for large datasets.
method Proposes MIMONets, which augment neural network architectures with variable binding mechanisms to handle multiple inputs in superposition.
result Achieves significant speedups (2-4x) with minimal accuracy loss, demonstrating adaptability across different architectures.
Gravitational instantons are constructed as superpositions of Atiyah-Hitchin and Taub-NUT geometries.
problem Constructing gravitational instantons from Atiyah-Hitchin and Taub-NUT geometries.
method A gluing construction that captures the superposition of moduli spaces of centred SU(2) monopoles and Taub-NUT manifolds.
result Gravitational instantons are explicitly shown to be superpositions of Atiyah-Hitchin and Taub-NUT geometries.
We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study…
Explores tensor products in hyperdimensional computing.
problem Understanding tensor products in hyperdimensional computing.
method Generalized results from graph embeddings to vector symbolic architectures and hyperdimensional computing.
result Tensor product is the most general and expressive representation with errorless unbinding and detection.
Market strategies minimize Fisher information to minimize risk.
problem Applying minimum Fisher information principle to market dynamics.
method Analytical extension to quantum harmonic oscillator eigenstates and Gibbs distribution.
result Minimizing Fisher information reduces information and risk.
We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of structured superposition models, and propose a method which provably recovers t…