A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New machine learning method detects quantum separability in large-scale systems.
New framework for cyclic quantum causal models with graph separation property.
Quantum states associated with subsets of product manifolds are separable.
Quantum computers outperform classical methods in density modeling.
Quantum correlations enhance generative models, providing a new resource for machine learning.
Geodesic flows on Kähler manifolds are quantum integrable when metrics are c-projectively equivalent.
Quantum speedup for Monte Carlo integration reduces integrand calls.
New method uses single quantum state for machine learning tasks, improving accuracy.
Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.
We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number …
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
This work restricts hidden cardinality in causal models to infer causal relations.
The statistical complexity of quantum circuits is studied using Rademacher complexity.
Infinite families of quantum modular invariants for 3-manifolds are discovered.
Global EQG sums boundary states over manifold diffeomorphism classes.
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed o…
Quantum computing poses a threat to Bitcoin and Ethereum, but only to spending and not mining.
Few quantum measurements limit learning entanglement.
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalizat…
Quantum computing improves copula-based risk aggregation models.
Quantum algorithm improves sparse vector recovery from noisy measurements.
New kernels allow learning from non-separable data.
Develops trace class operators and inverse Laplacian theory for infinite dimensions.
In this paper, we present the idea that the formalism of string theory is connected with the dimension 4 in a new way, not covered by phenomenological or model-building approaches. The main connection is given by structures induced by small exotic smooth R^4's having intrinsic meaning for physics in dimension 4. We ext…
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
Unified approach for quantum and classical learning from evaluation oracles.
Calculates Dehn twist actions on conformal blocks for modular categories.
Introduces a continuous version of LWE problem.
We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics …
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group,…
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario, referred to as extreme clustering, datasets are enormous and the number of represent…
We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is re…
Pipeline decomposes portfolio optimization problems into smaller, solvable subproblems.
Optimal transport theory applied to quantum states on Grassmannians.
Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of the associated representations in cohomol- ogy. Furthermore, we observe that the …
We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use the unsupervised TN machine learning algorithm to obtain the entangled state $|Ψ…
Paper presents quantum algorithms for pricing financial derivatives using complex models.
Detects causal scenarios with inequality constraints among classical correlations.
Deep RNNs excel at capturing long-term dependencies in sequential data.
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspond…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the…
Study on kernels of SO(3) WRT representations for surfaces of genus g≥3.
We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of rational homology 3-spheres at roots of unity of order co-prime with the torsion. As an…
The Zeeman-Hamilton operators of free charged particles are identified with the Laplacians of certain Riemannian manifolds, called Zeeman manifolds. The quantum Hilbert space decomposes into subspaces (Zeeman zones) which are invariant under the actions both of the Zeeman operator and the natural Heisenberg group repre…
In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=φP_{ab}$, $\lieΠ_{ab}=χΠ_{ab}$ where , are orthogonal and complementary…