Reflection principles for harmonic and holomorphic maps from Hermitian symmetric spaces.
problem Establishing reflection principles for harmonic and holomorphic maps between Riemannian manifolds.
method Introducing recursive real forms and proving reflection principles for harmonic and holomorphic maps from Hermitian symmetric spaces.
result Reflection principles for harmonic and holomorphic maps from a class of Hermitian symmetric spaces.
Paper improves multi-step traffic flow prediction performance.
problem Predicting multiple time-steps into the future based on finite history.
method Introduces a model for recursive prediction and a data augmentation method for multi-output setting.
result Improves multi-step traffic flow prediction in recursive and multi-output settings.
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form solution. By recursively solving these sub-problems in an analytical way, an ef…
Theoretical study on AI models' resilience to data contamination during recursive training.
problem Data contamination in recursive training of generative AI models.
method General framework with minimal assumptions on real data distribution and flexible generative models.
result Contaminated recursive training converges with a rate equal to the minimum of baseline model's rate and contamination fraction.
Paper proposes a recursive GPSSM for efficient online learning.
problem Efficient online learning for dynamical models with limited prior information.
method Recursive Gaussian Process State-Space Model with adaptive capabilities for domains and hyperparameters.
result Superior accuracy, computational efficiency, and adaptability compared to state-of-the-art methods.
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface S, and fix a number of points F on its boundary. We ask: how many configurations of disjoint arcs are there on S whose boundary is F? We find that thi…
Study uses reinforcement learning to optimize portfolios under recursive utility.
problem Improving portfolio allocation using risk-sensitive objectives.
method Approximated certainty equivalent via Monte Carlo, trained actor-critic algorithms (PPO, A2C).
result Recursive-utility agent outperforms discounted baseline in Sharpe ratio, max drawdown, and cumulative return.
New findings on stable commutator lengths in recursively presented groups.
problem Understanding stable commutator lengths in recursively presented groups.
method Analyzing recursively presented groups and infinitely presented small cancellation groups.
result All non-negative algebraic or computable numbers are in the set of stable commutator lengths.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
Paper offers fast, accurate pricing for long-dated contracts using real-world probability measure.
problem Inaccurate pricing of long-dated contracts in insurance and pension funds.
method Applies RMQ and JRMQ algorithms under real-world measure, using benchmark approach.
result Prices are less expensive than risk-neutral valuation, highlighting departure from traditional methods.
Paper tackles model collapse in recursive generative models using a weighted training scheme.
problem Model collapse in recursive generative models trained on synthetic data.
method Iteratively trains models on real and synthetic data, evaluates weighted training schemes.
result Optimal weighting scheme for synthetic data follows a unified expression, revealing a trade-off with model performance.
Recursive prediction of graph signals with new nodes added.
problem Predicting graph signals with new nodes added over time.
method Recursive prediction of graph signals using incoming nodes.
result Recursive method results in good prediction performance close to full graph knowledge.
The paper computes a knot's Kauffman bracket polynomial using recursive concatenation of a 4-tangle shadow.
problem Computing the Kauffman bracket polynomial for complex knots.
method Recursive concatenation of a 4-tangle shadow, followed by a closure operation and polynomial computation.
result A method to compute the Kauffman bracket polynomial for knots formed from 4-tangle shadows.
We define and calculate the HOMFLY polynomial for a specific type of quiver.
problem Calculating the HOMFLY polynomial for forest quivers.
method Recursive definition and closed-form expression for forest quivers.
result Closed-form expression for the HOMFLY polynomial of a forest quiver.
Improved real-time UAV terrain following with RVM-RLS filter.
problem Accurate real-time waypoints estimation under measurement noise in nonlinear, time-varying systems.
method Residual Variance Matching Recursive Least Squares (RVM-RLS) filter guided by RVME criterion.
result Improved waypoints estimation accuracy by approximately 88% compared to benchmarks.
AdaVol adapts QML for real-time GARCH volatility prediction.
problem Real-time estimation of GARCH volatility in streaming data.
method Adaptive recursive estimation routine with Variance Targeting Estimation.
result AdaVol provides a stable and adaptive method for real-life data.
This paper reformulates double Hurwitz numbers using topological recursion.
problem Enumerating branched covers with specific ramification over zero and infinity.
method Topological recursion framework applied to double Hurwitz numbers.
result Double Hurwitz numbers are governed by the topological recursion.
Benchmarking recursive collapse claims with a new framework under false-positive control.
problem Evaluating recursive systems for failure patterns and warning claims.
method Developed Loopzero framework for testing recursive failures, specified claim boundaries in Lean, evaluated under FP constraint, and compared with standard detectors.
result No standard detectors or Loopzero's pre-registered quantile detector achieved the required operating point under the false-positive contract.
Paper presents novel online MTL methods using WRLS and OSLSSVR.
problem Online Multi-Task Learning (MTL) Regression Problems
method Develops recursive versions of WRLS and OSLSSVR for MTL.
result Achieves exact and approximate recursions with quadratic cost.
Using the duality between Wilson loop expectation values of SU(N) Chern-Simons theory on S3 and topological open-string amplitudes on the local mirror of the resolved conifold, we study knots on S3 and their invariants encoded in colored HOMFLY polynomials by means of topological recursion. In the context of the …
This research connects combinatorial Teichmüller space geometry to Weil-Petersson geometry.
problem Understanding the geometry of combinatorial Teichmüller space.
method Developed a parallel between combinatorial Teichmüller space and Weil-Petersson geometry, using measured foliations and Fenchel-Nielsen coordinates.
result Established a geometric recursion and topological recursion for mapping class group invariants.
Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.
problem Model collapse in recursive training of generative models
method Recursive training on their own outputs
result Recursive training converges to a unique limiting distribution
We extend topological recursion to twisted Higgs bundles with singularities.
problem Computing Taylor expansions of period matrices for twisted Higgs bundles.
method We introduce a twisted topological recursion on the spectral curve of a twisted Higgs bundle, encoding singularities and performing the recursion explicitly.
result The g=0 twisted Eynard-Orantin differentials compute the Taylor expansion of the spectral curve's period matrix, independent of the ambient space. We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal ℓ1,∞-penalized recursive least squares (R…
Study volumes of Klein surfaces, extending Mirzakhani's recursion.
problem Volumes of moduli spaces of bordered Klein surfaces.
method Generalization of Mirzakhani's recursion, integration over regularised moduli space.
result Explicit formula for Klein bottle moduli space volumes, recursion for arbitrary topologies.
Paper develops efficient recursive learning for multi-channel systems with heterogeneous dynamics.
problem Accurately learning system dynamics in complex, multi-channel systems with nonlinear and noisy data.
method Formulates system as Gaussian process state-space models (GPSSMs), introduces heterogeneous multi-output kernel, and develops recursive inference framework.
result Matches SOTA offline GPSSMs in accuracy with 1/100 runtime, and outperforms SOTA online GPSSMs by 70% in accuracy under noise with 1/20 runtime.
Deep learning solves dynamic programming with recursive utility.
problem Challenges in solving high-dimensional discrete-time dynamic programming problems with recursive utility.
method Certainty Equivalent Learning (CEL) algorithm that learns certainty-equivalent value directly with neural networks.
result Accurate value and policy approximations in high-dimensional problems, comparable to VFI in some cases.
Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.
problem State estimation in systems with noisy measurements and non-Gaussian noise.
method Recursive KalmanNet uses a recurrent neural network to estimate states with consistent error covariance, optimizing for Gaussian negative log-likelihood.
result Recursive KalmanNet outperforms conventional Kalman filters and deep learning-based estimators in non-Gaussian noise conditions.
Novel method recursively partitions sample space for density estimation.
problem Estimating complex density functions efficiently and accurately.
method Recursive partitioning of the sample space, asymptotically exact.
result Asymptotically exact approximation of any density function.
New methods learn from PU data with non-representative positives.
problem Learning from PU data with non-representative positive classes.
method Integrates negative-unlabeled and unlabeled-unlabeled learning, or uses a recursive risk estimator.
result Effective across various real-world datasets and forms of positive bias.
New method reduces errors in causal discovery from data.
problem Errors in causal discovery from limited data.
method Hierarchical wrapper for constraint-based algorithms.
result Significantly fewer tests, more accurate graphs, shorter run-times.
DiCoLa recursively decomposes causal structure learning for latent variables.
problem Learning causal structures in high-dimensional settings with latent variables.
method Recursive decomposition framework for divide-and-conquer causal discovery.
result Theoretical soundness and completeness of DiCoLa framework.
Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that combines two key ideas. The first one, which is deeply rooted in the Expectation-Maxim…
Proposes a novel method for estimating parameters in simulator-based models with intractable likelihood.
problem Parameter estimation for simulator-based models with unfeasible likelihood calculations.
method Recursive application of kernel ABC and kernel herding to observed data.
result The method converges to the true parameter as recursion proceeds, outperforming existing approaches in numerical experiments.
Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local an…
Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
The paper investigates model collapse in language models from a probabilistic perspective.
problem Understanding and preventing model collapse in language model training.
method Investigates recursive parametric model training from a probabilistic standpoint, characterizing conditions for model collapse and proposing mitigation strategies.
result Progressively increasing sample size is necessary to prevent model collapse, with a superlinear growth rate required in the asymptotic regime.
Paper proposes a recursive PLS model for optimal response to security threats.
problem Optimal response to security threats after violations have occurred.
method Recursive Partial Least Squares (PLS) model with factorial analysis of security events.
result The model optimally estimates security administrators' responses to threats.
Bayesian method improves online NARMAX model identification.
problem Online identification of nonlinear systems with small sample sizes and low noise.
method Variational Bayesian inference using message passing algorithm for polynomial NARMAX models.
result Variational Bayesian estimator outperforms recursive and offline least-squares methods.
A new method infers neural trajectories in real-time, improving experimental design.
problem Real-time inference of neural trajectories for immediate feedback.
method Exponential family variational Kalman filter (eVKF) for online learning.
result eVKF achieves competitive performance on synthetic and real-world data.
Unified framework for observables in n-plectic geometry.
problem Quantization of extended objects in higher geometric contexts.
method Develops a semi-simplicial set model for observables, using a Grassmann variable to encode submanifold codimensions.
result Establishes a categorified pre-n-Hilbert space and a quantization scheme matching multisymplectic geometry.
Adds recursion to deep learning frameworks for better handling of recursive data structures.
problem Lack of support for recursion in existing deep learning frameworks.
method Complements existing frameworks with recursive execution of dataflow graphs and APIs for recursive definitions.
result Recursive implementation reduces training and inference time by more effectively using resources.
This paper develops efficient algorithms for multibody dynamics using screw and Lie group theory.
problem Efficient modeling and computation of multibody systems.
method Recursive algorithms and Lie group formulations for multibody dynamics.
result Derivation of efficient Newton-Euler and Lagrange equations for multibody systems.
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization…
An efficient method to compute a single linkage dendrogram.
problem Computing a single linkage dendrogram efficiently.
method Form an edge-weighted graph, calculate MST, recursively split longest edge.
result Efficiently determine vertices of subtrees without additional cost.
We prove that the general fibre of the i-th Gauss map has dimension m if and only if at the general point the (i+1)-th fundamental form consists of cones with vertex a fixed Pm−1, extending a known theorem for the usual Gauss map. We prove this via a recursive formula for expressing higher fundamenta…
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
Recursive sketches summarize deep networks, aiding quick analysis and learning.
problem Understanding and analyzing complex deep learning models.
method Developed a recursive sketch mechanism to summarize inputs and outputs of modular deep networks.
result Sketches can identify key components and summarize essential information, even if partially erased.