Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.
A technique identifies memoryless algorithms approximating memory-dependent optimization methods.
problem Understanding how memory in optimization algorithms affects loss and generalization.
method Introducing a general technique to replace past iterates with the current one and adding a correction term.
result Lion does not have the same implicit anti-regularization as AdamW, explaining its better generalization performance.
Paper proposes efficient inference for hidden Markov models with memory decay.
problem Challenges in scalability due to dependencies in hidden Markov model observation data.
method Utilizes memory decay to carry out forward and backward probabilities with subsequences, enabling efficient inference over long sequences.
result Developed an efficient algorithm to numerically estimate the gap of top Lyapunov exponents, which determines the length of subsequences.
Paper proposes JEDI teaching framework for adaptive crowd teaching.
problem Adaptive crowd teaching in crowdsourcing applications.
method Exponentially decayed memory model for teaching and balancing diversity and accuracy.
result JEDI teaching framework outperforms state-of-the-art techniques.
New framework analyzes temporal features in state space models.
problem Understanding temporal dependencies in data streams.
method Proposes a framework for rigorous analysis of state representations in ESNs, using temporal feature spaces and kernel machines.
result Phase transition in kernel richness for cycle reservoir topology.
The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.
problem Prediction errors in stochastic dynamical systems with memory kernels.
method Analysis of generalized Langevin equations (GLEs) with Volterra equations, integrating synchronized noise coupling and weighted norms.
result Prediction discrepancies decay at a rate determined by the memory kernel's decay, quantitatively bounded by kernel estimation errors.
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form momen…
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …
Adafactor optimizes neural networks with less memory and similar performance.
problem Memory constraints in adaptive optimization methods.
method Adafactor uses row and column sums of moving averages to estimate per-parameter second moments, reducing memory usage.
result Adafactor achieves similar performance to Adam with minimal auxiliary storage.
Random walks on hyperbolic spaces show linear progress with exponential decay.
problem Understanding progress and decay in random walks on hyperbolic spaces.
method Analyzing random walks on separable, geodesic hyperbolic metric spaces with specific step distributions.
result Exponential decay in progress is extended to non-acylindrical actions.
A new method selects PCA components based on residual memory, outperforming existing techniques.
problem Selecting the optimal number of components in PCA for data with long memory effects.
method Sequentially removes components, stopping when maximum memory accounted for.
result Our method outperforms existing techniques in computational efficiency and accuracy.
Exponential decay observed between two metrics on a moduli space.
problem Analyzing the difference between two metrics on a moduli space.
method Proving exponential decay along generic rays in the Hitchin moduli space.
result Exponential decay of the difference between gL2 and gsf. Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
problem Modeling correlated volatility in financial time series with heavy tails and long memory.
method Superstatistical dynamics, Bayesian Inference, Metropolis-Hasting sampling.
result The log-Normal model is reliable for short timescales, while inverse-Gamma is preferred for long timescales.
Study finite rank bundle over J-Holomorphic map moduli spaces with exponential decay.
problem Understanding the structure of J-Holomorphic map moduli spaces.
method Prove exponential decay of derivative of gluing maps for a finite rank bundle.
result Exponential decay of the derivative of the gluing maps for the finite rank bundle.
New magnetic memory effects found in gravitational waves and memory.
problem Understanding new effects in gravitational waves and memory.
method Analyzing asymptotically-flat spacetimes with slow decay.
result Diverging magnetic memory sourced by curvature and neutrino cloud.
The study identifies persistent motifs in stock correlations for sector-neutral portfolio diversification.
problem Forecasting and diversification of sector-neutral portfolios using long-term correlations.
method Analysis of Triangulated Maximally Filtered Graphs (TMFG) generated from rolling windows of stock price log-returns, identifying persistent motifs.
result Persistent motifs in stock correlations can be used to forecast and diversify sector-neutral portfolios, reducing volatility.
Improved RNNs reduce memory decay and enhance language tasks.
problem Memory decay in RNNs affects performance in sequence prediction tasks.
method Introduced trainable scaling factors and a dependent bidirectional RNN to mitigate memory decay and improve performance.
result The proposed ELSTM and DBRNN models achieved up to 30% improvement in LAS compared to LSTM and GRU in dependency parsing.
Paper shows existence of vortex solutions with specific decay properties.
problem Existence of solutions to Seiberg-Witten equations with specific decay properties.
method Dimensional reduction of Seiberg-Witten equations on the plane.
result Contains both exponentially decayed and polynomial growth solutions.
Market makers use a new method to predict and respond to RFQs in the OTC market.
problem Predicting and managing RFQs in the OTC market with Hawkes kernels.
method Developed a hierarchy of Volterra-Riccati approximations for path-dependent control problems.
result The state-feedback Volterra-Riccati policy closely tracks the exact benchmark and improves inventory and P&L risk control.
MSTGD optimizes gradient descent with stratified sampling for faster convergence.
problem Fluctuation in gradient expectation and variance between iterations.
method Memory Stochastic Stratified Gradient Descent (MSTGD) with stratified sampling and variance reduction.
result MSTGD achieves an exponential convergence rate independent of dataset size and batch size.
We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution Pq(τ) and the volatility return intervals τ as Pq(τ)=1/τˉf(τ/τˉ) to obtain a uniform scaling curve for different threshold value q. The scali…
We show that the probability that a finitely supported random walk on a non-elementary subgroup of the the mapping class group gives a non-pseudo-Anosov element decays exponentially in the length of the random walk. More generally, we show that if R is a set of mapping class group elements with an upper bound on their …
In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length T of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary pun…
Paper questions RNN and LSTM's long-term memory and introduces a new definition.
problem Whether RNN and LSTM have long-term memory.
method Introduced a new definition of long-term memory and modified RNN and LSTM to test it.
result RNN and LSTM do not meet the new definition of long-term memory.
We prove exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.
AdamNX improves Adam's stability by adjusting its learning rate.
problem Adam's tendency to converge to non-flat minima in large-scale models.
method Proposes a novel exponential decay mechanism for Adam's second-order moment estimate.
result AdamNX outperforms Adam and its variants in stability and performance.
New quantization methods improve accuracy of Random Fourier Features.
problem Improving accuracy of Random Fourier Features for machine learning.
method Sigma-Delta and distributed noise-shaping quantization methods for 1-bit and low bit-depth quantization.
result Quantized RFFs allow high accuracy approximation of underlying kernels with polynomial error decay.
A new accelerated method with simpler momentum update rules.
problem Optimizing parameters in machine learning models.
method Proposes a novel accelerated stochastic gradient method with simpler momentum update rules.
result The method outperforms Sgdm and Adam in practical problems.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
New exponential decay estimate for Hermitian Yang-Mills metrics near branch points.
problem Understanding the behavior of Hermitian Yang-Mills metrics near branch points.
method Local radial solutions, global gluing construction, exponential estimate near branch points.
result Exponential decay estimate for local radial solutions near branch points.
In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragmén-Lindelöf principle we prove exponential decay of the eigenfunctions corresponding to the non-threshold eigenvalues of t…
The goal of this paper is to prove a result conjectured in Föllmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then …
Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative…
Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.
problem Deviation of U-statistics with heavy-tailed samples.
method Exponential tail bounds and Large Deviation Principle (LDP) for U-statistics.
result Obtained an exponential upper bound for U-statistics tail decay, showing two regions of decay.
Improved online FDR control with decaying memory.
problem Online multiple testing with temporal data.
method Generalized alpha-investing algorithms (GAI) with decaying memory FDR (mem-FDR).
result New algorithms reduce false discovery rate and improve power.
Study improves the exponential rate of metric difference in Higgs bundles.
problem Improving the exponential rate of metric difference in Higgs bundles.
method Analyzes the Hitchin metric and semi-flat metric in rank two Higgs bundles.
result Exponential rate of metric difference is improved.
Global stability proved for Navier-Stokes equations on hyperbolic space.
problem Stability of the Navier-Stokes equations on hyperbolic space.
method Proved global stability with exponential decay rate for small initial data.
result Exponential decay rate of $μλ_\Def^{(3)}$ for Navier-Stokes equations on hyperbolic space.
Unified algorithm Q(σ,λ) combines eligibility traces to improve memory and computation efficiency.
problem Memory and computation inefficiency in multi-step temporal-difference learning.
method Introduced Q(σ) algorithm, combined with eligibility traces to propose Q(σ,λ). result Proposed algorithm Q(σ,λ) converges to optimal value function exponentially. New memory effect discovered in gravitational wave behavior.
problem Understanding gravitational wave behavior in spacetimes with angular momentum.
method Mathematical analysis of Minkowski spacetime and Kerr black holes.
result Angular momentum memory effect observed at future null infinity.
The paper explores how the probability of default estimation changes with temporal correlation decay.
problem Difficulty in estimating the probability of default due to correlations between borrowers.
method Hierarchical Bayesian estimation using beta binomial distribution with temporal correlation.
result A phase transition occurs in the PD estimator, with convergence depending on the power decay index of temporal correlation.
The paper explores the limits of deep neural networks in approximating various function classes.
problem Characterizing the limits of deep neural networks in function approximation.
method Develops a theory relating function complexity and network complexity, using Kolmogorov complexity.
result Deep networks are optimal approximants for various function classes and provide exponential approximation accuracy.
New method SF-AdamW trains large models without decay phases or memory overhead.
problem Inadequate fixed compute budgets for large-scale training.
method Schedule-Free (SF) method revisited and refined.
result SF-AdamW effectively navigates loss landscape without decay phases or memory overhead.
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.
The paper studies Teichmüller TQFT for hyperbolic knots, proving exponential decay of partition functions.
problem Analyzing Teichmüller TQFT for hyperbolic knots with generalized FAMED triangulations.
method Introducing generalized FAMED property, proving exponential decay of partition functions in semi-classical limit.
result Partition functions decay exponentially with the volume of knot complements, and the 1-loop invariant emerges.
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …
New bounds for KRR condition number reveal overfitting phenomena.
problem Characterizing overfitting in KRR with varying kernel spectral decay.
method Derived new bounds for kernel matrices, enhanced test error bounds, and identified feature independence role.
result Identified tempered and catastrophic overfitting phenomena.
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…