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.
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when w…
New learning dynamics achieve fast convergence in games without needing to know utility scales.
problem Fast convergence guarantees in learning games require prior knowledge of utility scales.
method Developed scale-free and scale-invariant learning dynamics using optimistic follow-the-regularized-leader with adaptive learning rates and clipping techniques.
result Achieved fast convergence rates to Nash and correlated equilibria without prior utility scale knowledge.
We introduce a new weight-decay scaling rule to maintain sublayer gains across different widths in modern scale-invariant architectures.
problem In modern scale-invariant architectures, training quickly enters a steady state where normalization layers create backward scale sensitivity, degrading learning-rate transfer.
method We introduce a weight-decay scaling rule for AdamW that preserves sublayer gain across widths by equalizing the effective learning rate.
result Our empirical weight-decay scaling rule λ2∝d approximately keeps sublayer gains width invariant, enabling zero-shot transfer of learning rate and weight decay.
Critical points of scale-invariant curvature energies in 4D are analytic.
problem Analyzing critical points of curvature energies in 4D manifolds.
method Applying Noether's theorem to identify conservation laws and lower order elliptic system of PDEs, then using integrability by compensation and interpolation theory.
result Critical points of scale-invariant curvature energies in 4D are analytic.
We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are fini…
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
The paper develops a regularity theory for O'hara knot energies, focusing on Möbius energy.
problem Developing a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara.
method Reinterpreting O'hara knot energies as a nonlinear, nonlocal Lp-energy acting on the unit tangent of the knot parametrization, drawing a connection to the theory of (fractional) harmonic maps into spheres.
result Proves regularity for minimizers and critical knots of the scale-invariant O'hara knot energies.
The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale, providing direct evidence of the existence of sca…
SAM improves generalization in overparameterized models, but its behavior in tensorized models is less understood.
problem Understanding the implicit regularization of SAM in tensorized models.
method Scale-invariance analysis and gradient flow analysis to derive Norm Deviation as a measure of core norm imbalance, and propose Deviation-Aware Scaling (DAS).
result DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.
Generalized algorithm for translation and scale-invariant prediction.
problem Sequential prediction with expert advice, focusing on translation and scale invariance.
method Designing a generalized online algorithm using the universal prediction perspective to compete against a generic class of expert selection strategies.
result No preliminary knowledge of loss sequences is required; performance bounds are stable under arbitrary scalings and translations.
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…
We study the concept of coarse disjointness and large scale n-to-1 functions. As a byproduct, we obtain an Ostrand-type characterization of asymptotic dimension for coarse structures. It is shown that properties like finite asymptotic dimension, coarse finitism, large scale weak paracompactness, ect. are all invari…
The results of R^2 dynamical random surface model (2-dimensional quantum gravity with a R2 term) are applied to explain the personal income distribution. A scale invariance exists if there is not the R2 term in the action. The R^2 term provides a typical scale and breaks the scale invariance explicitly in the low…