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.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.
problem Learning modular addition with two-layer neural networks.
method Introduced and analyzed sine activation functions, providing theoretical and empirical evidence.
result Sine activation functions allow for constant-width network realizations of modular addition, whereas ReLU networks require linear width scaling.
The paper tackles fairness in forecasting and learning linear dynamical systems.
problem Under-representation bias in training data for multiple subgroups.
method Introducing subgroup-fair and instant-fair learning of LDS from multiple trajectories of varying lengths, using hierarchies of convexifications of non-commutative polynomial optimisation problems.
result Empirical results show both the beneficial impact of fairness considerations on statistical performance and encouraging effects of exploiting sparsity on run time.
We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…
PSiLON Net uses L1 weight normalization and 1-path-norm regularization for efficient learning and sparsity.
problem Efficient learning and sparsity in neural networks with limited data.
method PSiLON Net employs L1 weight normalization and 1-path-norm regularization to simplify the 1-path-norm and achieve efficient learning and near-sparse parameters.
result PSiLON Net achieves reliable optimization and strong performance in the small data regime.
Enhances financial time series forecasting with a multi-period learning framework.
problem Accurate financial time series forecasting requires considering both short-term and long-term trends.
method Proposes a Multi-period Learning Framework (MLF) with three modules: Inter-period Redundancy Filtering, Learnable Weighted-average Integration, and Multi-period self-Adaptive Patching.
result Improves financial time series forecasting accuracy and efficiency.
Proposes a new tail risk measure based on the most probable maximum risk event size.
problem Current risk measures like VaR and ES are limited in their applicability and require specifying a confidence level.
method Develops a new risk measure called MPMR that does not require a confidence level and scales with the length of the time interval.
result The new risk measure, MPMR, scales with the number of observations by a power law, allowing for reliable estimations of long-term risks based on short-term estimations.
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
It has been noticed that some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand index (R…
Filling length measures the length of the contracting closed loops in a null-homotopy. The filling length function of Gromov for a finitely presented group measures the filling length as a function of length of edge-loops in the Cayley 2-complex. We give a bound on the filling length function in terms of the log of an …