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.
A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and principled estimation procedure even without the missing completely at random (M…
Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical results show that the efficiency of DA algorithms depends on their capacity of …
The paper explores grokking in various models, revealing it's not limited to neural networks.
problem Understanding grokking in different models and its mechanism.
method Empirical exploration of grokking in neural networks, Gaussian processes, linear regression, and Bayesian neural networks. Inducing grokking through spurious dimensions.
result Grokking occurs in non-neural architectures, indicating it's not model-specific.
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…
New findings show neural network training loss follows a power law over time.
problem Understanding the optimization process of neural networks during training.
method Spectral analysis of the integral operator representing the linearized evolution of a large network.
result The loss function in neural network training follows a power law behavior, L(t)∼t−ξ, with exponent ξ determined by network parameters and data characteristics.
We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a low-rank matrix from various information deficits by using the principle of low-ran…
The paper addresses adversarial robustness in in-context learning models.
problem Adversarial distribution shifts threaten the reliability of in-context learning models.
method A distributionally robust meta-learning framework is introduced to provide worst-case performance guarantees under Wasserstein-based distribution shifts.
result Model robustness scales with the square root of its capacity and is penalized by the square of the perturbation magnitude.
Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowa- days. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and practical implementations of such tasks, in particular of clustering, is very rudi…
ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of shallow (one hidden-layer) networks. For example, in the task of memorizing a ran…
Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In spite of the usefulness of GBM in practice, our current theoretical un…
Variational inference is a very efficient and popular heuristic used in various forms in the context of latent variable models. It's closely related to Expectation Maximization (EM), and is applied when exact EM is computationally infeasible. Despite being immensely popular, current theoretical understanding of the eff…
A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
problem Formulating the Raychaudhuri equation in non-Riemannian geometries.
method Established a formal connection between the expansion scalar and the cross-sectional volume of the congruence. Derived a Lagrangian and Hamiltonian formulation.
result The expansion scalar equals the fractional rate of change of volume, weighted by a scalar factor.
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the ℓ1- and ℓ2-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…
Genetic algorithms are a well-known method for tackling the problem of variable selection. As they are non-parametric and can use a large variety of fitness functions, they are well-suited as a variable selection wrapper that can be applied to many different models. In almost all cases, the chromosome formulation used …
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…