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.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…
In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schrödinger equation and non-linear heat system to the…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction func…
Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…
A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and i…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear features on the original input space. After a finite number of iterations N, the n…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings o…
Capacity analysis has been recently introduced as a way to analyze how linear models distribute their modelling capacity across the input space. In this paper, we extend the notion of capacity allocation to the case of neural networks with non-linear layers. We show that under some hypotheses the problem is equivalent …
A basic problem in machine learning is to find a mapping f from a low dimensional latent space Y to a high dimensional observation space X. Modern tools such as deep neural networks are capable to represent general non-linear mappings. A learner can easily find a mapping which perfectly fits a…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Po…
We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed not in line element space but in point-Finsler space. In this view we recognize …
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as …
The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix Completion where the predicted rating is modeled as an inner product of the user and …
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes that capture across-task dependencies. We propose two different methods for segmen…
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.