Related papers: Proofs and additional experiments on Second order …

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the…

Online learning has gained popularity in recent years due to the urgent need to analyse large-scale streaming data, which can be collected in perpetuity and serially dependent. This motivates us to develop the online generalized method of…

The stability of recursively trained large language models (LLMs) is a foundational problem for AI safety. Prevailing theory predicts model collapse, a progressive degradation when models are trained on their own output. We challenge this…

We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…

Human recursive numeral systems (i.e., counting systems such as English base-10 numerals), like many other grammatical systems, are highly regular. Following prior work that relates cross-linguistic tendencies to biases in learning, we ask…

Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…

Can autoregressive large language models (LLMs) learn consistent probability distributions when trained on sequences in different token orders? We prove formally that for any well-defined probability distribution, sequence perplexity is…

Being able to quickly adapt to changes in dynamics is paramount in model-based control for object manipulation tasks. In order to influence fast adaptation of the inverse dynamics model's parameters, data efficiency is crucial. Given…

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are…

Various methods using machine and deep learning have been proposed to tackle different tasks in predictive process monitoring, forecasting for an ongoing case e.g. the most likely next event or suffix, its remaining time, or an…

This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based…

Due to the inherent imbalance in real-world datasets, na\"ive Empirical Risk Minimization (ERM) tends to bias the learning process towards the majority classes, hindering generalization to minority classes. To rebalance the learning…

We prove the existence of secondary terms of order $X^{3/4}$, with power saving error terms, in the counting functions of $|{\rm Sel}_2(E)|$, the 2-Selmer group of E, for elliptic curves E having height bounded by X. This is the first…

Offline reinforcement learning, which learns solely from datasets without environmental interaction, has gained attention. This approach, similar to traditional online deep reinforcement learning, is particularly promising for robot control…

We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test…

In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine learning literature, where they are used in random forest…