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.
Paper introduces NumLLM for better financial text understanding with numeric variables.
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition and Poisson's equation with mixed boundary conditions. The principal advantage o…
Improved financial sentiment analysis using simple instruction tuning of LLMs.
Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for modelling numerals with language models, such as memorisation and digit-by-digit composi…
This paper compares analytical and numerical solutions of the Black-Scholes model.
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and some non-simple m…
Method extracts governing laws from non-Gaussian stochastic systems data.
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional over conformal immersions from compact surfaces.
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding. The go…
This paper simplifies ANS for statisticians, making it easier to use.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
Financial markets provide a natural quantitative lab for understanding some of the most advanced human behaviours. Among them is the use of mathematical tools known as financial instruments. Besides money, the two most fundamental financial instruments are bonds and equities. More than 30 years ago Mehra and Prescott f…
Linear models can grok without understanding, improving generalization.
Understanding optimal prompts for binary sequence predictors is challenging.
Researchers improve transformer networks' optimization and understanding.
Grokking occurs at numerical stability edge, requiring regularization to prevent.
Genomic models learn DNA sequences to predict functions.
This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous ap…
Meta learning works well with overparameterized models, a phenomenon called 'benign overfitting'.
We consider the numerical stability of the parameter recovery problem in Linear Structural Equation Model ($\LSEM$) of causal inference. A long line of work starting from Wright (1920) has focused on understanding which sub-classes of $\LSEM$ allow for efficient parameter recovery. Despite decades of study, this questi…
This paper tackles Bayesian system identification with probabilistic numerical methods.
Asynchronous momentum stochastic gradient descent algorithms (Async-MSGD) is one of the most popular algorithms in distributed machine learning. However, its convergence properties for these complicated nonconvex problems is still largely unknown, because of the current technical limit. Therefore, in this paper, we pro…
Numerical models based on physics represent the state-of-the-art in earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest-generation computers, reducing the ability of …
Introduces Gaussian Processes and Relevance Vector Machines, connecting them to Kalman filtering.
Machine learning models predict the behavior of negatively buoyant jets from wastewater.
Enhances SDR via Hellinger correlation for better data dependency understanding.
This paper rates robustness of multi-modal time-series forecasting models.
Introduces MFCNs for better understanding manifold neural networks.
Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem through training a simple two-layer convolutional neural network model. Although trai…
Agent Trading Arena trains LLMs in real-time financial markets to improve numerical reasoning.
SAGE quantifies feature importance in machine learning models.
We introduce the new "Goldilocks" class of activation functions, which non-linearly deform the input signal only locally when the input signal is in the appropriate range. The small local deformation of the signal enables better understanding of how and why the signal is transformed through the layers. Numerical result…
Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is still lacking. We derive a theoretically motivated approach to explore the preimag…
A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to the theory of learning in deep neural nets. There has also been a recent intere…
We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…
Quantum reservoir computing needs coherence influx for effective information processing.
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should seek alternatives. Fortunately, many of the laws of behaviour of the physical wor…
Theoretical framework for neural network compression using sparsity norms.
The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More specific, we have shown that if that the Lie-Trotter integrator is obtained, in case o…
Improves understanding of neural network predictions using influence functions.
This article reviews mathematical insights into neural networks and machine learning.
Generative Adversarial Networks (GANs) have become a powerful framework to learn generative models that arise across a wide variety of domains. While there has been a recent surge in the development of numerous GAN architectures with distinct optimization metrics, we are still lacking in our understanding on how far aw…
New method reduces PDE surrogate model training costs by selectively acquiring time steps.
This study uses continuous-time analysis to understand how momentum affects the optimisation of diagonal linear networks.
State-of-art deep neural networks (DNN) are vulnerable to attacks by adversarial examples: a carefully designed small perturbation to the input, that is imperceptible to human, can mislead DNN. To understand the root cause of adversarial examples, we quantify the probability of adversarial example existence for linear …
Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…
In this paper, we propose and study a Nyström based approach to efficient large scale kernel principal component analysis (PCA). The latter is a natural nonlinear extension of classical PCA based on considering a nonlinear feature map or the corresponding kernel. Like other kernel approaches, kernel PCA enjoys good mat…
This is a brief survey of the research performed by Grandata Labs in collaboration with numerous academic groups around the world on the topic of human mobility. A driving theme in these projects is to use and improve Data Science techniques to understand mobility, as it can be observed through the lens of mobile phone…